From ae51d8cf4a1b814211c2fb0df054171e54d38423 Mon Sep 17 00:00:00 2001 From: Omid Bodaghi <42227752+omibo@users.noreply.github.com> Date: Fri, 27 Feb 2026 17:18:05 -0800 Subject: [PATCH 1/5] Implement Hachi PCS protocol with required primitives (#1) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * chore: add toolchain and formatting config Pin Rust 1.88 with minimal profile (cargo, rustc, clippy, rustfmt). Co-authored-by: Cursor * chore(ci): switch to actions-rust-lang/setup-rust-toolchain Respects rust-toolchain.toml automatically. Also normalize clippy flags to use --all --all-targets consistently. Co-authored-by: Cursor * feat(primitives): add u128/i128 serialization support Required by the Fp128 field backend. Co-authored-by: Cursor * feat(algebra): add prime fields, extensions, and modules Introduces the algebra module with: - Fp32/Fp64/Fp128 prime field backends with branchless constant-time add/sub/neg and rejection-sampled random - U256 helper for Fp128 wide multiplication - Fp2/Fp4 tower extensions with Karatsuba-ready structure - VectorModule fixed-length vector module over any field - Poly fixed-size polynomial container Co-authored-by: Cursor * feat(algebra): add NTT small-prime arithmetic and CRT helpers Adds the ntt submodule with: - NttPrime: per-prime Montgomery-like fpmul, Barrett-like fpred, branchless csubq/caddq/center - LimbQ/QData: radix-2^14 limb arithmetic for big-q coefficients - logq=32 parameter preset (six NTT-friendly primes, CRT constants) Co-authored-by: Cursor * test(algebra): add comprehensive algebra test suite 24 tests covering: - Field arithmetic, identities, and distributivity (Fp32/Fp64/Fp128) - Zero inversion returns None - Serialization round-trips (all field types, extensions, VectorModule) - Fp2 conjugate, norm, and distributivity - U256 wide multiply and bit access - LimbQ round-trip and add/sub inverse - QData consistency with preset constants - NTT normalize range and fpmul commutativity - Poly add/sub/neg Co-authored-by: Cursor * docs: add and update progress tracking document Records Phase 0 status: all field types, extensions, NTT scaffolding, constant-time arithmetic, and 24-test suite. Reflects the fields/ntt/module/poly directory layout. Co-authored-by: Cursor * refactor(ntt): Rust-ify NTT/CRT port from C Overhaul the NTT small-prime arithmetic and CRT modules: - Add MontCoeff newtype (#[repr(transparent)] i16 wrapper) to enforce Montgomery-domain vs canonical-domain separation at the type level - NttPrime methods now take/return MontCoeff instead of bare i16: fpmul→mul, fpred→reduce, csubq→csubp, caddq→caddp - Add domain conversion: from_canonical (i16→Mont), to_canonical (Mont→i16) - Delete free functions (pointwise_mul etc), replaced by methods on NttPrime - LimbQ: replace add_limbs/sub_limbs/less_than with std Add/Sub/Ord impls - LimbQ: replace from_u128/to_u128 with From/TryFrom for u128 - LimbQ: add Display impl, branchless csub_mod - Rename all LABRADOR* constants to project-native Q32_* names - Add #[cfg(test)] verification that re-derives pinv/v/mont/montsq from p - Add MontCoeff round-trip and LimbQ ordering tests (28 total) Co-authored-by: Cursor * chore: remove section banners, update progress doc Remove // ---- Section ---- banner comments from prime.rs and crt.rs. Add non-negotiable rules to HACHI_PROGRESS.md: - No section-banner comments - No commit/push without explicit user approval Co-authored-by: Cursor * feat(ring): add CyclotomicRing, CyclotomicNtt, and NTT butterfly Milestone 1 - CyclotomicRing (coefficient form): - Schoolbook negacyclic convolution Mul (X^D = -1) - Add/Sub/Neg/AddAssign/SubAssign/MulAssign, scale, zero/one/x - HachiSerialize/HachiDeserialize Milestone 2 - NTT butterfly + CyclotomicNtt: - Merged negacyclic Cooley-Tukey forward NTT (twist folded into twiddles) - Gentleman-Sande inverse NTT with D^{-1} scaling - Runtime primitive-root finder and twiddle table computation (TODO: migrate to compile-time const tables) - CyclotomicNtt with per-prime pointwise Add/Sub/Neg/Mul - Ring<->Ntt transforms with CRT reconstruction Co-authored-by: Cursor * test(algebra): add ring and NTT tests, wrap in mod tests Add 12 new tests: - CyclotomicRing: negacyclic X^D=-1, mul identity/zero, commutativity, distributivity, associativity, additive inverse, serde, degree-64 - NTT: forward/inverse round-trip (single prime + all primes), NTT mul matches schoolbook cross-check Wrap all integration tests in a single mod tests block and remove section-banner comments. Co-authored-by: Cursor * fix(algebra): harden ring-NTT conversion and field decoding Constrain ring/NTT conversions to explicit field backends and replace fragile CRT reconstruction with deterministic modular lifting. Enforce canonical deserialization checks in validated field decoding paths to reject malformed encodings. Co-authored-by: Cursor * test(algebra): add CRT round-trip and serialization guard coverage Add end-to-end ring->NTT->ring CRT round-trip tests plus reduced-ops stability checks. Expand serialization coverage for Fp4/Poly and verify checked deserialization rejects non-canonical field encodings. Co-authored-by: Cursor * chore(bench): add ring_ntt benchmark target and CT tracking docs Add a dedicated ring/NTT benchmark harness and register it in Cargo metadata. Record current constant-time review status and sync the implementation progress board with new milestones and test coverage. Co-authored-by: Cursor * refactor(field): split core, canonical, and sampling capabilities Break the monolithic Field trait into FieldCore, CanonicalField, and FieldSampling, and update algebra primitives to depend on explicit capabilities for cleaner semantics and future backend integration. Co-authored-by: Cursor * feat(fields): add pow2-offset pseudo-mersenne registry and checks Introduce the curated 2^k-offset prime registry and typed field aliases, then add dedicated Miller-Rabin regression tests to enforce probable primality for all enabled profiles. Co-authored-by: Cursor * refactor(ring): introduce crt-ntt backend/domain layering Rename the ring NTT representation to explicit CRT+NTT semantics and route conversions through backend traits, adding scalar backend and domain aliases for a cleaner representation-vs-execution boundary. Co-authored-by: Cursor * test(algebra): cover backend parity and pow2-offset invariants Expand algebra tests to validate default-vs-backend CRT+NTT equivalence, sampling bounds, and pow2-offset registry consistency under the new field and ring abstractions. Co-authored-by: Cursor * docs(algebra): update progress notes and add prime analysis references Refresh progress and constant-time notes to match the new CRT+NTT naming and field scope, and add the NTT prime analysis document plus local NIST standards artifacts used for parameter rationale. Co-authored-by: Cursor * fix(algebra): harden fp128 reduction and CRT reconstruction arithmetic Make Fp128 reduction and CRT inner accumulation paths more timing-stable with branchless modular operations, and refresh ring/docs/tests status after the hardening cleanup pass. Co-authored-by: Cursor * feat(protocol): add transcript and commitment scaffold Introduce Hachi protocol-layer interfaces and placeholder types with Blake2b/Keccak transcript backends plus phase-aligned labels, while making transcript absorption label-directed at call sites. Co-authored-by: Cursor * test(protocol): add transcript and commitment contract coverage Add deterministic transcript schedule checks (including keccak) and protocol commitment contract tests so transcript ordering and challenge derivation behavior are locked down. Co-authored-by: Cursor * docs(protocol): align transcript spec and progress status Document the protocol scaffold as in-progress, capture the commitment-focused transcript label vocabulary, and clarify deferred Jolt adapter expectations. Co-authored-by: Cursor * feat(protocol): add ring commitment core and seeded matrix derivation Implement the ring-native commitment setup/commit core with config validation, utility modules, and seeded domain-separated public matrix derivation, while wiring prover/verifier stub modules for the next open-check phase. Co-authored-by: Cursor * test(protocol): consolidate ring commitment and stub contract coverage Unify ring commitment core and config validation checks in one test file and add explicit prover/verifier stub contract tests to lock current placeholder behavior before open-check implementation. Co-authored-by: Cursor * docs(progress): update phase 2 status after commitment core landing Record that ring-native §4.1 commitment setup/commit and protocol wiring are in place, and clarify that open-check prove/verify remains the next unfinished protocol milestone. Co-authored-by: Cursor * fix(algebra): harden CT inversion path and CRT final projection Add a constant-time inversion helper for prime fields and replace scalar CRT's final `% q` projection with a division-free fixed-iteration reducer, so secret-bearing arithmetic paths avoid variable-latency behavior. Co-authored-by: Cursor * refactor(algebra): rename inversion helper API without ct suffix Rename the secret-path inversion helper to `Invertible::inv_or_zero` while preserving constant-time semantics via doc contracts, and update CT tracking docs to match the new API names. Co-authored-by: Cursor * test(algebra): clean inversion test naming and normalize formatting Rename the inversion helper test to match the new API naming and keep the ring commitment test formatting consistent after linting. Co-authored-by: Cursor * feat(protocol): add sumcheck core module and tests Introduce core sumcheck building blocks (univariate messages, compression, and transcript-driving prover/verifier driver) and add unit/integration tests. Update progress doc to reflect sumcheck core landing. Co-authored-by: Cursor * Add reference PDF papers * Add local agent instruction files * Add Hachi and SuperNOVA digest docs * Add general field, ring, and multilinear utilities * Add sparse Fiat-Shamir challenge sampling * Implement Polynomail Evaluation as Quadradic Equation * Rename stub to prover and verifier * Refactor code organization * Replace decopose with balanced decompose * Transform polynomial over Fq to ring * Refactor function names * Impl commitment_scheme API * Add SolinasFp128 backend for sparse 128-bit primes Introduce `SolinasFp128` with two-fold Solinas reduction for `p = 2^128 - c` (sparse `c`), plus `U256::sqr_u128`. Export descriptive prime aliases, add BigUint-backed correctness tests, and include a Criterion bench for mul/inv. Co-authored-by: Cursor * Tighten docs and minor clippy cleanups Add missing rustdoc Errors/Panics sections and apply small simplifications suggested by clippy. Co-authored-by: Cursor * Add reduction steps to iteration prover * Optimize Solinas mul/add/sub: fused u64-limb schoolbook + csel canonicalize Rewrite mul_raw as a fused 2×2 schoolbook multiply with two-fold Solinas reduction using explicit u64 limbs and mac helper, bypassing U256. Replace mask-based canonicalize with carry-flag-based pattern that compiles to adds+adcs+csel+csel (4 insns) instead of 10 on AArch64. Add pure-mul, sqr, and throughput microbenchmarks. Made-with: Cursor * Switch SolinasFp128 repr from u128 to [u64; 2] for 8-byte alignment Storage is now [u64; 2] (lo, hi) which halves alignment from 16 to 8 bytes, improving struct packing. Arithmetic hot paths convert to u128 for LLVM-optimal codegen (adds/adcs pairs), so no perf regression. Made-with: Cursor * Fuse overflow correction with canonicalize in fold2_canonicalize When fold-2 overflows, the wrapped value s < C², so s + C < C(C+1) < P — meaning s + C is already canonical. This lets us replace the separate overflow-correction + canonicalize (3 + 4 insns) with a single fused `if (overflow | carry) { s + C } else { s }` select, saving 2 instructions on the critical path. Add compile-time assertion enforcing C(C+1) < P. Made-with: Cursor * Unify Fp128 with Solinas-optimized arithmetic, delete SolinasFp128 Replace the generic Fp128 (binary-long-division via U256) with the Solinas-optimized implementation. Fp128 now uses [u64; 2] storage, fused schoolbook 2x2 + two-fold Solinas reduction (~23 cycles/mul on AArch64/x86-64), and compile-time validation that P = 2^128 - C with C < 2^64. Delete SolinasFp128, SolinasParams, solinas128.rs, and u256.rs. All call sites updated; prime type aliases (Prime128M13M4P0 etc.) are now simple Fp128<...> aliases in fp128.rs. Blanket PseudoMersenneField impl for all Fp128

. Made-with: Cursor * Use git deps for ark-bn254/ark-ff instead of local paths Switch from local path dependencies to the a16z/arkworks-algebra git repo (branch dev/twist-shout) so collaborators can compile without needing a local checkout of arkworks-algebra-jolt. Made-with: Cursor * Add template for sumchecks * Optimize Fp128 mul path and expand Rust field benchmarks. Refine Fp128 multiply/fold carry handling for better generated code and add isolated, passthrough, independent, and long-chain Rust microbenches to separate latency and throughput effects when comparing against BN254. Made-with: Cursor * Add 2^a±1 Fp128 reduction specialization and benches. Detect C = 2^a ± 1 at compile time and route fold multiplications through a specialized shift-based path with generic fallback, plus add benchmark coverage for sparse 128-bit primes using this shape. Made-with: Cursor * Add packed Fp128 field backend scaffolding and focused benchmarks. This introduces AArch64-first packed field abstractions with a scalar fallback and adds dedicated field-only validation/benchmark coverage before any ring or protocol integration. Made-with: Cursor * Refactor packed Fp128 backend to true SoA layout and stabilize benchmarking. This switches packed lane storage to SoA with NEON add/sub kernels and a SoA mul path, and updates packed-field APIs and benches so scalar-vs-packed latency/throughput comparisons are measured consistently. Made-with: Cursor * Optimize packed Fp128 mul throughput with array-backed SoA lanes. This keeps mul in true SoA form while removing repeated vector transmute overhead and inlining the limb-level Solinas lane kernel, improving packed mul throughput and latency against scalar baselines. Made-with: Cursor * Add Fp128 widening multiply API and specialized Solinas reduction Expose mul_wide_u64, mul_wide, mul_wide_u128, solinas_reduce, and to_limbs for deferred-reduction patterns needed by jolt-hachi. Hand-optimized reduce paths for 3/4/5 limbs avoid generic loop overhead. Refactor mul_raw to reuse mul_wide + reduce_4 (zero overhead). Add 9 unit tests and widening/accumulator benchmarks. Made-with: Cursor * Clean up fp128: remove section banners, hoist std::ops imports, rename mul_wide free fn Rename free function mul_wide → mul64_wide to avoid shadowing Fp128::mul_wide. Move reduce_4 next to fold2_canonicalize. Replace fully qualified std::ops::{Add,Sub,Mul,Neg} with use imports. Made-with: Cursor * Constrain Fp32/Fp64 to pseudo-Mersenne primes with Solinas reduction Rework fp32.rs and fp64.rs to require p = 2^k - c (small c), matching fp128's design. Compile-time constants BITS/C/MASK derived from P with static assertions. Replace bit-serial reduction with two-fold Solinas reduction (reduce_product for hot path, loop-based reduce_u64/u128 for arbitrary inputs). Add widening ops (mul_wide, square, solinas_reduce). Fix FieldSampling to use direct modular reduction instead of rejection sampling. Blanket-impl PseudoMersenneField, remove manual impls. Rename const generic MODULUS -> P at all call sites. Add latency + throughput benchmarks. Hoist mid-function imports in tests/algebra.rs. Made-with: Cursor * Specialize Fp64 sub-word primes to u64-only arithmetic For BITS < 64 (e.g. 2^40-195), avoid u128 intermediates in reduce_product, add_raw, and sub_raw. Use mul_c_narrow which splits C*high into u32x32->u64 widening multiplies (umaddl on AArch64), preventing LLVM from promoting to u128. Brings 40-bit mul throughput within 4% of 64-bit (690 vs 716 Melem/s), up from ~20% gap. Made-with: Cursor * Add 2^30 and 2^31 pseudo-Mersenne primes and expand benchmarks Add Pow2Offset30Field (2^30-35) and Pow2Offset31Field (2^31-19) prime definitions and type aliases. Refactor fp32/fp64 latency benchmarks with chain_bench! macro, add throughput benchmarks for all new primes. Made-with: Cursor * Add NEON packed backends for Fp32 (4-wide) and Fp64 (2-wide) PackedFp32Neon: 4 lanes in uint32x4_t with full NEON Solinas reduction for mul (vmull_u32 + 2-fold reduce), umin trick for add/sub (BITS<=31), overflow-aware paths for BITS==32. C_SHIFT_KIND optimization for C=2^a+/-1. PackedFp64Neon: 2 lanes in uint64x2_t with NEON add/sub (conditional P for BITS<=62, carry-aware for BITS>=63), scalar-per-lane mul (no native 64x64->128 on NEON). Fp32 packed achieves 2.4-3.5x mul throughput and 3.5-5.0x add/sub throughput over scalar. Includes HasPacking impls, type aliases, NoPacking fallbacks, 7 correctness tests, and throughput benchmarks. Made-with: Cursor * Optimize packed Fp32/Fp64 Solinas multiply hot paths on NEON For packed Fp32, remove the shift/add C-special-case in the Solinas fold and always use vmull_u32 with a hoisted C broadcast, which improves stability and removes the 24-bit mul regression. For packed Fp64, replace per-lane Fp64 wrapper multiplication with packed-local per-lane 64x64->128 products plus specialized Solinas reduction (including the sub-word u64 fold path), reducing mul overhead for both 40-bit and 64-bit packed variants. Made-with: Cursor * Tune packed Fp64 mul folding and add reducer/codegen probes Switch packed Fp64 sub-word fold multiplication to direct `C*x`, which improves packed mul throughput in repeated A/B runs. Add dedicated reducer and codegen probe benches so we can compare 40-bit and 64-bit fold paths with instruction-level visibility. Made-with: Cursor * Optimize x86 BMI2 multiply paths for fp64/fp128 fields Use BMI2 widening multiplies in scalar field hot paths and specialize x86 sub-word fold multiplication to a single 64-bit multiply, improving 40-bit fp64 throughput while keeping 64-bit and 128-bit paths stable. Made-with: Cursor * Optimize fp128 wide-limb multiply path for Jolt integration Raise Hachi MSRV to 1.88, add specialized Fp128 mul_wide_limbs kernels for M={3,4} and OUT={4,5,6}, and add field_arith benches that track mul_wide_limbs-only and roundtrip costs to catch regressions. Made-with: Cursor * Specialize Fp128 CanonicalField small-int constructors Make from_u64 use a direct canonical limb construction (no reduction path), fix from_i64 to use unsigned_abs to avoid i64::MIN overflow, and add a regression test for the min-value case. Made-with: Cursor * Impl sumchecks for hachi * Add optimized one-hot commitment path for regular sparse witnesses Exploits the structure of one-hot vectors (T chunks of K field elements, each chunk with exactly one 1) to eliminate all inner ring multiplications. Gadget decomposition of {0,1} coefficients is trivial (only level-0 digit is nonzero), and the inner Ajtai t = A*s reduces to summing selected columns of A with O(D) negacyclic rotations instead of O(D^2) ring muls. Handles both K >= D and D >= K as long as one divides the other: - K >= D: each nonzero ring element is a monomial X^j (single rotation) - D >= K: each ring element is a sum of D/K monomials (multiple rotations) Total inner cost: N_A * T * D coefficient additions (zero multiplications), vs N_A * 2^M * delta * D^2 coefficient multiplications in the dense path. Made-with: Cursor * Apply rustfmt formatting to fp128 and field_arith bench Made-with: Cursor * Inject sumchecks to Hachi prover * Add commitment to w to transcript * Add AVX2 and AVX-512 packed field backends for Fp32, Fp64, Fp128 Implement vectorized SIMD arithmetic for x86_64: - AVX2: 8-wide Fp32, 4-wide Fp64, 2-wide Fp128 (scalar delegation) - AVX-512: 16-wide Fp32, 8-wide Fp64, 4-wide Fp128 (scalar delegation) Fp32 uses even/odd lane split with 2-fold Solinas reduction. Fp64 uses vectorized 64×64→128 schoolbook multiply (adapted from plonky3 Goldilocks) with custom Solinas reduction for pseudo-Mersenne primes p = 2^k - c. Also: extract NEON backend into packed_neon.rs, add cfg-gated module selection (AVX-512 > AVX2 > NEON > NoPacking), enable nightly stdarch_x86_avx512 feature, add sumcheck-mix benchmark, and fix minor clippy lints in fp64/fp128. Made-with: Cursor * Vectorize Fp128 packed add/sub on AVX-512 (8-wide) and AVX2 (4-wide) Convert Fp128 packed backends from scalar delegation (AoS) to SoA layout with vectorized add/sub via __m512i / __m256i. Mul remains scalar per-lane. Add FIELD_OPS_PERF.md with Zen 5 benchmark results. Fp128 packed add: +114% (1.08 → 2.31 Gelem/s on Zen 5 AVX-512) Fp128 packed sub: +137% (1.34 → 3.18 Gelem/s) Made-with: Cursor * Add M4 Pro NEON benchmarks, remove mul_add experiment Populate FIELD_OPS_PERF.md with Apple M4 Pro (NEON) results for all primes across scalar, packed, and sumcheck MACC workloads. Remove the experimental mul_add trait method (vectorized add already optimal after inlining; scalar fused approach was 16% slower). Made-with: Cursor * Change sumcheck API * Separate ring switch logic * Rename sumchecks to NormSumcheck and RelationSumcheck * Remove iteration prover * Eliminate O(D^2) schoolbook ring multiplication from protocol hot paths At production parameters (D=256/1024), schoolbook CyclotomicRing multiplication is catastrophically expensive. Every protocol hot path has exploitable operand structure that avoids the full D^2 cost: - Add CyclotomicRing::mul_by_sparse for O(omega*D) sparse challenge multiplication (90-140x speedup in compute_z_hat) - Change RingOpeningPoint to store Vec scalars; use scale() instead of ring mul in compute_w_hat (256-1024x speedup) - Add kron_scalars, kron_row_scale, kron_sparse_scale; refactor generate_m to use scalar-aware Kronecker products - Add zero-skip and scalar-detect in compute_r_via_poly_division - Add sample_sparse_challenges, store Vec in QuadraticEquation throughout prover and verifier paths Made-with: Cursor * lint: section banner removal, naming hoist, cfg(test) for test-only paths - Remove section banner comments (----, =====) repo-wide in src, tests, benches - commitment_scheme: hoist RingCommitment, RingOpeningPoint, transcript labels to top-level use; add #[cfg(test)] use for rederive_alpha_and_m_a body (Blake2bTranscript, eval_ring_matrix_at, expand_m_a, labels) so that function uses short names without polluting lib build - Leave mod tests imports in place (no hoisting of test-module use blocks) Made-with: Cursor * Fix CI issues --------- Co-authored-by: Quang Dao Co-authored-by: Cursor --- .github/workflows/ci.yml | 14 +- AGENTS.md | 35 + CLAUDE.md | 1 + CONSTANT_TIME_NOTES.md | 42 + Cargo.lock | 401 ++++- Cargo.toml | 21 +- HACHI_PROGRESS.md | 200 +++ NTT_PRIME_ANALYSIS.md | 146 ++ README.md | 4 + benches/field_arith.rs | 1448 ++++++++++++++++++ benches/fp64_reduce_probe.rs | 118 ++ benches/ring_ntt.rs | 67 + docs/FIELD_EMBEDDINGS_SUPERNEO_VS_HACHI.md | 698 +++++++++ docs/FIELD_OPS_PERF.md | 237 +++ docs/HACHI_DIGEST.md | 1362 ++++++++++++++++ docs/SUPERNEO_DIGEST.md | 271 ++++ docs/TRANSCRIPT_COMMITMENT_COMPAT_SPEC.md | 106 ++ examples/codegen_probe_special.rs | 143 ++ paper/fri-binius.pdf | Bin 0 -> 819617 bytes paper/greyhound.pdf | Bin 0 -> 557273 bytes paper/labrador.pdf | Bin 0 -> 569118 bytes paper/standards/NIST.FIPS.203.pdf | Bin 0 -> 1252341 bytes paper/standards/NIST.FIPS.204.pdf | Bin 0 -> 3291746 bytes paper/superneo.pdf | Bin 0 -> 740185 bytes rust-toolchain.toml | 4 + rustfmt.toml | 5 + src/algebra/backend/mod.rs | 7 + src/algebra/backend/scalar.rs | 191 +++ src/algebra/backend/traits.rs | 56 + src/algebra/domains/coeff.rs | 6 + src/algebra/domains/crt_ntt.rs | 6 + src/algebra/domains/mod.rs | 7 + src/algebra/fields/ext.rs | 446 ++++++ src/algebra/fields/fp128.rs | 1032 +++++++++++++ src/algebra/fields/fp32.rs | 455 ++++++ src/algebra/fields/fp64.rs | 604 ++++++++ src/algebra/fields/lift.rs | 43 + src/algebra/fields/mod.rs | 40 + src/algebra/fields/packed.rs | 434 ++++++ src/algebra/fields/packed_avx2.rs | 704 +++++++++ src/algebra/fields/packed_avx512.rs | 666 ++++++++ src/algebra/fields/packed_neon.rs | 731 +++++++++ src/algebra/fields/pseudo_mersenne.rs | 177 +++ src/algebra/mod.rs | 34 + src/algebra/module.rs | 202 +++ src/algebra/ntt/butterfly.rs | 155 ++ src/algebra/ntt/crt.rs | 189 +++ src/algebra/ntt/mod.rs | 10 + src/algebra/ntt/prime.rs | 180 +++ src/algebra/ntt/tables.rs | 149 ++ src/algebra/poly.rs | 95 ++ src/algebra/ring/crt_ntt_repr.rs | 246 +++ src/algebra/ring/cyclotomic.rs | 439 ++++++ src/algebra/ring/mod.rs | 9 + src/algebra/ring/sparse_challenge.rs | 164 ++ src/lib.rs | 20 +- src/primitives/arithmetic.rs | 56 +- src/primitives/mod.rs | 1 + src/primitives/multilinear_evals.rs | 155 ++ src/primitives/poly.rs | 15 +- src/primitives/serialization.rs | 2 + src/primitives/transcript.rs | 4 +- src/protocol/challenges/mod.rs | 6 + src/protocol/challenges/sparse.rs | 121 ++ src/protocol/commitment/commit.rs | 146 ++ src/protocol/commitment/config.rs | 186 +++ src/protocol/commitment/mod.rs | 17 + src/protocol/commitment/onehot.rs | 268 ++++ src/protocol/commitment/scheme.rs | 277 ++++ src/protocol/commitment/transcript_append.rs | 13 + src/protocol/commitment/types.rs | 157 ++ src/protocol/commitment/utils/linear.rs | 44 + src/protocol/commitment/utils/math.rs | 14 + src/protocol/commitment/utils/matrix.rs | 131 ++ src/protocol/commitment/utils/mod.rs | 6 + src/protocol/commitment/utils/norm.rs | 48 + src/protocol/commitment_scheme.rs | 425 +++++ src/protocol/mod.rs | 30 + src/protocol/opening_point.rs | 20 + src/protocol/proof.rs | 59 + src/protocol/quadratic_equation.rs | 744 +++++++++ src/protocol/ring_switch.rs | 453 ++++++ src/protocol/sumcheck/mod.rs | 641 ++++++++ src/protocol/sumcheck/norm_sumcheck.rs | 255 +++ src/protocol/sumcheck/relation_sumcheck.rs | 345 +++++ src/protocol/transcript/blake2b.rs | 82 + src/protocol/transcript/keccak.rs | 82 + src/protocol/transcript/labels.rs | 69 + src/protocol/transcript/mod.rs | 37 + src/test_utils.rs | 123 ++ tests/algebra.rs | 1058 +++++++++++++ tests/commitment_contract.rs | 236 +++ tests/hachi_sumcheck.rs | 225 +++ tests/label_schedule.rs | 63 + tests/onehot_commitment.rs | 145 ++ tests/primality.rs | 124 ++ tests/ring_commitment_core.rs | 184 +++ tests/sparse_challenge.rs | 98 ++ tests/sumcheck_core.rs | 304 ++++ tests/sumcheck_prover_driver.rs | 98 ++ tests/transcript.rs | 136 ++ 101 files changed, 20489 insertions(+), 34 deletions(-) create mode 100644 AGENTS.md create mode 120000 CLAUDE.md create mode 100644 CONSTANT_TIME_NOTES.md create mode 100644 HACHI_PROGRESS.md create mode 100644 NTT_PRIME_ANALYSIS.md create mode 100644 benches/field_arith.rs create mode 100644 benches/fp64_reduce_probe.rs create mode 100644 benches/ring_ntt.rs create mode 100644 docs/FIELD_EMBEDDINGS_SUPERNEO_VS_HACHI.md create mode 100644 docs/FIELD_OPS_PERF.md create mode 100644 docs/HACHI_DIGEST.md create mode 100644 docs/SUPERNEO_DIGEST.md create mode 100644 docs/TRANSCRIPT_COMMITMENT_COMPAT_SPEC.md create mode 100644 examples/codegen_probe_special.rs create mode 100644 paper/fri-binius.pdf create mode 100644 paper/greyhound.pdf create mode 100644 paper/labrador.pdf create mode 100644 paper/standards/NIST.FIPS.203.pdf create mode 100644 paper/standards/NIST.FIPS.204.pdf create mode 100644 paper/superneo.pdf create mode 100644 rust-toolchain.toml create mode 100644 rustfmt.toml create mode 100644 src/algebra/backend/mod.rs create mode 100644 src/algebra/backend/scalar.rs create mode 100644 src/algebra/backend/traits.rs create mode 100644 src/algebra/domains/coeff.rs create mode 100644 src/algebra/domains/crt_ntt.rs create mode 100644 src/algebra/domains/mod.rs create mode 100644 src/algebra/fields/ext.rs create mode 100644 src/algebra/fields/fp128.rs create mode 100644 src/algebra/fields/fp32.rs create mode 100644 src/algebra/fields/fp64.rs create mode 100644 src/algebra/fields/lift.rs create mode 100644 src/algebra/fields/mod.rs create mode 100644 src/algebra/fields/packed.rs create mode 100644 src/algebra/fields/packed_avx2.rs create mode 100644 src/algebra/fields/packed_avx512.rs create mode 100644 src/algebra/fields/packed_neon.rs create mode 100644 src/algebra/fields/pseudo_mersenne.rs create mode 100644 src/algebra/mod.rs create mode 100644 src/algebra/module.rs create mode 100644 src/algebra/ntt/butterfly.rs create mode 100644 src/algebra/ntt/crt.rs create mode 100644 src/algebra/ntt/mod.rs create mode 100644 src/algebra/ntt/prime.rs create mode 100644 src/algebra/ntt/tables.rs create mode 100644 src/algebra/poly.rs create mode 100644 src/algebra/ring/crt_ntt_repr.rs create mode 100644 src/algebra/ring/cyclotomic.rs create mode 100644 src/algebra/ring/mod.rs create mode 100644 src/algebra/ring/sparse_challenge.rs create mode 100644 src/primitives/multilinear_evals.rs create mode 100644 src/protocol/challenges/mod.rs create mode 100644 src/protocol/challenges/sparse.rs create mode 100644 src/protocol/commitment/commit.rs create mode 100644 src/protocol/commitment/config.rs create mode 100644 src/protocol/commitment/mod.rs create mode 100644 src/protocol/commitment/onehot.rs create mode 100644 src/protocol/commitment/scheme.rs create mode 100644 src/protocol/commitment/transcript_append.rs create mode 100644 src/protocol/commitment/types.rs create mode 100644 src/protocol/commitment/utils/linear.rs create mode 100644 src/protocol/commitment/utils/math.rs create mode 100644 src/protocol/commitment/utils/matrix.rs create mode 100644 src/protocol/commitment/utils/mod.rs create mode 100644 src/protocol/commitment/utils/norm.rs create mode 100644 src/protocol/commitment_scheme.rs create mode 100644 src/protocol/mod.rs create mode 100644 src/protocol/opening_point.rs create mode 100644 src/protocol/proof.rs create mode 100644 src/protocol/quadratic_equation.rs create mode 100644 src/protocol/ring_switch.rs create mode 100644 src/protocol/sumcheck/mod.rs create mode 100644 src/protocol/sumcheck/norm_sumcheck.rs create mode 100644 src/protocol/sumcheck/relation_sumcheck.rs create mode 100644 src/protocol/transcript/blake2b.rs create mode 100644 src/protocol/transcript/keccak.rs create mode 100644 src/protocol/transcript/labels.rs create mode 100644 src/protocol/transcript/mod.rs create mode 100644 src/test_utils.rs create mode 100644 tests/algebra.rs create mode 100644 tests/commitment_contract.rs create mode 100644 tests/hachi_sumcheck.rs create mode 100644 tests/label_schedule.rs create mode 100644 tests/onehot_commitment.rs create mode 100644 tests/primality.rs create mode 100644 tests/ring_commitment_core.rs create mode 100644 tests/sparse_challenge.rs create mode 100644 tests/sumcheck_core.rs create mode 100644 tests/sumcheck_prover_driver.rs create mode 100644 tests/transcript.rs diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 7aa166de..5715a7f5 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -20,7 +20,7 @@ jobs: runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - - uses: dtolnay/rust-toolchain@stable + - uses: actions-rust-lang/setup-rust-toolchain@v1 with: components: rustfmt - name: Check formatting @@ -31,20 +31,20 @@ jobs: runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - - uses: dtolnay/rust-toolchain@stable + - uses: actions-rust-lang/setup-rust-toolchain@v1 with: components: clippy - name: Clippy (all features) - run: cargo clippy -q --message-format=short --all-features --all-targets -- -D warnings + run: cargo clippy --all --all-targets --all-features -- -D warnings - name: Clippy (no default features) - run: cargo clippy -q --message-format=short --no-default-features --lib -- -D warnings + run: cargo clippy --all --all-targets --no-default-features -- -D warnings doc: name: Documentation runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - - uses: dtolnay/rust-toolchain@stable + - uses: actions-rust-lang/setup-rust-toolchain@v1 - name: Build documentation run: cargo doc -q --no-deps --all-features env: @@ -55,8 +55,8 @@ jobs: runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - - uses: dtolnay/rust-toolchain@stable + - uses: actions-rust-lang/setup-rust-toolchain@v1 - name: Install cargo-nextest uses: taiki-e/install-action@nextest - name: Run tests - run: cargo nextest run -q --all-features + run: cargo nextest run --all-features diff --git a/AGENTS.md b/AGENTS.md new file mode 100644 index 00000000..68f667fa --- /dev/null +++ b/AGENTS.md @@ -0,0 +1,35 @@ +# AGENTS.md + +**Compatibility notice (explicit): This repo makes NO backward-compatibility guarantees. Breaking changes are allowed and expected.** + +## Project Overview + +Hachi is a lattice-based polynomial commitment scheme (PCS) with transparent setup and post-quantum security. Built in Rust. Intended to replace Dory in Jolt. + +## Essential Commands + +```bash +cargo clippy --all --message-format=short -q -- -D warnings +cargo fmt -q +cargo test # no nextest yet +``` + +## Crate Structure + +Two workspace members: `hachi-pcs` (root) and `derive` (proc macros). + +- `src/primitives/` — Core traits: `FieldCore`, `Module`, `MultilinearLagrange`, `Transcript`, serialization +- `src/algebra/` — Concrete backends: prime fields, extension fields, cyclotomic rings, NTT, domains +- `src/protocol/` — Protocol layer: commitment, prover, verifier, opening (ring-switch), challenges, transcript +- `src/error.rs` — Error types + +## Key Abstractions + +- `CommitmentScheme` / `StreamingCommitmentScheme` — top-level PCS traits +- `FieldCore` + `PseudoMersenneField` + `Module` — arithmetic over lattice-friendly fields and rings +- `MultilinearLagrange` — multilinear polynomial in Lagrange basis +- `Transcript` — Fiat-Shamir + +## Feature Flags + +- `parallel` — Rayon parallelization diff --git a/CLAUDE.md b/CLAUDE.md new file mode 120000 index 00000000..47dc3e3d --- /dev/null +++ b/CLAUDE.md @@ -0,0 +1 @@ +AGENTS.md \ No newline at end of file diff --git a/CONSTANT_TIME_NOTES.md b/CONSTANT_TIME_NOTES.md new file mode 100644 index 00000000..dac24600 --- /dev/null +++ b/CONSTANT_TIME_NOTES.md @@ -0,0 +1,42 @@ +# Constant-Time Review Notes (Phase 0/1 Algebra) + +This note tracks timing-sensitive implementation decisions for the current +algebra and ring stack. + +## Reviewed Components + +- `src/algebra/fields/fp32.rs` +- `src/algebra/fields/fp64.rs` +- `src/algebra/fields/fp128.rs` +- `src/algebra/ntt/prime.rs` +- `src/algebra/ntt/butterfly.rs` +- `src/algebra/ring/cyclotomic.rs` +- `src/algebra/ring/crt_ntt_repr.rs` + +## Current State + +- Branchless primitives are in place for: + - `Fp32/Fp64/Fp128` add/sub/neg raw helpers. + - `Fp128` multiplication reduction (`reduce_u256`) with branchless conditional subtract. + - `Fp32/Fp64` multiplication reduction (division-free fixed-iteration paths). + - NTT helper operations `csubp`, `caddp`, and `center`. +- NTT butterfly arithmetic runs in fixed loop structure independent of data. +- Ring multiplication (`CyclotomicRing`) is fixed-structure schoolbook over `D`. +- CRT reconstruction inner accumulation now uses fixed-trip, branchless + modular add/mul-by-small-factor helpers. +- Prime fields now expose `Invertible::inv_or_zero()` for secret-bearing + inversion use-cases without input-dependent branching on zero. +- CRT reconstruction final projection now uses a division-free fixed-iteration + reducer (`reduce_u128_divfree`) instead of `% q`. + +## Known Timing Risks / Follow-ups + +- `FieldCore::inv()` still returns `Option` and therefore branches on zero; + treat that API as public-value oriented. Use `Invertible::inv_or_zero()` + in secret-dependent paths. + +## Action Items Before Production-Critical Use + +1. Wire secret-bearing call sites to `Invertible::inv_or_zero()` as + protocol code matures. +2. Add dedicated CT review tests/checklists for any arithmetic subsystem changes. diff --git a/Cargo.lock b/Cargo.lock index a505ce5c..e184f5cc 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -2,6 +2,18 @@ # It is not intended for manual editing. version = 3 +[[package]] +name = "ahash" +version = "0.8.12" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "5a15f179cd60c4584b8a8c596927aadc462e27f2ca70c04e0071964a73ba7a75" +dependencies = [ + "cfg-if", + "once_cell", + "version_check", + "zerocopy", +] + [[package]] name = "aho-corasick" version = "1.1.4" @@ -11,6 +23,33 @@ dependencies = [ "memchr", ] +[[package]] +name = "allocative" +version = "0.3.4" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "8fac2ce611db8b8cee9b2aa886ca03c924e9da5e5295d0dbd0526e5d0b0710f7" +dependencies = [ + "allocative_derive", + "ctor", +] + +[[package]] +name = "allocative_derive" +version = "0.3.3" +source = 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[ + "proc-macro2", + "quote", + "syn 2.0.110", ] diff --git a/Cargo.toml b/Cargo.toml index 47abb4d8..d6e45663 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -6,7 +6,7 @@ resolver = "2" name = "hachi-pcs" version = "0.1.0" edition = "2021" -rust-version = "1.75" +rust-version = "1.88" authors = [ "Markos Georghiades ", ] @@ -37,14 +37,31 @@ parallel = ["dep:rayon"] [dependencies] thiserror = "2.0" -rand_core = "0.6" +rand_core = { version = "0.6", features = ["getrandom"] } hachi-derive = { version = "0.1.0", path = "derive" } tracing = "0.1" rayon = { version = "1.10", optional = true } +blake2 = "0.10.6" +sha3 = "0.10.8" [dev-dependencies] rand = "0.8" criterion = { version = "0.5", features = ["html_reports"] } +num-bigint = "0.4.6" +ark-bn254 = { git = "https://github.com/a16z/arkworks-algebra", branch = "dev/twist-shout", features = ["scalar_field"] } +ark-ff = { git = "https://github.com/a16z/arkworks-algebra", branch = "dev/twist-shout" } + +[[bench]] +name = "ring_ntt" +harness = false + +[[bench]] +name = "field_arith" +harness = false + +[[bench]] +name = "fp64_reduce_probe" +harness = false [lints.rust] missing_docs = "warn" diff --git a/HACHI_PROGRESS.md b/HACHI_PROGRESS.md new file mode 100644 index 00000000..afca63e6 --- /dev/null +++ b/HACHI_PROGRESS.md @@ -0,0 +1,200 @@ +## Hachi PCS implementation progress + +This file is the **single source of truth** for implementation status and near-term priorities. + +### Goals (project-level) + +- **Production-ready implementation**: correctness, security, maintainability, and performance are first-class goals. +- **Standalone codebase**: implementation and comments should stand on their own; external acknowledgements live in `README.md`. +- **Constant-time cryptographic core**: arithmetic and protocol-critical paths must be constant-time with respect to secret data. +- **No shortcuts / no fallback design**: avoid temporary or degraded code paths in the core implementation. + +### Non-negotiable requirements + +- **Constant-time discipline** + - No secret-dependent branches or memory access patterns in cryptographic hot paths. + - No secret-indexed table lookups; table access patterns must be independent of secret data. + - Keep data representations and reductions explicit and auditable for timing behavior. + - Add targeted tests/reviews for constant-time-sensitive code as features land. +- **Code quality bar** + - Clear naming, explicit invariants, small cohesive modules, and API docs for public interfaces. + - No placeholder crypto logic in mainline code (no "temporary" arithmetic shortcuts). + - Tests are required for correctness-critical arithmetic before dependent protocol code is built. + - No section-banner comments (e.g., `// ---- Section ----`, `// === ... ===`). Let the code and doc-comments speak for themselves. +- **Standalone implementation policy** + - Do not mention external inspirations/ports in core code comments. + - Keep terminology and structure internally coherent and project-native. + - Keep external attribution limited to dedicated docs (for now: `README.md` acknowledgements). +- **Git discipline** + - Do not commit or push without explicit user approval. + +### Implementation workflow (cautious + approval-driven) + +- Before each major subsystem, present implementation options with trade-offs. +- Seek explicit approval before proceeding with a selected option. +- Pause at milestone boundaries for review and feedback before continuing. +- Prefer slow, verifiable progress over rapid, high-risk changes. +- Ask for user input frequently when requirements are ambiguous or involve design trade-offs. + +### Definition of Done (all crypto-critical work) + +- **Security / constant-time** + - Secret-independent control flow and memory access in cryptographic paths. + - Constant-time review notes included for non-trivial arithmetic/ring changes. +- **Correctness** + - Unit tests for edge cases and algebraic identities. + - Cross-check vectors/reference checks added where practical. +- **Code quality** + - Clear naming, explicit invariants, and no placeholder logic in core paths. + - Public interfaces documented sufficiently for safe usage. +- **Performance** + - Hot-path performance impact evaluated (benchmark or measured rationale). +- **Tooling + CI** + - `cargo fmt --all --check` passes. + - `cargo clippy --all --all-targets --all-features` passes. + - `cargo test` (or targeted suite for touched modules) passes. +- **Process** + - Implementation options reviewed with user before major subsystem changes. + - Milestone update recorded in this file. + +### Scope (current) + +- **Implemented so far (Phase 0 + Phase 1 functional core)**: prime fields (32/64/128-bit representations), extension fields, cyclotomic `R_q = Z_q[X]/(X^d + 1)`, CRT+NTT representation, backend/domain layering, ring automorphisms, and functional gadget decomposition. +- **Phase 2+ protocol status**: interface scaffold plus ring-native §4.1 commitment core are present (`Transcript`, Blake2b/Keccak backends, phase-grounded labels, `RingCommitmentScheme`, config layer, and setup/commit implementation). Sumcheck core building blocks (univariate messages + transcript-driving prover/verifier driver) are now implemented, with tests. Open-check prover/verifier paths remain stubbed. +- **Deferred future phase**: integration into Jolt (replacement of Dory with Hachi) is intentionally out of current execution scope; cross-repo analysis is design input only. + +### Critical review snapshot (2026-02-13) + +- **Phase 1 functional milestone appears complete** + - Ring/gadget components listed in Phase 1 are implemented and currently checked off. + - Conversion and arithmetic paths in coefficient and CRT+NTT domains are exercised by passing tests. +- **Not yet "production-ready" despite functional completion** + - Constant-time hardening follow-ups narrowed: secret-bearing call-sites still need to migrate from `FieldCore::inv()` to `Invertible::inv_or_zero()` as protocol code lands (see `CONSTANT_TIME_NOTES.md`). + - Current ring multiplication in coefficient form remains `O(D^2)` schoolbook (`src/algebra/ring/cyclotomic.rs`), with CRT+NTT available as the faster domain path. +- **Tooling/quality gate status (current branch snapshot)** + - `cargo test` passes, including protocol transcript/label/commitment contract tests and new ring-commitment core/config/stub tests. + - `cargo fmt --all --check` passes. + - `cargo clippy --all --all-targets --all-features` passes. +- **Phase 2 scaffold + commitment core landed; proof-system work still pending** + - `src/protocol/*` now provides transcript + commitment abstraction boundaries with `Transcript` naming. + - Two transcript backends are wired (`Blake2bTranscript`, `KeccakTranscript`) with deterministic replay/order/reset tests. + - Hachi-native labels are now calibrated to paper-stage phases (§4.1, §4.2, §4.3, §4.5). + - Commitment absorption is label-directed at call sites (`AppendToTranscript` no longer hardcodes commitment labels). + - Ring-native commitment setup/commit flow for §4.1 is implemented in `src/protocol/commitment/commit.rs` behind `RingCommitmentScheme`. + - Sumcheck core module landed (`src/protocol/sumcheck.rs`) with unit/integration tests (`tests/sumcheck_core.rs`, `tests/sumcheck_prover_driver.rs`). + - Prover/verifier split folders are wired with explicit stubs (`src/protocol/prover/stub.rs`, `src/protocol/verifier/stub.rs`) for future open-check implementation. +- **Conclusion** + - Treat **Phase 1 as functionally complete**. + - Treat **Phase 2 as active/in-progress** (commitment core implemented; prove/verify and later reductions still open). + - Remaining strict CT follow-ups stay tracked in `CONSTANT_TIME_NOTES.md`. + +### Status board + +#### Phase 0 — Algebra + +- [x] Prime field `Fp32` (u32 storage; u64 mul) implementing `FieldCore + CanonicalField` (`src/algebra/fields/fp32.rs`) +- [x] Prime field `Fp64` (u64 storage; u128 mul) implementing `FieldCore + CanonicalField` (`src/algebra/fields/fp64.rs`) +- [x] Prime field `Fp128` (u128 storage; 256-bit intermediate) implementing `FieldCore + CanonicalField` (`src/algebra/fields/fp128.rs`, `src/algebra/fields/u256.rs`) +- [x] Branchless constant-time `add_raw`, `sub_raw`, `neg` for all field types +- [x] Constant-time inversion helper for prime fields: `Invertible::inv_or_zero()` (`src/primitives/arithmetic.rs`, `src/algebra/fields/fp*.rs`) +- [x] Division-free fixed-iteration reduction for `Fp32/Fp64` multiplication paths +- [x] Division-free fixed-iteration CRT final projection (replaced `% q` in scalar reconstruction path) +- [x] Rejection-sampled `FieldSampling::sample()` for all field types (no modular bias) +- [x] Pow2Offset pseudo-Mersenne registry + aliases (`q = 2^k - offset`, bounded `k <= 128`, `q % 8 == 5`) (`src/algebra/fields/pseudo_mersenne.rs`) +- [x] Constant-time review notes for current algebra/ring paths (`CONSTANT_TIME_NOTES.md`) +- [x] Deterministic parameter presets + - [x] `q = 2^32 - 99` constants scaffold (`src/algebra/ntt/tables.rs`) + - [x] `Pow2Offset` presets selected for 64/128-bit path: + - `q = 2^64 - 59` (`POW2_OFFSET_MODULUS_64`) + - `q = 2^128 - 275` (`POW2_OFFSET_MODULUS_128`) + - source: `src/algebra/fields/pseudo_mersenne.rs` +- [x] `Module` implementations: + - [x] `VectorModule` (fixed-length vectors; `Module` via scalar*vector mul) (`src/algebra/module.rs`) + - [x] `PolyModule` removed from current scope (not needed for near-term Hachi milestones) +- [ ] Extension fields: + - [x] `Fp2` quadratic extension (`src/algebra/fields/ext.rs`) + - [x] `Fp4` tower extension (`src/algebra/fields/ext.rs`) +- [x] Serialization for algebra types (`HachiSerialize` / `HachiDeserialize`) (+ `u128/i128` primitives in `src/primitives/serialization.rs`) +- [x] NTT small-prime arithmetic: Montgomery-like `fpmul`, Barrett-like `fpred`, branchless `csubq`/`caddq`/`center` (`src/algebra/ntt/prime.rs`) +- [x] CRT limb arithmetic: `LimbQ`, `QData` (`src/algebra/ntt/crt.rs`) +- [x] Tests (49 total in `tests/algebra.rs`): + - [x] field arithmetic, identities, distributivity (Fp32/Fp64/Fp128) + - [x] zero inversion returns None + - [x] serialization round-trips (all field types, extensions, Poly, VectorModule) + - [x] Fp2 conjugate, norm, distributivity + - [x] U256 wide multiply and bit access + - [x] LimbQ round-trip, add/sub inverse, QData consistency + - [x] NTT normalize range, fpmul commutativity + - [x] Poly add/sub/neg + - [x] Cyclotomic ring identities and serialization (D=4, D=64) + - [x] NTT forward/inverse round-trips (single prime and all Q32 primes) + - [x] Cyclotomic CRT+NTT full round-trip (`from_ring` -> `to_ring`) + - [x] Scalar backend path equivalence (`*_with_backend` vs default path) + - [x] Pow2Offset profile invariants (`q = 2^k - offset`, `q % 8 == 5`) + - [x] `FieldSampling::sample()` output bound checks + - [x] Checked deserialization rejects non-canonical field encodings + - [x] Galois automorphism checks (`sigma` composition + multiplicativity) + - [x] Functional gadget decompose/recompose round-trip checks + - [x] Sparse `+/-1` challenge support checks (`hamming_weight = omega`) +- [x] Dedicated Pow2Offset primality regression tests (`tests/primality.rs`) + - [x] Miller-Rabin probable-prime checks for all registered Pow2Offset moduli + - [x] Composite sanity rejection checks + +#### Phase 1 — Ring + gadgets (functional core) + +- [x] Cyclotomic ring `Rq` with `X^D = -1` (`src/algebra/ring/cyclotomic.rs`) +- [x] CRT+NTT-domain ring representation + CRT conversion (`src/algebra/ring/crt_ntt_repr.rs`) +- [x] Backend/domain layering for ring execution (`src/algebra/backend/*`, `src/algebra/domains/*`) +- [x] Galois automorphisms `sigma_i: X ↦ X^i` (odd `i`) +- [x] Functional gadget decomposition/recomposition (`G^{-1}` / `G` behavior) for base-`2^d` digits, without materializing dense gadget matrices +- [x] sparse short challenges (paper: `||c||_1 ≤ ω`, sparse ±1) + +#### Phase 2+ — Protocol (later) + +- [x] Protocol module scaffold (`src/protocol/*`) and top-level re-exports +- [x] Transcript interface (`Transcript`) plus Blake2b/Keccak implementations +- [x] Hachi-native transcript label schedule aligned to paper phases (§4.1/§4.2/§4.3/§4.5) +- [x] Commitment trait surface + streaming trait surface + contract tests +- [x] Label-directed transcript absorption for commitments (`AppendToTranscript` takes label at call site) +- [x] ring-native commitment core (`RingCommitmentScheme`, `commit.rs`, config wiring) for §4.1 setup/commit +- [x] protocol prover/verifier folder split with explicit stubs (`prover/stub.rs`, `verifier/stub.rs`) +- [x] ring-commitment tests (`ring_commitment_core`, `ring_commitment_config`, `prover_verifier_stub_contract`) +- [x] sumcheck core building blocks (univariate messages + transcript-driving prover/verifier driver) (`src/protocol/sumcheck.rs`) +- [x] sumcheck core tests (`tests/sumcheck_core.rs`, `tests/sumcheck_prover_driver.rs`) +- [ ] commitment open-check prove/verify implementation (currently stubs) +- [ ] evaluation → linear relation (paper §4.2) +- [ ] ring-switching constraints as sumcheck instances (paper §4.3, Fig. 4–7) +- [ ] recursion / “stop condition” + optional Greyhound composition (§4.5) + +#### Phase 3 — Integration into Jolt (deferred; not active now) + +- [ ] Define compatibility boundary document (what must match Jolt/Dory behavior vs what can remain Hachi-native) +- [ ] Provide Jolt-facing transcript adapter design (`Jolt` transcript pattern ↔ Hachi transcript object) +- [ ] Provide Jolt-facing PCS shim design (`CommitmentScheme`/`StreamingCommitmentScheme` mapping) +- [ ] Add transcript/commitment compatibility tests for integration-readiness (without wiring into Jolt yet) + +### Conventions + +- **Correctness first**: lock arithmetic with tests before touching protocol code. +- **Security first**: enforce constant-time behavior for secret-dependent operations. +- **Lean deps**: avoid heavyweight crypto crates until there is a clear need. +- **Explicit parameter sets**: each field/ring preset lives in code with a clear name and rationale. + +### Module layout + +``` +src/algebra/ +├── backend/ Backend execution traits + scalar backend +├── domains/ Domain-level aliases (coefficient / CRT+NTT) +├── fields/ Prime fields, pseudo-mersenne registry, u256, and extensions +├── ntt/ NTT kernels (butterfly), prime kernels (prime), CRT helpers (crt), presets (tables) +├── module.rs VectorModule +├── poly.rs Poly container +└── ring/ Cyclotomic ring and CRT+NTT representation +``` + +### References + +- Hachi paper: `paper/hachi.pdf` +- Core traits: `src/primitives/arithmetic.rs`, `src/primitives/serialization.rs` + diff --git a/NTT_PRIME_ANALYSIS.md b/NTT_PRIME_ANALYSIS.md new file mode 100644 index 00000000..e6b9c85c --- /dev/null +++ b/NTT_PRIME_ANALYSIS.md @@ -0,0 +1,146 @@ +# NTT Prime Analysis (Pow2Offset / Solinas Context) + +This note records the current analysis for small NTT primes and CRT coverage targets. + +## References + +- NIST ML-KEM: `paper/standards/NIST.FIPS.203.pdf` +- NIST ML-DSA: `paper/standards/NIST.FIPS.204.pdf` +- Current small-prime table: `src/algebra/ntt/tables.rs` +- Labrador generator heuristic: `../labrador/data.py` + +## Why does `2D` divide `p - 1`? + +For negacyclic NTT on `Z_p[X]/(X^D + 1)`, we need a primitive `2D`-th root `psi` such that: + +- `psi^D = -1 (mod p)` +- `psi^(2D) = 1 (mod p)` + +Over prime fields, `F_p^*` is cyclic of size `p - 1`, so an element of order `2D` exists iff: + +- `2D | (p - 1)` + +So yes, the `128 | (p - 1)` condition is directly tied to `D = 64`. + +## What if `D = 1024`? + +Then requirement becomes: + +- `2D = 2048`, so `2048 | (p - 1)`. + +Under the current "small prime" cap (`p < 2^14`), this is extremely restrictive. + +## Why `< 2^14` in current code? + +This is a backend implementation constraint, not a hard NTT math requirement: + +- Current small-prime NTT backend stores modulus/coefficients in signed 16-bit lanes (`i16`). +- It relies on centered signed arithmetic and butterfly add/sub before full normalization. +- Keeping `p < 2^14` leaves practical headroom in those 16-bit operations. +- Current CRT limb code is also radix-`2^14`, matching this design style. + +So the `2^14` cap is about the present `i16` scalar kernel design. If we introduce an `i32` backend, this cap can be raised substantially. + +## Exhaustive counts (for `p < 2^14`) + +We classify exact Solinas as: + +- `p = 2^x - 2^y + 1`. + +Results: + +- `D = 64` (`128 | p-1`) + - all small NTT primes: **31** + - exact Solinas NTT primes: **6** + - all-prime set: + - `257, 641, 769, 1153, 1409, 2689, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857, 10369, 10753, 11393, 11777, 12161, 12289, 13313, 13441, 13697, 14081, 14593, 15233, 15361, 16001` + - Solinas set: `257, 769, 7681, 7937, 12289, 15361` +- `D = 256` (`512 | p-1`) + - all small NTT primes: **6** + - exact Solinas NTT primes: **3** + - Solinas set: `7681, 12289, 15361` +- `D = 1024` (`2048 | p-1`) + - all small NTT primes: **1** + - exact Solinas NTT primes: **1** + - Solinas set: `12289` + +Conclusion: for higher `D`, the small-prime pool shrinks rapidly. + +## 30-bit exploration (`p < 2^30`) with NTT constraints + +To assess a larger-prime backend direction, we scanned for primes under `2^30` with: + +- `p ≡ 1 (mod 2D)`. + +Below are the **full outputs of the bounded search run** (top 30 largest primes found by descending scan): + +### `D = 64` (`2D = 128`) + +- Top-30 list: + - `1073741441, 1073739649, 1073738753, 1073736449, 1073735297, 1073734913, 1073732993, 1073732609, 1073731201, 1073731073, 1073730817, 1073728897, 1073727617, 1073726977, 1073722753, 1073719681, 1073717377, 1073716993, 1073713409, 1073712769, 1073712257, 1073710721, 1073708929, 1073707009, 1073703809, 1073702657, 1073702401, 1073698817, 1073696257, 1073693441` +- Coverage for `q = 2^128 - 275`: + - `P > q`: **5** limbs + - `P > 128*q^2`: **9** limbs + +### `D = 1024` (`2D = 2048`) + +- Top-30 list: + - `1073707009, 1073698817, 1073692673, 1073682433, 1073668097, 1073655809, 1073651713, 1073643521, 1073620993, 1073600513, 1073569793, 1073563649, 1073551361, 1073539073, 1073522689, 1073510401, 1073508353, 1073479681, 1073453057, 1073442817, 1073440769, 1073430529, 1073412097, 1073391617, 1073385473, 1073354753, 1073350657, 1073330177, 1073299457, 1073268737` +- Coverage for `q = 2^128 - 275`: + - `P > q`: **5** limbs + - `P > 128*q^2`: **9** limbs + +### Bit-estimate sanity check + +- `ceil(128 / 30) = 5` +- `ceil(263 / 30) = 9` (for `128*q^2 ~ 2^263`) + +This matches the concrete product counts above. + +## CRT size targets for `q = 2^128 - 275` + +Two common thresholds: + +1. Minimal uniqueness target: + - `P = prod(p_i) > q` +2. Labrador conservative heuristic: + - `P > 128 * q^2` (from `data.py`, with `FIXME` comment) + +### Limb counts at `D = 64` with current small-prime pool + +- Using all small NTT primes (`31` available): + - `P > q` achievable with **10** limbs + - `P > 128*q^2` achievable with **20** limbs +- Using only exact Solinas NTT primes (`6` available): + - `P > q`: **not achievable** + - `P > 128*q^2`: **not achievable** + - total product is only about `2^70` + +### Limb counts at `D = 1024` with current small-prime pool + +- Only one qualifying prime (`12289`) under `p < 2^14`, so neither threshold is achievable. + +## What is Labrador's safety margin doing? + +In Labrador code, prime selection stops at: + +- `P > 128 * q^2` + +Interpretation: + +- `q^2` tracks product-scale growth, +- extra factor `128` gives additional headroom (for `N=64`, this is `2N`), +- but their own `FIXME` comment indicates this is a conservative engineering bound, not a tight proof. + +So treat this as a robust heuristic rather than a formal minimum. + +## Practical implication for Hachi + +- If we stay with `D=64` and small i16-ish primes, we need non-Solinas primes in the CRT set. +- If we push to `D=1024`, we must either: + - lift prime size beyond `<2^14`, or + - change CRT strategy (fewer larger limbs / different backend), or + - avoid strict small-prime CRT-NTT at that degree. +- A mixed backend model is sensible: + - keep the current `i16` backend for small-prime kernels, + - add an `i32`/wider backend for larger-prime kernels (e.g., up to ~30-bit). diff --git a/README.md b/README.md index 492b4d12..8036344f 100644 --- a/README.md +++ b/README.md @@ -3,3 +3,7 @@ A high performance and modular implementation of the Hachi polynomial commitment scheme. Hachi is a lattice-based polynomial commitment scheme with transparent setup and post-quantum security. + +## Acknowledgements + +The CRT/NTT and small-prime arithmetic design in this repository is informed by the Labrador/Greyhound C implementation family. In particular, the current pseudo-Mersenne profile uses moduli of the form `q = 2^k - offset` (smallest prime below `2^k` with `q % 8 == 5`). Hachi provides a Rust-native architecture and APIs, while drawing algorithmic inspiration from those implementations. diff --git a/benches/field_arith.rs b/benches/field_arith.rs new file mode 100644 index 00000000..9caf70d8 --- /dev/null +++ b/benches/field_arith.rs @@ -0,0 +1,1448 @@ +#![allow(missing_docs)] + +use ark_bn254::Fr as BN254Fr; +use ark_ff::{AdditiveGroup, Field}; +use criterion::{black_box, criterion_group, criterion_main, Criterion, Throughput}; +use hachi_pcs::algebra::fields::fp128::{Prime128M18M0, Prime128M54P0}; +use hachi_pcs::algebra::fields::fp32::Fp32; +use hachi_pcs::algebra::{HasPacking, PackedField, PackedValue, Prime128M13M4P0, Prime128M8M4M1M0}; +use hachi_pcs::algebra::{ + Pow2Offset24Field, Pow2Offset30Field, Pow2Offset31Field, Pow2Offset32Field, Pow2Offset40Field, + Pow2Offset48Field, Pow2Offset56Field, Pow2Offset64Field, +}; +use hachi_pcs::{CanonicalField, FieldCore, FieldSampling, Invertible}; +use rand::{rngs::StdRng, RngCore, SeedableRng}; +use std::env; +#[cfg(feature = "parallel")] +use std::thread; + +#[cfg(feature = "parallel")] +use rayon::prelude::*; +#[cfg(feature = "parallel")] +use rayon::ThreadPoolBuilder; + +fn rand_u128(rng: &mut R) -> u128 { + let lo = rng.next_u64() as u128; + let hi = rng.next_u64() as u128; + lo | (hi << 64) +} + +fn env_usize(name: &str, default: usize) -> usize { + env::var(name) + .ok() + .and_then(|v| v.parse::().ok()) + .unwrap_or(default) +} + +fn bench_mul(c: &mut Criterion) { + type F13 = Prime128M13M4P0; + type F275 = Prime128M8M4M1M0; + type F2p18p1 = Prime128M18M0; + type F2p54m1 = Prime128M54P0; + + let mut rng = StdRng::seed_from_u64(0x5eed); + let inputs_u128: Vec = (0..2048).map(|_| rand_u128(&mut rng)).collect(); + + let inputs_f13: Vec = inputs_u128 + .iter() + .copied() + .map(F13::from_canonical_u128_reduced) + .collect(); + + let inputs_f275: Vec = inputs_u128 + .iter() + .copied() + .map(F275::from_canonical_u128_reduced) + .collect(); + let inputs_f2p18p1: Vec = inputs_u128 + .iter() + .copied() + .map(F2p18p1::from_canonical_u128_reduced) + .collect(); + let inputs_f2p54m1: Vec = inputs_u128 + .iter() + .copied() + .map(F2p54m1::from_canonical_u128_reduced) + .collect(); + + let mut group = c.benchmark_group("field_mul"); + + group.bench_function("fp128_prime128m13m4p0", |b| { + b.iter(|| { + let mut acc = F13::one(); + for x in inputs_f13.iter() { + acc = acc * *x + acc; + } + black_box(acc) + }) + }); + + group.bench_function("fp128_prime128m8m4m1m0", |b| { + b.iter(|| { + let mut acc = F275::one(); + for x in inputs_f275.iter() { + acc = acc * *x + acc; + } + black_box(acc) + }) + }); + + group.bench_function("fp128_prime128m18m0_shift_special", |b| { + b.iter(|| { + let mut acc = F2p18p1::one(); + for x in inputs_f2p18p1.iter() { + acc = acc * *x + acc; + } + black_box(acc) + }) + }); + + group.bench_function("fp128_prime128m54p0_shift_special", |b| { + b.iter(|| { + let mut acc = F2p54m1::one(); + for x in inputs_f2p54m1.iter() { + acc = acc * *x + acc; + } + black_box(acc) + }) + }); + + group.finish(); +} + +fn bench_mul_only(c: &mut Criterion) { + type F13 = Prime128M13M4P0; + type F2p18p1 = Prime128M18M0; + type F2p54m1 = Prime128M54P0; + + let mut rng = StdRng::seed_from_u64(0x5eed); + let inputs_f13: Vec = (0..2048) + .map(|_| F13::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + let inputs_f2p18p1: Vec = (0..2048) + .map(|_| F2p18p1::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + let inputs_f2p54m1: Vec = (0..2048) + .map(|_| F2p54m1::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + + let mut group = c.benchmark_group("field_mul_only"); + + group.bench_function("mul_chain_2048", |b| { + b.iter(|| { + let mut acc = F13::one(); + for x in inputs_f13.iter() { + acc = acc * *x; + } + black_box(acc) + }) + }); + + group.bench_function("mul_chain_16384", |b| { + b.iter(|| { + let mut acc = F13::one(); + for _ in 0..8 { + for x in inputs_f13.iter() { + acc = acc * *x; + } + } + black_box(acc) + }) + }); + + group.bench_function("mul_parallel_1024", |b| { + b.iter(|| { + let mut sum = F13::zero(); + for pair in inputs_f13.chunks_exact(2) { + sum = sum + pair[0] * pair[1]; + } + black_box(sum) + }) + }); + + group.bench_function("mul_chain_2048_special_m18m0", |b| { + b.iter(|| { + let mut acc = F2p18p1::one(); + for x in inputs_f2p18p1.iter() { + acc = acc * *x; + } + black_box(acc) + }) + }); + + group.bench_function("mul_chain_2048_special_m54p0", |b| { + b.iter(|| { + let mut acc = F2p54m1::one(); + for x in inputs_f2p54m1.iter() { + acc = acc * *x; + } + black_box(acc) + }) + }); + + group.finish(); +} + +fn bench_mul_isolated(c: &mut Criterion) { + use ark_ff::UniformRand; + + type F13 = Prime128M13M4P0; + + let mut rng = StdRng::seed_from_u64(0x5eed); + let a_fp128 = F13::from_canonical_u128_reduced(rand_u128(&mut rng)); + let b_fp128 = F13::from_canonical_u128_reduced(rand_u128(&mut rng)); + let a_bn254 = BN254Fr::rand(&mut rng); + let b_bn254 = BN254Fr::rand(&mut rng); + + let mut group = c.benchmark_group("field_mul_isolated"); + + group.bench_function("fp128_black_box_only", |b| b.iter(|| black_box(a_fp128))); + + group.bench_function("bn254_black_box_only", |b| b.iter(|| black_box(a_bn254))); + + group.bench_function("fp128_pair_passthrough", |b| { + b.iter(|| { + let x = black_box(a_fp128); + let y = black_box(b_fp128); + black_box((x, y)) + }) + }); + + group.bench_function("bn254_pair_passthrough", |b| { + b.iter(|| { + let x = black_box(a_bn254); + let y = black_box(b_bn254); + black_box((x, y)) + }) + }); + + group.bench_function("fp128_mul_single", |b| { + b.iter(|| { + let x = black_box(a_fp128); + let y = black_box(b_fp128); + black_box(x * y) + }) + }); + + group.bench_function("bn254_mul_single", |b| { + b.iter(|| { + let x = black_box(a_bn254); + let y = black_box(b_bn254); + black_box(x * y) + }) + }); + + let lanes_fp128: [(F13, F13); 8] = std::array::from_fn(|_| { + ( + F13::from_canonical_u128_reduced(rand_u128(&mut rng)), + F13::from_canonical_u128_reduced(rand_u128(&mut rng)), + ) + }); + let lanes_bn254: [(BN254Fr, BN254Fr); 8] = + std::array::from_fn(|_| (BN254Fr::rand(&mut rng), BN254Fr::rand(&mut rng))); + + group.bench_function("fp128_mul_8way_independent", |b| { + b.iter(|| { + let lanes = black_box(&lanes_fp128); + let p0 = lanes[0].0 * lanes[0].1; + let p1 = lanes[1].0 * lanes[1].1; + let p2 = lanes[2].0 * lanes[2].1; + let p3 = lanes[3].0 * lanes[3].1; + let p4 = lanes[4].0 * lanes[4].1; + let p5 = lanes[5].0 * lanes[5].1; + let p6 = lanes[6].0 * lanes[6].1; + let p7 = lanes[7].0 * lanes[7].1; + black_box([p0, p1, p2, p3, p4, p5, p6, p7]) + }) + }); + + group.bench_function("fp128_8way_passthrough", |b| { + b.iter(|| { + let lanes = black_box(&lanes_fp128); + let p0 = lanes[0].0; + let p1 = lanes[1].0; + let p2 = lanes[2].0; + let p3 = lanes[3].0; + let p4 = lanes[4].0; + let p5 = lanes[5].0; + let p6 = lanes[6].0; + let p7 = lanes[7].0; + black_box([p0, p1, p2, p3, p4, p5, p6, p7]) + }) + }); + + group.bench_function("bn254_mul_8way_independent", |b| { + b.iter(|| { + let lanes = black_box(&lanes_bn254); + let p0 = lanes[0].0 * lanes[0].1; + let p1 = lanes[1].0 * lanes[1].1; + let p2 = lanes[2].0 * lanes[2].1; + let p3 = lanes[3].0 * lanes[3].1; + let p4 = lanes[4].0 * lanes[4].1; + let p5 = lanes[5].0 * lanes[5].1; + let p6 = lanes[6].0 * lanes[6].1; + let p7 = lanes[7].0 * lanes[7].1; + black_box([p0, p1, p2, p3, p4, p5, p6, p7]) + }) + }); + + group.bench_function("bn254_8way_passthrough", |b| { + b.iter(|| { + let lanes = black_box(&lanes_bn254); + let p0 = lanes[0].0; + let p1 = lanes[1].0; + let p2 = lanes[2].0; + let p3 = lanes[3].0; + let p4 = lanes[4].0; + let p5 = lanes[5].0; + let p6 = lanes[6].0; + let p7 = lanes[7].0; + black_box([p0, p1, p2, p3, p4, p5, p6, p7]) + }) + }); + + group.finish(); +} + +fn bench_sqr(c: &mut Criterion) { + type F13 = Prime128M13M4P0; + + let mut rng = StdRng::seed_from_u64(0x5eed); + let start = F13::from_canonical_u128_reduced(rand_u128(&mut rng)); + + let mut group = c.benchmark_group("field_sqr"); + + group.bench_function("sqr_chain_2048", |b| { + b.iter(|| { + let mut acc = start; + for _ in 0..2048 { + acc = acc.square(); + } + black_box(acc) + }) + }); + + group.bench_function("mul_self_chain_2048", |b| { + b.iter(|| { + let mut acc = start; + for _ in 0..2048 { + acc = acc * acc; + } + black_box(acc) + }) + }); + + group.finish(); +} + +fn bench_inv(c: &mut Criterion) { + type F13 = Prime128M13M4P0; + + let mut rng = StdRng::seed_from_u64(0x1a2b_3c4d_5e6f_7788); + let inputs: Vec = (0..256) + .map(|_| F13::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + + c.bench_function("fp128_inv_or_zero_prime128m13m4p0", |b| { + b.iter(|| { + let mut acc = F13::one(); + for x in inputs.iter() { + acc = acc * x.inv_or_zero(); + } + black_box(acc) + }) + }); +} + +fn bench_bn254(c: &mut Criterion) { + use ark_ff::UniformRand; + + let mut rng = StdRng::seed_from_u64(0x5eed); + let inputs: Vec = (0..2048).map(|_| BN254Fr::rand(&mut rng)).collect(); + + let mut group = c.benchmark_group("bn254_fr"); + + group.bench_function("mul_add_chain_2048", |b| { + b.iter(|| { + let mut acc = BN254Fr::ONE; + for x in inputs.iter() { + acc = acc * x + acc; + } + black_box(acc) + }) + }); + + group.bench_function("mul_chain_2048", |b| { + b.iter(|| { + let mut acc = BN254Fr::ONE; + for x in inputs.iter() { + acc *= x; + } + black_box(acc) + }) + }); + + group.bench_function("mul_chain_16384", |b| { + b.iter(|| { + let mut acc = BN254Fr::ONE; + for _ in 0..8 { + for x in inputs.iter() { + acc *= x; + } + } + black_box(acc) + }) + }); + + group.bench_function("mul_parallel_1024", |b| { + b.iter(|| { + let mut sum = BN254Fr::ZERO; + for pair in inputs.chunks_exact(2) { + sum += pair[0] * pair[1]; + } + black_box(sum) + }) + }); + + group.bench_function("sqr_chain_2048", |b| { + b.iter(|| { + let mut acc = inputs[0]; + for _ in 0..2048 { + acc.square_in_place(); + } + black_box(acc) + }) + }); + + group.bench_function("inv_256", |b| { + b.iter(|| { + let mut acc = BN254Fr::ONE; + for x in inputs[..256].iter() { + acc *= x.inverse().unwrap_or(BN254Fr::ZERO); + } + black_box(acc) + }) + }); + + group.finish(); +} + +fn bench_packed_fp128_backend(c: &mut Criterion) { + type F = Prime128M13M4P0; + type PF = ::Packing; + let packed_streams = env_usize("HACHI_BENCH_PACKED_STREAMS", 8); + let latency_iters = env_usize("HACHI_BENCH_LATENCY_ITERS", 4096); + let throughput_iters = env_usize("HACHI_BENCH_THROUGHPUT_ITERS", 256); + let stream_iters = env_usize("HACHI_BENCH_STREAM_ITERS", 2048); + let mix_iters = env_usize("HACHI_BENCH_MIX_ITERS", 256); + let mix_muls = env_usize("HACHI_BENCH_MIX_MULS", 3); + let mix_adds = env_usize("HACHI_BENCH_MIX_ADDS", 1); + let mix_subs = env_usize("HACHI_BENCH_MIX_SUBS", 1); + + assert!(packed_streams > 0, "HACHI_BENCH_PACKED_STREAMS must be > 0"); + assert!(latency_iters > 0, "HACHI_BENCH_LATENCY_ITERS must be > 0"); + assert!( + throughput_iters > 0, + "HACHI_BENCH_THROUGHPUT_ITERS must be > 0" + ); + assert!(stream_iters > 0, "HACHI_BENCH_STREAM_ITERS must be > 0"); + assert!(mix_iters > 0, "HACHI_BENCH_MIX_ITERS must be > 0"); + + let muls_per_stream = throughput_iters + 1; + let mix_ops = mix_muls + mix_adds + mix_subs; + assert!(mix_ops > 0, "at least one mix operation must be enabled"); + + let backend = if cfg!(all(target_arch = "aarch64", target_feature = "neon")) { + "aarch64_neon" + } else { + "scalar_fallback" + }; + let mut group = c.benchmark_group(format!("field_packed_backend/{backend}/w{}", PF::WIDTH)); + + let mut rng = StdRng::seed_from_u64(0xd00d_f00d_1122_3344); + let scalar_stream_len = PF::WIDTH * stream_iters; + let lhs: Vec = (0..scalar_stream_len) + .map(|_| F::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + let rhs: Vec = (0..scalar_stream_len) + .map(|_| F::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + + let packed_lhs: Vec = PF::pack_slice(&lhs); + let packed_rhs: Vec = PF::pack_slice(&rhs); + let scalar_latency_inputs: Vec = (0..latency_iters) + .map(|_| F::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + let packed_latency_inputs: Vec = (0..latency_iters) + .map(|_| PF::from_fn(|_| F::from_canonical_u128_reduced(rand_u128(&mut rng)))) + .collect(); + + let scalar_streams = packed_streams * PF::WIDTH; + let scalar_lanes: Vec<(F, F)> = (0..scalar_streams) + .map(|_| { + ( + F::from_canonical_u128_reduced(rand_u128(&mut rng)), + F::from_canonical_u128_reduced(rand_u128(&mut rng)), + ) + }) + .collect(); + let packed_lanes: Vec<(PF, PF)> = (0..packed_streams) + .map(|_| { + ( + PF::from_fn(|_| F::from_canonical_u128_reduced(rand_u128(&mut rng))), + PF::from_fn(|_| F::from_canonical_u128_reduced(rand_u128(&mut rng))), + ) + }) + .collect(); + + group.throughput(Throughput::Elements(scalar_stream_len as u64)); + group.bench_function("scalar_add_stream", |b| { + let mut out = lhs.clone(); + b.iter(|| { + for (dst, src) in out.iter_mut().zip(rhs.iter()) { + *dst = *dst + *src; + } + black_box(out[0]) + }) + }); + + group.throughput(Throughput::Elements(scalar_stream_len as u64)); + group.bench_function("packed_add_stream", |b| { + let mut out = packed_lhs.clone(); + b.iter(|| { + for (dst, src) in out.iter_mut().zip(packed_rhs.iter()) { + *dst = *dst + *src; + } + black_box(out[0].extract(0)) + }) + }); + + group.throughput(Throughput::Elements(latency_iters as u64)); + group.bench_function("scalar_mul_latency_chain", |b| { + b.iter(|| { + let mut acc = F::one(); + for x in scalar_latency_inputs.iter() { + acc = acc * *x; + } + black_box(acc) + }) + }); + + group.throughput(Throughput::Elements((latency_iters * PF::WIDTH) as u64)); + group.bench_function("packed_mul_latency_chain", |b| { + b.iter(|| { + let mut acc = PF::broadcast(F::one()); + for x in packed_latency_inputs.iter() { + acc = acc * *x; + } + black_box(acc.extract(0)) + }) + }); + + group.throughput(Throughput::Elements( + (scalar_streams * muls_per_stream) as u64, + )); + group.bench_function("scalar_mul_throughput_8way", |b| { + b.iter(|| { + let lanes = black_box(&scalar_lanes); + let mut acc: Vec = lanes.iter().map(|(a, b)| *a * *b).collect(); + for _ in 0..throughput_iters { + for (acc_i, lane) in acc.iter_mut().zip(lanes.iter()) { + *acc_i = *acc_i * lane.0; + } + } + black_box(acc[0]) + }) + }); + + group.throughput(Throughput::Elements( + (packed_streams * muls_per_stream * PF::WIDTH) as u64, + )); + group.bench_function("packed_mul_throughput_8way", |b| { + b.iter(|| { + let lanes = black_box(&packed_lanes); + let mut acc: Vec = lanes.iter().map(|(a, b)| *a * *b).collect(); + for _ in 0..throughput_iters { + for (acc_i, lane) in acc.iter_mut().zip(lanes.iter()) { + *acc_i = *acc_i * lane.0; + } + } + black_box(acc[0].extract(0)) + }) + }); + + group.throughput(Throughput::Elements( + (scalar_streams * mix_iters * mix_ops) as u64, + )); + group.bench_function("scalar_mix_sumcheck_like", |b| { + b.iter(|| { + let lanes = black_box(&scalar_lanes); + let mut acc: Vec = lanes.iter().map(|(a, b)| *a + *b).collect(); + for _ in 0..mix_iters { + for (acc_i, lane) in acc.iter_mut().zip(lanes.iter()) { + let (x, y) = *lane; + for _ in 0..mix_muls { + *acc_i = *acc_i * x; + } + for _ in 0..mix_adds { + *acc_i = *acc_i + y; + } + for _ in 0..mix_subs { + *acc_i = *acc_i - x; + } + } + } + black_box(acc[0]) + }) + }); + + group.throughput(Throughput::Elements( + (packed_streams * PF::WIDTH * mix_iters * mix_ops) as u64, + )); + group.bench_function("packed_mix_sumcheck_like", |b| { + b.iter(|| { + let lanes = black_box(&packed_lanes); + let mut acc: Vec = lanes.iter().map(|(a, b)| *a + *b).collect(); + for _ in 0..mix_iters { + for (acc_i, lane) in acc.iter_mut().zip(lanes.iter()) { + let (x, y) = *lane; + for _ in 0..mix_muls { + *acc_i = *acc_i * x; + } + for _ in 0..mix_adds { + *acc_i = *acc_i + y; + } + for _ in 0..mix_subs { + *acc_i = *acc_i - x; + } + } + } + black_box(acc[0].extract(0)) + }) + }); + + group.finish(); +} + +fn bench_fp32_fp64_mul(c: &mut Criterion) { + let mut rng = StdRng::seed_from_u64(0x3264_3264); + let n = 2048; + + let inputs_24: Vec = + (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let inputs_30: Vec = + (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let inputs_31: Vec = + (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let inputs_32: Vec = + (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let inputs_40: Vec = + (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let inputs_64: Vec = + (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + + let mut group = c.benchmark_group("fp32_fp64_mul"); + + macro_rules! chain_bench { + ($name:expr, $ty:ty, $inputs:expr) => { + group.bench_function(concat!($name, "_mul_chain_2048"), |b| { + b.iter(|| { + let mut acc = <$ty>::one(); + for x in $inputs.iter() { + acc = acc * *x; + } + black_box(acc) + }) + }); + group.bench_function(concat!($name, "_mul_add_chain_2048"), |b| { + b.iter(|| { + let mut acc = <$ty>::one(); + for x in $inputs.iter() { + acc = acc * *x + acc; + } + black_box(acc) + }) + }); + }; + } + + chain_bench!("fp32_2pow24m3", Pow2Offset24Field, inputs_24); + chain_bench!("fp32_2pow30m35", Pow2Offset30Field, inputs_30); + chain_bench!("fp32_2pow31m19", Pow2Offset31Field, inputs_31); + chain_bench!("fp32_2pow32m99", Pow2Offset32Field, inputs_32); + chain_bench!("fp64_2pow40m195", Pow2Offset40Field, inputs_40); + chain_bench!("fp64_2pow64m59", Pow2Offset64Field, inputs_64); + + group.finish(); +} + +fn bench_widening_ops(c: &mut Criterion) { + type F = Prime128M8M4M1M0; + + let mut rng = StdRng::seed_from_u64(0x01de_be0c_0001); + let a = F::from_canonical_u128_reduced(rand_u128(&mut rng)); + let b = F::from_canonical_u128_reduced(rand_u128(&mut rng)); + let b_u64 = rng.next_u64(); + + let mut group = c.benchmark_group("widening_ops"); + + group.bench_function("mul_wide_u64_only", |bench| { + bench.iter(|| black_box(black_box(a).mul_wide_u64(black_box(b_u64)))) + }); + + group.bench_function("mul_wide_only", |bench| { + bench.iter(|| black_box(black_box(a).mul_wide(black_box(b)))) + }); + + let limbs3 = [rng.next_u64(), rng.next_u64(), rng.next_u64()]; + let limbs4 = [ + rng.next_u64(), + rng.next_u64(), + rng.next_u64(), + rng.next_u64(), + ]; + + group.bench_function("mul_wide_limbs_3_to_5_only", |bench| { + bench.iter(|| black_box(black_box(a).mul_wide_limbs::<3, 5>(black_box(limbs3)))) + }); + group.bench_function("mul_wide_limbs_3_to_4_only", |bench| { + bench.iter(|| black_box(black_box(a).mul_wide_limbs::<3, 4>(black_box(limbs3)))) + }); + group.bench_function("mul_wide_limbs_4_to_5_only", |bench| { + bench.iter(|| black_box(black_box(a).mul_wide_limbs::<4, 5>(black_box(limbs4)))) + }); + group.bench_function("mul_wide_limbs_4_to_4_only", |bench| { + bench.iter(|| black_box(black_box(a).mul_wide_limbs::<4, 4>(black_box(limbs4)))) + }); + + group.bench_function("full_mul_u64_reduce", |bench| { + bench.iter(|| black_box(black_box(a) * F::from_u64(black_box(b_u64)))) + }); + + group.bench_function("full_mul_reduce", |bench| { + bench.iter(|| black_box(black_box(a) * black_box(b))) + }); + + let wide3 = a.mul_wide_u64(b_u64); + let wide4 = a.mul_wide(b); + let wide5 = { + let mut l = [0u64; 5]; + l[..3].copy_from_slice(&wide3); + l[4] = rng.next_u64() & 0xFF; + l + }; + + group.bench_function("solinas_reduce_3_limbs", |bench| { + bench.iter(|| black_box(F::solinas_reduce(black_box(&wide3)))) + }); + + group.bench_function("solinas_reduce_4_limbs", |bench| { + bench.iter(|| black_box(F::solinas_reduce(black_box(&wide4)))) + }); + + group.bench_function("solinas_reduce_5_limbs", |bench| { + bench.iter(|| black_box(F::solinas_reduce(black_box(&wide5)))) + }); + + group.bench_function("mul_wide_u64_roundtrip", |bench| { + bench.iter(|| { + let x = black_box(a); + let y = black_box(b_u64); + black_box(F::solinas_reduce(&x.mul_wide_u64(y))) + }) + }); + + group.bench_function("mul_wide_roundtrip", |bench| { + bench.iter(|| { + let x = black_box(a); + let y = black_box(b); + black_box(F::solinas_reduce(&x.mul_wide(y))) + }) + }); + + group.bench_function("mul_wide_limbs_3_to_5_roundtrip", |bench| { + bench.iter(|| { + let x = black_box(a); + let m = black_box(limbs3); + black_box(F::solinas_reduce(&x.mul_wide_limbs::<3, 5>(m))) + }) + }); + group.bench_function("mul_wide_limbs_3_to_4_roundtrip", |bench| { + bench.iter(|| { + let x = black_box(a); + let m = black_box(limbs3); + black_box(F::solinas_reduce(&x.mul_wide_limbs::<3, 4>(m))) + }) + }); + group.bench_function("mul_wide_limbs_4_to_5_roundtrip", |bench| { + bench.iter(|| { + let x = black_box(a); + let m = black_box(limbs4); + black_box(F::solinas_reduce(&x.mul_wide_limbs::<4, 5>(m))) + }) + }); + group.bench_function("mul_wide_limbs_4_to_4_roundtrip", |bench| { + bench.iter(|| { + let x = black_box(a); + let m = black_box(limbs4); + black_box(F::solinas_reduce(&x.mul_wide_limbs::<4, 4>(m))) + }) + }); + + group.finish(); +} + +fn bench_accumulator_pattern(c: &mut Criterion) { + type F = Prime128M8M4M1M0; + + let mut rng = StdRng::seed_from_u64(0xacc0_1a70_0002); + let inputs_a: Vec = (0..256) + .map(|_| F::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + let inputs_b_u64: Vec = (0..256).map(|_| rng.next_u64()).collect(); + let inputs_b_f: Vec = (0..256) + .map(|_| F::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + + let mut group = c.benchmark_group("accumulator_pattern"); + + for &n in &[16, 64, 256] { + group.bench_function(format!("eager_mul_u64_{n}"), |bench| { + bench.iter(|| { + let a_s = black_box(&inputs_a[..n]); + let b_s = black_box(&inputs_b_u64[..n]); + let mut acc = F::zero(); + for i in 0..n { + acc = acc + a_s[i] * F::from_u64(b_s[i]); + } + black_box(acc) + }) + }); + + group.bench_function(format!("widening_accum_u64_{n}"), |bench| { + bench.iter(|| { + let a_s = black_box(&inputs_a[..n]); + let b_s = black_box(&inputs_b_u64[..n]); + let mut acc = [0u64; 5]; + for i in 0..n { + let wide = a_s[i].mul_wide_u64(b_s[i]); + let mut carry: u64 = 0; + for j in 0..3 { + let sum = acc[j] as u128 + wide[j] as u128 + carry as u128; + acc[j] = sum as u64; + carry = (sum >> 64) as u64; + } + for item in &mut acc[3..5] { + let sum = *item as u128 + carry as u128; + *item = sum as u64; + carry = (sum >> 64) as u64; + } + } + black_box(F::solinas_reduce(&acc)) + }) + }); + + group.bench_function(format!("eager_mul_full_{n}"), |bench| { + bench.iter(|| { + let a_s = black_box(&inputs_a[..n]); + let b_s = black_box(&inputs_b_f[..n]); + let mut acc = F::zero(); + for i in 0..n { + acc = acc + a_s[i] * b_s[i]; + } + black_box(acc) + }) + }); + + group.bench_function(format!("widening_accum_full_{n}"), |bench| { + bench.iter(|| { + let a_s = black_box(&inputs_a[..n]); + let b_s = black_box(&inputs_b_f[..n]); + let mut acc = [0u64; 6]; + for i in 0..n { + let wide = a_s[i].mul_wide(b_s[i]); + let mut carry: u64 = 0; + for j in 0..4 { + let sum = acc[j] as u128 + wide[j] as u128 + carry as u128; + acc[j] = sum as u64; + carry = (sum >> 64) as u64; + } + for item in &mut acc[4..6] { + let sum = *item as u128 + carry as u128; + *item = sum as u64; + carry = (sum >> 64) as u64; + } + } + black_box(F::solinas_reduce(&acc)) + }) + }); + } + + group.finish(); +} + +fn bench_throughput(c: &mut Criterion) { + let n = 4096u64; + let mut rng = StdRng::seed_from_u64(0xdead_cafe); + + type M31 = Fp32<{ (1u32 << 31) - 1 }>; + + let a24: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b24: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let a30: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b30: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let a31: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b31: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let am31: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let bm31: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let a32: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b32: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let a40: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b40: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let a48: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b48: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let a56: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b56: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let a64: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b64: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let a128: Vec = (0..n) + .map(|_| Prime128M8M4M1M0::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + let b128: Vec = (0..n) + .map(|_| Prime128M8M4M1M0::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + + let mut out24 = vec![Pow2Offset24Field::zero(); n as usize]; + let mut out30 = vec![Pow2Offset30Field::zero(); n as usize]; + let mut out31 = vec![Pow2Offset31Field::zero(); n as usize]; + let mut outm31 = vec![M31::zero(); n as usize]; + let mut out32 = vec![Pow2Offset32Field::zero(); n as usize]; + let mut out40 = vec![Pow2Offset40Field::zero(); n as usize]; + let mut out48 = vec![Pow2Offset48Field::zero(); n as usize]; + let mut out56 = vec![Pow2Offset56Field::zero(); n as usize]; + let mut out64 = vec![Pow2Offset64Field::zero(); n as usize]; + let mut out128 = vec![Prime128M8M4M1M0::zero(); n as usize]; + + let mut group = c.benchmark_group("throughput"); + group.throughput(Throughput::Elements(n)); + + macro_rules! bench_op { + ($name:expr, $a:expr, $b:expr, $out:expr, $op:tt) => { + group.bench_function($name, |bench| { + bench.iter(|| { + let a = black_box(&$a); + let b = black_box(&$b); + let out = &mut $out; + for i in 0..n as usize { + out[i] = a[i] $op b[i]; + } + }) + }); + }; + } + + bench_op!("fp32_24b_mul", a24, b24, out24, *); + bench_op!("fp32_24b_add", a24, b24, out24, +); + bench_op!("fp32_30b_mul", a30, b30, out30, *); + bench_op!("fp32_30b_add", a30, b30, out30, +); + bench_op!("fp32_31b_mul", a31, b31, out31, *); + bench_op!("fp32_31b_add", a31, b31, out31, +); + bench_op!("fp32_m31_mul", am31, bm31, outm31, *); + bench_op!("fp32_m31_add", am31, bm31, outm31, +); + bench_op!("fp32_32b_mul", a32, b32, out32, *); + bench_op!("fp32_32b_add", a32, b32, out32, +); + bench_op!("fp64_40b_mul", a40, b40, out40, *); + bench_op!("fp64_40b_add", a40, b40, out40, +); + bench_op!("fp64_48b_mul", a48, b48, out48, *); + bench_op!("fp64_48b_add", a48, b48, out48, +); + bench_op!("fp64_56b_mul", a56, b56, out56, *); + bench_op!("fp64_56b_add", a56, b56, out56, +); + bench_op!("fp64_64b_mul", a64, b64, out64, *); + bench_op!("fp64_64b_add", a64, b64, out64, +); + bench_op!("fp128_mul", a128, b128, out128, *); + bench_op!("fp128_add", a128, b128, out128, +); + + group.finish(); +} + +fn bench_packed_throughput(c: &mut Criterion) { + use hachi_pcs::algebra::{Fp128Packing, Fp32Packing, Fp64Packing}; + + let n = 4096u64; + let mut rng = StdRng::seed_from_u64(0xbeef_cafe); + + macro_rules! packed_bench { + ($group:expr, $label:expr, $field:ty, $packing:ty, $rng:expr, $n:expr) => {{ + let lhs: Vec<$field> = (0..$n).map(|_| FieldSampling::sample($rng)).collect(); + let rhs: Vec<$field> = (0..$n).map(|_| FieldSampling::sample($rng)).collect(); + let lhs_p = <$packing>::pack_slice(&lhs); + let rhs_p = <$packing>::pack_slice(&rhs); + let mut out_p = vec![<$packing>::broadcast(<$field>::zero()); lhs_p.len()]; + + $group.bench_function(concat!($label, "_packed_mul"), |b| { + b.iter(|| { + let a = black_box(&lhs_p); + let b_v = black_box(&rhs_p); + let out = &mut out_p; + for i in 0..out.len() { + out[i] = a[i] * b_v[i]; + } + }) + }); + $group.bench_function(concat!($label, "_packed_add"), |b| { + b.iter(|| { + let a = black_box(&lhs_p); + let b_v = black_box(&rhs_p); + let out = &mut out_p; + for i in 0..out.len() { + out[i] = a[i] + b_v[i]; + } + }) + }); + $group.bench_function(concat!($label, "_packed_sub"), |b| { + b.iter(|| { + let a = black_box(&lhs_p); + let b_v = black_box(&rhs_p); + let out = &mut out_p; + for i in 0..out.len() { + out[i] = a[i] - b_v[i]; + } + }) + }); + }}; + } + + let mut group = c.benchmark_group("packed_throughput"); + group.throughput(Throughput::Elements(n)); + + use hachi_pcs::algebra::fields::pseudo_mersenne::*; + type M31 = Fp32<{ (1u32 << 31) - 1 }>; + + type P24 = Fp32Packing<{ POW2_OFFSET_MODULUS_24 }>; + type P30 = Fp32Packing<{ POW2_OFFSET_MODULUS_30 }>; + type P31 = Fp32Packing<{ POW2_OFFSET_MODULUS_31 }>; + type PM31 = Fp32Packing<{ (1u32 << 31) - 1 }>; + type P32 = Fp32Packing<{ POW2_OFFSET_MODULUS_32 }>; + type P40 = Fp64Packing<{ POW2_OFFSET_MODULUS_40 }>; + type P48 = Fp64Packing<{ POW2_OFFSET_MODULUS_48 }>; + type P56 = Fp64Packing<{ POW2_OFFSET_MODULUS_56 }>; + type P64 = Fp64Packing<{ POW2_OFFSET_MODULUS_64 }>; + type P128 = Fp128Packing<{ POW2_OFFSET_MODULUS_128 }>; + + packed_bench!(group, "fp32_24b", Pow2Offset24Field, P24, &mut rng, n); + packed_bench!(group, "fp32_30b", Pow2Offset30Field, P30, &mut rng, n); + packed_bench!(group, "fp32_31b", Pow2Offset31Field, P31, &mut rng, n); + packed_bench!(group, "fp32_m31", M31, PM31, &mut rng, n); + packed_bench!(group, "fp32_32b", Pow2Offset32Field, P32, &mut rng, n); + packed_bench!(group, "fp64_40b", Pow2Offset40Field, P40, &mut rng, n); + packed_bench!(group, "fp64_48b", Pow2Offset48Field, P48, &mut rng, n); + packed_bench!(group, "fp64_56b", Pow2Offset56Field, P56, &mut rng, n); + packed_bench!(group, "fp64_64b", Pow2Offset64Field, P64, &mut rng, n); + packed_bench!(group, "fp128", Prime128M8M4M1M0, P128, &mut rng, n); + + group.finish(); +} + +#[cfg(feature = "parallel")] +fn bench_parallel_throughput(c: &mut Criterion) { + use hachi_pcs::algebra::{Fp32Packing, Fp64Packing}; + + let profile = env::var("HACHI_BENCH_PAR_PROFILE").unwrap_or_else(|_| "dev".to_string()); + let default_n = match profile.as_str() { + "scale" | "large" => 1 << 20, + "xlarge" => 1 << 22, + _ => 1 << 15, + }; + let n = env_usize("HACHI_BENCH_PAR_N", default_n); + let default_chunk = match profile.as_str() { + "scale" | "large" => 1 << 14, + "xlarge" => 1 << 15, + _ => 1 << 12, + }; + let chunk = env_usize("HACHI_BENCH_PAR_CHUNK", default_chunk); + let threads = env_usize( + "HACHI_BENCH_PAR_THREADS", + thread::available_parallelism() + .map(|v| v.get()) + .unwrap_or(1), + ); + + assert!(threads > 0, "HACHI_BENCH_PAR_THREADS must be > 0"); + assert!(n > 0, "HACHI_BENCH_PAR_N must be > 0"); + assert!(chunk > 0, "HACHI_BENCH_PAR_CHUNK must be > 0"); + assert!(n % 4 == 0, "HACHI_BENCH_PAR_N must be divisible by 4"); + + let pool = ThreadPoolBuilder::new() + .num_threads(threads) + .build() + .expect("failed to build rayon pool"); + + let mut rng = StdRng::seed_from_u64(0xfeed_face); + + let lhs31: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let rhs31: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let lhs64: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let rhs64: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let lhs128: Vec = (0..n) + .map(|_| Prime128M13M4P0::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + let rhs128: Vec = (0..n) + .map(|_| Prime128M13M4P0::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + + type P31 = Fp32Packing<{ hachi_pcs::algebra::fields::pseudo_mersenne::POW2_OFFSET_MODULUS_31 }>; + type P64 = Fp64Packing<{ hachi_pcs::algebra::fields::pseudo_mersenne::POW2_OFFSET_MODULUS_64 }>; + type F128 = Prime128M13M4P0; + type P128 = ::Packing; + let chunk31_p = (chunk / P31::WIDTH).max(1); + let chunk64_p = (chunk / P64::WIDTH).max(1); + let chunk128_p = (chunk / P128::WIDTH).max(1); + + let lhs31_p = P31::pack_slice(&lhs31); + let rhs31_p = P31::pack_slice(&rhs31); + let lhs64_p = P64::pack_slice(&lhs64); + let rhs64_p = P64::pack_slice(&rhs64); + let lhs128_p = P128::pack_slice(&lhs128); + let rhs128_p = P128::pack_slice(&rhs128); + + let mut out31 = vec![Pow2Offset31Field::zero(); n]; + let mut out64 = vec![Pow2Offset64Field::zero(); n]; + let mut out128 = vec![F128::zero(); n]; + let mut out31_p = vec![P31::broadcast(Pow2Offset31Field::zero()); lhs31_p.len()]; + let mut out64_p = vec![P64::broadcast(Pow2Offset64Field::zero()); lhs64_p.len()]; + let mut out128_p = vec![P128::broadcast(F128::zero()); lhs128_p.len()]; + + let mut group = c.benchmark_group(format!( + "parallel_throughput/{profile}/t{threads}/n{n}/c{chunk}" + )); + group.throughput(Throughput::Elements(n as u64)); + + group.bench_function("fp32_31b_mul_seq", |b| { + b.iter(|| { + let a = black_box(&lhs31); + let b_v = black_box(&rhs31); + let out = &mut out31; + for i in 0..out.len() { + out[i] = a[i] * b_v[i]; + } + black_box(out[0]) + }) + }); + + group.bench_function("fp32_31b_mul_par_zip", |b| { + b.iter(|| { + let a = black_box(&lhs31); + let b_v = black_box(&rhs31); + let out = &mut out31; + pool.install(|| { + out.par_iter_mut() + .zip(a.par_iter()) + .zip(b_v.par_iter()) + .for_each(|((dst, lhs), rhs)| *dst = *lhs * *rhs); + }); + black_box(out[0]) + }) + }); + + group.bench_function("fp32_31b_mul_par_chunked", |b| { + b.iter(|| { + let a = black_box(&lhs31); + let b_v = black_box(&rhs31); + let out = &mut out31; + pool.install(|| { + out.par_chunks_mut(chunk) + .zip(a.par_chunks(chunk)) + .zip(b_v.par_chunks(chunk)) + .for_each(|((dst, lhs), rhs)| { + for i in 0..dst.len() { + dst[i] = lhs[i] * rhs[i]; + } + }); + }); + black_box(out[0]) + }) + }); + + group.bench_function("fp32_31b_packed_mul_seq", |b| { + b.iter(|| { + let a = black_box(&lhs31_p); + let b_v = black_box(&rhs31_p); + let out = &mut out31_p; + for i in 0..out.len() { + out[i] = a[i] * b_v[i]; + } + black_box(out[0].extract(0)) + }) + }); + + group.bench_function("fp32_31b_packed_mul_par_zip", |b| { + b.iter(|| { + let a = black_box(&lhs31_p); + let b_v = black_box(&rhs31_p); + let out = &mut out31_p; + pool.install(|| { + out.par_iter_mut() + .zip(a.par_iter()) + .zip(b_v.par_iter()) + .for_each(|((dst, lhs), rhs)| *dst = *lhs * *rhs); + }); + black_box(out[0].extract(0)) + }) + }); + + group.bench_function("fp32_31b_packed_mul_par_chunked", |b| { + b.iter(|| { + let a = black_box(&lhs31_p); + let b_v = black_box(&rhs31_p); + let out = &mut out31_p; + pool.install(|| { + out.par_chunks_mut(chunk31_p) + .zip(a.par_chunks(chunk31_p)) + .zip(b_v.par_chunks(chunk31_p)) + .for_each(|((dst, lhs), rhs)| { + for i in 0..dst.len() { + dst[i] = lhs[i] * rhs[i]; + } + }); + }); + black_box(out[0].extract(0)) + }) + }); + + group.bench_function("fp64_64b_mul_seq", |b| { + b.iter(|| { + let a = black_box(&lhs64); + let b_v = black_box(&rhs64); + let out = &mut out64; + for i in 0..out.len() { + out[i] = a[i] * b_v[i]; + } + black_box(out[0]) + }) + }); + + group.bench_function("fp64_64b_mul_par_zip", |b| { + b.iter(|| { + let a = black_box(&lhs64); + let b_v = black_box(&rhs64); + let out = &mut out64; + pool.install(|| { + out.par_iter_mut() + .zip(a.par_iter()) + .zip(b_v.par_iter()) + .for_each(|((dst, lhs), rhs)| *dst = *lhs * *rhs); + }); + black_box(out[0]) + }) + }); + + group.bench_function("fp64_64b_mul_par_chunked", |b| { + b.iter(|| { + let a = black_box(&lhs64); + let b_v = black_box(&rhs64); + let out = &mut out64; + pool.install(|| { + out.par_chunks_mut(chunk) + .zip(a.par_chunks(chunk)) + .zip(b_v.par_chunks(chunk)) + .for_each(|((dst, lhs), rhs)| { + for i in 0..dst.len() { + dst[i] = lhs[i] * rhs[i]; + } + }); + }); + black_box(out[0]) + }) + }); + + group.bench_function("fp64_64b_packed_mul_seq", |b| { + b.iter(|| { + let a = black_box(&lhs64_p); + let b_v = black_box(&rhs64_p); + let out = &mut out64_p; + for i in 0..out.len() { + out[i] = a[i] * b_v[i]; + } + black_box(out[0].extract(0)) + }) + }); + + group.bench_function("fp64_64b_packed_mul_par_zip", |b| { + b.iter(|| { + let a = black_box(&lhs64_p); + let b_v = black_box(&rhs64_p); + let out = &mut out64_p; + pool.install(|| { + out.par_iter_mut() + .zip(a.par_iter()) + .zip(b_v.par_iter()) + .for_each(|((dst, lhs), rhs)| *dst = *lhs * *rhs); + }); + black_box(out[0].extract(0)) + }) + }); + + group.bench_function("fp64_64b_packed_mul_par_chunked", |b| { + b.iter(|| { + let a = black_box(&lhs64_p); + let b_v = black_box(&rhs64_p); + let out = &mut out64_p; + pool.install(|| { + out.par_chunks_mut(chunk64_p) + .zip(a.par_chunks(chunk64_p)) + .zip(b_v.par_chunks(chunk64_p)) + .for_each(|((dst, lhs), rhs)| { + for i in 0..dst.len() { + dst[i] = lhs[i] * rhs[i]; + } + }); + }); + black_box(out[0].extract(0)) + }) + }); + + group.bench_function("fp128_mul_seq", |b| { + b.iter(|| { + let a = black_box(&lhs128); + let b_v = black_box(&rhs128); + let out = &mut out128; + for i in 0..out.len() { + out[i] = a[i] * b_v[i]; + } + black_box(out[0]) + }) + }); + + group.bench_function("fp128_mul_par_chunked", |b| { + b.iter(|| { + let a = black_box(&lhs128); + let b_v = black_box(&rhs128); + let out = &mut out128; + pool.install(|| { + out.par_chunks_mut(chunk) + .zip(a.par_chunks(chunk)) + .zip(b_v.par_chunks(chunk)) + .for_each(|((dst, lhs), rhs)| { + for i in 0..dst.len() { + dst[i] = lhs[i] * rhs[i]; + } + }); + }); + black_box(out[0]) + }) + }); + + group.bench_function("fp128_packed_mul_seq", |b| { + b.iter(|| { + let a = black_box(&lhs128_p); + let b_v = black_box(&rhs128_p); + let out = &mut out128_p; + for i in 0..out.len() { + out[i] = a[i] * b_v[i]; + } + black_box(out[0].extract(0)) + }) + }); + + group.bench_function("fp128_packed_mul_par_chunked", |b| { + b.iter(|| { + let a = black_box(&lhs128_p); + let b_v = black_box(&rhs128_p); + let out = &mut out128_p; + pool.install(|| { + out.par_chunks_mut(chunk128_p) + .zip(a.par_chunks(chunk128_p)) + .zip(b_v.par_chunks(chunk128_p)) + .for_each(|((dst, lhs), rhs)| { + for i in 0..dst.len() { + dst[i] = lhs[i] * rhs[i]; + } + }); + }); + black_box(out[0].extract(0)) + }) + }); + + group.finish(); +} + +#[cfg(not(feature = "parallel"))] +fn bench_parallel_throughput(_: &mut Criterion) {} + +fn bench_packed_sumcheck_mix(c: &mut Criterion) { + use hachi_pcs::algebra::{Fp128Packing, Fp32Packing, Fp64Packing}; + + let n = 4096u64; + let mut rng = StdRng::seed_from_u64(0xface_bead); + + macro_rules! sumcheck_bench { + ($group:expr, $label:expr, $field:ty, $packing:ty, $rng:expr, $n:expr) => {{ + let eq: Vec<$field> = (0..$n).map(|_| FieldSampling::sample($rng)).collect(); + let poly: Vec<$field> = (0..$n).map(|_| FieldSampling::sample($rng)).collect(); + let eq_p = <$packing>::pack_slice(&eq); + let poly_p = <$packing>::pack_slice(&poly); + let mut acc = <$packing>::broadcast(<$field>::zero()); + + $group.bench_function(concat!($label, "_packed_macc"), |b| { + b.iter(|| { + let e = black_box(&eq_p); + let p_v = black_box(&poly_p); + acc = <$packing>::broadcast(<$field>::zero()); + for i in 0..e.len() { + acc = acc + e[i] * p_v[i]; + } + black_box(acc) + }) + }); + }}; + } + + let mut group = c.benchmark_group("packed_sumcheck_mix"); + group.throughput(Throughput::Elements(n)); + + use hachi_pcs::algebra::fields::pseudo_mersenne::*; + type M31 = Fp32<{ (1u32 << 31) - 1 }>; + + type P24 = Fp32Packing<{ POW2_OFFSET_MODULUS_24 }>; + type P30 = Fp32Packing<{ POW2_OFFSET_MODULUS_30 }>; + type P31 = Fp32Packing<{ POW2_OFFSET_MODULUS_31 }>; + type PM31 = Fp32Packing<{ (1u32 << 31) - 1 }>; + type P32 = Fp32Packing<{ POW2_OFFSET_MODULUS_32 }>; + type P40 = Fp64Packing<{ POW2_OFFSET_MODULUS_40 }>; + type P48 = Fp64Packing<{ POW2_OFFSET_MODULUS_48 }>; + type P56 = Fp64Packing<{ POW2_OFFSET_MODULUS_56 }>; + type P64 = Fp64Packing<{ POW2_OFFSET_MODULUS_64 }>; + type P128 = Fp128Packing<{ POW2_OFFSET_MODULUS_128 }>; + + sumcheck_bench!(group, "fp32_24b", Pow2Offset24Field, P24, &mut rng, n); + sumcheck_bench!(group, "fp32_30b", Pow2Offset30Field, P30, &mut rng, n); + sumcheck_bench!(group, "fp32_31b", Pow2Offset31Field, P31, &mut rng, n); + sumcheck_bench!(group, "fp32_m31", M31, PM31, &mut rng, n); + sumcheck_bench!(group, "fp32_32b", Pow2Offset32Field, P32, &mut rng, n); + sumcheck_bench!(group, "fp64_40b", Pow2Offset40Field, P40, &mut rng, n); + sumcheck_bench!(group, "fp64_48b", Pow2Offset48Field, P48, &mut rng, n); + sumcheck_bench!(group, "fp64_56b", Pow2Offset56Field, P56, &mut rng, n); + sumcheck_bench!(group, "fp64_64b", Pow2Offset64Field, P64, &mut rng, n); + sumcheck_bench!(group, "fp128", Prime128M8M4M1M0, P128, &mut rng, n); + + group.finish(); +} + +criterion_group!( + field_arith, + bench_mul, + bench_mul_only, + bench_mul_isolated, + bench_sqr, + bench_inv, + bench_packed_fp128_backend, + bench_bn254, + bench_fp32_fp64_mul, + bench_widening_ops, + bench_accumulator_pattern, + bench_throughput, + bench_packed_throughput, + bench_packed_sumcheck_mix, + bench_parallel_throughput +); +criterion_main!(field_arith); diff --git a/benches/fp64_reduce_probe.rs b/benches/fp64_reduce_probe.rs new file mode 100644 index 00000000..073544a9 --- /dev/null +++ b/benches/fp64_reduce_probe.rs @@ -0,0 +1,118 @@ +#![allow(missing_docs)] + +use criterion::{black_box, criterion_group, criterion_main, Criterion, Throughput}; + +const P40: u64 = hachi_pcs::algebra::fields::pseudo_mersenne::POW2_OFFSET_MODULUS_40; +const P64: u64 = hachi_pcs::algebra::fields::pseudo_mersenne::POW2_OFFSET_MODULUS_64; +const C40: u64 = (1u64 << 40) - P40; // 195 +const C64: u64 = 0u64.wrapping_sub(P64); // 59 +const MASK40: u64 = (1u64 << 40) - 1; +const MASK64_U128: u128 = u64::MAX as u128; + +#[inline(always)] +fn mul_c40_split(x: u64) -> u64 { + let c = C40 as u32; + let x_lo = x as u32; + let x_hi = (x >> 32) as u32; + (c as u64 * x_lo as u64).wrapping_add((c as u64 * x_hi as u64) << 32) +} + +#[inline(always)] +fn reduce40_split(lo: u64, hi: u64) -> u64 { + let high = (lo >> 40) | (hi << 24); + let f1 = (lo & MASK40).wrapping_add(mul_c40_split(high)); + let f2 = (f1 & MASK40).wrapping_add(mul_c40_split(f1 >> 40)); + let reduced = f2.wrapping_sub(P40); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & P40) +} + +#[inline(always)] +fn reduce40_direct(lo: u64, hi: u64) -> u64 { + let high = (lo >> 40) | (hi << 24); + let f1 = (lo & MASK40).wrapping_add(C40.wrapping_mul(high)); + let f2 = (f1 & MASK40).wrapping_add(C40.wrapping_mul(f1 >> 40)); + let reduced = f2.wrapping_sub(P40); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & P40) +} + +#[inline(always)] +fn reduce64(lo: u64, hi: u64) -> u64 { + let f1 = (lo as u128) + (C64 as u128) * (hi as u128); + let f2 = (f1 & MASK64_U128) + (C64 as u128) * ((f1 >> 64) as u64 as u128); + let reduced = f2.wrapping_sub(P64 as u128); + let borrow = reduced >> 127; + reduced.wrapping_add(borrow.wrapping_neg() & (P64 as u128)) as u64 +} + +#[inline(always)] +fn next_u64(state: &mut u64) -> u64 { + let mut x = *state; + x ^= x << 13; + x ^= x >> 7; + x ^= x << 17; + *state = x; + x +} + +fn bench_fp64_reduce_probe(c: &mut Criterion) { + let n = 1 << 13; + let mut seed = 0x9e37_79b9_7f4a_7c15u64; + + let mut pairs40 = Vec::with_capacity(n); + let mut pairs64 = Vec::with_capacity(n); + for _ in 0..n { + let a40 = next_u64(&mut seed) % P40; + let b40 = next_u64(&mut seed) % P40; + let x40 = (a40 as u128) * (b40 as u128); + pairs40.push((x40 as u64, (x40 >> 64) as u64)); + + let a64 = next_u64(&mut seed); + let b64 = next_u64(&mut seed); + let x64 = (a64 as u128) * (b64 as u128); + pairs64.push((x64 as u64, (x64 >> 64) as u64)); + } + + for &(lo, hi) in &pairs40 { + assert_eq!(reduce40_split(lo, hi), reduce40_direct(lo, hi)); + } + + let mut group = c.benchmark_group("fp64_reduce_probe"); + group.throughput(Throughput::Elements(n as u64)); + + group.bench_function("reduce40_split", |b| { + b.iter(|| { + let mut acc = 0u64; + for &(lo, hi) in black_box(&pairs40) { + acc ^= reduce40_split(lo, hi); + } + black_box(acc) + }) + }); + + group.bench_function("reduce40_direct", |b| { + b.iter(|| { + let mut acc = 0u64; + for &(lo, hi) in black_box(&pairs40) { + acc ^= reduce40_direct(lo, hi); + } + black_box(acc) + }) + }); + + group.bench_function("reduce64", |b| { + b.iter(|| { + let mut acc = 0u64; + for &(lo, hi) in black_box(&pairs64) { + acc ^= reduce64(lo, hi); + } + black_box(acc) + }) + }); + + group.finish(); +} + +criterion_group!(fp64_reduce_probe, bench_fp64_reduce_probe); +criterion_main!(fp64_reduce_probe); diff --git a/benches/ring_ntt.rs b/benches/ring_ntt.rs new file mode 100644 index 00000000..546f9b9d --- /dev/null +++ b/benches/ring_ntt.rs @@ -0,0 +1,67 @@ +#![allow(missing_docs)] + +use criterion::{black_box, criterion_group, criterion_main, Criterion}; +use hachi_pcs::algebra::ntt::butterfly::{forward_ntt, inverse_ntt, NttTwiddles}; +use hachi_pcs::algebra::tables::{Q32_DATA, Q32_MODULUS, Q32_NUM_PRIMES, Q32_PRIMES}; +use hachi_pcs::algebra::{CyclotomicCrtNtt, CyclotomicRing, Fp64, MontCoeff}; +use hachi_pcs::CanonicalField; + +type F = Fp64<{ Q32_MODULUS }>; +type R = CyclotomicRing; +type N = CyclotomicCrtNtt; + +fn sample_ring(seed: u64) -> R { + let coeffs = std::array::from_fn(|i| { + let x = seed + .wrapping_mul(31) + .wrapping_add((i as u64).wrapping_mul(17)); + F::from_u64(x % Q32_MODULUS) + }); + R::from_coefficients(coeffs) +} + +fn bench_ring_schoolbook_mul(c: &mut Criterion) { + let lhs = sample_ring(3); + let rhs = sample_ring(11); + c.bench_function("ring_schoolbook_mul_d64", |b| { + b.iter(|| black_box(lhs) * black_box(rhs)) + }); +} + +fn bench_ntt_single_prime_round_trip(c: &mut Criterion) { + let prime = Q32_PRIMES[0]; + let tw = NttTwiddles::<64>::compute(prime); + let base: [MontCoeff; 64] = + std::array::from_fn(|i| prime.from_canonical(((i * 5 + 7) as i16) % prime.p)); + + c.bench_function("ntt_single_prime_forward_inverse_d64", |b| { + b.iter(|| { + let mut a = base; + forward_ntt(&mut a, prime, &tw); + inverse_ntt(&mut a, prime, &tw); + black_box(a) + }) + }); +} + +fn bench_crt_round_trip(c: &mut Criterion) { + let ring = sample_ring(19); + let twiddles: [NttTwiddles<64>; Q32_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::<64>::compute(Q32_PRIMES[k])); + + c.bench_function("ring_ntt_crt_round_trip_d64_k6", |b| { + b.iter(|| { + let ntt = N::from_ring(black_box(&ring), &Q32_PRIMES, &twiddles); + let back: R = ntt.to_ring(&Q32_PRIMES, &twiddles, &Q32_DATA); + black_box(back) + }) + }); +} + +criterion_group!( + ring_ntt, + bench_ring_schoolbook_mul, + bench_ntt_single_prime_round_trip, + bench_crt_round_trip +); +criterion_main!(ring_ntt); diff --git a/docs/FIELD_EMBEDDINGS_SUPERNEO_VS_HACHI.md b/docs/FIELD_EMBEDDINGS_SUPERNEO_VS_HACHI.md new file mode 100644 index 00000000..90b631c2 --- /dev/null +++ b/docs/FIELD_EMBEDDINGS_SUPERNEO_VS_HACHI.md @@ -0,0 +1,698 @@ +# Field embeddings in SuperNeo vs Hachi (math-first notes) + +This note focuses **only** on the math in the two papers: + +- `docs/superneo.pdf` (“Neo and SuperNeo: Post-quantum folding with pay-per-bit costs over small fields”) +- `paper/hachi.pdf` (“Hachi: Efficient Lattice-Based Multilinear Polynomial Commitments over Extension Fields”) + +The shared theme is: lattice commitments naturally live over **cyclotomic rings**, but we want the *interactive proof logic* (sum-check, norm checks, etc.) to live over a **(small) field or a small extension field**. Both works build *embeddings/reductions* that let you: + +- commit in a ring/module world (Ajtai/Module-SIS commitments), while +- proving the needed algebraic statements using field arithmetic, and +- keeping norms under control (for binding) and enabling linear-combination/folding operations. + +--- + +## 1) Common background and notation (as used in SuperNeo) + +SuperNeo sets up a base field \(F = \mathbb{F}_q\), an extension field \(K/F\) of minimal degree such that \(1/|K| = \mathrm{negl}(\lambda)\), and a cyclotomic ring + +\[ +R_F := F[X]/(\Phi(X)), \quad R_K := K[X]/(\Phi(X)), +\] + +where \(\Phi(X)\) is an \(\eta\)-th cyclotomic polynomial of degree \(d\). It explicitly treats + +\[ +F \subseteq R_F \subseteq R_K, \qquad F \subseteq K +\] + +as nested substructures (SuperNeo, Def. 1; `docs/superneo.pdf`, p. 19–20: “-- 19 of 60 --”, “-- 20 of 60 --”). + +Two coefficient maps show up everywhere: + +- coefficient vector: \(\mathrm{cf}(a)\in F^d\) for \(a\in R_F\), +- constant term: \(\mathrm{ct}(a)\in F\) for \(a\in R_F\), + +and similarly over \(R_K\) (SuperNeo, Def. 2; `docs/superneo.pdf`, p. 20: “-- 20 of 60 --”). + +### 1.1 What I mean by the “Gram operator” in this note + +Fix: + +- an \(F\)-basis \(\{e_0,\dots,e_{d-1}\}\) of the \(F\)-vector space \(R_F\) (most often \(e_i = X^i\), the coefficient basis), and +- a bilinear form \(B: R_F\times R_F \to F\). + +Typical examples in these papers are: + +- \(B(u,v)=\mathrm{ct}(u\cdot v)\) (SuperNeo’s constant-term functional), possibly with an automorphism inserted, or +- \(B(u,v)=\mathrm{Tr}_H(u\cdot \sigma_{-1}(v))\) (Hachi’s trace-to-subfield functional). + +Then the **Gram matrix** of \(B\) in the basis \(\{e_i\}\) is the \(d\times d\) matrix +\[ +G_{ij} := B(e_i,e_j). +\] +This matrix encodes the pairing: +if \(u=\sum_i a_i e_i\) and \(v=\sum_j b_j e_j\), then +\[ +B(u,v) = a^\top\, G\, b. +\] + +The corresponding **Gram operator** is just the linear map \(g: F^d\to F^d\) given by +\[ +g(b) := G\,b, +\] +so that \(B(u,v)=a^\top g(b)\). + +When SuperNeo says “there exists a linear transform \(T\) such that \(\mathrm{ct}(T(a)\cdot b)=\langle a,b\rangle\)” (Thm. 3), +one way to interpret it is: choose a bilinear form \(B_0(u,v)=\mathrm{ct}(u\cdot v)\) (or a close variant), write down its Gram matrix \(G\) in the coefficient basis, and take \(T = G^{-{\top}}\). This makes the pairing become the standard dot product in coordinates. + +--- + +## 2) What “field embedding” means in SuperNeo (the core problem) + +### 2.1 The Ajtai-commitment mismatch + +Ajtai/Module-SIS style commitments are *ring-module* commitments: + +- Commit to \(z \in R_F^n\) via a linear map \(c = A z\) over \(R_F\). + +But CCS witnesses (and CCS arithmetic) are naturally vectors over \(F\). So you need a map: + +\[ +\iota: F^{N} \longrightarrow R_F^n +\] + +that is compatible with: + +- **norm constraints** (binding only holds for “small-norm” openings), +- **field constraint checking** via sum-check over \(F\) or \(K\), +- **folding** (random linear combinations of commitments and claims). + +SuperNeo frames this as “embed field vectors (CCS witnesses) into the ring vectors that Ajtai commitments operate over” and calls out that the embedding must preserve **norm bounds** and an **evaluation homomorphism** needed for sum-check-based folding (SuperNeo, §1.2; `docs/superneo.pdf`, p. 5–6: “-- 5 of 60 --”, “-- 6 of 60 --”). + +### 2.2 What went wrong before (NTT embedding) + +Prior lattice folding used an NTT/SIMD isomorphism that maps ring elements into a product of extension fields; this makes field-constraint checking look “ring-native”, but: + +- the NTT map is **not norm-preserving**, so small bit-width witnesses become arbitrary-norm ring elements, +- the commitment must then decompose regardless of bit-width ⇒ **no pay-per-bit**, +- packing efficiency is limited by the factor \(t\) in \(F_{q^t}\) (SuperNeo, §1.2.1; `docs/superneo.pdf`, p. 6–7: “-- 6 of 60 --”, “-- 7 of 60 --”). + +--- + +## 3) SuperNeo’s key innovation: *norm-preserving embeddings + evaluation homomorphism* + +SuperNeo’s abstract summarizes the core as: + +> “two new norm-preserving embeddings of field vectors into ring vectors that respect an evaluation homomorphism required for folding” +(`docs/superneo.pdf`, p. 1: “-- 1 of 60 --”). + +The paper describes both a “Neo embedding” (SIMD-friendly) and a “SuperNeo embedding” (general, non-SIMD), and then focuses the rest of the paper on SuperNeo (see `docs/superneo.pdf`, p. 10–11: “-- 10 of 60 --”, “-- 11 of 60 --”). + +### 3.1 Neo embedding (high level: “coefficients-as-SIMD lanes”) + +Neo’s embedding idea: pack **\(d\) field vectors** \(z^{(1)},\dots,z^{(d)}\in F^n\) into the **coefficient slots** of a ring vector \(z \in R_F^n\), so the coefficient matrix \(\mathrm{cf}(z)\in F^{d\times n}\) literally equals those \(d\) vectors (SuperNeo, §1.2.2 “Contribution 1”; `docs/superneo.pdf`, p. 8–10: “-- 8 of 60 --”, “-- 9 of 60 --”, “-- 10 of 60 --”). + +Key consequences: + +- **norm-preserving**: small field entries ⇒ small ring coefficients ⇒ binding is aligned with bit-width. +- **optimal SIMD packing**: achieves \(d\cdot n\) field elements per length-\(n\) ring vector (under a SIMD constraint system). +- **evaluation homomorphism for folding**: if you fold commitments with a *short ring* challenge \(\delta\in R_F\), the embedded evaluation claims can be folded consistently by embedding the \(d\) field evaluations as a ring element \(y=\sum_i y^{(i)}X^{i-1}\) (SuperNeo, p. 9: “-- 9 of 60 --”). + +But Neo still needs SIMD constraints: “the same constraint system must be applied to all \(d\) underlying field vectors” (SuperNeo, p. 10: “-- 10 of 60 --”). + +### 3.2 SuperNeo embedding (formal: coefficient embedding of **one** length-\(d n_R\) vector) + +SuperNeo removes SIMD by embedding a **single** long field vector \(z\in F^{n_F}\) where \(n_F = d\cdot n_R\), by chunking it into \(n_R\) blocks of length \(d\), and mapping each block to one ring element’s coefficient vector. + +This is defined formally as “Coefficient Embedding” (SuperNeo, §5, Def. 7; `docs/superneo.pdf`, p. 23: “-- 23 of 60 --”): + +- element: \(v\in F^d \mapsto \mathbf{v}\in R_F\) with \(\mathrm{cf}(\mathbf{v})=v\) +- vector: \(z\in F^{d n_R}\mapsto \mathbf{z}\in R_F^{n_R}\) by splitting into \(d\)-sized blocks +- matrix: \(M\in F^{m\times d n_R}\mapsto \mathbf{M}\in R_F^{m\times n_R}\) row-wise. + +**Why this matters:** + +- **optimal packing without SIMD**: you pack \(d\cdot n_R\) field elements into \(n_R\) ring elements. +- **norm-preserving**: the committed object’s coefficients are exactly the witness entries. +- **field-native checks become possible**: you can write constraints directly over the underlying field vector \(z\) and use sum-check over \(F\) or \(K\). + +### 3.3 The nontrivial part: lifting *field* products to *ring* products while keeping folding linear + +SuperNeo’s obstacle is: commitments/folding live over the ring, but sum-check outputs **field** multilinear evaluation claims like + +\[ +M z \;\widetilde{}\; (r) \in K +\] + +for some random \(r\), and folding wants to take ring-linear combinations \(z'' = z + \delta z'\) with \(\delta \in R_F\) and have the **claims** fold “the same way”. + +SuperNeo’s main embedding tool is Section 5 “Embedding products with evaluation homomorphism”: + +1. Use a cyclotomic **inner-product automorphism trick** to turn coefficient inner products into ring constant terms. + +SuperNeo states an “Inner Product Transform” (Thm. 3; `docs/superneo.pdf`, p. 23: “-- 23 of 60 --”): + +> there exists a linear transform \(\bar{\cdot}: F^d \to F^d\) such that for all \(a,b\in F^d\), +> \[ +> \mathrm{ct}(\overline{a}\cdot \mathbf{b}) = \langle a,b\rangle. +> \] + +Conceptually: cyclotomic rings have many Galois automorphisms (e.g. “conjugation” \(X\mapsto X^{-1}\)), and by applying an appropriate automorphism/linear transform to one operand, the constant coefficient of a ring product recovers a dot product of coefficient vectors. (SuperNeo explicitly attributes this to “(Galois, conjugation, or inner product) automorphism trick” in §1.2.2; `docs/superneo.pdf`, p. 10–11: “-- 10 of 60 --”, “-- 11 of 60 --”.) + +2. Extend this transform blockwise to vectors/matrices (Def. 8; `docs/superneo.pdf`, p. 23: “-- 23 of 60 --”). + +3. Obtain a **matrix-vector product transform** (Thm. 4; `docs/superneo.pdf`, p. 23–24: “-- 23 of 60 --”, “-- 24 of 60 --”): + +> For \(M\in F^{m\times n_F}\), \(z\in F^{n_F}\), +> \[ +> M z = \mathrm{ct}(\overline{M}\,\mathbf{z}), +> \] +> i.e. the field product equals the vector of constant terms of a ring product. + +4. Lift this to evaluation claims and prove the **evaluation homomorphism** (Thm. 5; `docs/superneo.pdf`, p. 24: “-- 24 of 60 --”): + +Roughly: if you linearly combine committed ring vectors with ring scalars \(\rho_i\in R_F\), then the lifted ring-evaluation objects combine linearly as well, and constant terms track the underlying field evaluations. + +This is the formal engine that makes “field-native sum-check + ring-linear folding” composable. + +### 3.3.1 Explicit inner-product transforms for two cyclotomics you care about + +SuperNeo’s Theorem 3 is an *existence* statement: there is a linear map \(T: F^d \to F^d\) (write \(T(a)=\bar a\)) such that for all \(a,b\in F^d\), + +\[ +\mathrm{ct}(\mathbf{\bar a}\cdot \mathbf{b}) = \langle a,b\rangle +\] + +where \(\mathbf{v}\in R_F\) denotes the coefficient embedding of \(v\in F^d\). + +Below are **concrete closed forms** for \(T\) in two important special cases. + +#### (A) Power-of-two cyclotomic: \(\Phi(X)=X^d+1\) (negacyclic ring) + +Let \(R_F = F[X]/(X^d+1)\), and write +\(a(X)=\sum_{i=0}^{d-1} a_i X^i\), \(b(X)=\sum_{i=0}^{d-1} b_i X^i\). + +Define \(\bar a(X)\) by the coefficient rule: + +- \(\bar a_0 := a_0\) +- for \(i=1,\dots,d-1\): \(\bar a_i := -a_{d-i}\) + +Equivalently, +\[ +\bar a(X)=a_0 - \sum_{i=1}^{d-1} a_i X^{d-i}. +\] + +Then in \(R_F\), +\[ +\mathrm{ct}(\bar a(X)\,b(X)) = \sum_{i=0}^{d-1} a_i b_i. +\] + +Reason (one-line): the term \((-a_i X^{d-i})(b_i X^i)=-a_i b_i X^d\) contributes \(+a_i b_i\) to the constant term since \(X^d=-1\); other cross-terms cannot reduce to constants without leaving a nonzero power of \(X\). + +This is exactly the classical “conjugation/inversion automorphism” trick specialized to \(X^d+1\). + +#### (B) Trinomial cyclotomic: \(\Phi_{81}(X)=X^{54}+X^{27}+1\) + +Let \(R_F = F[X]/(X^{54}+X^{27}+1)\) (so \(d=54\)). Write +\(a(X)=\sum_{i=0}^{53} a_i X^i\), \(b(X)=\sum_{i=0}^{53} b_i X^i\). + +One valid “inner product transform” \(T(a)=\bar a\) with +\(\mathrm{ct}(\bar a(X)\,b(X))=\sum_i a_i b_i\) +is: + +- \(\bar a_0 := a_0\) +- for \(i=1,\dots,26\): \(\bar a_i := -(a_{27-i} + a_{54-i})\) +- for \(i=27,\dots,53\): \(\bar a_i := -a_{54-i}\) + +(indices are in \(\{0,\dots,53\}\)). + +Notable features: + +- **extremely sparse**: each output coefficient depends on at most 2 input coefficients, +- **\(O(d)\)** time with only adds + sign flips, matching SuperNeo’s efficiency remark for power-of-two / trinomial cyclotomics. + +--- + +### 3.4 Why this is the “field-embedding innovation” (in one sentence) + +SuperNeo’s innovation on the embedding side is: + +- **embed a single field witness vector into ring coefficients in a norm-preserving way**, and +- **systematically lift field matrix products/evaluations to ring expressions whose constant terms recover the field values**, so that +- **ring-linear folding preserves the field evaluation claims** (evaluation homomorphism), + +thereby enabling a HyperNova-like folding architecture where *sum-check and norm checks run over \(K\)* rather than over the ring, while commitments still live over \(R_F\). + +--- + +## 4) What “field embedding” means in Hachi (the PCS perspective) + +Hachi is not a folding scheme; it is a **multilinear PCS**. But the verification bottleneck is similar: classic lattice PCS machinery lives in cyclotomic rings \(R_q = \mathbb{Z}_q[X]/(X^d+1)\), whereas sum-check is naturally over a field. + +Hachi’s abstract states its two embedding/reduction ideas (Hachi, Abstract; `paper/hachi.pdf`, p. 1: “-- 1 of 33 --”): + +1. **Ring-switching + sum-check**: integrate Greyhound with ring-switching so the verifier avoids ring multiplication. +2. **Generic reduction (extension field → ring)**: convert evaluation proofs over \( \mathbb{F}_{q^k}\) into statements over cyclotomic rings \(R_q\). + +### 4.1 Embedding extension fields inside cyclotomic rings (fixed rings under automorphisms) + +In Hachi’s technical overview (Hachi, §1.3; `paper/hachi.pdf`, p. 4–5: “-- 4 of 33 --”, “-- 5 of 33 --”), it identifies finite fields \( \mathbb{F}_{q^k}\) *inside* \(R_q\) using fixed subrings under a subgroup of the Galois group: + +- Let \(R = \mathbb{Z}[X]/(X^d+1)\) and \(R_q = R/(q)\) with \(d=2^\alpha\). +- For automorphisms \(\sigma_i: X\mapsto X^i\), define the fixed ring + \[ + R_q^H := \{x\in R_q : \forall \sigma\in H,\;\sigma(x)=x\}. + \] + +Then (Lemma 1, informal; `paper/hachi.pdf`, p. 5: “-- 5 of 33 --”): + +> for suitable \(q\) (notably \(q\equiv 5\pmod 8\)) and \(k\mid d/2\), there exists \(H\) such that \(R_q^H\) is a **subfield** of \(R_q\) isomorphic to \(\mathbb{F}_{q^k}\). + +This is a literal *field embedding into the ring*: \(\mathbb{F}_{q^k}\hookrightarrow R_q\) realized as a fixed subring. + +### 4.2 Inner products via trace + automorphisms (a close cousin of SuperNeo’s transform) + +Hachi then uses a trace map \(\mathrm{Tr}_H:R_q\to R_q^H\) and an automorphism (notably \(\sigma_{-1}\)) to turn ring products into **field inner products** (Theorem 1, informal; `paper/hachi.pdf`, p. 5: “-- 5 of 33 --”): + +> there exists a bijection \(\psi:(R_q^H)^{d/k}\to R_q\) such that +> \[ +> \mathrm{Tr}_H\big(\psi(a)\cdot \sigma_{-1}(\psi(b))\big) = (d/k)\cdot \langle a,b\rangle. +> \] + +This is structurally very similar to SuperNeo’s “inner product transform → constant term” idea, except Hachi uses: + +- a **trace to a subfield** \(R_q^H \cong \mathbb{F}_{q^k}\), +- whereas SuperNeo phrases it as a **linear transform** on coefficient vectors whose ring-product constant term recovers the dot product. + +### 4.3 Ring-switching: from ring equations to extension-field equations (so the verifier stays field-native) + +Hachi’s “ring switching and sum-check over extension fields” overview (Hachi, §1.3; `paper/hachi.pdf`, p. 6–7: “-- 6 of 33 --”, “-- 7 of 33 --”) sketches: + +- lift a relation over \(R_q\) to an identity over \(\mathbb{Z}_q[X]\) with an explicit multiple of \((X^d+1)\), +- sample \(\alpha \leftarrow \mathbb{F}_{q^k}\) and substitute \(X=\alpha\), +- reducing the ring relation to a **field inner product / sum-check-type claim** over \(\mathbb{F}_{q^k}\), +- then run sum-check over the field and recurse. + +This is the PCS analogue of “avoid ring operations during sum-check”: Hachi’s verifier can avoid cyclotomic ring multiplications even though the underlying assumption/commitments are lattice/ring-based. + +--- + +## 5) Same vs different (embedding viewpoint) + +### 5.1 The same (high-level mathematical pattern) + +- **Cyclotomic rings + automorphisms are the bridge.** + - SuperNeo: an automorphism/linear transform makes \(\mathrm{ct}(\bar{a}\cdot b)\) become \(\langle a,b\rangle\) (SuperNeo Thm. 3; `docs/superneo.pdf`, p. 23: “-- 23 of 60 --”). + - Hachi: trace + automorphisms make \(\mathrm{Tr}_H(\psi(a)\cdot \sigma_{-1}(\psi(b)))\) become \(\langle a,b\rangle\) (Hachi Thm. 1; `paper/hachi.pdf`, p. 5: “-- 5 of 33 --”). + +- **Field-native sum-check is the goal.** + - SuperNeo explicitly targets “field-native arithmetic” where “sum-check and norm checks run purely over a small field” (SuperNeo Abstract; `docs/superneo.pdf`, p. 1: “-- 1 of 60 --”). + - Hachi’s verifier similarly reduces to sum-check over \(\mathbb{F}_{q^k}\) after ring switching (Hachi §1.3; `paper/hachi.pdf`, p. 6–7: “-- 6 of 33 --”, “-- 7 of 33 --”). + +- **Linearity matters.** + Both constructions rely on the fact that the commitment operation is linear in the ring/module, and they build embeddings/reductions so the *claimed evaluations* transform linearly under the same combinations (SuperNeo Thm. 5; `docs/superneo.pdf`, p. 24: “-- 24 of 60 --”). + +### 5.2 The different (what each paper is optimizing for) + +- **Direction of “embedding”:** + - **SuperNeo**: embeds *field witnesses* into *ring vectors* to make Ajtai commitments “pay-per-bit” and folding-friendly. + - **Hachi**: embeds *extension-field evaluation statements* into *ring statements* (and back), to make PCS verification fast via sum-check. + +- **Primary object being preserved:** + - **SuperNeo**: preserves **norm** (for binding/pay-per-bit) *and* preserves **evaluation homomorphism** (for folding). + - **Hachi**: preserves the **truth of evaluation claims** (over \(\mathbb{F}_{q^k}\)) when translated into ring relations; norm constraints are handled via sum-check after ring switching. + +- **Ring family emphasis:** + - **Hachi**’s core ring is explicitly power-of-two cyclotomic \(X^d+1\) (Hachi Abstract; `paper/hachi.pdf`, p. 1: “-- 1 of 33 --”). + - **SuperNeo** broadens to more general cyclotomics to support fields like Goldilocks without “full splitting” issues, and explicitly mentions supporting trinomials in parameter sets (SuperNeo intro + parameters discussion; `docs/superneo.pdf`, p. 1–4 and later “concrete parameters” sections). + +- **Protocol role:** + - **SuperNeo** needs an embedding compatible with **folding** (random linear combination of instances/commitments). + - **Hachi** needs a reduction compatible with **PCS recursion and verifier-time reduction** (ring switching + sum-check). + +### 5.3 Are the embeddings “the same”, mathematically? + +It depends what you mean by “same”. There are two distinct layers: + +- **Layer 1: the raw embedding map(s) \(F^{dn}\to R_F^n\) vs \(F_{q^k}\to R_q\)** + These are **not the same functions**. + - SuperNeo’s core embedding is literally the **coefficient embedding** (Def. 7 in their §5), i.e. *place field coordinates into ring coefficients* (`docs/superneo.pdf`, “Definition 7”; see the quote range in this repo at lines 1222–1238 of the extracted text). + - Hachi’s key “field embedding” is to realize \(F_{q^k}\) as a **fixed subfield** \(R_q^H \subseteq R_q\), then use a **basis-dependent bijection** \(\psi:(R_q^H)^{d/k}\to R_q\) (`paper/hachi.pdf`, lines 290–300 in the extracted text). + +- **Layer 2: the algebraic *mechanism* (automorphisms/trace giving inner products, and linearity of evaluations)** + At this layer, they are **the same underlying idea**: both are exploiting a canonical bilinear pairing on cyclotomic rings derived from Galois automorphisms (e.g. \(\sigma_{-1}\)) plus a linear functional (constant term or trace). + - SuperNeo packages it as “there exists a linear transform \(T\) so that \(\mathrm{ct}(T(a)\cdot b)=\langle a,b\rangle\)” (Thm. 3). + - Hachi packages it as “there exists a bijection \(\psi\) so that \(\mathrm{Tr}_H(\psi(a)\cdot\sigma_{-1}(\psi(b)))=(d/k)\langle a,b\rangle\)” (Thm. 1). + +Concretely: SuperNeo’s \(T\) is (mathematically) the **inverse Gram operator** of the ring’s trace/constant-term pairing *expressed in the coefficient basis*. Hachi’s \(\psi\) is a **choice of basis** that identifies \(R_q\) as a free module over a subfield \(R_q^H\cong F_{q^k}\), so that the same pairing looks like a scaled dot product over that subfield. + +So the correct crisp statement is: + +- **Not identical as maps** (different domains/codomains and different basis choices), but +- **equivalent in the sense that both instantiate the same cyclotomic “automorphism + linear functional = inner product” backbone**, just presented in different coordinates. + +--- + +## 6) Practical mental model (how to read both papers through one lens) + +Both papers can be read as building “interfaces” between three layers: + +1. **Ring/module commitment layer** (Ajtai / Module-SIS commitments) +2. **Field arithmetic layer** (sum-check, equality tests, low-degree checks) +3. **Embedding/reduction layer** (the math glue) + +SuperNeo’s embedding layer is primarily: + +- coefficient embedding \(F^{d n_R} \leftrightarrow R_F^{n_R}\), +- inner-product transform + constant-term extraction, +- evaluation homomorphism for ring-linear combinations. + +Hachi’s embedding layer is primarily: + +- fixed-field embedding \( \mathbb{F}_{q^k} \cong R_q^H \subseteq R_q\), +- trace + automorphisms for inner products, +- ring-switching by evaluation \(X=\alpha\) to move verifier work into \( \mathbb{F}_{q^k}\). + +If you want a single phrase: + +> **SuperNeo**: “make folding happen over small fields even though commitments live over rings.” +> **Hachi**: “make PCS verification happen over extension fields even though commitments live over rings.” + + +--- + +## 7) SuperNeo's bilinear form, explicitly identified + +SuperNeo's Theorem 3 states existence of a linear transform \(T\) but never identifies it as a Galois automorphism. Here we close that gap. + +### 7.1 Claim: \(T = \sigma_{-1}\) for \(\Phi(X) = X^d + 1\) + +In \(R_q = F_q[X]/(X^d+1)\), we have \(X^d = -1\), so \(X^{-1} = -X^{d-1}\). The automorphism \(\sigma_{-1}: X \mapsto X^{-1}\) acts on monomials as: + +\[ +\sigma_{-1}(X^0) = 1, \qquad \sigma_{-1}(X^i) = X^{-i} = -X^{d-i} \;\text{ for } 1 \le i \le d-1. +\] + +So on a polynomial \(a(X) = \sum_i a_i X^i\): + +\[ +\sigma_{-1}(a) = a_0 - \sum_{i=1}^{d-1} a_i\, X^{d-i}. +\] + +This is *exactly* the transform \(\bar{a}(X)\) from §3.3.1(A). + +### 7.2 Why the Gram matrix is the identity + +Consider the bilinear form \(B(a,b) = \mathrm{ct}(\sigma_{-1}(a)\cdot b)\) in the monomial basis \(\{1, X, \dots, X^{d-1}\}\). The Gram matrix is: + +\[ +G_{ij} = \mathrm{ct}\big(X^{j-i} \bmod (X^d+1)\big). +\] + +For \(j = i\): \(\mathrm{ct}(1) = 1\). + +For \(j \ne i\): the exponent \(j-i\) satisfies \(-(d-1) \le j-i \le d-1\) and \(j-i \ne 0\). +- If \(j > i\): \(\mathrm{ct}(X^{j-i}) = 0\) since \(1 \le j-i \le d-1\). +- If \(j < i\): \(X^{j-i} = X^{j-i+d}\cdot X^{-d} = -X^{d+j-i}\) where \(1 \le d+j-i \le d-1\), so \(\mathrm{ct}(-X^{d+j-i}) = 0\). + +Therefore \(G = I\) (the identity matrix). This means: + +\[ +\mathrm{ct}(\sigma_{-1}(a)\cdot b) = \mathrm{cf}(a)^\top\, I\, \mathrm{cf}(b) = \langle \mathrm{cf}(a),\,\mathrm{cf}(b)\rangle. +\] + +No Gram correction is needed. The pairing \((\sigma_{-1}, \mathrm{ct})\) gives the standard dot product directly. + +### 7.3 For the trinomial \(\Phi_{81}(X) = X^{54}+X^{27}+1\), the Gram matrix is NOT the identity + +Here \(X^{81} = 1\) but \(X^{27} \ne 1\) in \(R_F\). So \(X^{-27} = X^{54} = -X^{27}-1\), which gives: + +\[ +\mathrm{ct}(X^{-27}) = \mathrm{ct}(-X^{27}-1) = -1. +\] + +The Gram matrix \(G_{ij} = \mathrm{ct}(X^{j-i} \bmod \Phi_{81})\) therefore has off-diagonal entries \(G_{i,\,i+27} = -1\) (and their transposes). The inner-product transform for the trinomial (§3.3.1(B)) is \(T = G^{-1}\circ \sigma_{-1}\), which is why its formula involves sums like \(-(a_{27-i}+a_{54-i})\) rather than a simple sign flip. + +### 7.4 Bottom line + +SuperNeo's bilinear form is: + +\[ +B_{\mathrm{SuperNeo}}(a,b) = \mathrm{ct}\big(\sigma_{-1}(a)\cdot b\big) \in F_q. +\] + +Hachi's bilinear form is: + +\[ +B_{\mathrm{Hachi}}(a,b) = \mathrm{Tr}_H\big(a\cdot \sigma_{-1}(b)\big) \in R_q^H \cong \mathbb{F}_{q^k}. +\] + +Same involution \(\sigma_{-1}\). Different linear functional (\(\mathrm{ct}\) vs \(\mathrm{Tr}_H\)). Different target (\(F_q\) vs \(\mathbb{F}_{q^k}\)). + +--- + +## 8) Classification of non-degenerate bilinear forms on cyclotomic rings + +### 8.1 The general template + +For a cyclotomic ring \(R_q = F_q[X]/(\Phi(X))\) of degree \(d\), with Galois group \(\mathrm{Gal} = (\mathbb{Z}/\eta\mathbb{Z})^\times\) acting by \(\sigma_i: X\mapsto X^i\), the general bilinear form from an automorphism + linear functional is: + +\[ +B_{\sigma,\lambda}(a,b) = \lambda\big(a\cdot \sigma(b)\big) +\] + +where \(\sigma \in \mathrm{Gal}\) and \(\lambda: R_q \to T\) is a linear functional into some target \(T\). + +### 8.2 When is this non-degenerate? (Frobenius algebra theory) + +\(R_q = F_q[X]/(\Phi(X))\) is a **Frobenius algebra** over \(F_q\) (since cyclotomic polynomials are squarefree). This gives a clean classification: + +**Theorem (Frobenius classification)**: A linear functional \(\lambda: R_q \to F_q\) makes the bilinear form \(B(a,b) = \lambda(a\cdot b)\) non-degenerate if and only if \(\lambda\) is a **generating functional**, meaning the induced map \(R_q \to R_q^\vee\) (sending \(a\) to the functional \(b\mapsto \lambda(ab)\)) is an isomorphism. + +Moreover: **the set of all generating functionals is \(\{\lambda(g\,\cdot\,{-}) : g \in R_q^\times\}\)**. Once you have one non-degenerate form, all others come from pre-multiplying by a unit. + +For the form \(B_{\sigma,\lambda}(a,b)=\lambda(a\cdot\sigma(b))\), non-degeneracy reduces to: \(\lambda\circ(\text{mult by }\sigma(\cdot))\) is generating. Since \(\sigma\) is an automorphism (hence maps units to units), \(B_{\sigma,\lambda}\) is non-degenerate iff \(\lambda\) is generating. + +### 8.3 Complete menu of linear functionals + +The dual space \(R_q^\vee = \mathrm{Hom}_{F_q}(R_q, F_q)\) is \(d\)-dimensional. Here are the "natural" families: + +#### (A) Coefficient extraction: \(\mathrm{ct}_j(a) = [X^j](a)\) + +Target: \(F_q\). There are \(d\) such functionals (one per coefficient index \(j\)). + +\(\mathrm{ct} = \mathrm{ct}_0\) is the constant term. For \(\Phi = X^d+1\) with \(\sigma_{-1}\), the Gram matrix of \(\mathrm{ct}_0\) is the identity (§7.2). Other \(\mathrm{ct}_j\) give non-degenerate forms too, but with permuted/signed Gram matrices. + +*Generating?* Yes for many cyclotomics including \(X^d+1\). Can fail for pathological factorizations. + +#### (B) Absolute trace: \(\mathrm{Tr}_{R_q/F_q}(a) = \sum_{\sigma\in\mathrm{Gal}} \sigma(a)\) + +Target: \(F_q\). This is the canonical choice from algebraic number theory. + +*Generating?* Always yes for separable algebras (which cyclotomic rings are). + +Relation to \(\mathrm{ct}\): since both are generating, \(\mathrm{Tr}(a) = \mathrm{ct}(g\cdot a)\) for some explicit unit \(g\in R_q^\times\) (related to the "different ideal" of the cyclotomic extension). + +#### (C) Relative/partial trace: \(\mathrm{Tr}_H(a) = \sum_{\sigma\in H}\sigma(a) \in R_q^H\) + +Target: \(R_q^H \cong \mathbb{F}_{q^k}\) (the fixed subfield under a subgroup \(H \subseteq \mathrm{Gal}\)). + +This is what Hachi uses. The key upgrade: the target is an extension field \(\mathbb{F}_{q^k}\), not just \(F_q\). You get an \(\mathbb{F}_{q^k}\)-valued bilinear form, which means inner products live natively in the sumcheck domain. + +*Generating?* As a map \(R_q \to R_q^H\), yes: the induced \(R_q^H\)-bilinear form on \(R_q\) (viewed as a free \(R_q^H\)-module of rank \(d/k\)) is non-degenerate. + +Trace tower: \(\mathrm{Tr}_{R_q/F_q} = \mathrm{Tr}_{R_q^H/F_q}\circ \mathrm{Tr}_H\). So the relative trace "refines" the absolute trace. + +#### (D) Evaluation at a root: \(\mathrm{ev}_\zeta(a) = a(\zeta)\) for \(\zeta\) a root of \(\Phi\) in some \(\mathbb{F}_{q^t}\) + +Target: \(\mathbb{F}_{q^t}\). + +*Generating?* If \(\Phi\) is irreducible over \(F_q\) (so \(R_q \cong \mathbb{F}_{q^d}\)), every nonzero functional is generating. If \(\Phi\) factors, \(\mathrm{ev}_\zeta\) projects onto one CRT slot and annihilates the others, so it is **not** generating. + +**Fatal for norms**: the evaluation map is equivalent to NTT, which is not norm-preserving. This is exactly the problem SuperNeo identifies with prior approaches (§2.2). + +#### (E) CRT-slot projection: \(\pi_s: R_q \twoheadrightarrow \mathbb{F}_{q^t}\) + +When \(\Phi = \prod_i \phi_i\) factors over \(F_q\) (each \(\phi_i\) irreducible of degree \(t\)), \(R_q \cong \prod_i \mathbb{F}_{q^t}\). The projection \(\pi_s\) onto one factor is: + +Target: \(\mathbb{F}_{q^t}\). + +*Generating?* **No** --- it annihilates the other factors. + +**Same norm problem as (D)**: the CRT isomorphism is an NTT-like map. + +#### (F) Arbitrary \(F_q\)-linear combinations of the above + +Any \(\lambda = \sum_j c_j \,\mathrm{ct}_j\) for scalars \(c_j \in F_q\) gives a functional. It is generating iff the associated element \(g = \sum_j c_j X^j \in R_q\) is a unit. + +### 8.4 Practical takeaway + +If you want **norm preservation**, you must stay in "coefficient-land" (functionals A, B, C, F). Evaluation-based functionals (D, E) destroy norms. + +If you want **extension-field-valued inner products** (for native sumcheck over \(\mathbb{F}_{q^k}\)), the only natural coefficient-land option is **(C) the relative trace** \(\mathrm{Tr}_H\). + +--- + +## 9) The evaluation homomorphism (SuperNeo Theorem 5), spelled out + +This is the key property that makes SuperNeo's folding work. The paper states it abstractly; here is the fully explicit version. + +### 9.1 Setup + +Fix: +- Base field \(F = \mathbb{F}_q\), extension \(K = \mathbb{F}_{q^2}\) (or any extension with \(1/|K| = \mathrm{negl}(\lambda)\)). +- Cyclotomic ring \(R_F = F[X]/(\Phi(X))\), \(R_K = K[X]/(\Phi(X))\), degree \(d\). +- A CCS matrix \(M \in F^{m\times n_F}\) with \(n_F = d\cdot n_R\). +- Witness vectors \(z_1, \dots, z_\ell \in F^{n_F}\), coefficient-embedded as \(\mathbf{z}_i \in R_F^{n_R}\). +- Folding challenges \(\rho_1, \dots, \rho_\ell \in C \subset R_F\) (short ring elements). +- An evaluation point \(r \in K^{\log m}\) (from a prior sumcheck round). +- Any \(R_F\)-module homomorphisms \(L: R_F^{n_R}\to C\) (commitment) and \(\mathrm{Lin}: R_F^{n_R}\to R_F^{n_{R,\mathrm{in}}}\) (input extraction). + +### 9.2 Per-instance "lifted" claims + +For each instance \(i\in[\ell]\), define three objects: + +- **Commitment**: \(c_i := L(\mathbf{z}_i) \in C\) (Ajtai commitment of the ring vector). +- **Input**: \(x_i := \mathrm{Lin}(\mathbf{z}_i) \in R_F^{n_{R,\mathrm{in}}}\) (public input part). +- **Lifted evaluation**: \(y_i := \overline{M}\,\widetilde{\mathbf{z}_i}(r) \in R_K\) (apply the transformed matrix \(\overline{M}\) to the multilinear extension of the ring vector \(\mathbf{z}_i\), evaluated at \(r\)). + +The lifted evaluation \(y_i\) is a **ring element in \(R_K\)** (not a field element in \(K\)). Its constant term recovers the field-level evaluation (by Theorem 4 / Remark 2): + +\[ +\mathrm{ct}(y_i) = M\,\widetilde{z_i}(r) \in K. +\] + +In other words: \(y_i\) has \(d\) coefficients in \(K\); the constant coefficient is the "real" field evaluation; the other \(d-1\) coefficients carry extra information that is needed for folding consistency. + +### 9.3 The evaluation homomorphism (Theorem 5) + +**Statement**: Define the folded objects: + +\[ +\mathbf{z} := \sum_{i\in[\ell]} \rho_i\,\mathbf{z}_i \in R_F^{n_R}, \quad +c := \sum_{i\in[\ell]} \rho_i\, c_i \in C, \quad +x := \sum_{i\in[\ell]} \rho_i\, x_i \in R_F^{n_{R,\mathrm{in}}}, +\quad +y := \sum_{i\in[\ell]} \rho_i\, y_i \in R_K. +\] + +Then **all three of the following hold simultaneously**: + +1. **Commitment homomorphism**: \(c = L(\mathbf{z})\). +2. **Lifted-evaluation homomorphism**: \(y = \overline{M}\,\widetilde{\mathbf{z}}(r)\). +3. **Field-evaluation consistency**: \(\mathrm{ct}(y) = M\,\widetilde{z}(r) \in K\) where \(z = \sum_i \rho_i z_i \in F^{n_F}\). + +(1) holds because \(L\) is \(R_F\)-linear. (2) holds because multilinear extension is \(K\)-linear and matrix multiplication is \(R_K\)-linear. (3) follows from applying \(\mathrm{ct}\) to (2) and invoking Theorem 4. + +### 9.4 Why ring-level claims are essential (the subtle point) + +The folding challenge \(\rho_i \in R_F\) is a **ring** scalar, not a field scalar. At the field level, multiplying by \(\rho_i\) acts on the coefficient vector \(z_i \in F^{n_F}\) by **convolution** (polynomial multiplication scrambles coefficients), not by coordinate-wise scaling. + +This means: +- **At the field level**: after folding, the individual CCS constraints \(Mz = 0\) do NOT hold in any simple sense. The "meaning" of the folded witness as a CCS satisfier is lost. +- **At the ring level**: the commitment, lifted evaluation claims, and input extraction all fold cleanly. The accumulator stores \((c, x, r, y)\) as ring-level objects. + +This is why SuperNeo's accumulator relation is **CE (CCS Evaluation)**, not CCS itself: it stores ring-level evaluation claims \(y_j \in R_K\), and the decider checks them by opening the commitment and verifying ring-level equalities. The \(\mathrm{ct}\) extraction (field-level check) happens only once, at decision time. + +### 9.5 Contrast with Hachi + +Hachi does not need an "evaluation homomorphism" in SuperNeo's sense because Hachi does not fold multiple instances. Instead: + +- Hachi's protocol reduces a *single* opening claim by splitting the coefficient table into blocks, folding with a sparse ring challenge \(c\), and then using ring-switching + sumcheck. +- The analogue of "linearity under ring multiplication" in Hachi is the fold relations (Eq. (18)--(19)): \(a^\top G_{2^m} z = (c^\top\otimes G_1)\hat{w}\) and \(Az = (c^\top\otimes G_{n_A})\hat{t}\), which are linear in the sparse challenge \(c\). + +Both papers exploit the same algebraic fact (ring multiplication is \(R_F\)-linear), but for different protocol purposes: folding (SuperNeo) vs opening reduction (Hachi). + +--- + +## 10) Unified embedding framework (best of both worlds) + +### 10.1 The core observation + +The two bilinear forms use the **same involution** \(\sigma_{-1}\) and differ only in the "readout functional": + +| | SuperNeo | Hachi | +|---|---|---| +| Form | \(\mathrm{ct}(\sigma_{-1}(a)\cdot b)\) | \(\mathrm{Tr}_H(\sigma_{-1}(a)\cdot b)\) | +| Target | \(F_q\) | \(\mathbb{F}_{q^k}\) | +| Gram (for \(X^d+1\)) | \(I\) (identity) | Non-trivial (absorbed into \(\psi\)) | + +These are **compatible**: they use the same product \(\sigma_{-1}(a)\cdot b\) in \(R_q\) and differ only in what you project onto. The trace tower connects them: + +\[ +\mathrm{Tr}_{R_q/F_q} = \mathrm{Tr}_{\mathbb{F}_{q^k}/F_q} \circ \mathrm{Tr}_H. +\] + +### 10.2 The unified pairing abstraction + +**Definition (Cyclotomic Pairing).** Given: +- cyclotomic ring \(R_q\) of degree \(d\), +- a subfield \(S \cong \mathbb{F}_{q^k}\) realized as \(R_q^H \subseteq R_q\) (or \(S = F_q\) as the trivial case \(k=1\)), +- the involution \(\sigma_{-1} \in \mathrm{Aut}(R_q)\), +- the relative trace \(\mathrm{Tr}_H: R_q \to S\), + +define the **level-\(k\) pairing**: + +\[ +B_k(a,b) := \mathrm{Tr}_H\big(\sigma_{-1}(a)\cdot b\big) \in S \cong \mathbb{F}_{q^k}. +\] + +Special cases: +- **\(k = 1\)** (\(H = \mathrm{Gal}\), \(S = F_q\)): \(B_1\) is (up to unit scaling) the absolute-trace pairing. Closely related to SuperNeo's \(\mathrm{ct}\)-based form. +- **\(k = d\)** (\(H = \{1\}\), \(S = R_q\)): \(B_d(a,b) = \sigma_{-1}(a)\cdot b\) (the ring product itself, no projection). +- **\(1 < k < d\)** (\(H\) a proper subgroup): Hachi's setting. \(B_k\) is an \(\mathbb{F}_{q^k}\)-valued non-degenerate bilinear form on the free \(\mathbb{F}_{q^k}\)-module \(R_q \cong \mathbb{F}_{q^k}^{d/k}\). + +### 10.3 Combined embedding pipeline + +``` +Field witness z ∈ F_q^{d·n_R} + │ coefficient embedding (SuperNeo Def. 7, norm-preserving) + ▼ +Ring vector z ∈ R_q^{n_R} ← ‖z‖_∞ preserved + │ Ajtai commit: c = Az + ▼ +Commitment c ∈ R_q^κ + │ + ├── MODE A (SuperNeo-style folding): + │ Use B_1: ct(σ_{-1}(a)·b) = ⟨cf(a), cf(b)⟩ ∈ F_q + │ → sumcheck over K = F_{q²}, fold with ρ ∈ R_F, track ring-level claims y ∈ R_K + │ + └── MODE B (Hachi-style PCS opening): + Use B_k: Tr_H(σ_{-1}(a)·b) ∈ F_{q^k} + → ring-switch at α ∈ F_{q^k}, sumcheck over F_{q^k}, recurse on smaller instance +``` + +The committed object \(\mathbf{z}\in R_q^{n_R}\) is the same in both modes. The choice of functional only affects how you read out inner products and run the interactive proof. + +### 10.4 What you gain + +| Property | SuperNeo alone | Hachi alone | Unified | +|---|---|---|---| +| Norm-preserving embedding | Yes | N/A (PCS, not CCS) | Yes | +| Pay-per-bit commitments | Yes | No | Yes | +| Extension-field inner products | No (\(\mathrm{ct}\to F_q\)) | Yes (\(\mathrm{Tr}_H\to \mathbb{F}_{q^k}\)) | Yes | +| Sumcheck natively over \(\mathbb{F}_{q^k}\) | No (needs \(K\) externally) | Yes | Yes | +| Power-of-two cyclotomics | Supported | Required | Supported | +| General cyclotomics (trinomials) | Supported | Not discussed | Supported (Gram \(\ne I\)) | + +### 10.5 The Gram cost of switching from \(\mathrm{ct}\) to \(\mathrm{Tr}_H\) + +For \(\Phi = X^d+1\) with \(\sigma_{-1}\): +- \(\mathrm{ct}\): Gram = \(I\). No correction needed. Beautifully simple. +- \(\mathrm{Tr}_H\): Gram \(\ne I\). Hachi absorbs this into the packing map \(\psi:(R_q^H)^{d/k}\to R_q\) (Theorem 2, Eq. (8)). + +If you use \(\mathrm{Tr}_H\) instead of \(\mathrm{ct}\), you need: +- the packing map \(\psi\) (one \(O(d)\) linear map per block), +- its inverse \(\psi^{-1}\) (for verification). + +Both are explicit, \(O(d)\)-time, and defined once per parameter set. The Galois subgroup \(H\) and the map \(\psi\) are static public data. + +### 10.6 When you would want each mode + +- **Folding** (SuperNeo-style IVC) with pay-per-bit: use \(\mathrm{ct}\) mode. The evaluation homomorphism (§9) works cleanly because the Gram is trivial. +- **PCS opening** (Hachi-style recursive reduction): switch to \(\mathrm{Tr}_H\) mode when you need ring-switching at \(\alpha \in \mathbb{F}_{q^k}\). +- **Hybrid fold-then-open**: fold in \(\mathrm{ct}\) mode (accumulating ring-level claims), then at the end, open the accumulated commitment using \(\mathrm{Tr}_H\) mode for efficient PCS verification. + +The handoff between modes is seamless because the committed object \(\mathbf{z}\in R_q^{n_R}\) is the same either way. diff --git a/docs/FIELD_OPS_PERF.md b/docs/FIELD_OPS_PERF.md new file mode 100644 index 00000000..13a90846 --- /dev/null +++ b/docs/FIELD_OPS_PERF.md @@ -0,0 +1,237 @@ +# Field Operations Performance + +Benchmark results for scalar and packed (SIMD) field arithmetic across +platforms. All numbers are **element throughput** (median) reported by +`criterion` over 4096-element arrays (`cargo bench --bench field_arith`). + +## Prime selection + +All primes (except M31) are pseudo-Mersenne: `q = 2^k − c` where `c` is +the **smallest positive offset** such that `q` is prime and `q ≡ 5 +(mod 8)`. The congruence `q ≡ 5 (mod 8)` is required so that the +cyclotomic ring `Z_q[X]/(X^d + 1)` splits fully via NTT when `d` is a +power of two (equivalently, `−1` is a quadratic residue but not a quartic +residue mod `q`). + +The constraint `q ≡ 5 (mod 8)` forces `c ≡ 2^k − 5 (mod 8)`: + +| k mod 8 | required c mod 8 | examples | +|---------|------------------|----------| +| 0 | 3 | k=24,32,40,48,56,64,128 | +| 6 | 1 | k=30 | +| 7 | 2 | k=31 | + +For each `k`, smaller candidates were checked and found composite. For +instance at `k = 31` (`c ≡ 3 mod 8`): `2^31 − 3 = 5 × 429496729`, +`2^31 − 11 = 3 × 715827879`, so the first prime is `2^31 − 19`. + +**M31** (`2^31 − 1`, Mersenne prime, `q ≡ 7 mod 8`) is included for +comparison with plonky3 even though it does not satisfy `q ≡ 5 (mod 8)`. + +## Primes benchmarked + +| Label | Modulus | Offset | Rust type | SIMD width | +|-------|---------|--------|-----------|------------| +| fp32_24b | `2^24 − 3` | 3 | `Fp32` | AVX-512: 16, AVX2: 8, NEON: 4 | +| fp32_30b | `2^30 − 35` | 35 | `Fp32` | AVX-512: 16, AVX2: 8, NEON: 4 | +| fp32_31b | `2^31 − 19` | 19 | `Fp32` | AVX-512: 16, AVX2: 8, NEON: 4 | +| fp32_m31 | `2^31 − 1` | 1 | `Fp32` | AVX-512: 16, AVX2: 8, NEON: 4 | +| fp32_32b | `2^32 − 99` | 99 | `Fp32` | AVX-512: 16, AVX2: 8, NEON: 4 | +| fp64_40b | `2^40 − 195` | 195 | `Fp64` | AVX-512: 8, AVX2: 4, NEON: 2 | +| fp64_48b | `2^48 − 59` | 59 | `Fp64` | AVX-512: 8, AVX2: 4, NEON: 2 | +| fp64_56b | `2^56 − 27` | 27 | `Fp64` | AVX-512: 8, AVX2: 4, NEON: 2 | +| fp64_64b | `2^64 − 59` | 59 | `Fp64` | AVX-512: 8, AVX2: 4, NEON: 2 | +| fp128 | `2^128 − 275` | 275 | `Fp128` | AVX-512: 8 (SoA), AVX2: 4 (SoA), NEON: 2 (SoA) | + +--- + +## AMD Zen 5 (Ryzen 9950X / leopard) + +Backend: **AVX-512** (16-wide Fp32, 8-wide Fp64, 8-wide Fp128 SoA with +vectorized add/sub and scalar-per-lane mul). +`RUSTFLAGS='-C target-cpu=native'`, nightly toolchain. + +### Scalar (`throughput/`) + +| Field | mul | add | +|-------|-----|-----| +| fp32_24b | 1.224 Gelem/s | 2.050 Gelem/s | +| fp32_30b | 1.220 Gelem/s | 2.026 Gelem/s | +| fp32_31b | 1.212 Gelem/s | 1.866 Gelem/s | +| fp32_m31 | 1.355 Gelem/s | 1.993 Gelem/s | +| fp32_32b | 1.219 Gelem/s | 1.955 Gelem/s | +| fp64_40b | 1.018 Gelem/s | 2.074 Gelem/s | +| fp64_48b | 1.021 Gelem/s | 2.073 Gelem/s | +| fp64_56b | 0.945 Gelem/s | 2.060 Gelem/s | +| fp64_64b | 0.927 Gelem/s | 1.840 Gelem/s | +| fp128 | 0.452 Gelem/s | 1.127 Gelem/s | + +### Packed (`packed_throughput/`) + +| Field | mul | add | sub | +|-------|-----|-----|-----| +| fp32_24b | 5.362 Gelem/s | 12.76 Gelem/s | 12.74 Gelem/s | +| fp32_30b | 6.145 Gelem/s | 13.53 Gelem/s | 13.55 Gelem/s | +| fp32_31b | 6.187 Gelem/s | 13.53 Gelem/s | 13.54 Gelem/s | +| fp32_m31 | 6.943 Gelem/s | 13.56 Gelem/s | 13.50 Gelem/s | +| fp32_32b | 6.785 Gelem/s | 13.02 Gelem/s | 12.66 Gelem/s | +| fp64_40b | 1.961 Gelem/s | 5.847 Gelem/s | 5.861 Gelem/s | +| fp64_48b | 1.942 Gelem/s | 5.852 Gelem/s | 5.853 Gelem/s | +| fp64_56b | 1.937 Gelem/s | 5.847 Gelem/s | 5.796 Gelem/s | +| fp64_64b | 1.742 Gelem/s | 5.278 Gelem/s | 5.760 Gelem/s | +| fp128 | 0.284 Gelem/s | 2.314 Gelem/s | 3.175 Gelem/s | + +### Packed speedup over scalar + +| Field | mul | add | +|-------|-----|-----| +| fp32_24b | **4.4x** | **6.2x** | +| fp32_30b | **5.0x** | **6.7x** | +| fp32_31b | **5.1x** | **7.3x** | +| fp32_m31 | **5.1x** | **6.8x** | +| fp32_32b | **5.6x** | **6.7x** | +| fp64_40b | **1.9x** | **2.8x** | +| fp64_48b | **1.9x** | **2.8x** | +| fp64_56b | **2.0x** | **2.8x** | +| fp64_64b | **1.9x** | **2.9x** | +| fp128 | **0.6x** | **2.1x** | + +### Sumcheck MACC (`packed_sumcheck_mix/`) + +`acc += eq[i] * poly[i]` loop (dominant inner loop in sumcheck provers). + +| Field | MACC | % of pure mul | +|-------|------|---------------| +| fp32_24b | 4.764 Gelem/s | 89% | +| fp32_30b | 5.352 Gelem/s | 87% | +| fp32_31b | 5.351 Gelem/s | 86% | +| fp32_m31 | 6.097 Gelem/s | 88% | +| fp32_32b | 3.409 Gelem/s | 50% | +| fp64_40b | 1.488 Gelem/s | 76% | +| fp64_48b | 1.492 Gelem/s | 77% | +| fp64_56b | 1.491 Gelem/s | 77% | +| fp64_64b | 1.141 Gelem/s | 65% | +| fp128 | 0.323 Gelem/s | 114% | + +--- + +## Apple M4 Pro (macOS / aarch64) + +Backend: **NEON** (4-wide Fp32, 2-wide Fp64, 2-wide Fp128 SoA). +`RUSTFLAGS='-C target-cpu=native'`, nightly toolchain. + +### Scalar (`throughput/`) + +| Field | mul | add | +|-------|-----|-----| +| fp32_24b | 1.129 Gelem/s | 1.426 Gelem/s | +| fp32_30b | 1.133 Gelem/s | 1.425 Gelem/s | +| fp32_31b | 1.043 Gelem/s | 1.433 Gelem/s | +| fp32_m31 | 1.319 Gelem/s | 1.435 Gelem/s | +| fp32_32b | 1.135 Gelem/s | 1.423 Gelem/s | +| fp64_40b | 0.871 Gelem/s | 1.446 Gelem/s | +| fp64_48b | 0.886 Gelem/s | 1.385 Gelem/s | +| fp64_56b | 0.891 Gelem/s | 1.442 Gelem/s | +| fp64_64b | 0.923 Gelem/s | 1.443 Gelem/s | +| fp128 | 0.444 Gelem/s | 0.938 Gelem/s | + +### Packed (`packed_throughput/`) + +| Field | mul | add | sub | +|-------|-----|-----|-----| +| fp32_24b | 3.717 Gelem/s | 5.272 Gelem/s | 5.278 Gelem/s | +| fp32_30b | 3.719 Gelem/s | 5.281 Gelem/s | 5.275 Gelem/s | +| fp32_31b | 3.719 Gelem/s | 5.283 Gelem/s | 5.268 Gelem/s | +| fp32_m31 | 3.720 Gelem/s | 5.263 Gelem/s | 5.263 Gelem/s | +| fp32_32b | 2.524 Gelem/s | 5.296 Gelem/s | 5.253 Gelem/s | +| fp64_40b | 1.253 Gelem/s | 2.648 Gelem/s | 2.645 Gelem/s | +| fp64_48b | 1.254 Gelem/s | 2.650 Gelem/s | 2.643 Gelem/s | +| fp64_56b | 1.255 Gelem/s | 2.632 Gelem/s | 2.650 Gelem/s | +| fp64_64b | 1.399 Gelem/s | 2.639 Gelem/s | 2.602 Gelem/s | +| fp128 | 0.480 Gelem/s | 1.724 Gelem/s | 2.107 Gelem/s | + +### Packed speedup over scalar + +| Field | mul | add | +|-------|-----|-----| +| fp32_24b | **3.3x** | **3.7x** | +| fp32_30b | **3.3x** | **3.7x** | +| fp32_31b | **3.6x** | **3.7x** | +| fp32_m31 | **2.8x** | **3.7x** | +| fp32_32b | **2.2x** | **3.7x** | +| fp64_40b | **1.4x** | **1.8x** | +| fp64_48b | **1.4x** | **1.9x** | +| fp64_56b | **1.4x** | **1.8x** | +| fp64_64b | **1.5x** | **1.8x** | +| fp128 | **1.1x** | **1.8x** | + +### Sumcheck MACC (`packed_sumcheck_mix/`) + +| Field | MACC | % of pure mul | +|-------|------|---------------| +| fp32_24b | 2.652 Gelem/s | 71% | +| fp32_30b | 2.660 Gelem/s | 72% | +| fp32_31b | 2.662 Gelem/s | 72% | +| fp32_m31 | 2.661 Gelem/s | 72% | +| fp32_32b | 1.991 Gelem/s | 79% | +| fp64_40b | 0.990 Gelem/s | 79% | +| fp64_48b | 0.991 Gelem/s | 79% | +| fp64_56b | 0.993 Gelem/s | 79% | +| fp64_64b | 0.795 Gelem/s | 57% | +| fp128 | 0.450 Gelem/s | 94% | + +--- + +## Notes + +### Zen 5 AVX-512 observations + +- **Fp32 add/sub** saturate at ~13–13.5 Gelem/s, close to 1 cycle per + 16-wide vector at 5 GHz. +- **M31 is the fastest Fp32 prime** for packed mul (6.94 Gelem/s) and + sumcheck MACC (6.10 Gelem/s), because `C = 1` minimizes the reduction + chain. +- **Fp32 mul** is latency-bound by the 2-fold Solinas reduction chain + (~18 cycles per vector). +- **Fp64 sub-word** primes (40b, 48b, 56b) show nearly identical packed + mul throughput (~1.94 Gelem/s), since the vectorized schoolbook + multiply + Solinas reduction dominates regardless of bit-width. +- **Fp64 64b** is slower than sub-word variants due to multi-stage + overflow tracking in the Solinas reduction. +- **Fp32 32b sumcheck MACC** drops to 50% of pure mul, the worst ratio, + because the carry-based add correction creates additional dependencies + in the `acc += eq * poly` loop. +- **Fp128** packed backend now uses SoA layout (8-wide) with vectorized + add/sub via `__m512i`. Add improved **2.1x** (1.13 → 2.31 Gelem/s), + sub improved **2.4x** (1.34 → 3.18 Gelem/s). Mul remains scalar + per-lane and regressed 0.6x (0.45 → 0.28 Gelem/s) due to SoA + pack/unpack overhead. Sumcheck MACC is -7% (0.35 → 0.32 Gelem/s); + MACC exceeds pure-mul throughput (114%) because the accumulation loop + avoids the SoA store overhead that the throughput benchmark incurs. + +### M4 Pro NEON observations + +- **NEON is 4-wide for Fp32, 2-wide for Fp64/Fp128**, so maximum + speedup is 4x and 2x respectively (vs 16x/8x for AVX-512). +- **Fp32 packed mul** is uniform at ~3.72 Gelem/s for all sub-word + primes (24b–31b, including M31), unlike Zen 5 where M31 is notably + faster. The 4-wide NEON `vmull_u32` + reduction is the bottleneck. +- **Fp32 32b packed mul** drops to 2.52 Gelem/s (carry-based path). +- **Fp64 packed mul** ~1.25 Gelem/s for all sub-word primes, ~1.40 + for 64b — the 64b prime is *faster* on NEON, opposite to Zen 5. +- **Fp128 packed add** 1.72 Gelem/s = **1.8x** scalar speedup; sub + 2.11 Gelem/s = **2.2x**, both close to the theoretical 2x from + 2-wide `uint64x2_t`. Mul 0.48 Gelem/s ≈ **1.1x** (scalar per-lane). +- **Sumcheck MACC** is 71–72% of pure mul for sub-word Fp32, 79% for + Fp64 sub-word, and 94% for Fp128 — higher than Zen 5 ratios. + +### Reduction strategy by field width + +| Field | Reduction method | +|-------|-----------------| +| Fp32, BITS ≤ 31 | `min(t, t−P)` — single unsigned compare + blend | +| Fp32, BITS = 32 | carry-based: detect overflow, conditionally add `C`, then subtract `P` if `≥ P` | +| Fp64, BITS ≤ 62 | 2-fold Solinas in u64: `(lo & mask) + c * (lo >> k)`, repeat | +| Fp64, BITS = 64 | vectorized schoolbook 64×64→128 + multi-stage Solinas with overflow tracking | +| Fp128 add/sub | vectorized 128-bit add/sub with carry/borrow propagation via `__m512i` | +| Fp128 mul | scalar per-lane: 9-limb Solinas via u64 decomposition | diff --git a/docs/HACHI_DIGEST.md b/docs/HACHI_DIGEST.md new file mode 100644 index 00000000..c0d0328b --- /dev/null +++ b/docs/HACHI_DIGEST.md @@ -0,0 +1,1362 @@ +# Hachi Digest (for side-by-side comparison with SuperNeo) + +This file captures the parts of `paper/hachi.pdf` that are most actionable for understanding Hachi’s **parameterization** and **protocol shape**, in a compact AI-readable format. + +Primary source: `paper/hachi.pdf` (“Hachi: Efficient Lattice-Based Multilinear Polynomial Commitments over Extension Fields”). + +## Canonical parameter tuples (from paper) + +The paper gives a concrete benchmark parameter set (ℓ = 30) in Figure 9 and uses it to estimate proof size (~55KB) in §5.2. + +```yaml +hachi_parameter_tuples: + - id: l30_benchmark_first_round + witness_num_vars_ell: 30 + base_field: + q: 4294967197 # ~2^32, prime (paper Fig. 9) + ring_coeffs: "Z_q (aka F_q)" + extension_field_for_sumcheck: + k: 4 + field: "F_{q^4}" # paper §5.1, §5.4 + cyclotomic_ring: + phi: "X^d + 1" + alpha: 10 + d: 1024 + ring: "R_q = Z_q[X]/(X^d + 1)" + split_and_fold_params: + m: 10 + r: 10 + commitment_matrices_heights: + nA: 1 + nB: 1 + nD: 1 + decomposition_and_challenges: + decomposition_base_b: 16 + delta: 8 # decomposition length (Fig. 9) + tau: 4 # expansion factor for decomposing z (Fig. 9) + omega_L1: 16 + c_nonzero_coeffs_in_challenge: 16 + norm_bounds: + z_Linf_bound: 30583 + next_witness_Linf_bound: 8 + next_round_witness: + size: 226 + proof_size_estimate: + first_round_sumcheck: "~7.3KB" + adaptation_overhead: "~4.8KB" + greyhound_subproof: "~43KB" + total: "~55.1KB" + timings_reported: + verify_ms_server: 227 # paper §5.2 narrative (first round), plus Fig. 8 context + verify_ms_server_greyhound: 130 # cited as Greyhound estimate in §5.2 narrative +``` + +Notes: + +- The paper’s 55.1KB estimate is explicitly derived in §5.2 (“To conclude, the total evaluation proof can be estimated to be 7.3 + 4.8 + 43 KB = 55.1KB.”). +- This tuple is the “Hachi + compose with Greyhound” estimate for ℓ = 30, not “Hachi alone forever”; Hachi’s design explicitly allows switching to Greyhound/LaBRADOR at small witness sizes. + +## Exact counts (from the paper’s concrete section) + +- Total explicit concrete parameter tables in the paper: **1** (Figure 9; ℓ = 30). +- Concrete benchmark variable counts shown: **3** (ℓ ∈ {26, 28, 30} in Figure 8 timings), but only ℓ = 30 is fully parameterized in Figure 9. +- Unique cyclotomic family used: **1** (`X^d + 1` with `d` power of two). + +## What Hachi suggests (for its purpose) + +High-level message (from the abstract + technical overview): + +- Use **sum-check** to get fast verification, but avoid doing sum-check “over the ring”. +- Use **ring switching** (evaluate at a random α in an extension field) so that the verifier’s checks are field-native and do not require expensive \(R_q\) multiplication. +- Use a **generic reduction** to convert evaluation proofs over extension fields \(F_{q^k}\) into equivalent ring statements over \(R_q\), enabling extension-field evaluation support for lattice PCS. + +Concrete implication (paper §5.3–§5.4): + +- Hachi can pick **larger ring dimensions** (e.g. \(d=1024\)) than Greyhound’s typical \(d=64\) and still keep verification efficient; larger \(d\) helps commitment time (fewer ring mults, NTT-friendly structure) and enables very sparse challenges. + +## Fit into this repo design (easy vs harder) + +- Easy fit (already aligned): + - Hachi’s core ring family is power-of-two cyclotomic \(R_q = Z_q[X]/(X^d+1)\), which matches this repo’s existing algebra/ring direction. +- Harder pieces (protocol-level, not yet fully implemented here): + - Ring switching pipeline (lifting ring equations to \(Z_q[X]\), evaluate at random α in \(F_{q^k}\), sum-check over \(F_{q^k}\)). + - The “compose with Greyhound” handoff (treating the reduced witness as a short ring instance for an existing PCS/proof system). + +## Notation glossary (from `paper/hachi.pdf`) + +Hachi’s paper reuses common lattice-proof-system symbols; here are the ones that tend to confuse on first read. + +### Base objects + +- **\(q\)**: prime modulus; base ring/field is \(Z_q\) (paper treats \(Z_q\) and \(F_q\) interchangeably). +- **\(d = 2^\alpha\)**: cyclotomic ring dimension (power of two). +- **\(\alpha\)**: shorthand for \(\log_2 d\) (used heavily in §3’s “variable count after transformation” formulas). +- **\(R\)**: integer cyclotomic ring \(Z[X]/(X^d+1)\). +- **\(R_q\)**: cyclotomic ring mod \(q\): \(Z_q[X]/(X^d+1)\). +- **\(F_{q^k}\)**: extension field used to run sum-check with negligible soundness error. +- **\(\kappa\)**: shorthand for \(\log_2 k\) when \(k\) is a power of two (this is the \(\kappa\) used in §3.2 and in the “\(\ell-\alpha+\kappa\)” variable-count formulas). +- **\(\sigma_i\)**: Galois automorphism \(X \mapsto X^i\) on \(R\) / \(R_q\) (with \(i\in (\mathbb{Z}/2d\mathbb{Z})^\times\)). +- **\(R_q^H\)**: fixed ring under a subgroup \(H\) of automorphisms; becomes a subfield isomorphic to \(F_{q^k}\) under conditions (Lemma 1 informal in §1.3). +- **\(\mathrm{Tr}_H\)**: trace map \(R_q \to R_q^H\). +- **\(\psi\)**: an efficiently computable bijection \((R_q^H)^{d/k} \to R_q\) used to turn trace-of-product into inner products (Theorem 1 informal in §1.3). + +### Multilinear polynomials / sizes + +- **\(\ell\)**: number of variables of the multilinear polynomial (so witness length is \(2^\ell\)). +- **\(L := 2^\ell\)**: number of coefficients / evaluation-table length. + +### Split-and-fold / decomposition parameters (Figure 9) + +The paper uses **\(m, r\)** as “folding parameters” (they are *not* the same \(m\) as “#constraints” in SuperNeo’s CCS section). + +- **\(m, r\)**: split-and-fold parameters controlling the shape of the quadratic relation after one reduction step. +- **\(b\)**: decomposition base (e.g. 16 in Fig. 9). +- **\(\delta\)**: decomposition length for base witness (e.g. 8 in Fig. 9; essentially \(\lceil \log_b q\rceil\) in spirit). +- **\(\tau\)**: expansion factor / extra length parameter for decomposing intermediate vectors (e.g. 4 in Fig. 9). +- **\(\omega\)**: \(\ell_1\)-norm bound on a sparse challenge (Fig. 9). +- **\(c\)**: number of nonzero coefficients in a sparse challenge polynomial (Fig. 9). + +### Commitment matrix “heights” (Figure 9) + +Hachi uses commitment matrices \(A,B,D\) (not the same “Ajtai A” notation as in SuperNeo). + +- **\(n_A, n_B, n_D\)**: heights (row counts) of the corresponding commitment matrices in the composed relation (Fig. 9 uses all 1). + +## Protocol overview (what is proved, and what is sent) + +This is an end-to-end walkthrough of the **full Hachi protocol**, in the order it’s built in `paper/hachi.pdf`. + +### What Hachi is (PCS statement + design goal, **field-first**) + +The digest previously jumped straight to the §4 “ring PCS statement”. That is **not the full picture**: the paper’s *natural* PCS interface is the usual one where the **witness coefficients are in the base field** \(Z_q \cong F_q\) but the **evaluation point is in an extension field** \(F_{q^k}\) (because sumcheck / batching wants negligible soundness error). + +Concretely, the “true” opening statement the paper starts from (Intro + §3.2) is: + +- **Witness polynomial (true witness)**: \(f \in Z_q^{\le 1}[X_1,\dots,X_\ell]\) (equivalently \(F_q^{\le1}[\cdot]\)), with coefficient table \((f_i)_{i\in\{0,1\}^\ell}\subset Z_q\). +- **Claim (extension-field point/value)**: for a public point \(x=(x_1,\dots,x_\ell)\in F_{q^k}^\ell\), prove \(f(x)=y\in F_{q^k}\). + +Hachi is engineered so that the verifier’s heavy checking runs as **sumcheck over \(F_{q^k}\)** (fast), while commitments / Module-SIS structure remain over the cyclotomic ring \(R_q = Z_q[X]/(X^d+1)\). + +### Step 0 (paper §3.2 → §3.1): the missing “embedding” step (from **\(F_q\)-witness @ \(F_{q^k}\)-point** to a ring statement) + +The paper’s §3 is exactly the bridge from the “true” statement above to the §4 ring PCS statement. + +#### 0.A (paper §3.2): reduce **\(f\in Z_q[\cdot]\)** at **\(x\in F_{q^k}^\ell\)** to one evaluation over \(F_{q^k}\) + +Assume \(k\) is a power of two and write \(k = 2^\kappa\) (this \(\kappa\) is the one used in §3). Split variables into the first \(\kappa\) and the remaining \(\ell-\kappa\). The evaluation can be rewritten (paper Eq. (11)) as: + +\[ +y \;=\;\sum_{i\in\{0,1\}^\kappa}\Big(\prod_{t=1}^{\kappa} x_t^{i_t}\Big)\cdot y_i, +\quad\text{where}\quad +y_i \;:=\; f_{i}(\,x_{\kappa+1},\dots,x_\ell\,)\in F_{q^k}. +\] + +So the prover can send the \(k=2^\kappa\) *partial evaluations* \((y_i)_i\) (and the verifier checks the recombination); what remains is to prove each \(y_i\) is well-formed. + +Paper detail (§3.2, right after Eq. (11)): the verifier can compute \(y_{0\ldots 0}\) from the claimed \(y\) and the other \(y_i\), so in principle only **\(k-1\)** of the partial evaluations need to be transmitted. + +To make that “prove all \(y_i\)” look like **one** extension-field evaluation, §3.2 defines \(F_{q^k} := F_q[Z]/\varphi(Z)\) and builds an \((\ell-\kappa)\)-variate multilinear polynomial \(f' \in F_{q^k}[X_{\kappa+1},\dots,X_\ell]\) by *embedding* the \(k\) slices \((f_i)_i\) into the \(F_q\)-basis \(1,Z,Z^2,\dots,Z^{k-1}\) (paper §3.2): + +\[ +f'(X_{\kappa+1},\dots,X_\ell) +:=\sum_{i\in\{0,1\}^\kappa} +f_i(X_{\kappa+1},\dots,X_\ell)\cdot Z^{\sum_{t=1}^{\kappa} i_t 2^{t-1}}. +\] + +Then \(f'(x_{\kappa+1},\dots,x_\ell)=\sum_i y_i\cdot Z^{(\cdot)}\) holds as an algebraic identity. + +**Critical caveat (security / binding):** it is **not** generally sound to claim that “proving the single packed value \(f'(x_{\kappa+1},\dots,x_\ell)\)” suffices to prove that *each* \(y_i\) is correct, because the coefficients \(y_i\) live in \(F_{q^k}\) (not in the ground field \(F_q\)). + +Concretely, the linear map + +\[ +(y_i)_{i\in\{0,1\}^\kappa}\in (F_{q^k})^{2^\kappa} +\;\longmapsto\; +\sum_i y_i \cdot Z^{(\cdot)} \in F_{q^k} +\] + +is **\(F_{q^k}\)-linear** and therefore has a large kernel whenever \(2^\kappa>1\). So many distinct tuples \((y_i)_i\) produce the *same* packed sum. A toy example for \(k=2\) (basis \(\{1,Z\}\)): the two different pairs \((y_0,y_1)\) and \((y_0+Z,\; y_1-1)\) satisfy + +\[ +(y_0+Z) + (y_1-1)\cdot Z \;=\; y_0 + y_1\cdot Z, +\] + +so the packed value alone does not pin down \(y_0,y_1\). + +This is exactly the “basis is only independent over the ground field” pitfall called out in `paper/fri-binius.pdf`, where they explain that a basis \((\beta_v)\) is linearly independent over \(K\) but **not** over its extension \(L\); hence basis-combining \(L\)-valued claims is insecure. See the strawman discussion around Figure 1 in: + +- `paper/fri-binius.pdf` §1.3 “Ring-Switching”, “A strawman approach”, Figure 1, and the paragraph beginning “While this protocol is complete, it’s not secure.” (pages 4–6 in this PDF copy). + +**How to fix (high-level, sumcheck-style):** you must reduce the “\(y_i\) are well-formed” constraints into **ground-field (\(F_q\)) constraints** before basis-combining / packing them. + +The standard way (as in Fri-Binius ring-switching) is: + +1. **Basis-decompose each \(y_i\) over \(F_q\)**: write \(y_i = \sum_{u=0}^{k-1} y_{u,i}\,Z^u\) with \(y_{u,i}\in F_q\). +2. Also basis-decompose the extension-field weights (the equality-polynomial weights / monomial weights) into \(F_q\) coefficients. +3. Check the resulting family of \(F_q\)-valued equalities “slice-wise” (over the \(u\) index), and then **batch them with an additional sumcheck** so the verifier only pays polylog overhead. + +After this extra sumcheck layer pins down the \(F_q\)-slices, packing becomes injective again (because it is now combining **\(F_q\)-vectors** against an \(F_q\)-basis), and the reduction from “many partial claims” to “one packed claim” becomes sound. + +##### 0.A.1 Concrete “extra sumcheck” shape (Fri-Binius Eq. (12) style), and how many rounds it costs + +This subsection spells out the *exact* reason the extra sumcheck has \(\ell\) rounds (and how it fits the objects already in §3.2). + +Let \(K:=F_q\) and \(L:=F_{q^k}\), and assume \(k=2^\kappa\) for some \(\kappa\) (as in §3.2). Fix a \(K\)-basis \((\beta_u)_{u\in\{0,1\}^\kappa}\) of \(L\) (in §3.2 the paper chooses \(1,Z,\dots,Z^{k-1}\), which is just one such basis). + +The goal is to prove the family of claims (paper after Eq. (11)): + +\[ +\forall v\in\{0,1\}^\kappa:\quad +y_v \stackrel{?}{=} f_v(x_{\kappa+1},\dots,x_\ell)\in L, +\] + +where \(f_v\in K^{\le1}[X_{\kappa+1},\dots,X_\ell]\) is the “slice” of \(f\) with the first \(\kappa\) variables fixed to \(v\). + +The unsafe step is to basis-combine these \(L\)-valued equalities directly. The safe replacement is to basis-decompose everything so the equalities become \(K\)-valued first. + +1) **Basis-decompose the prover’s \(L\)-claims**: for each \(v\in\{0,1\}^\kappa\), write + +\[ +y_v = \sum_{u\in\{0,1\}^\kappa} y_{u,v}\,\beta_u, +\quad\text{with } y_{u,v}\in K. +\] + +2) **Expand \(f_v(x_{\kappa+1},\dots,x_\ell)\) as a \(K\)-weighted sum.** Let \(\ell':=\ell-\kappa\) and index \(w\in\{0,1\}^{\ell'}\). Then + +\[ +f_v(x_{\kappa+1},\dots,x_\ell) += +\sum_{w\in\{0,1\}^{\ell'}} +\mathrm{eq}(x_{\kappa+1},\dots,x_\ell;\,w)\cdot f(v,w), +\] + +where \(f(v,w)\in K\) is the \((v,w)\) Lagrange coefficient of \(f\), and \(\mathrm{eq}(\cdot;\,w)\in L\) is the multilinear equality indicator value. + +3) **Basis-decompose the (public) weights**: for each \(w\), decompose the \(L\)-element \(\mathrm{eq}(x_{\kappa+1},\dots,x_\ell;\,w)\) in the same basis: + +\[ +\mathrm{eq}(x_{\kappa+1},\dots,x_\ell;\,w) += +\sum_{u\in\{0,1\}^\kappa} A_{w,u}\,\beta_u, +\quad\text{with } A_{w,u}\in K, +\] + +where the \(A_{w,u}\) are deterministically computable from the public point \((x_{\kappa+1},\dots,x_\ell)\) and the chosen basis. + +4) **Now each coordinate is a \(K\)-statement**: equating coefficients of \(\beta_u\) yields the family of \(K\)-equalities + +\[ +\forall u,v\in\{0,1\}^\kappa:\quad +y_{u,v} \stackrel{?}{=} \sum_{w\in\{0,1\}^{\ell'}} A_{w,u}\cdot f(v,w). +\] + +5) **Pack the \(f(v,w)\) table into one \(L\)-multilinear** (this is the same “packing” idea as §3.2, but applied to a \(K\)-table so it is information-preserving): + +\[ +f'(w) := \sum_{v\in\{0,1\}^\kappa} f(v,w)\,\beta_v \in L, +\] + +so \(f'\) has \(\ell'=\ell-\kappa\) variables over \(L\). + +6) **Batch and sumcheck.** Define the combined \(L\)-valued claims (these are the secure analog of the strawman’s linear combination step): + +\[ +\hat y_u := \sum_{v\in\{0,1\}^\kappa} y_{u,v}\,\beta_v \in L. +\] + +Then the \(K\)-equalities above imply the \(L\)-equalities + +\[ +\forall u\in\{0,1\}^\kappa:\quad +\hat y_u \stackrel{?}{=} \sum_{w\in\{0,1\}^{\ell'}} A_{w,u}\cdot f'(w). +\] + +Finally, batch over \(u\) with a random point \(r''\in L^\kappa\) and apply sumcheck to the identity + +\[ +\sum_{u\in\{0,1\}^\kappa} \mathrm{eq}(u;\,r'')\cdot \hat y_u +\stackrel{?}{=} +\sum_{w\in\{0,1\}^{\ell'}} +\Big(\sum_{u\in\{0,1\}^\kappa}\mathrm{eq}(u;\,r'')\cdot A_{w,u}\Big)\cdot f'(w). +\] + +This is exactly the structural form of Fri-Binius Eq. (12). The sum ranges over \((u,w)\in\{0,1\}^\kappa\times\{0,1\}^{\ell'}\), so the sumcheck has **\(\kappa+\ell'=\ell\) rounds**, i.e. it costs **\(+\kappa=\log_2 k\)** more rounds than a hypothetical scheme that only needed to open \(f'\) (which has \(\ell'\) variables). + +Asymptotically, prover time for this added sumcheck is linear in the domain size \(2^{\kappa+\ell'}=2^\ell\) (times poly\((\ell,k)\) factors), i.e. \(\Theta(2^\ell)\) field operations in \(L\) for the sumcheck layer, plus one opening of the \(L\)-PCS on \(f'\) at the final point. + +#### 0.B (paper §3.1): embed \(F_{q^k}\) inside \(R_q\) and turn extension-field inner products into trace statements over \(R_q\) + +Now treat the remaining claim as an evaluation over \(F_{q^k}\) (equivalently over the subfield \(R_q^H \cong F_{q^k}\) from Lemma 5). §3.1 then provides: + +- **A subfield of \(R_q\)**: for \(q \equiv 5 \pmod 8\) and \(k\mid d/2\), define \(H=\langle\sigma^{-1},\sigma^{4k+1}\rangle\subset\mathrm{Aut}(R)\). Then the fixed ring \(R_q^H\) is a field and \(R_q^H \cong F_{q^k}\). (Lemma 5.) +- **A packing bijection** \(\psi:(R_q^H)^{d/k}\to R_q\). (Eq. (8), Theorem 2.) +- **A trace/inner-product identity** (Theorem 2): + + \[ + \mathrm{Tr}_H\big(\psi(a)\cdot \sigma^{-1}(\psi(b))\big) \;=\; \frac{d}{k}\cdot \langle a,b\rangle, + \quad a,b \in (R_q^H)^{d/k}. + \] + +Concretely (paper around Eq. (10)), pick \(\alpha:=\log_2 d\) and split the \(\ell\) variables into an “outer” prefix of length \(\ell-\alpha+\kappa\) and an “inner” suffix of length \(\alpha-\kappa\). Write indices as \(i\in\{0,1\}^{\ell-\alpha+\kappa}\) and \(j\in\{0,1\}^{\alpha-\kappa}\). Define: + +- **Packed coefficient blocks**: \(F_i := \psi\big((f_{i\parallel j})_{j\in\{0,1\}^{\alpha-\kappa}}\big)\in R_q\). +- **Packed monomial block at the suffix**: + + \[ + v := \psi\Big(\big(\prod_{t=1}^{\alpha-\kappa} x_{\ell-\alpha+\kappa+t}^{\,j_t}\big)_{j\in\{0,1\}^{\alpha-\kappa}}\Big)\in R_q. + \] + +Then the extension-field evaluation is reduced to checking a **single trace equation** in \(R_q\) involving: + +\[ +Y \;:=\; \sum_{i\in\{0,1\}^{\ell-\alpha+\kappa}} +\Big(\prod_{t=1}^{\ell-\alpha+\kappa} x_t^{i_t}\Big)\cdot F_i +\;\in\; R_q, +\] + +namely \(\mathrm{Tr}_H\big(Y\cdot \sigma^{-1}(v)\big)=\tfrac{d}{k}\,y\). The prover sends this single ring element \(Y\). + +What remains is to prove that \(Y\) is well-formed, i.e. that it is *exactly* the evaluation of the \((\ell-\alpha+\kappa)\)-variate ring polynomial \(F := (F_i)_i \in R_q^{\le 1}[X_1,\dots,X_{\ell-\alpha+\kappa}]\) at the point \((x_1,\dots,x_{\ell-\alpha+\kappa})\) (viewing those \(x_t\) as elements of the subfield \(R_q^H\subset R_q\)). This is the “smaller multilinear evaluation claim over \(R_q\)” that becomes the input to the §4 core PCS. + +### Step 1 (paper §4): the internal ring PCS statement Hachi actually proves + +After §3’s transformation, Hachi reduces extension-field evaluation claims to the §4 “core” ring PCS statement: + +- **Witness polynomial (ring core)**: \(f \in R_q^{\le 1}[X_1,\dots,X_{\ell'}]\) with coefficients in \(R_q\) (this \(f\) is the reduced ring polynomial constructed in Step 0.B; i.e., it is the \(F := (F_i)_i\) from above, just returning to the paper’s §4 notation), +- **Claim**: for a public point \(x\in R_q^{\ell'}\) (in the reduction flow, typically \(x\in (R_q^H)^{\ell'}\subset R_q^{\ell'}\)), prove \(f(x)=u\in R_q\), + +where (per §3.2) \(\ell' = \ell - \alpha\) in the important special case “coefficients in \(Z_q\), point in \(F_{q^k}\)”, with \(d=2^\alpha\). + +From here on, we are *inside* §4. The paper continues to write the ring instance as \(\ell\)-variate; in digest notation, you can read the \(\ell\) used in Steps A/B/C below as \(\ell'\) (the post-§3 reduced variable count). + +### Step A (paper §4.1): Commit to the coefficient table (inner + outer commitments) + +Hachi’s commitment structure is Greyhound-style: it commits to the coefficient table in blocks using two Ajtai commitments. + +Split \(\ell = m + r\) with \(m \approx r\). Define the block slices \(f_i^\top := (f_{i\|j})_{j\in\{0,1\}^m}\in R_q^{2^m}\) for each outer index \(i\in\{0,1\}^r\). (This is the “\(f_i\)” notation right below Equation (12).) + +Commitment construction (Equations (13)–(14)): + +- **Decompose each slice**: \(s_i := G^{-1}_{2^m}(f_i)\in R_q^{2^m\delta}\), where \(\delta=\lceil \log_b q\rceil\). (Eq. (13).) +- **Inner Ajtai commit**: \(t_i := A s_i \in R_q^{n_A}\) for all \(i\in[2^r]\). +- **Decompose the inner commit**: \(\hat t_i := G^{-1}_{n_A}(t_i)\). +- **Outer Ajtai commit**: stack all \(\hat t_i\) and commit: + - \(u := B[\hat t_1;\dots;\hat t_{2^r}] \in R_q^{n_B}\). (Eq. (14).) + +So: + +- **Commitment** is \(u \in R_q^{n_B}\). +- **Opening witness** (conceptually) is \((s_i,\hat t_i)_i\). +- Knowledge/binding is phrased in terms of “weak openings” (definition right after Eq. (14), Lemma 7). + +### Step B (paper §4.2): Reduce “open \(f(x)=u\)” to “prove knowledge of short vectors satisfying a public linear system” + +This is the core reduction pipeline of Hachi’s opening proof. + +#### B.0. Descriptive names for the “hat” variables (implementation-minded) + +The paper uses “hats” (\(\hat{\cdot}\)) for **digit-decomposed** objects (small coefficients), and uses a few single-letter vectors that are easy to lose track of. Here is a naming map that matches the paper’s definitions in §4.1–§4.2 and is meant to be used as docstring text during implementation. + +- **\(s_i\)** = **block_digits** (digits of the \(i\)-th coefficient block): + - \(s_i = G^{-1}_{2^m}(f_i)\). (Eq. (13).) + - Shape: vector of ring elements, length \(2^m\cdot\delta\). + +- **\(t_i\)** = **inner_commitment_block_i** (Ajtai commit of the \(i\)-th block digits): + - \(t_i := A s_i \in R_q^{n_A}\). + +- **\(\hat t_i\)** = **inner_commitment_digits_block_i** (digits of \(t_i\)): + - \(\hat t_i := G^{-1}_{n_A}(t_i)\). + +- **\(u\)** = **outer_commitment** (the actual PCS commitment output): + - \(u := B[\hat t_1;\dots;\hat t_{2^r}] \in R_q^{n_B}\). (Eq. (14).) + +- **\(w_i\)** = **block_partial_eval_i** (block \(i\)’s contribution after plugging the “\(a\)” half of the opening point): + - \(w_i := a^\top G_{2^m} s_i \in R_q\). (Defined right before Eq. (16).) + +- **\(\hat w_i\)** = **block_partial_eval_digits_i** (digits of \(w_i\)): + - \(\hat w_i := G^{-1}_1(w_i) \in R_q^\delta\). + +- **\(v\)** = **aux_commitment_to_block_partials** (commitment to all \(\hat w_i\)): + - \(v := D\hat w \in R_q^{n_D}\). (Eq. (16).) + +- **\(c\)** = **fold_challenge_vector** (short/sparse ring challenge used to fold blocks): + - \(c=(c_1,\dots,c_{2^r})\in C^{2^r}\), with \(\|c_i\|_1\le \omega\). + +- **\(z\)** = **folded_block_digits** (folded witness over block digits): + - \(z := \sum_{i=1}^{2^r} c_i s_i\). (Eq. (18)/(19) discussion.) + - This is the key “compress all blocks into one witness” object. + +- **\(\hat z\)** = **folded_block_digits_redecomposed** (extra decomposition of \(z\) after coefficient growth): + - \(\hat z := J^{-1}_{2^m}(z)\), where \(J\) is the gadget matrix sized for \(\tau\) digits (so \(\hat z\) has length \(2^m\cdot\delta\cdot\tau\)). (Right after Eq. (20).) + +- **\(r\)** = **modulus_quotient_witness** / **slack_witness** (ring-switching quotient): + - \(Mz = y + (X^d+1)\cdot r\) over \(Z_q[X]\). (§4.3.) + - In the “real” protocol, \(r\) is digit-decomposed as \(r=\sum_u b^u r_u\) and the prover commits to the digit vectors \(r_u\). (See §4.3 and our C.2.1.) + +#### B.1. Rewrite evaluation as a bilinear form (Eq. (12)) + +Define the monomial vectors from the evaluation point \(x\): + +- \(b^\top := (x_1^{i_1}\cdots x_r^{i_r})_{i\in\{0,1\}^r}\in R_q^{2^r}\) +- \(a^\top := (x_{r+1}^{j_1}\cdots x_\ell^{j_m})_{j\in\{0,1\}^m}\in R_q^{2^m}\) + +Then the evaluation can be written as Equation (12), which motivates everything that follows. + +#### B.2. Introduce intermediate values \(w_i\) and commit to them (Eq. (16)) + +Using the decomposed slices \(s_i\), Equation (15) rewrites the opening equation using \(s_i\). + +Define the intermediate ring elements: + +- \(w_i := a^\top G_{2^m} s_i \in R_q\). (Defined right before Eq. (16).) + +Then: + +- \(u = b^\top w\). (Eq. (17).) + +The prover also commits to \(w\) using another Ajtai-style commitment (Eq. (16)): + +- decompose \(w_i\) to \(\hat w_i := G^{-1}_1(w_i)\in R_q^\delta\), +- stack \(\hat w := (\hat w_1,\dots,\hat w_{2^r})\), +- compute **\(v := D \hat w \in R_q^{n_D}\)**. (Eq. (16).) + +This is the first prover message in Figure 3: + +- **P → V**: send \(v\). + +#### B.3. Fold all the \(s_i\) using a short challenge vector \(c\) (Eqs. (18)–(19)) + +The verifier samples a short/sparse challenge vector: + +- **V → P**: \(c=(c_1,\dots,c_{2^r}) \leftarrow C^{2^r}\), where \(C \subset \{c\in R_q : \|c\|_1 \le \omega\}\). (See the paragraph introducing \(c\).) + +The prover folds the witness: + +- \(z := \sum_{i=1}^{2^r} c_i s_i \in R_q^{2^m\delta}\). (Immediately after defining \(c\).) + +Two crucial linear identities then hold: + +- \(a^\top G_{2^m} z = (c^\top \otimes G_1)\hat w\). (Eq. (18).) +- \(A z = (c^\top \otimes G_{n_A})\hat t\). (Eq. (19).) + +These relate the folded witness \(z\) to the already-committed objects \(\hat w,\hat t\). + +#### B.4. Decompose \(z\) further and form one big “unstructured linear relation” (Eq. (20)) + +Because coefficients of \(z\) are larger, the prover further decomposes \(z\) using another gadget matrix \(J\): + +- pick a bound \(\beta\) on \(\|z\|_\infty\), define \(\tau:=\lceil \log_b \beta\rceil\), +- compute \(\hat z := J^{-1}_{2^m}(z)\in R_q^{2^m\delta\tau}\). + +At this point, the prover’s remaining task becomes: + +> prove knowledge of a short vector \((\hat w,\hat t,\hat z)\) satisfying a public linear system over \(R_q\). (Eq. (20).) + +Equation (20) is exactly that public linear system: + +- it includes the matrices \(D,B,A\), +- it includes the evaluation-derived vectors \(a,b\), +- it includes the verifier challenge \(c\), +- and it enforces: (i) consistency with the commitments \(u,v\), (ii) the opening equation, and (iii) the fold relations (18)–(19). + +##### B.4.1 Eq. (20) rewritten as a list of constraints (no hats, descriptive meaning) + +Mentally, Eq. (20) is just a *bundling* of several checks into one linear system \(M_{\text{big}}\cdot \text{witness} = \text{statement}\). Written as explicit constraints, the prover is proving existence of **small** objects: + +- **`block_partial_eval_digits`** = \(\hat w\) +- **`inner_commitment_digits`** = \(\hat t\) +- **`folded_block_digits_redecomposed`** = \(\hat z\) (and implicitly \(z = J\hat z\)) + +such that all of the following hold: + +1. **Aux-commitment consistency (ties \(\hat w\) to the sent commitment \(v\))**: + - \(D\hat w = v\). (Eq. (16).) + +2. **Main commitment consistency (ties \(\hat t\) to the sent commitment \(u\))**: + - \(B\hat t = u\). (Eq. (14).) + +3. **Evaluation equation (ties the claimed opening value \(u\) to the partials \(w\))**: + - If \(w := G_{2^r}\hat w\) then \(b^\top w = u\). (Eq. (17).) + +4. **Fold-consistency: partial-eval folding matches the folded witness \(z\)**: + - Let \(z := J\hat z\) (so \(z\) is the “recomposed” folded block-digits witness). + - Then \(a^\top G_{2^m} z = (c^\top\otimes G_1)\hat w\). (Eq. (18).) + +5. **Fold-consistency: inner-commitment folding matches the same folded witness \(z\)**: + - \(A z = (c^\top\otimes G_{n_A})\hat t\). (Eq. (19).) + +6. **Smallness/range constraints (coefficient bounds)**: + - Coefficients of \(\hat w,\hat t,\hat z\) lie in the intended digit ranges (bounded by the gadget decomposition), and the protocol’s range-check machinery in §4.3 ultimately enforces these via the \(H_0\) constraint. + +Figure 3 shows this “conceptual protocol”, ending with the prover *sending* \((\hat w,\hat t,\hat z)\), but the paper immediately notes: + +- in the **final scheme**, the prover does not send these in the clear; instead it proves knowledge of them. + +### Step C (paper §4.3): Prove the unstructured linear relation + coefficient smallness via ring switching + sumcheck over \(F_{q^k}\) + +This is the main verifier-efficiency trick: transform ring relations into field relations (via evaluation at a random \(\alpha\)), then apply sumcheck over \(F_{q^k}\). + +#### C.1. The generic linear relation they want to prove + +They define: + +- \(R^{\mathrm{lin}}_{q,d,n,\mu,b}\): given public \(M\in R_q^{n\times \mu}\), \(y\in R_q^n\), prove knowledge of \(z\in R_q^\mu\) such that \(Mz=y\) and \(\|z\|_\infty \le b-1\). + +Eq. (20) is an instance of this relation (with \(z=(\hat w,\hat t,\hat z)\)). + +#### C.2. Ring switching (Figure 4): lift equality in \(R_q\) to an identity in \(Z_q[X]\), then evaluate at random \(\alpha\) + +Because \(R_q = Z_q[X]/(X^d+1)\), the ring equation \(Mz=y\) holds iff there exists a “slack” polynomial vector \(r\) such that (paper §4.3, “Ring switching.”): + +- \(Mz = y + (X^d+1)\cdot r\) over \(Z_q[X]\). + +##### C.2.1 Critical “hidden detail”: \(r\) is gadget-decomposed, and the protocol commits to the digits + +The paper explicitly notes that **both \(z\) and \(r\)** are prover witnesses, and while the verifier ultimately needs a check involving \(r\), the prover *does not* want to commit to a large-\(q\) object and then range-check it “as-is”. + +So, for “notation and implementation simplicity”, Hachi performs a base-\(b\) gadget decomposition of the quotient witness \(r\) (paper §4.3): + +- \(r = \sum_u b^u \cdot r_u\), +- the prover commits to \((z, r_1, \dots, r_{\log_b(q)})\) instead of \((z,r)\), +- and the prover proves \(\|r_u\|_\infty \le b-1\) for every digit-vector \(r_u\). + +The paper then says it **omits the subscript \(u\)** from this point on, and that to incorporate this in the sumcheck view, “we can modify the multilinear extension correspondingly.” + +Concretely, the “real” linear constraint is: + +\[ +Mz = y + (X^d+1)\cdot \sum_u b^u r_u \quad\text{over } Z_q[X], +\] + +and the “real” smallness constraints are: + +\[ +\|z\|_\infty \le b-1 +\quad\text{and}\quad +\|r_u\|_\infty \le b-1 \ \forall u. +\] + +Protocol idea (Figure 4): + +- **P → V**: commit to \((z,r)\): \(t := \mathrm{Com}(z,r)\). (In the “real” protocol: commit to \((z,(r_u)_u)\) as above; the paper keeps writing \((z,r)\) after omitting the digit index.) +- **V → P**: sample \(\alpha \leftarrow F_{q^k}\). +- Reduce to checking the *field* equations: + - \(M(\alpha)z(\alpha) = y(\alpha) + (\alpha^d+1)r(\alpha)\) over \(F_{q^k}\). (Figure 4.) + +Soundness of this “evaluate at random \(\alpha\)” step is formalized as \(2d\)-special soundness (Lemma 9), reflecting degree \(\le 2d-1\). + +They also need to enforce that the witness coefficients are genuinely in \(Z_q\) and small (not arbitrary in \(F_{q^k}\)), and they fold those checks into the next “sumcheck view”. + +#### C.3. Represent the constraints as multilinear polynomials and batch them (Eqs. (21)–(23), Figure 5) + +This is where the **full constraint system** (including the range check) is spelled out in the paper. + +##### C.3.1 The witness polynomial \(\tilde w\) (Eq. (21)) + +The prover’s committed witness for sumcheck is a multilinear polynomial \(\tilde w\) that encodes coefficient tables. + +**Important:** because of §4.3’s hidden gadget decomposition \(r=\sum_u b^u r_u\), the *real* committed witness should be thought of as encoding coefficient tables of: + +- the vector of polynomials \(z\), and +- all digit-vectors \(r_u\), + +not just a single undigitized \(r\). The paper immediately omits the digit index \(u\) and keeps writing \((z,r)\); this is why Eq. (21) below only has one \(r\). + +The paper defines a multilinear polynomial \(e_w\) (same role as \(\tilde w\) in our prose) as: + +- \(e_w(u,\ell) = z_{u,\ell}\) if \(u \le \mu\), +- \(e_w(u,\ell) = r_{u-\mu,\ell}\) if \(\mu < u \le \mu+n\). (Eq. (21).) + +Here \(u\) and \(\ell\) are treated as binary strings indexing \([\,\mu+n\,]\) and \([\,d\,]\). + +To “incorporate the gadget decomposition” in the exact same shape, one natural flattened encoding is: + +- let \(\delta := \lceil \log_b(q)\rceil\) be the number of digits, +- treat the committed table as indexed by \([\,\mu + n\cdot \delta\,]\times[\,d\,]\), +- keep \(e_w(u,\ell)=z_{u,\ell}\) for \(u\in[\mu]\), +- and set \(e_w(\mu + u'\cdot n + i,\ell) := (r_{u'})_{i,\ell}\) for digit index \(u'\in[\delta]\) and row index \(i\in[n]\). + +With this flattening, the “range check” constraints apply to **every** coordinate of \(z\) and **every** coordinate of every digit vector \(r_{u'}\). + +##### C.3.1.1 Digit-aware \(e_{M_\alpha}\): the fully expanded constraint coefficient function + +The paper’s simplified definition (after Eq. (21)) encodes the linear constraint at \(\alpha\) by defining a public function \(e_{M_\alpha}(i,u)\) that (informally) gives the coefficient multiplying the polynomial \(w_u(\alpha)\) inside row \(i\). + +Once you flatten the digit vectors \((r_{u'})_{u'\in[\delta]}\) into the witness index \(u\in[\,\mu+n\delta\,]\), the *literal* digit-aware version is: + +- Let \(u\in[\,\mu+n\delta\,]\). +- Define the “decoded” witness coordinate \(W_u(\alpha)\) by: + - for \(1 \le u \le \mu\): \(W_u(\alpha) := z_u(\alpha)\), + - for \(\mu + (u'-1)n + i\) with \(u'\in[\delta]\) and \(i\in[n]\): \(W_{\mu + (u'-1)n + i}(\alpha) := (r_{u'})_i(\alpha)\). + +Then define: + +\[ +e^{\text{dig}}_{M_\alpha}(i,u) := +\begin{cases} +M_{i,u}(\alpha) & \text{if } 1 \le u \le \mu, \\ +-\,b^{u'-1}\cdot(\alpha^d+1) & \text{if } u = \mu + (u'-1)n + i \text{ for some } u'\in[\delta], \\ +0 & \text{otherwise.} +\end{cases} +\] + +With this explicit \(e^{\text{dig}}_{M_\alpha}\), the digitized ring-switch check for each row \(i\in[n]\) is exactly: + +\[ +\sum_{u=1}^{\mu+n\delta} e^{\text{dig}}_{M_\alpha}(i,u)\cdot W_u(\alpha) \;=\; y_i(\alpha). +\] + +This is just the statement: + +\[ +\sum_{j=1}^{\mu} M_{i,j}(\alpha)\,z_j(\alpha)\;-\;(\alpha^d+1)\sum_{u'=1}^{\delta} b^{u'-1}\,(r_{u'})_i(\alpha) \;=\; y_i(\alpha), +\] + +which is equivalent to the “real” lifted identity \(Mz = y + (X^d+1)\sum_{u'}b^{u'-1}r_{u'}\) after evaluation at \(X=\alpha\). + +##### C.3.2 The two *literal* constraints before batching (paper right before Eq. (22)/(23)) + +For a fixed ring-switch challenge \(\alpha\in F_{q^k}\), the verifier wants to enforce: + +1. **Linear constraints (ring switching at \(\alpha\))**: for each row \(i\in[n]\), + + \[ + \sum_{u=1}^{\mu+n} e_{M_\alpha}(i,u)\cdot \sum_{\ell} e_w(u,\ell)\cdot e_\alpha(\ell)\;=\;y_i(\alpha), + \] + + where \(e_\alpha(\ell)=\alpha^\ell\) and \(e_{M_\alpha}(i,u)\) is the public multilinear encoding of \(M(\alpha)\) plus the extra \(-(\alpha^d+1)\) term on the \(r\)-coordinates. (This is the first bullet list item under Figure 5 in the paper.) + + With the hidden gadget decomposition \(r=\sum_u b^u r_u\), the same constraint is enforced except the right-hand side becomes \(y_i(\alpha) + (\alpha^d+1)\sum_u b^u r_{i,u}(\alpha)\). In the “\(e_{M_\alpha}\cdot e_w\)” encoding, this is handled by: + + - expanding \(e_w\) to include all digit-vectors \((r_u)_u\) (as described in C.3.1), and + - modifying the \(-(\alpha^d+1)\) part of \(e_{M_\alpha}\) to include the appropriate digit weights \(-b^u(\alpha^d+1)\) on the digit blocks. + +2. **Smallness / range constraints (this is the “range check”)**: for *every* coordinate \((u,\ell)\), + + \[ + P_b\big(e_w(u,\ell)\big) = 0 + \quad\text{where}\quad + P_b(T) := \prod_{t=-(b-1)}^{b-1}(T-t). + \] + + The paper writes this explicitly as the vanishing product: + \(e_w(u,\ell)\cdot(e_w(u,\ell)-1)\cdot(e_w(u,\ell)+1)\cdots(e_w(u,\ell)-b+1)\cdot(e_w(u,\ell)+b-1)=0\). + +This is **not optional**: it is exactly how Hachi enforces that the coefficients the prover is claiming for \(z\) (and the \(r\)-side witness they commit) are small integers (embedded into \(F_{q^k}\)), i.e. a range/membership proof via a root-check polynomial. + +##### C.3.3 Batching with equality polynomials: the exact \(H_\alpha\) and \(H_0\) (Eqs. (22)–(23)) + +Let the multilinear equality polynomial be: + +- \(e_{eq}(t,i) = \prod_j (t_j i_j + (1-t_j)(1-i_j))\). + +Then the paper defines: + +- **Linear constraint batch** \(H_\alpha(t)\) (Eq. (22)): + + \[ + H_\alpha(t) := + \sum_{i\in[n]} e_{eq}(t,i)\cdot + \Big(\sum_{u,\ell} e_{M_\alpha}(i,u)\cdot e_w(u,\ell)\cdot e_\alpha(\ell) - y_i(\alpha)\Big). + \] + +- **Smallness/range batch** \(H_0(t)\) (Eq. (23)): + + \[ + H_0(t) := + \sum_{u,\ell} e_{eq}\big(t,(u,\ell)\big)\cdot P_b\big(e_w(u,\ell)\big). + \] + +The goal is to prove both are **identically zero polynomials**, which they reduce (Figure 5) to random-point checks: + +- **V → P**: send random points \(\tau_0,\tau_1\), +- prove \(H_0(\tau_0)=0\) and \(H_\alpha(\tau_1)=0\). + +#### C.4. Use sumcheck to prove the remaining batched sums (Figure 6) + +After fixing \(\tau_0,\tau_1\), they rewrite \(H_0(\tau_0)\) and \(H_\alpha(\tau_1)\) as sums over \((u,\ell)\) of polynomials \(F_{0,\tau_0}\) and \(F_{\alpha,\tau_1}\), and then apply **sumcheck** over \(F_{q^k}\) (discussion right after Eq. (23)). + +Figure 6 gives the “single-round view” of sumcheck: prover sends univariate \(g_i\), verifier sends random challenge scalars \(a_i\), and in the end the verifier reduces everything to checking an evaluation of the witness polynomial \(\tilde w\) at one final random point. + +Crucially, the sumcheck ends in: + +- a **final evaluation claim** of the committed \(\tilde w\) at a random point \(r^\*\), +- plus the requirement to prove this evaluation is consistent with the commitment \(t\). + +That “prove the evaluation claim for \(\tilde w\)” is exactly where recursion happens: you invoke the PCS again on the smaller committed object. + +##### C.4.1 Full message flow (Figure 7), spelled out + +Figure 7 in the paper is the full composition of Figures 4, 5, and 6. Written as an explicit transcript skeleton: + +- **P → V**: \(t := \mathrm{Com}(z,r)\). (In the “real” protocol: \(t := \mathrm{Com}(z,(r_u)_u)\) with \(r=\sum_u b^u r_u\).) +- **V → P**: sample challenges: + - \(\alpha \leftarrow F_{q^k}\), + - \(\tau_0 \leftarrow F_{q^k}^{\log(\mu)+\log(d)}\), + - \(\tau_1 \leftarrow F_{q^k}^{\log(n)}\). +- **P ↔ V (sumcheck)**: run sumcheck to prove \(H_0(\tau_0)=0\) and \(H_\alpha(\tau_1)=0\): + - in each sumcheck round, **P → V** sends a univariate polynomial \(g_i(X_i)\), + - and **V → P** responds with a random scalar challenge \(a_i \leftarrow F_{q^k}\). (Figure 6.) +- **P → V (final opening)**: open the commitment \(t\) at the final point determined by \((a_1,\dots,a_\ell)\) to provide the needed value(s) of \(\tilde w\). +- **V (final checks)**: + - evaluate the public multilinear extensions (notably \(e_{M_\alpha}\) / \(e_\alpha\)) at the same final point, + - and check the final sumcheck identities (Figure 6’s last-round checks). + +### Step D (paper §3 + §5): recursion shape and concrete proof-size accounting + +Recursion shape (high-level): + +- One invocation reduces the big opening proof into opening proofs for **smaller** committed objects (smaller \(\ell\), smaller coefficient domains after decomposition, and evaluation points living in \(F_{q^k}\)). +- Eventually, Hachi suggests switching to different sub-proofs when the witness is small (paper discusses both switching to LaBRADOR/JL and composing with Greyhound). + +Concrete proof-size estimate for \(\ell=30\) (paper §5.2): + +- Sumcheck for the first round: ~7.3KB. +- “Adaptation + Greyhound subproof” gives total ~55.1KB for an evaluation proof. + +This is the explicit estimate in §5.2: + +- first-round sumcheck: \(7.3\)KB, +- plus preparation/adaptation \(4.8\)KB, +- plus Greyhound evaluation subproof \(43\)KB, +- total \(7.3 + 4.8 + 43 = 55.1\)KB. + +#### D.1 What the “adaptation to Greyhound” actually means (paper §4.5, §5.2) + +When the witness becomes small enough, Hachi can stop running its own §4.3 ring-switch + sumcheck recursion and instead reduce the remaining claim into a **Greyhound-native** opening proof. + +The key shape (paper §4.5 and the concrete instantiation in §5.2) is: + +- you end up with an evaluation claim where the verifier has reduced everything to checking that a committed multilinear object \(\tilde w\) evaluates correctly at a random point; +- the prover groups / “packs” the needed coefficients into extension-field elements, and then uses the §3 embedding machinery (the \(\psi\) map and trace identity) to turn the remaining check into a ring statement supported by Greyhound. + +In the concrete accounting, the additional prover communication for this handoff is bounded as (Equation (28) in the paper excerpted in §4.5): + +- \((k-1)\cdot k \cdot \log q\) bits for the sent partial evaluations \((y_i)\), plus +- \(d'\cdot \log q\) bits for sending one ring element \(p\in R'_{q}\) (where \(d'\) is the Greyhound ring dimension, e.g. \(d'=64\) in §5.2). + +This is why §5.2 reports the “adaptation overhead” as small (~0.3KB for the non-commitment part), and then adds the cost to **commit** to the new Greyhound witness element(s). + +### Message flow summary (first / dominant round) + +If you want a “wire-format mental model” aligned to Figures 3–6, the dominant first round contains: + +- **Ring commitments**: the main commitment \(u\in R_q^{n_B}\) (Eq. (14)) and the auxiliary commitment \(v\in R_q^{n_D}\) (Eq. (16)). +- **Ring challenge**: short/sparse \(c\in C^{2^r}\) used to fold the opening witness (Eq. (18)–(19)). +- **Field challenge**: \(\alpha\in F_{q^k}\) for ring switching (Figure 4), and random points \(\tau_0,\tau_1\) (Figure 5). +- **Sumcheck transcript**: univariate polynomials \(g_i\) and challenge scalars \(a_i\) (Figure 6), ending in a point \(r^\*\) and an evaluation value \(\tilde w(r^\*)\). +- **Opening proof(s)**: recursive PCS openings that prove the claimed evaluations of the committed \(\tilde w\) values match the commitments. + +## Implementation-oriented PCS flow spec (what we need before coding) + +This section re-states the end-to-end PCS as a **software spec**: what the prover/verifier compute, what objects exist (and their “witness” roles), and what must be pinned down *before* we implement §4.3 “witness table embedding” or the ring-switch sumcheck instances. + +### E.0 The key mental model: “stacked linear relation” → “ring switch” → “sumcheck” → “new opening claim” + +The paper explains §4.3 in the simplified setting \(Mz=y\) for \(z\in R_q^\mu\). In the actual PCS opening proof, §4.2 produces exactly such a relation, but with: + +- a **stacked witness vector** \(z\) that bundles multiple unknowns (notably \(\hat w,\hat t,\hat z\) from Eq. (20)), and +- a stacked statement \(y\) and matrix \(M\) derived from public matrices \(A,B,D\), the opening point \(x\) (via \(a,b\)), the claimed opening value, and the verifier challenge \(c\). + +Once the prover and verifier agree on that concrete \((M,y)\), §4.3 proceeds as: + +1. **Ring switching introduces a quotient witness** \(r\) such that: + + \[ + Mz = y + (X^d+1)\cdot r \quad \text{over } Z_q[X]. + \] + +2. **Digitize the quotient witness** \(r = \sum_{u'=0}^{\delta-1} b^{u'} r_{u'}\) and range-check each digit block. +3. Encode the (digitized) coefficient tables of \((z,(r_{u'})_{u'})\) into one multilinear object \(\tilde w\) (paper Eq. (21), with the digit index omitted in the paper’s notation). +4. Prove the linear and range constraints by sumcheck, which ends in an evaluation claim \(\tilde w(r^\*)\) at a random point \(r^\*\). +5. **Recursion boundary**: the next PCS subproblem is “open the commitment to \(\tilde w\) at point \(r^\*\)”. + +### E.1 What the prover’s “witness” is after the first interaction rounds (ring switching + sumcheck) + +If by “after the first rounds” you mean “after the verifier samples \(\alpha,\tau_0,\tau_1\) and sumcheck begins”, then the prover’s relevant witnesses are: + +- **The stacked linear-relation witness** \(z\) from §4.2 (Eq. (20)’s unknown vector; in the paper’s naming, this is \((\hat w,\hat t,\hat z)\) with the implicit recomposition \(z := J\hat z\)). +- **The ring-switch quotient witness digits** \((r_{u'})_{u'\in[\delta]}\) satisfying: + + \[ + Mz - y = (X^d+1)\sum_{u'} b^{u'} r_{u'}. + \] + +These are not sent directly. Instead they are **committed** and then accessed *only* through: + +- evaluations of the committed multilinear object \(\tilde w\) during sumcheck, and finally +- one PCS opening of \(\tilde w\) at the final sumcheck point \(r^\*\). + +So the short answer is: + +> After ring switching starts, the “PCS witness” (for the next recursion layer) is the committed multilinear polynomial \(\tilde w\) that encodes the coefficient table of the stacked witness \(z\) and the digitized quotient witness \((r_{u'})_{u'}\). Sumcheck reduces everything to opening \(\tilde w\) at one random point \(r^\*\). + +### E.2 What “witness table embedding” (Eq. (21)) really must encode in the full PCS (not the simplified \(Mz=y\) story) + +Eq. (21) defines \(e_w(u,\ell)\) in the simplified \((z,r)\) notation. For implementation, the important points are: + +- The “\(z\)” rows are not just “some vector”; in the PCS they are the **stacked unknowns** of Eq. (20), i.e. the prover’s hidden objects that tie together: + - the main commitment \(u\), + - the aux commitment \(v\), + - the opening equation, + - the fold identities (18)–(19), + - and the redecomposition via \(J\). +- The “\(r\)” rows are not optional: they are the **quotient witness** for the lifted equation over \(Z_q[X]\), and in the real protocol are digitized as \((r_{u'})_{u'}\) and range-checked. + +In other words, the witness-table encoder we build should take as input: + +- the stacked witness vector (call it `linear_relation_witness` instead of paper’s `z`), and +- the digitized quotient witness blocks `quotient_digits` (instead of paper’s `r`), + +and output a padded, evaluation-form multilinear object \(\tilde w\). + +### E.3 Why the PoC’s “next witness” contains “extra quotient terms” (and why they don’t contradict the paper) + +The PoC does not implement §4.3 for a single abstract relation \(Mz=y\). It already constructs (a variant of) Eq. (20)’s **stacked linear system**, which bundles multiple constraints. + +Each lifted constraint row contributes its own quotient polynomial(s) when you rewrite it as: + +\[ +\text{(row LHS)} - \text{(row RHS)} = (X^d+1)\cdot r_i(X), +\] + +so the PoC ends up with several quotient vectors (for several different stacked sub-constraints), and it concatenates them into the “next witness table” before padding to a power of two. + +This is an implementation manifestation of the same principle the paper uses: + +- §4.2 stacks many checks into one linear system (Eq. (20)), +- §4.3 introduces quotient witnesses for that system when lifted to \(Z_q[X]\), +- §4.3 then commits to a single coefficient-table object \(\tilde w\) representing *all* witness coordinates and *all* quotient-digit coordinates. + +So: seeing “more quotient chunks” in a prototype is expected whenever you expand the simplified \(Mz=y\) exposition into the concrete PCS relation. + +### E.4 Concrete “before we code” checklist (MVP up through §4.3) + +To avoid implementing §4.3 machinery “in the dark”, we should pin down the following concrete spec items first. + +#### E.4.1 Fix the exact stacked linear relation produced by §4.2 + +We need a concrete `LinearRelationInstance` spec with: + +- **Public statement**: + - the stacked matrix \(M\in R_q^{n\times \mu}\), + - the stacked right-hand side \(y\in R_q^n\), + - and the coefficient smallness parameters (base \(b\), digit length \(\delta\), and any redecomposition \(\tau\) where relevant). +- **Witness semantics**: + - what each coordinate of the stacked witness vector means (e.g., slices corresponding to \(\hat w,\hat t,\hat z\)), + - and which coordinates are subject to the range-check polynomial \(P_b\). + +Without this, we cannot correctly define how many “\(z\) rows” Eq. (21) has (the paper’s \(\mu\)). + +#### E.4.2 Fix the quotient witness structure introduced by ring switching + +For the chosen \((M,y)\), ring switching requires: + +- the quotient witness vector \(r\in (Z_q[X]_{ idx\) to become “evaluations on the hypercube”. + +This is the “witness table embedding” deliverable: it is the object whose commitment is opened at the end of sumcheck (Figure 6 / Figure 7). + +#### E.4.4 Fix the public multilinear encodings needed by §4.3 constraints + +To define \(H_\alpha\) and \(H_0\) (Eqs. (22)–(23)), we need: + +- `AlphaPowers`: the table \(e_\alpha(\ell)=\alpha^\ell\), +- `LinearCoeffEncoding`: the digit-aware coefficient function \(e^{dig}_{M_\alpha}(i,u)\) (i.e., how \(M(\alpha)\) and \(-(\alpha^d+1)\cdot b^{u'}\) are encoded), +- and the equality polynomials \(e_{eq}\) used for batching. + +#### E.4.5 Fix how sumcheck’s final oracle check becomes a PCS opening claim + +Our sumcheck core deliberately stops at “here is the final point \(r^\*\)”; the ring-switch module must: + +- compute the expected final value using the public parts, and +- reduce to a **single opening claim** of the committed \(\tilde w\) at \(r^\*\). + +This is exactly where the PCS prover/verifier “open-check” logic plugs in (currently stubbed in this repo). + +## Modulus switching / cross-prime sumcheck (Jolt-motivated extension; not in the Hachi paper) + +This section sketches how to adapt the Hachi “ring switch \(\to\) sumcheck” pipeline to the setting where: + +- **Commitments** are over a *small* prime field / ring modulus \(q\) (e.g. \(\approx 2^{32}\)), because that makes commitment-time arithmetic and NTT/CRT layouts fast. +- **Sumcheck / arithmetization** must run over a *large* prime field \(F_{q'}\) (e.g. 128-bit prime), because the application (e.g. Jolt) requires characteristic large enough to avoid wrap-around in \(u64\cdot u64\) accumulation. + +This is *similar in spirit* to §3’s extension-field story, but **strictly harder**: there is no field embedding \(F_q \hookrightarrow F_{q'}\) that preserves addition/multiplication mod the prime, so we must explicitly control an **integer lift** via range checks. + +### F.0 Target statement (“foreign-field opening”) + +Let \(q\) be a small prime, \(q'\) a large prime, and let \(f\) be an \(\ell\)-variate multilinear with **small coefficients**, ideally bits: + +\[ +f \in F_q^{\le 1}[X_1,\dots,X_\ell],\quad f_i \in \{0,1\}\subset F_q. +\] + +We commit to the coefficient table \((f_i)_{i\in\{0,1\}^\ell}\) using the Hachi/Greyhound-style commitment core over \(R_q\) (or over \(F_q\) as the \(d=1\) special case). + +The opening claim we want to support is over the **large prime field**: + +\[ +\text{given } x\in F_{q'}^\ell,\ y\in F_{q'},\ \text{prove } f(x)=y\ \text{(interpreting the coefficients as small integers in }F_{q'}\text{).} +\] + +Because the coefficients are in \(\{0,1\}\), there is a canonical injection \(\iota:\{0,1\}\to F_{q'}\) (map to the same integers). The only remaining job is to enforce that the committed coefficients are indeed in \(\{0,1\}\) (bitness) and that every algebraic check is performed with respect to this integer lift. + +#### F.0.1 Important clarification: this is **not** “digit-decompose \(x,y\)” + +It is tempting to think “we have an evaluation claim \(f(x)=y\) in the large field \(F_{q'}\), so we should decompose \(x\) and \(y\) into base-\(b\) digits and prove digit-wise subclaims.” That is **not** what the modulus-switching reduction does, and it generally does not work (polynomial evaluation does not decompose into independent digit evaluations). + +Instead: + +- The evaluation point \(x\in F_{q'}^\ell\) and claimed value \(y\in F_{q'}\) are already *native* to the field where Jolt runs sumcheck. There is typically no reason to decompose them. +- The lift issue arises because the **committed objects** live over the *small* modulus \(q\) (i.e. values are only defined modulo \(q\)), while the verifier wants to check equations **inside \(F_{q'}\)**. + +So the purpose of \(\mathrm{lift}_q\) is to assign a **canonical integer meaning** to committed mod-\(q\) values (made unambiguous by range constraints like “bitness”), so those values can be interpreted inside \(F_{q'}\). + +Warm-up (scalar version). For integers \(\tilde A,\tilde B\in Z\), the statement “\(A=B\) in \(Z_q\)” is exactly: + +\[ +\tilde A \equiv \tilde B \pmod q +\quad\Longleftrightarrow\quad +\exists s\in Z:\ \tilde A - \tilde B = q\cdot s. +\] + +The \(q\cdot s\) term is the “modulus switching slack”. The ring/polynomial version in F.1 is the same idea applied coefficient-wise (and with an additional cyclotomic slack \((X^d+1)\cdot r\) for the ring quotient). + +#### F.0.2 How this plugs into Hachi’s six core constraints (B.4.1) in the Jolt Stage-8 setting + +Jolt Stage 8 asks the PCS to prove openings of the form “\(P(\mathbf r)=v\)” where both the point \(\mathbf r\) and value \(v\) live in the **Jolt field** \(F\) (in your target case, \(F=F_{q'}\)). See: + +- `../jolt/jolt-core/src/poly/opening_proof.rs`: `pub type Opening = (OpeningPoint<..., F>, F);` +- `../jolt/jolt-core/src/zkvm/prover.rs`: Stage 8 calls `PCS::prove(..., &opening_point.r, ...)` where `opening_point.r` is a vector of field challenges. + +Hachi’s Step B constraints (the six items in B.4.1) are written as equalities over the **ring** \(R_q\). To use a Hachi-style PCS under Jolt’s interface, we keep the *same witness objects* \((\hat w,\hat t,\hat z,\dots)\) and the *same logical constraints*, but we do **not** expect the verifier to check them natively in \(R_q\) (and we cannot even form the “\(a,b\in R_q\) from the opening point” parts when \(\mathbf r\in F_{q'}^\ell\)). + +Instead, the PCS opening proof checks these constraints **after ring switching**, i.e. after applying an evaluation map + +\[ +\mathrm{ev}_\alpha: R_q \to F_{q'} +\] + +at a random \(\alpha\in F_{q'}\) (and including the modulus-switch slack \(q\cdot s\) to make “mod \(q\)” equalities meaningful in \(F_{q'}\)). + +Concretely: + +- Constraints **(1), (2), and the purely ring-linear parts** of (4),(5) are still “ring equations”, but they are verified in \(F_{q'}\) by checking \(\mathrm{ev}_\alpha(\text{LHS}-\text{RHS})=0\) (with quotient witnesses for \((X^d+1)\) and \(q\) as in F.1). +- Constraints **(3)–(5)** are the ones that *mention the evaluation point* (via the monomial vectors \(a,b\)) and therefore must be interpreted in the **field**: + - compute \(a,b\) directly from the Stage-8 opening point \(\mathbf r\in F_{q'}^\ell\), + - treat unknown ring elements like \(w_i\in R_q\) only through their field images \(w_i(\alpha):=\mathrm{ev}_\alpha(w_i)\in F_{q'}\), + - and enforce the same algebraic equalities (Eq. (17)–(19)) in \(F_{q'}\). + +So the “generalization to account for \(q'\)” is not “change a few constraints while keeping the rest in \(q\)”; it is: + +> keep the constraint *structure*, but **move their verification domain** from \(R_q\) to \(F_{q'}\) via ring switching (plus a \(q\cdot s\) slack), because Stage 8’s statement lives in \(F_{q'}\). + +#### F.0.3 Why you cannot keep the *entire* opening proof “purely in \(F_q/R_q\)” under Jolt’s interface + +Under Jolt, the opening point \(\mathbf r\) is sampled as transcript challenges in the **same field as the sumchecks**, i.e. \(\mathbf r\in F_{q'}^m\) (see `OpeningPoint<..., F>` in `../jolt/jolt-core/src/poly/opening_proof.rs`). + +Any PCS that plugs into Stage 8 must therefore convince the verifier of a statement that is *parameterized by* these \(F_{q'}\) elements: + +\[ +P(\mathbf r)=v\quad\text{for }\mathbf r,v\in F_{q'}. +\] + +If a verifier refuses to do any \(F_{q'}\) arithmetic, it cannot even *evaluate the public weights* (equality polynomials) at \(\mathbf r\), nor can it check the final identity that defines “evaluation at \(\mathbf r\)”. The only way around this would be to represent every \(F_{q'}\) element (including \(\mathbf r\), \(v\), and all derived weights) as **non-native data** over \(F_q\) (e.g. base-\(b\) limbs) and then prove that these limbs satisfy the mod-\(q'\) arithmetic via additional quotient/carry constraints. + +That “all-\(F_q\) verification” route is a different, much heavier design: it is essentially a SNARK for \(F_{q'}\) arithmetic implemented over \(F_q\), and it introduces digit/carry constraints for every multiplication/addition in the opening protocol. This is *not* what Hachi’s ring switching is optimizing for. + +So the realistic design space is: + +- commitments / witness representation over \(F_q\) / \(R_q\) for performance, +- but verifier-side checking (sumcheck challenges, equality weights, and final identities) in \(F_{q'}\). + +#### F.0.4 Recursion / “next folding steps” in the cross-prime setting + +In Hachi, the “recursion boundary” is: sumcheck reduces a large set of constraints to **one new opening claim** for a committed multilinear object (the \(\tilde w\) table). The next layer repeats the same pattern on a smaller witness. + +In the cross-prime Stage-8 adaptation: + +- the **commitment domain stays** \(F_q/R_q\) at every layer (you keep committing to digitized tables over the small modulus), +- the **opening points stay** in \(F_{q'}\) at every layer, because they are derived from sumcheck challenges / transcript in \(F_{q'}\), +- and the verifier continues to check constraints in \(F_{q'}\) via ring switching (evaluation at \(\alpha\in F_{q'}\) plus the \((X^d+1)\cdot r\) and \(q\cdot s\) quotient witnesses). + +So “continuing in \(F_{q'}\)” does not mean “switch commitments to \(q'\)”; it means the *interactive checking algebra* (sumcheck, batching, evaluation weights) remains in the Jolt field where the statement is expressed. + +#### F.0.5 One full “folding/recursion step” of the adapted PCS (clean, end-to-end) + +This subsection gives a clean one-layer view: how we go from **one opening claim at point \(\mathbf r\in F_{q'}^m\)** to **a smaller opening claim at a new point \(\mathbf r^\*\in F_{q'}^{m'}\)**, and why that output is amenable to repeating the same procedure. + +We describe this as a PCS protocol (what Stage 8 wants), independent of Jolt’s earlier stages. + +##### Inputs (statement) and commitment domain + +- **Commitment domain** (small): commitments are to coefficient tables over \(F_q\) (or ring elements over \(R_q\)) using Hachi’s §4.1 Ajtai-style structure. +- **Opening statement domain** (large): the opening point \(\mathbf r\) and claimed value \(v\) are in \(F_{q'}\) (Jolt’s `JoltField`). + +So the opening statement is: + +\[ +\text{Given commitment } C \text{ to a multilinear table } P,\ \text{and public } \mathbf r\in F_{q'}^m,\ v\in F_{q'},\ \text{prove } P(\mathbf r)=v. +\] + +Here \(P(\mathbf r)\) is defined by interpreting the committed coefficients as integers (via \(\mathrm{lift}_q\)) and reducing them into \(F_{q'}\); for bit/one-hot tables, this interpretation is canonical. + +##### Step 1 (Hachi Step B “split-and-fold”): reduce evaluation to a structured linear relation witness + +This step is unchanged in *spirit* from Hachi: we rewrite “\(P(\mathbf r)=v\)” into a small set of algebraic constraints involving intermediate witnesses (partial evaluations, decomposed digits, and folded combinations). + +The key point in the two-field setting is typing: + +- any time the original §4.2 constraints multiply “point-derived scalars” into witness quantities, those scalars are in \(F_{q'}\) and we interpret the witness quantities through their images in \(F_{q'}\) (via ring switching in Step 2), rather than trying to multiply \(F_{q'}\) scalars by \(R_q\) elements directly. + +Operationally, the prover still constructs the same witness objects (\(\hat w,\hat t,\hat z\), folded \(z\), etc.) and commits to the same ring elements (\(u,v\), etc.). The verifier will not check the ring equations directly; it will check their *ring-switched* images in Step 2. + +##### Step 2 (Hachi Step C generalized): ring switching + modulus switching to get field-native constraints + +The verifier samples a random \(\alpha\leftarrow F_{q'}\) and defines the evaluation map: + +\[ +\mathrm{ev}_\alpha: R_q \to F_{q'} +\] + +as “lift coefficients to integers (per chosen \(\mathrm{lift}_q\)), then evaluate the polynomial at \(X=\alpha\) in \(F_{q'}\)”. + +Now take each ring equation from the Step B constraint set (the six constraints in B.4.1) and convert it into a field equation at \(\alpha\) by: + +1. lifting it from \(R_q\) to \(Z[X]\) with a cyclotomic quotient witness \(r\) (as in the paper), and +2. adding a modulus quotient witness \(s\) so that “mod \(q\) equality” becomes an *integer* equality plus a \(q\cdot s\) slack (Section F.1). + +After evaluating at \(X=\alpha\), every check becomes an identity in \(F_{q'}\) involving: + +- public scalars derived from \(\mathbf r\) (equality weights / monomial vectors), +- the prover’s unknowns only through \(\mathrm{ev}_\alpha(\cdot)\), +- and the quotient witnesses \(r(\alpha), s(\alpha)\). + +##### Step 3 (Hachi §4.3 sumcheck): batch all constraints and reduce to one oracle evaluation + +Exactly as in Hachi, we encode the relevant coefficient tables into one committed multilinear object \(\tilde w\) (“witness table embedding”), except that in the cross-prime setting \(\tilde w\) must encode the extra modulus quotient witness \(s\) as well as \(r\). + +Then we define batched constraint polynomials (the analogs of \(H_\alpha\) and \(H_0\)), and run sumcheck over **\(F_{q'}\)** (not over \(R_q\)). The sumcheck transcript produces a final random point: + +\[ +\mathbf r^\* \in F_{q'}^{m'} +\] + +and reduces verification to a **single evaluation claim** of the committed witness-table multilinear: + +\[ +\tilde w(\mathbf r^\*) = v^\*\in F_{q'}. +\] + +##### Step 4 (recursion boundary): output a smaller opening claim of the same type + +This is the crucial “amenable to further folding” point: + +- The new claim “\(\tilde w(\mathbf r^\*)=v^\*\)” has the **same shape** as the original opening claim, just on a different committed multilinear and a different point. +- The commitment to \(\tilde w\) is again over the **small modulus domain** (it is built from digitized tables over \(F_q/R_q\)). +- The opening point \(\mathbf r^\*\) is again in the **large field** \(F_{q'}\), because it is derived from the sumcheck challenges (and thus from the Jolt transcript). + +Therefore, we can repeat the same 4-step pipeline on \(\tilde w\): + +\[ +P(\mathbf r)=v +\ \leadsto\ +\tilde w(\mathbf r^\*)=v^\* +\ \leadsto\ +\tilde w^{(2)}(\mathbf r^{\*\*})=v^{\*\*} +\ \leadsto\ \cdots +\] + +and eventually hand off to a base PCS / small-instance prover once the witness table is small enough (exactly the same “stop recursion when small” design choice as Hachi’s §5 composition discussion). + +#### F.0.6 Option B (for comparison): decompose the \(F_{q'}\) opening point/value and prove everything over \(F_q/R_q\) + +This subsection works out the alternative you asked for: **avoid doing any verifier arithmetic in \(F_{q'}\)** by representing all \(F_{q'}\) elements (the opening point \(\mathbf r\) and claimed value \(v\), plus all derived weights) as *digits/limbs* over the small field. + +This is not “ring switching”; it is **non-native (foreign-field) arithmetic**: we simulate mod-\(q'\) arithmetic inside a proof system whose native arithmetic is mod-\(q\). + +##### Why this is a different interface than Jolt Stage 8 + +In Jolt, Stage 8’s opening statement is parameterized by an actual \(\mathbf r\in F_{q'}^m\) sampled from the transcript (see `OpeningPoint<..., F>`). + +Option B instead treats \(\mathbf r\) and \(v\) as **public limb vectors over \(F_q\)**. To plug this into Jolt unchanged, you would need to either: + +- change Jolt’s transcript/challenges to live in the small field (not compatible with the stated “char \(> u64\cdot u64\)” requirement), or +- keep \(\mathbf r\in F_{q'}\) as usual but additionally provide a limb decomposition of \(\mathbf r\) and then **prove inside the PCS** that those limbs reconstruct the same \(\mathbf r\) (which reintroduces \(F_{q'}\) operations unless you also non-natively model the transcript). + +So Option B is best viewed as a “theoretical comparison point”, not a drop-in Stage-8 replacement. + +##### Representation: limbs for \(F_{q'}\) elements + +Fix a radix \(B=2^t\) (e.g. \(B=2^{16}\) so limbs fit comfortably under a 32-bit-ish \(q\)), and let + +\[ +L := \left\lceil \log_B(q') \right\rceil +\] + +be the limb count (for a 128-bit prime and \(B=2^{16}\), \(L\approx 8\)). + +We represent a field element \(a\in F_{q'}\) by an integer representative \(\tilde a\in[0,q')\) (canonical lift mod \(q'\)) and a limb decomposition: + +\[ +\tilde a = \sum_{j=0}^{L-1} a_j B^j,\quad a_j\in\{0,1,\dots,B-1\}. +\] + +All limbs \(a_j\) are then encoded as small elements of \(F_q\) (and range-checked to lie in \([0,B)\)). + +##### Non-native arithmetic constraints (core gadget) + +To simulate \(F_{q'}\) arithmetic, every operation becomes an integer identity plus a \(q'\)-multiple slack: + +- **Addition**: to enforce \(c \equiv a+b \pmod{q'}\), prove + + \[ + \tilde a + \tilde b - \tilde c = q'\cdot k + \] + + for some integer \(k\) (with \(k\in\{0,1\}\) if \(\tilde a,\tilde b,\tilde c\in[0,q')\)). + +- **Multiplication**: to enforce \(c \equiv a\cdot b \pmod{q'}\), prove + + \[ + \tilde a\cdot \tilde b - \tilde c = q'\cdot k + \] + + for some integer \(k\) with \(0 \le k < q'\). + +In practice, you do not materialize \(\tilde a\) as a single huge integer; you enforce these identities **in base \(B\) with carries**: + +- introduce carry variables \(u_t\) so that the schoolbook convolution of limbs matches the target limbs, +- and range-check carries so that “equality mod \(q\)” implies “equality over integers” (no wrap-around) at the limb level. + +Cost model: one non-native multiplication of two \(L\)-limb numbers costs + +\[ +\Theta(L^2)\ \text{small-field multiplications} \quad + \quad \Theta(L)\ \text{carry/range constraints}. +\] + +##### How to prove an opening claim \(P(\mathbf r)=v\) using Option B + +Let \(P\) be a multilinear polynomial committed over \(F_q\) (or \(R_q\)) whose coefficients are small integers (bits/one-hot is the cleanest case). + +Public input for Option B: + +- limb decompositions of each coordinate \(r_i\in F_{q'}\) (so \(\tilde r_i=\sum_j r_{i,j}B^j\)), +- limb decomposition of \(v\in F_{q'}\), +- and the modulus \(q'\) itself (public constant). + +Prover witness: + +- limb decompositions for all intermediate \(F_{q'}\) values needed to evaluate \(P\) at \(\mathbf r\), +- plus all carry/quotient witnesses for the modular reduction constraints above. + +Then enforce, inside the proof system over \(F_q/R_q\): + +1. **Range**: every limb is in \([0,B)\) (bitness is the special case \(B=2\)). +2. **Recomposition**: the limb vectors correspond to integers in \([0,q')\) (often implemented by providing a quotient \(t\) such that \(\sum_j a_jB^j = \tilde a + q' t\) and constraining \(\tilde a CE(b,L)^(K+k) -- + | + Π_RLC + | + CE(B,L) + | + Π_DEC + | + next accumulator: CE(b,L)^k +``` + +### What the prover sends in each sub-protocol + +Below is the communication “payload” you should have in mind (Fiat–Shamir makes verifier randomness transcript-derived, but sizes are the same). + +#### Π_CCS (paper §7.3) + +Prover payload: + +- **Sum-check transcript over \(K\)** for \(\log m\) rounds (one univariate polynomial per round; degree is small in typical CCS, e.g. R1CS-like \(u=2\)). +- **Oracle answers after sum-check**: for every claim \(i\in[K+k]\) and every matrix \(j\in[t]\), send + \[ + y'_{i,j} = \bar M_j \tilde z_i(r') \in R_K. + \] + +Rule of thumb: the \(y'_{i,j}\) payload dominates. + +#### Π_RLC (paper §7.4) + +This is just random linear combination using \(\rho_i\in C\): + +\[ +c := \sum_i \rho_i c_i,\quad y_j := \sum_i \rho_i y_{i,j},\quad z := \sum_i \rho_i z_i. +\] + +Prover payload: essentially **nothing new** (the reduction is “algebraic bookkeeping”; in FS the \(\rho_i\) come from the transcript). + +#### Π_DEC (paper §7.5) + +Prover payload: + +- Decompose \(z\) into digits \((z_1,\dots,z_k)=\mathrm{split}_b(z)\). +- Send **\(k\) new commitments** \(c_i = L(z_i)\). +- Send **\(k\cdot t\)** new lifted evaluations \(y_{i,j} = \bar M_j \tilde z_i(r)\in R_K\). + +### Proof size accounting (symbolic, per fold step) + +Let: + +- commitment output be \(c\in R_F^\kappa\) (Ajtai: \(\kappa\) ring elements over \(R_F\)), +- each lifted evaluation be one ring element in \(R_K\) (degree \(d\) over \(K\)), +- \(\ell := \log m\) be the sum-check arity. + +Then per fold step, prover sends approximately: + +- **Π\_CCS**: + - sum-check: \(O(\ell)\) field elements in \(K\), + - evaluations: \((K+k)\cdot t\) ring elements in \(R_K\). +- **Π\_DEC**: + - commitments: \(k\cdot \kappa\) ring elements in \(R_F\), + - evaluations: \(k\cdot t\) ring elements in \(R_K\). + +Total (dominant terms): + +\[ +\text{#}(R_K\text{-elements}) \approx (K+k)t + kt = (K+2k)t, +\] +\[ +\text{#}(R_F\text{-elements}) \approx k\kappa, +\] +plus a small \(\tilde O(\log m)\) number of \(K\)-field elements from sum-check. + +To convert to bytes for appendix parameter sets where \(K=\mathbb{F}_{q^2}\) and \(q\) is 61–64 bits: + +- 1 \(F\)-element ≈ 8 bytes +- 1 \(K\)-element ≈ 16 bytes +- 1 \(R_F\)-element ≈ \(d\cdot 8\) bytes +- 1 \(R_K\)-element ≈ \(d\cdot 16\) bytes +- 1 commitment \(c\in R_F^\kappa\) ≈ \(\kappa\cdot d\cdot 8\) bytes + +So a back-of-the-envelope fold proof byte size is: + +\[ +\approx (K+2k)t\cdot(d\cdot 16)\;+\;k\kappa\cdot(d\cdot 8)\;+\;\tilde O(\log m)\cdot 16. +\] + +## Exact counts + +- Total concrete field/cyclotomic tuples in SuperNeo appendix: **3** +- Unique base fields in those tuples: **3** +- Unique cyclotomic polynomials in those tuples: **2** + - `X^64 + 1` + - `X^54 + X^27 + 1` +- Strict Solinas-only tuples (`q = 2^x - 2^y + 1`): **2 / 3** + - Goldilocks (`2^64 - 2^32 + 1`) + - Mersenne61 (`2^61 - 1 = 2^61 - 2^1 + 1`) +- Non-Solinas tuple: **1 / 3** + - Almost-Goldilocks (`2^64 - 2^32 - 31`) + +## What SuperNeo suggests (for their purpose) + +- Keep sum-check and norm-check over a small field (or small extension), not over ring arithmetic. +- Do not restrict to only power-of-two cyclotomics (`X^d + 1`); using broader cyclotomics can unlock better field compatibility. +- For Goldilocks/M61, the paper uses a trinomial cyclotomic (`X^54 + X^27 + 1`) instead of `X^d + 1`. +- They explicitly discuss why power-of-two cyclotomics are problematic for some small fields (full splitting / security issues in prior designs). + +## Fit into Hachi design (easy vs harder) + +- Easy fit now: + - Almost-Goldilocks-like setup with `d = 64` and `X^64 + 1` is structurally close to Hachi's current ring form. +- Requires refactor: + - Goldilocks and M61 with `X^54 + X^27 + 1` do not match the current hardcoded negacyclic `X^D + 1` shape. + +## Minimal integration plan into current architecture + +1. Add a cyclotomic profile abstraction (`CyclotomicProfile`) that defines modulus polynomial behavior. +2. Keep current profile as `Negacyclic` (`X^D + 1`) for existing NTT/CRT path. +3. Add a `Trinomial54` profile (`X^54 + X^27 + 1`) for SuperNeo-style field/ring experiments. +4. Keep backend split: + - current CRT+NTT backend for `Negacyclic` only, + - coefficient-domain backend first for `Trinomial54` (no forced NTT dependency). +5. Add explicit domain aliases for profile-bound rings so APIs remain clear (`CoeffDomain`). + +## Practical implication if we insist on Solinas-only fields + +- Within SuperNeo's concrete options, we still have **2 viable Solinas choices**: + - Goldilocks + `X^54 + X^27 + 1` + - M61 + `X^54 + X^27 + 1` +- If we also insist on power-of-two cyclotomics only (`X^d + 1`), SuperNeo's concrete Solinas count drops to **0**. diff --git a/docs/TRANSCRIPT_COMMITMENT_COMPAT_SPEC.md b/docs/TRANSCRIPT_COMMITMENT_COMPAT_SPEC.md new file mode 100644 index 00000000..03fceb7a --- /dev/null +++ b/docs/TRANSCRIPT_COMMITMENT_COMPAT_SPEC.md @@ -0,0 +1,106 @@ +# Transcript and Commitment Compatibility Spec (Hachi Core) + +This document specifies Hachi's protocol-layer transcript and commitment interfaces. + +## Scope + +- Applies to Hachi core (`src/protocol/*`). +- Uses **Hachi-native** transcript labels and ordering. +- Does **not** wire Hachi into Jolt in this phase. +- Any future cross-system interop (for example Jolt-facing adaptation) must be handled by an adapter layer outside core label definitions. + +## Transcript Contract + +Hachi protocol transcripts implement: + +- `new(domain_label)` +- `append_bytes(label, bytes)` +- `append_field(label, x)` +- `append_serde(label, s)` +- `challenge_scalar(label)` +- `reset(domain_label)` + +Current core implementations: + +- `Blake2bTranscript` (Blake2b-512) +- `KeccakTranscript` (Keccak-256, matching Jolt's `sha3` crate usage) + +### Byte Framing + +All absorbed bytes use deterministic framing: + +- `label || len_le64 || bytes` + +This framing is applied uniformly for raw bytes, fields, and serializable protocol objects. + +### Field Encoding + +- Field elements are encoded through canonical representatives (little-endian `u128` bytes). +- Challenge derivation maps transcript digest bytes into field elements via canonical reduction. + +### Label Namespace + +All labels are defined in `src/protocol/transcript/labels.rs` and are Hachi-native. + +Reserved core labels include: + +- Domain label: `hachi/protocol` +- Commitment phase (§4.1): commitment +- Reduction phase (§4.2): evaluation-claims + linear-relation challenge +- Ring-switch phase (§4.3): ring-switch-message + ring-switch challenge +- Sumcheck phase (§4.3): sumcheck-round + sumcheck-round challenge +- Recursion stop phase (§4.5): stop-condition + stop-condition challenge + +Forbidden in Hachi core transcript constants: + +- Dory label literals (for example `vmv_c`, `beta`, `alpha`, `gamma`, `final_e1`, `final_e2`, `d`) + +## Commitment Contract + +Hachi protocol commitment interfaces include: + +- `CommitmentScheme` +- `StreamingCommitmentScheme` +- `AppendToTranscript` + +The commitment layer defines: + +- setup split (`setup_prover`, `setup_verifier`) +- commitment/opening APIs (`commit`, `prove`, `verify`) +- homomorphic combination APIs (`combine_commitments`, `combine_hints`) +- optional streaming/chunked path for large inputs +- label-directed transcript absorption (`AppendToTranscript` call sites choose event labels) + +## Determinism Requirements + +- Prover and verifier must absorb the same labeled byte sequence in the same order. +- Transcript challenges must be reproducible for identical input schedules. +- Commitment/proof objects absorbed via `append_serde` must use deterministic `HachiSerialize` encoding. + +## Test Requirements + +Tests should enforce: + +- Transcript replay determinism (same schedule => same challenges). +- Label/order sensitivity (different labels/order => diverging challenges). +- Framing stability. +- No Dory-label leakage in Hachi label constants/schedules. +- Commitment/hint combination algebraic sanity. + +## Deferred Integration Note + +Integration into Jolt is a separate, deferred phase tracked in `HACHI_PROGRESS.md`. +When started, an adapter should translate between external transcript conventions and Hachi core interfaces without changing Hachi-native core labels. + +## Deferred Adapter Contract (Design Only) + +`JoltToHachiTranscript` is deferred, but its expected behavior is fixed now: + +- Owns a mutable reference to a Jolt transcript object. +- Implements Hachi `Transcript` by forwarding absorption/challenge calls. +- Performs label translation at the boundary (Jolt-side naming to Hachi-side API events). +- Never mutates or extends Hachi core label constants. +- Maintains deterministic call ordering: prover and verifier adapter paths must replay identical absorb/challenge sequences. +- Supports domain initialization and explicit reset semantics. + +This adapter lives outside Hachi core protocol modules and is not part of this phase's implementation. diff --git a/examples/codegen_probe_special.rs b/examples/codegen_probe_special.rs new file mode 100644 index 00000000..bc6d5b50 --- /dev/null +++ b/examples/codegen_probe_special.rs @@ -0,0 +1,143 @@ +#![allow(missing_docs)] + +//! Codegen probe for packed/scalar Fp64 multiply kernels. +//! +//! Build with: +//! `cargo rustc --example codegen_probe_special --release -- --emit=asm` + +use hachi_pcs::algebra::fields::pseudo_mersenne::{POW2_OFFSET_MODULUS_40, POW2_OFFSET_MODULUS_64}; +use hachi_pcs::algebra::{Fp64, Fp64Packing, PackedValue}; +use hachi_pcs::CanonicalField; + +const MASK40: u64 = (1u64 << 40) - 1; +const P40: u64 = POW2_OFFSET_MODULUS_40; +const C40: u64 = (1u64 << 40) - P40; // 195 +const P64: u64 = POW2_OFFSET_MODULUS_64; +const C64: u64 = 0u64.wrapping_sub(P64); // 59 + +#[inline(always)] +fn mul_c40_split(x: u64) -> u64 { + let c = C40 as u32; + let x_lo = x as u32; + let x_hi = (x >> 32) as u32; + (c as u64 * x_lo as u64).wrapping_add((c as u64 * x_hi as u64) << 32) +} + +#[inline(always)] +fn mul_c40_shiftadd(x: u64) -> u64 { + // 195x = (128 + 64 + 2 + 1) * x + (x << 7) + .wrapping_add(x << 6) + .wrapping_add(x << 1) + .wrapping_add(x) +} + +#[inline(always)] +fn reduce40_with_mulc(lo: u64, hi: u64, mulc: fn(u64) -> u64) -> u64 { + let high = (lo >> 40) | (hi << 24); + let f1 = (lo & MASK40).wrapping_add(mulc(high)); + let f2 = (f1 & MASK40).wrapping_add(mulc(f1 >> 40)); + let reduced = f2.wrapping_sub(P40); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & P40) +} + +#[inline(always)] +fn reduce64(lo: u64, hi: u64) -> u64 { + let f1 = (lo as u128) + (C64 as u128) * (hi as u128); + let f2 = (f1 as u64 as u128) + (C64 as u128) * ((f1 >> 64) as u64 as u128); + let reduced = f2.wrapping_sub(P64 as u128); + let borrow = reduced >> 127; + reduced.wrapping_add(borrow.wrapping_neg() & (P64 as u128)) as u64 +} + +#[inline(never)] +#[no_mangle] +pub extern "C" fn probe_reduce40_split(lo: u64, hi: u64) -> u64 { + reduce40_with_mulc(lo, hi, mul_c40_split) +} + +#[inline(never)] +#[no_mangle] +pub extern "C" fn probe_reduce40_shiftadd(lo: u64, hi: u64) -> u64 { + reduce40_with_mulc(lo, hi, mul_c40_shiftadd) +} + +#[inline(never)] +#[no_mangle] +pub extern "C" fn probe_reduce64(lo: u64, hi: u64) -> u64 { + reduce64(lo, hi) +} + +#[inline(never)] +#[no_mangle] +pub extern "C" fn probe_packed_fp64_40_mul(a0: u64, a1: u64, b0: u64, b1: u64) -> u64 { + type F = Fp64<{ POW2_OFFSET_MODULUS_40 }>; + type PF = Fp64Packing<{ POW2_OFFSET_MODULUS_40 }>; + + let a = PF::from_fn(|i| { + if i == 0 { + F::from_canonical_u64(a0) + } else { + F::from_canonical_u64(a1) + } + }); + let b = PF::from_fn(|i| { + if i == 0 { + F::from_canonical_u64(b0) + } else { + F::from_canonical_u64(b1) + } + }); + let c = a * b; + (c.extract(0).to_canonical_u128() as u64) ^ (c.extract(1).to_canonical_u128() as u64) +} + +#[inline(never)] +#[no_mangle] +pub extern "C" fn probe_packed_fp64_64_mul(a0: u64, a1: u64, b0: u64, b1: u64) -> u64 { + type F = Fp64<{ POW2_OFFSET_MODULUS_64 }>; + type PF = Fp64Packing<{ POW2_OFFSET_MODULUS_64 }>; + + let a = PF::from_fn(|i| { + if i == 0 { + F::from_canonical_u64(a0) + } else { + F::from_canonical_u64(a1) + } + }); + let b = PF::from_fn(|i| { + if i == 0 { + F::from_canonical_u64(b0) + } else { + F::from_canonical_u64(b1) + } + }); + let c = a * b; + (c.extract(0).to_canonical_u128() as u64) ^ (c.extract(1).to_canonical_u128() as u64) +} + +#[inline(never)] +#[no_mangle] +pub extern "C" fn probe_scalar_fp64_40_mul(a: u64, b: u64) -> u64 { + type F = Fp64<{ POW2_OFFSET_MODULUS_40 }>; + (F::from_canonical_u64(a) * F::from_canonical_u64(b)).to_canonical_u128() as u64 +} + +#[inline(never)] +#[no_mangle] +pub extern "C" fn probe_scalar_fp64_64_mul(a: u64, b: u64) -> u64 { + type F = Fp64<{ POW2_OFFSET_MODULUS_64 }>; + (F::from_canonical_u64(a) * F::from_canonical_u64(b)).to_canonical_u128() as u64 +} + +fn main() { + let x = probe_packed_fp64_40_mul(1, 2, 3, 4) + ^ probe_packed_fp64_64_mul(5, 6, 7, 8) + ^ probe_scalar_fp64_40_mul(9, 10) + ^ probe_scalar_fp64_64_mul(11, 12) + ^ probe_reduce40_split(13, 14) + ^ probe_reduce40_shiftadd(15, 16) + ^ probe_reduce64(17, 18); + std::hint::black_box(x); +} diff --git a/paper/fri-binius.pdf b/paper/fri-binius.pdf new file mode 100644 index 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zUQHVK!{j?bxkDqr8pa$uCxx1E#+*X;3HVPtiAFWOD^8MUMsFL2a%jBb)&yMl{{^fh zNt|Ve3{4BmU6b0leHl;SwW4(WGTwj^S}y<@Dtjgk-6f)xJ8Pf(E=Dm=c58Tlq%R{> zwRZ0y(^l!?!2JCh0<5sI&S(<#xahHlS*XxXZVTr2#K`q%L< zB?qxQUG=)t%?;cl)d!Ug_SH;+R%|<7OqsQ*ZCzyt?G3;8Ol1fw>4H8NC{&<#1tJhu zaXw}jFjXkONKDsjLnz+44>Moa#9v!h_-`h3GgEYybPsN5Y$k26US!mF?^hr=#^c}5 zl%V?m9EQ7NW4*YIgNs*#Us!qWrS>%|?&c_f>+;nM-kpF`>uBocqF}jria`CnMS+l8 zgLglw9!$9LZnFppwf(nIu~*MxOf7+W$iq-=I++6<6{jBd&I}QA`ZRB6<1j0*Tcu=_RDOXQH&7(9_ViZBq)S$ zY-BeC9bp`xHd%^oUG{ea{rES3KC(nEpT@neMeSh+?PdD>d83y1qnFJ-KDfTQ?x%G` zIH4N!--{%K)j0-jAnp7$3INEj6N#_sXdRK1WkG12>G4UR_ozGbP=^R_j7=%+cFf9u zi~|_Za~%-YMfzn7ao698_gioPg%gs0Qp^*~Q^}=jcUrSIA9zp NttPrimeOps for ScalarBackend { + #[inline] + fn from_canonical(prime: NttPrime, value: i16) -> MontCoeff { + prime.from_canonical(value) + } + + #[inline] + fn to_canonical(prime: NttPrime, value: MontCoeff) -> i16 { + prime.to_canonical(value) + } + + #[inline] + fn reduce(prime: NttPrime, value: MontCoeff) -> MontCoeff { + prime.reduce(value) + } + + #[inline] + fn pointwise_mul( + prime: NttPrime, + out: &mut [MontCoeff; D], + lhs: &[MontCoeff; D], + rhs: &[MontCoeff; D], + ) { + prime.pointwise_mul(out, lhs, rhs); + } +} + +impl NttTransform for ScalarBackend { + #[inline] + fn forward_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles) { + forward_ntt(limb, prime, twiddles); + } + + #[inline] + fn inverse_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles) { + inverse_ntt(limb, prime, twiddles); + } +} + +impl CrtReconstruct for ScalarBackend { + fn reconstruct( + primes: &[NttPrime; K], + canonical_limbs: &[[i16; D]; K], + qdata: &QData, + ) -> [F; D] { + let q = qdata.q_u128().expect("q must fit in u128"); + let prime_moduli: [u128; K] = std::array::from_fn(|k| { + u128::try_from(primes[k].p).expect("CRT prime modulus must be positive") + }); + let big_p = prime_moduli.iter().fold(1u128, |acc, p| { + acc.checked_mul(*p) + .expect("product of CRT primes must fit u128") + }); + let crt_m: [u128; K] = std::array::from_fn(|k| big_p / prime_moduli[k]); + let crt_inv: [u16; K] = std::array::from_fn(|k| { + let inv = mod_inverse( + (crt_m[k] % prime_moduli[k]) as i128, + prime_moduli[k] as i128, + ); + u16::try_from(inv).expect("CRT inverse must fit u16 for small-prime backend") + }); + + let mut coeffs = [F::zero(); D]; + for (d, coeff) in coeffs.iter_mut().enumerate() { + let mut acc: u128 = 0; + for k in 0..K { + let ck_i16 = canonical_limbs[k][d]; + debug_assert!(ck_i16 >= 0 && ck_i16 < primes[k].p); + let ck = u16::try_from(ck_i16).expect("canonical residue must fit u16"); + + // Multiply by tiny residues/inverses (<= 15 bits) in fixed-time + // loops, then accumulate modulo P. + let term = mul_mod_by_small_u16(crt_m[k], ck, big_p); + let term = mul_mod_by_small_u16(term, crt_inv[k], big_p); + acc = add_mod_u128(acc, term, big_p); + } + + // Final projection into [0, q) without variable-latency division. + let reduced = reduce_u128_divfree(acc, q); + *coeff = F::from_q_residue_u128(reduced); + } + + coeffs + } +} + +fn mod_inverse(a: i128, modulus: i128) -> i128 { + let (mut t, mut new_t) = (0i128, 1i128); + let (mut r, mut new_r) = (modulus, ((a % modulus) + modulus) % modulus); + + while new_r != 0 { + let q = r / new_r; + (t, new_t) = (new_t, t - q * new_t); + (r, new_r) = (new_r, r - q * new_r); + } + + assert_eq!(r, 1, "CRT inverse does not exist"); + (t % modulus + modulus) % modulus +} + +#[inline] +fn add_mod_u128(a: u128, b: u128, modulus: u128) -> u128 { + debug_assert!(a < modulus); + debug_assert!(b < modulus); + + let (sum_lo, carry) = a.overflowing_add(b); + let hi = carry as u128; + let (sub_lo, borrow) = sum_lo.overflowing_sub(modulus); + let sum_ge_modulus = (!borrow) as u128; + let should_sub = hi | sum_ge_modulus; + let mask = should_sub.wrapping_neg(); + (sum_lo & !mask) | (sub_lo & mask) +} + +#[inline] +fn mul_mod_by_small_u16(a: u128, b: u16, modulus: u128) -> u128 { + debug_assert!(a < modulus); + let mut acc = 0u128; + let mut cur = a; + for i in 0..16 { + let candidate = add_mod_u128(acc, cur, modulus); + let bit = ((b >> i) & 1) as u128; + let mask = bit.wrapping_neg(); + acc = (acc & !mask) | (candidate & mask); + cur = add_mod_u128(cur, cur, modulus); + } + acc +} + +#[inline] +fn reduce_u128_divfree(x: u128, modulus: u128) -> u128 { + debug_assert!(modulus > 0); + let mut rem = 0u128; + for i in (0..128).rev() { + rem = (rem << 1) | ((x >> i) & 1); + let (candidate, borrow) = rem.overflowing_sub(modulus); + let mask = 0u128.wrapping_sub((!borrow) as u128); + rem = (candidate & mask) | (rem & !mask); + } + rem +} + +#[cfg(test)] +mod tests { + use super::{add_mod_u128, mul_mod_by_small_u16, reduce_u128_divfree}; + + #[test] + fn add_mod_matches_native_when_sum_fits_u128() { + let modulus = (1u128 << 100) - 159; + for i in 0..4096u128 { + let a = (i * 104_729 + 17) % modulus; + let b = (i * 130_363 + 31) % modulus; + let expected = (a + b) % modulus; + assert_eq!(add_mod_u128(a, b, modulus), expected); + } + } + + #[test] + fn mul_mod_small_matches_native_when_product_fits_u128() { + let modulus = (1u128 << 100) - 159; + for i in 0..4096u128 { + let a = (i * 786_433 + 19) % modulus; + let b = ((i * 97 + 7) & 0xFFFF) as u16; + let expected = (a * (b as u128)) % modulus; + assert_eq!(mul_mod_by_small_u16(a, b, modulus), expected); + } + } + + #[test] + fn reduce_u128_divfree_matches_native_mod() { + let modulus = (1u128 << 100) - 159; + for i in 0..4096u128 { + let x = (i.wrapping_mul(1_146_989_321_207u128)) + ^ (i.rotate_left(37)) + ^ 0xA5A5_A5A5_A5A5_A5A5_A5A5_A5A5_A5A5_A5A5u128; + assert_eq!(reduce_u128_divfree(x, modulus), x % modulus); + } + } +} diff --git a/src/algebra/backend/traits.rs b/src/algebra/backend/traits.rs new file mode 100644 index 00000000..d6c8a5a0 --- /dev/null +++ b/src/algebra/backend/traits.rs @@ -0,0 +1,56 @@ +//! Backend traits for CRT+NTT execution semantics. + +use crate::algebra::ntt::butterfly::NttTwiddles; +use crate::algebra::ntt::crt::QData; +use crate::algebra::ntt::prime::{MontCoeff, NttPrime}; +use crate::algebra::ring::CrtNttConvertibleField; + +/// Per-prime arithmetic primitives used by CRT+NTT domains. +pub trait NttPrimeOps { + /// Convert canonical coefficient to backend prime representation. + fn from_canonical(prime: NttPrime, value: i16) -> MontCoeff; + + /// Convert backend prime representation back to canonical coefficient. + fn to_canonical(prime: NttPrime, value: MontCoeff) -> i16; + + /// Range-reduce one backend prime coefficient. + fn reduce(prime: NttPrime, value: MontCoeff) -> MontCoeff; + + /// Pointwise multiplication in backend prime representation. + fn pointwise_mul( + prime: NttPrime, + out: &mut [MontCoeff; D], + lhs: &[MontCoeff; D], + rhs: &[MontCoeff; D], + ); +} + +/// Forward/inverse transform kernels for one NTT limb. +pub trait NttTransform { + /// Forward transform from coefficient limb to NTT limb. + fn forward_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles); + + /// Inverse transform from NTT limb to coefficient limb. + fn inverse_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles); +} + +/// CRT reconstruction contract from per-prime canonical coefficients. +pub trait CrtReconstruct { + /// Reconstruct coefficient-domain values from canonical CRT residues. + fn reconstruct( + primes: &[NttPrime; K], + canonical_limbs: &[[i16; D]; K], + qdata: &QData, + ) -> [F; D]; +} + +/// Convenience composition trait for full ring backend capability. +pub trait RingBackend: + NttPrimeOps + NttTransform + CrtReconstruct +{ +} + +impl RingBackend for T where + T: NttPrimeOps + NttTransform + CrtReconstruct +{ +} diff --git a/src/algebra/domains/coeff.rs b/src/algebra/domains/coeff.rs new file mode 100644 index 00000000..461a2fd4 --- /dev/null +++ b/src/algebra/domains/coeff.rs @@ -0,0 +1,6 @@ +//! Coefficient-domain representation boundary. + +use crate::algebra::ring::CyclotomicRing; + +/// Coefficient-domain ring representation. +pub type CoeffDomain = CyclotomicRing; diff --git a/src/algebra/domains/crt_ntt.rs b/src/algebra/domains/crt_ntt.rs new file mode 100644 index 00000000..48fe2263 --- /dev/null +++ b/src/algebra/domains/crt_ntt.rs @@ -0,0 +1,6 @@ +//! CRT+NTT-domain representation boundary. + +use crate::algebra::ring::CyclotomicCrtNtt; + +/// CRT+NTT-domain ring representation. +pub type CrtNttDomain = CyclotomicCrtNtt; diff --git a/src/algebra/domains/mod.rs b/src/algebra/domains/mod.rs new file mode 100644 index 00000000..fa140308 --- /dev/null +++ b/src/algebra/domains/mod.rs @@ -0,0 +1,7 @@ +//! Explicit domain-layer aliases for ring representations. + +pub mod coeff; +pub mod crt_ntt; + +pub use coeff::CoeffDomain; +pub use crt_ntt::CrtNttDomain; diff --git a/src/algebra/fields/ext.rs b/src/algebra/fields/ext.rs new file mode 100644 index 00000000..29061e9b --- /dev/null +++ b/src/algebra/fields/ext.rs @@ -0,0 +1,446 @@ +//! Quadratic and quartic extension fields. + +use crate::algebra::module::VectorModule; +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; +use crate::{FieldCore, FieldSampling}; +use rand_core::RngCore; +use std::io::{Read, Write}; +use std::marker::PhantomData; +use std::ops::{Add, Mul, Neg, Sub}; + +/// Parameters for an `Fp2` quadratic extension over base field `F`. +pub trait Fp2Config { + /// Non-residue `NR` such that `u^2 = NR`. + fn non_residue() -> F; +} + +/// Quadratic extension element `c0 + c1 * u` with `u^2 = NR`. +pub struct Fp2> { + /// Constant term. + pub c0: F, + /// Coefficient of `u`. + pub c1: F, + _cfg: PhantomData C>, +} + +impl> Fp2 { + /// Construct `c0 + c1 * u`. + #[inline] + pub fn new(c0: F, c1: F) -> Self { + Self { + c0, + c1, + _cfg: PhantomData, + } + } + + /// Return the conjugate `c0 - c1 * u`. + #[inline] + pub fn conjugate(self) -> Self { + Self::new(self.c0, -self.c1) + } + + /// Return the norm in the base field: `c0^2 - NR * c1^2`. + #[inline] + pub fn norm(self) -> F { + let nr = C::non_residue(); + (self.c0 * self.c0) - (nr * (self.c1 * self.c1)) + } +} + +impl> Clone for Fp2 { + fn clone(&self) -> Self { + *self + } +} + +impl> Copy for Fp2 {} + +impl> Default for Fp2 { + fn default() -> Self { + Self::new(F::zero(), F::zero()) + } +} + +impl> PartialEq for Fp2 { + fn eq(&self, other: &Self) -> bool { + self.c0 == other.c0 && self.c1 == other.c1 + } +} + +impl> Add for Fp2 { + type Output = Self; + fn add(self, rhs: Self) -> Self::Output { + Self::new(self.c0 + rhs.c0, self.c1 + rhs.c1) + } +} +impl> Sub for Fp2 { + type Output = Self; + fn sub(self, rhs: Self) -> Self::Output { + Self::new(self.c0 - rhs.c0, self.c1 - rhs.c1) + } +} +impl> Neg for Fp2 { + type Output = Self; + fn neg(self) -> Self::Output { + Self::new(-self.c0, -self.c1) + } +} +impl> Mul for Fp2 { + type Output = Self; + fn mul(self, rhs: Self) -> Self::Output { + let nr = C::non_residue(); + let a0 = self.c0; + let a1 = self.c1; + let b0 = rhs.c0; + let b1 = rhs.c1; + Self::new((a0 * b0) + (nr * (a1 * b1)), (a0 * b1) + (a1 * b0)) + } +} + +impl<'a, F: FieldCore, C: Fp2Config> Add<&'a Self> for Fp2 { + type Output = Self; + fn add(self, rhs: &'a Self) -> Self::Output { + self + *rhs + } +} +impl<'a, F: FieldCore, C: Fp2Config> Sub<&'a Self> for Fp2 { + type Output = Self; + fn sub(self, rhs: &'a Self) -> Self::Output { + self - *rhs + } +} +impl<'a, F: FieldCore, C: Fp2Config> Mul<&'a Self> for Fp2 { + type Output = Self; + fn mul(self, rhs: &'a Self) -> Self::Output { + self * *rhs + } +} + +impl> Valid for Fp2 { + fn check(&self) -> Result<(), SerializationError> { + self.c0.check()?; + self.c1.check()?; + Ok(()) + } +} + +impl> HachiSerialize for Fp2 { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.c0.serialize_with_mode(&mut writer, compress)?; + self.c1.serialize_with_mode(&mut writer, compress)?; + Ok(()) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.c0.serialized_size(compress) + self.c1.serialized_size(compress) + } +} + +impl> HachiDeserialize for Fp2 { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let c0 = F::deserialize_with_mode(&mut reader, compress, validate)?; + let c1 = F::deserialize_with_mode(&mut reader, compress, validate)?; + let out = Self::new(c0, c1); + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +impl> FieldCore for Fp2 { + fn zero() -> Self { + Self::new(F::zero(), F::zero()) + } + + fn one() -> Self { + Self::new(F::one(), F::zero()) + } + + fn is_zero(&self) -> bool { + self.c0.is_zero() && self.c1.is_zero() + } + + fn add(&self, rhs: &Self) -> Self { + *self + *rhs + } + + fn sub(&self, rhs: &Self) -> Self { + *self - *rhs + } + + fn mul(&self, rhs: &Self) -> Self { + *self * *rhs + } + + fn inv(self) -> Option { + if self.is_zero() { + return None; + } + let inv_n = self.norm().inv()?; + Some(Self::new(self.c0 * inv_n, (-self.c1) * inv_n)) + } +} + +impl> FieldSampling for Fp2 { + fn sample(rng: &mut R) -> Self { + Self::new(F::sample(rng), F::sample(rng)) + } +} + +/// Parameters for an `Fp4` quadratic extension over `Fp2`. +pub trait Fp4Config> { + /// Non-residue `NR2` in `Fp2` such that `v^2 = NR2`. + fn non_residue() -> Fp2; +} + +/// Quartic extension element `c0 + c1 * v` over `Fp2`, where `v^2 = NR2`. +pub struct Fp4, C4: Fp4Config> { + /// Constant term. + pub c0: Fp2, + /// Coefficient of `v`. + pub c1: Fp2, + _cfg: PhantomData C4>, +} + +impl, C4: Fp4Config> Fp4 { + /// Construct `c0 + c1 * v`. + #[inline] + pub fn new(c0: Fp2, c1: Fp2) -> Self { + Self { + c0, + c1, + _cfg: PhantomData, + } + } + + /// Return the norm in `Fp2`: `c0^2 - NR2 * c1^2`. + #[inline] + pub fn norm(self) -> Fp2 { + let nr2 = C4::non_residue(); + (self.c0 * self.c0) - (nr2 * (self.c1 * self.c1)) + } +} + +impl, C4: Fp4Config> Clone for Fp4 { + fn clone(&self) -> Self { + *self + } +} + +impl, C4: Fp4Config> Copy for Fp4 {} + +impl, C4: Fp4Config> Default for Fp4 { + fn default() -> Self { + Self::new( + Fp2::new(F::zero(), F::zero()), + Fp2::new(F::zero(), F::zero()), + ) + } +} + +impl, C4: Fp4Config> PartialEq for Fp4 { + fn eq(&self, other: &Self) -> bool { + self.c0 == other.c0 && self.c1 == other.c1 + } +} + +impl, C4: Fp4Config> Add for Fp4 { + type Output = Self; + fn add(self, rhs: Self) -> Self::Output { + Self::new(self.c0 + rhs.c0, self.c1 + rhs.c1) + } +} +impl, C4: Fp4Config> Sub for Fp4 { + type Output = Self; + fn sub(self, rhs: Self) -> Self::Output { + Self::new(self.c0 - rhs.c0, self.c1 - rhs.c1) + } +} +impl, C4: Fp4Config> Neg for Fp4 { + type Output = Self; + fn neg(self) -> Self::Output { + Self::new(-self.c0, -self.c1) + } +} +impl, C4: Fp4Config> Mul for Fp4 { + type Output = Self; + fn mul(self, rhs: Self) -> Self::Output { + let nr2 = C4::non_residue(); + let a0 = self.c0; + let a1 = self.c1; + let b0 = rhs.c0; + let b1 = rhs.c1; + Self::new((a0 * b0) + (nr2 * (a1 * b1)), (a0 * b1) + (a1 * b0)) + } +} + +impl<'a, F: FieldCore, C2: Fp2Config, C4: Fp4Config> Add<&'a Self> for Fp4 { + type Output = Self; + fn add(self, rhs: &'a Self) -> Self::Output { + self + *rhs + } +} +impl<'a, F: FieldCore, C2: Fp2Config, C4: Fp4Config> Sub<&'a Self> for Fp4 { + type Output = Self; + fn sub(self, rhs: &'a Self) -> Self::Output { + self - *rhs + } +} +impl<'a, F: FieldCore, C2: Fp2Config, C4: Fp4Config> Mul<&'a Self> for Fp4 { + type Output = Self; + fn mul(self, rhs: &'a Self) -> Self::Output { + self * *rhs + } +} + +impl, C4: Fp4Config> Valid for Fp4 { + fn check(&self) -> Result<(), SerializationError> { + self.c0.check()?; + self.c1.check()?; + Ok(()) + } +} + +impl, C4: Fp4Config> HachiSerialize for Fp4 { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.c0.serialize_with_mode(&mut writer, compress)?; + self.c1.serialize_with_mode(&mut writer, compress)?; + Ok(()) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.c0.serialized_size(compress) + self.c1.serialized_size(compress) + } +} + +impl, C4: Fp4Config> HachiDeserialize + for Fp4 +{ + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let c0 = Fp2::::deserialize_with_mode(&mut reader, compress, validate)?; + let c1 = Fp2::::deserialize_with_mode(&mut reader, compress, validate)?; + let out = Self::new(c0, c1); + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +impl, C4: Fp4Config> FieldCore for Fp4 { + fn zero() -> Self { + Self::new(Fp2::zero(), Fp2::zero()) + } + + fn one() -> Self { + Self::new(Fp2::one(), Fp2::zero()) + } + + fn is_zero(&self) -> bool { + self.c0.is_zero() && self.c1.is_zero() + } + + fn add(&self, rhs: &Self) -> Self { + *self + *rhs + } + + fn sub(&self, rhs: &Self) -> Self { + *self - *rhs + } + + fn mul(&self, rhs: &Self) -> Self { + *self * *rhs + } + + fn inv(self) -> Option { + if self.is_zero() { + return None; + } + let inv_n = self.norm().inv()?; + Some(Self::new(self.c0 * inv_n, (-self.c1) * inv_n)) + } +} + +impl, C4: Fp4Config> FieldSampling + for Fp4 +{ + fn sample(rng: &mut R) -> Self { + Self::new(Fp2::sample(rng), Fp2::sample(rng)) + } +} + +// Scalar * VectorModule impls for extension scalars. + +impl Mul, N>> for Fp2 +where + F: FieldCore + Valid, + C: Fp2Config, +{ + type Output = VectorModule, N>; + fn mul(self, rhs: VectorModule, N>) -> Self::Output { + let mut out = rhs.0; + for coeff in &mut out { + *coeff = self * *coeff; + } + VectorModule(out) + } +} + +impl<'a, F, C, const N: usize> Mul<&'a VectorModule, N>> for Fp2 +where + F: FieldCore + Valid, + C: Fp2Config, +{ + type Output = VectorModule, N>; + fn mul(self, rhs: &'a VectorModule, N>) -> Self::Output { + self * *rhs + } +} + +impl Mul, N>> for Fp4 +where + F: FieldCore + Valid, + C2: Fp2Config, + C4: Fp4Config, +{ + type Output = VectorModule, N>; + fn mul(self, rhs: VectorModule, N>) -> Self::Output { + let mut out = rhs.0; + for coeff in &mut out { + *coeff = self * *coeff; + } + VectorModule(out) + } +} + +impl<'a, F, C2, C4, const N: usize> Mul<&'a VectorModule, N>> for Fp4 +where + F: FieldCore + Valid, + C2: Fp2Config, + C4: Fp4Config, +{ + type Output = VectorModule, N>; + fn mul(self, rhs: &'a VectorModule, N>) -> Self::Output { + self * *rhs + } +} diff --git a/src/algebra/fields/fp128.rs b/src/algebra/fields/fp128.rs new file mode 100644 index 00000000..09248062 --- /dev/null +++ b/src/algebra/fields/fp128.rs @@ -0,0 +1,1032 @@ +//! 128-bit prime field for primes of the form `p = 2^128 − c` with `c < 2^64`. +//! +//! Uses Solinas-style two-fold reduction: no Montgomery form, ~23 cycles/mul +//! on both AArch64 and x86-64. The offset `c` is computed at compile time +//! from the const-generic modulus `P`. +//! +//! ## Naming convention for built-in primes +//! +//! The built-in type names encode the **signed terms as they appear in the +//! modulus `p`** (excluding the leading `+2^128` term). For example, +//! `Prime128M13M4P0` denotes `p = 2^128 − 2^13 − 2^4 + 2^0`. + +use std::io::{Read, Write}; +use std::ops::{Add, Mul, Neg, Sub}; + +use rand_core::RngCore; + +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; +use crate::{CanonicalField, FieldCore, FieldSampling, Invertible, PseudoMersenneField}; + +/// Pack two u64 limbs into `[lo, hi]`. +#[inline(always)] +const fn pack(lo: u64, hi: u64) -> [u64; 2] { + [lo, hi] +} + +/// Convert `u128` → `[u64; 2]`. +#[inline(always)] +const fn from_u128(x: u128) -> [u64; 2] { + [x as u64, (x >> 64) as u64] +} + +/// Convert `[u64; 2]` → `u128`. +#[inline(always)] +const fn to_u128(x: [u64; 2]) -> u128 { + x[0] as u128 | (x[1] as u128) << 64 +} + +/// `a * b` widening to 128 bits; returns `(lo64, hi64)`. +#[inline(always)] +fn mul64_wide(a: u64, b: u64) -> (u64, u64) { + #[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] + { + // Safety: this block is compiled only when `bmi2` is enabled. + unsafe { mul64_wide_bmi2(a, b) } + } + #[cfg(not(all(target_arch = "x86_64", target_feature = "bmi2")))] + { + let prod = (a as u128) * (b as u128); + (prod as u64, (prod >> 64) as u64) + } +} + +#[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] +#[inline(always)] +unsafe fn mul64_wide_bmi2(a: u64, b: u64) -> (u64, u64) { + let mut hi = 0; + // Safety: caller guarantees CPU support via cfg-gated compilation. + let lo = unsafe { std::arch::x86_64::_mulx_u64(a, b, &mut hi) }; + (lo, hi) +} + +#[inline(always)] +const fn is_pow2_u64(x: u64) -> bool { + x != 0 && (x & (x - 1)) == 0 +} + +#[inline(always)] +const fn log2_pow2_u64(mut x: u64) -> u32 { + let mut k = 0u32; + while x > 1 { + x >>= 1; + k += 1; + } + k +} + +/// 128-bit prime field element for primes `p = 2^128 − c` with `c < 2^64`. +/// +/// Stored as `[u64; 2]` (lo, hi) for 8-byte alignment and direct limb access. +/// +/// The offset `c = 2^128 − p` and all derived constants are computed at +/// compile time from the const-generic `P`. Instantiating `Fp128` with a +/// modulus that is not of this form is a compile-time error. +#[derive(Debug, Clone, Copy, Default)] +pub struct Fp128(pub(crate) [u64; 2]); + +impl PartialEq for Fp128

{ + fn eq(&self, other: &Self) -> bool { + self.0 == other.0 + } +} + +impl Eq for Fp128

{} + +impl Fp128

{ + /// Offset `c = 2^128 − p`. Validated at compile time. + const C: u128 = { + let c = 0u128.wrapping_sub(P); + assert!(P != 0, "modulus must be nonzero"); + assert!(P & 1 == 1, "modulus must be odd"); + assert!(c < (1u128 << 64), "P must be 2^128 - c with c < 2^64"); + // Fused overflow+canonicalize requires C(C+1) < P. + assert!( + c * (c + 1) < P, + "C(C+1) < P required for fused canonicalize" + ); + c + }; + const C_LO: u64 = Self::C as u64; + /// +1 means `C = 2^a + 1`, -1 means `C = 2^a - 1`, 0 means generic. + const C_SHIFT_KIND: i8 = { + let c = Self::C_LO; + if c > 1 && is_pow2_u64(c - 1) { + 1 + } else if c == u64::MAX || is_pow2_u64(c + 1) { + -1 + } else { + 0 + } + }; + const C_SHIFT: u32 = { + let c = Self::C_LO; + if Self::C_SHIFT_KIND == 1 { + log2_pow2_u64(c - 1) + } else if Self::C_SHIFT_KIND == -1 { + if c == u64::MAX { + 64 + } else { + log2_pow2_u64(c + 1) + } + } else { + 0 + } + }; + + /// Multiply by `C = 2^128 - P`. For `C = 2^a ± 1`, this is shift/add or + /// shift/sub only; otherwise it falls back to generic widening multiply. + #[inline(always)] + fn mul_c_wide(x: u64) -> (u64, u64) { + if Self::C_SHIFT_KIND == 1 { + let v = ((x as u128) << Self::C_SHIFT) + x as u128; + (v as u64, (v >> 64) as u64) + } else if Self::C_SHIFT_KIND == -1 { + let v = ((x as u128) << Self::C_SHIFT) - x as u128; + (v as u64, (v >> 64) as u64) + } else { + mul64_wide(Self::C_LO, x) + } + } + + /// Create from a canonical representative in `[0, p)`. + #[inline] + pub fn from_canonical_u128(x: u128) -> Self { + debug_assert!(x < P); + Self(from_u128(x)) + } + + /// Return the canonical representative in `[0, p)`. + #[inline] + pub fn to_canonical_u128(self) -> u128 { + to_u128(self.0) + } + + #[inline(always)] + fn add_raw(a: [u64; 2], b: [u64; 2]) -> [u64; 2] { + let (s, carry) = to_u128(a).overflowing_add(to_u128(b)); + let (reduced, borrow) = s.overflowing_sub(P); + from_u128(if carry | !borrow { + reduced + } else { + reduced.wrapping_add(P) + }) + } + + #[inline(always)] + fn sub_raw(a: [u64; 2], b: [u64; 2]) -> [u64; 2] { + let (diff, borrow) = to_u128(a).overflowing_sub(to_u128(b)); + from_u128(if borrow { diff.wrapping_add(P) } else { diff }) + } + + /// Fold 2 + canonicalize: reduce `[t0, t1] + t2·2^128` into `[0, p)`. + /// + /// Correctness argument for the fused overflow+canonicalize: + /// + /// Let `v = base + C·t2` (mathematical, not mod 2^128). + /// From the fold-1 mac chain, `t2 ≤ C`, so `C·t2 ≤ C²`. + /// + /// - **No overflow** (`v < 2^128`): `s = v`, and the standard + /// canonicalize applies — `s + C` carries iff `s ≥ P`. + /// - **Overflow** (`v ≥ 2^128`): `s = v − 2^128`, so `s < C·t2 ≤ C²`. + /// The correct reduced value is `s + C` (since `2^128 ≡ C mod P`). + /// Because `s + C < C² + C = C(C+1)` and `C(C+1) < P` for all + /// `C < 2^64`, the value `s + C` is already in `[0, P)` — no + /// further canonicalization is needed, and `s + C < 2^128` so the + /// add does NOT carry. + /// + /// Therefore `if (overflow | carry) { s + C } else { s }` is correct + /// in both cases, fusing the overflow correction with canonicalization. + #[inline(always)] + fn fold2_canonicalize(t0: u64, t1: u64, t2: u64) -> [u64; 2] { + let (ct2_lo, ct2_hi) = Self::mul_c_wide(t2); + + let (s0, carry0) = t0.overflowing_add(ct2_lo); + let (s1a, carry1a) = t1.overflowing_add(ct2_hi); + let (s1, carry1b) = s1a.overflowing_add(carry0 as u64); + let overflow = carry1a | carry1b; + + let (r0, carry2) = s0.overflowing_add(Self::C_LO); + let (r1, carry3) = s1.overflowing_add(carry2 as u64); + + pack( + if overflow | carry3 { r0 } else { s0 }, + if overflow | carry3 { r1 } else { s1 }, + ) + } + + /// Solinas fold for exactly 4 limbs: `[r0,r1] + C·[r2,r3]` → 3 limbs, + /// then `fold2_canonicalize`. + #[inline(always)] + fn reduce_4(r0: u64, r1: u64, r2: u64, r3: u64) -> [u64; 2] { + let (cr2_lo, cr2_hi) = Self::mul_c_wide(r2); + let (cr3_lo, cr3_hi) = Self::mul_c_wide(r3); + + let t0_sum = r0 as u128 + cr2_lo as u128; + let t0 = t0_sum as u64; + let carryf = (t0_sum >> 64) as u64; + + let t1_sum = r1 as u128 + cr2_hi as u128 + cr3_lo as u128 + carryf as u128; + let t1 = t1_sum as u64; + + let t2_sum = cr3_hi as u128 + (t1_sum >> 64); + let t2 = t2_sum as u64; + debug_assert_eq!(t2_sum >> 64, 0); + + Self::fold2_canonicalize(t0, t1, t2) + } + + #[inline(always)] + fn mul_raw(a: [u64; 2], b: [u64; 2]) -> [u64; 2] { + let [r0, r1, r2, r3] = Self(a).mul_wide(Self(b)); + Self::reduce_4(r0, r1, r2, r3) + } + + #[inline(always)] + fn sqr_raw(a: [u64; 2]) -> [u64; 2] { + Self::mul_raw(a, a) + } + + /// Squaring, equivalent to `self * self`. + #[inline(always)] + pub fn square(self) -> Self { + Self(Self::sqr_raw(self.0)) + } + + fn pow_u128(self, mut exp: u128) -> Self { + let mut base = self; + let mut acc = Self::one(); + while exp > 0 { + if (exp & 1) == 1 { + acc = acc * base; + } + base = Self(Self::sqr_raw(base.0)); + exp >>= 1; + } + acc + } + + /// Extract the canonical `[lo, hi]` limb representation. + #[inline(always)] + pub fn to_limbs(self) -> [u64; 2] { + self.0 + } + + /// 128×64 → 192-bit widening multiply, **no reduction**. + /// + /// Returns `[lo, mid, hi]` representing `self · other` as a 192-bit + /// integer. Cost: 2 widening `mul64`. + #[inline(always)] + pub fn mul_wide_u64(self, other: u64) -> [u64; 3] { + let (a0, a1) = (self.0[0], self.0[1]); + let (p0_lo, p0_hi) = mul64_wide(a0, other); + let (p1_lo, p1_hi) = mul64_wide(a1, other); + let mid = p0_hi as u128 + p1_lo as u128; + let hi = p1_hi + (mid >> 64) as u64; + [p0_lo, mid as u64, hi] + } + + /// 128×128 → 256-bit widening multiply, **no reduction**. + /// + /// Returns `[r0, r1, r2, r3]` representing `self · other` as a 256-bit + /// integer. This is the schoolbook 2×2 portion of the Solinas multiply, + /// without the reduction fold. Cost: 4 widening `mul64`. + #[inline(always)] + pub fn mul_wide(self, other: Self) -> [u64; 4] { + let (a0, a1) = (self.0[0], self.0[1]); + let (b0, b1) = (other.0[0], other.0[1]); + let (p00_lo, p00_hi) = mul64_wide(a0, b0); + let (p01_lo, p01_hi) = mul64_wide(a0, b1); + let (p10_lo, p10_hi) = mul64_wide(a1, b0); + let (p11_lo, p11_hi) = mul64_wide(a1, b1); + + let row1 = p00_hi as u128 + p01_lo as u128 + p10_lo as u128; + let r0 = p00_lo; + let r1 = row1 as u64; + let carry1 = (row1 >> 64) as u64; + + let row2 = p01_hi as u128 + p10_hi as u128 + p11_lo as u128 + carry1 as u128; + let r2 = row2 as u64; + let carry2 = (row2 >> 64) as u64; + + let row3 = p11_hi as u128 + carry2 as u128; + let r3 = row3 as u64; + debug_assert_eq!(row3 >> 64, 0); + + [r0, r1, r2, r3] + } + + /// 128×128 → 256-bit widening multiply with a raw `u128` operand, + /// **no reduction**. + #[inline(always)] + pub fn mul_wide_u128(self, other: u128) -> [u64; 4] { + self.mul_wide(Self(from_u128(other))) + } + + /// 128×(64*M) → (64*OUT) widening multiply, **no reduction**. + /// + /// Multiplies a canonical Fp128 value (`[u64; 2]`) by an arbitrary + /// little-endian limb array and returns the little-endian product + /// truncated/extended to `OUT` limbs. + #[inline(always)] + pub fn mul_wide_limbs(self, other: [u64; M]) -> [u64; OUT] { + let (a0, a1) = (self.0[0], self.0[1]); + + // Hot-path specializations used by Jolt (M in {3,4}, OUT in {4,5}). + // These avoid loop/control-flow overhead in tight sumcheck FMAs. + if M == 3 && OUT == 5 { + let b0 = other[0]; + let b1 = other[1]; + let b2 = other[2]; + + let (p00_lo, p00_hi) = mul64_wide(a0, b0); + let (p01_lo, p01_hi) = mul64_wide(a0, b1); + let (p02_lo, p02_hi) = mul64_wide(a0, b2); + let (p10_lo, p10_hi) = mul64_wide(a1, b0); + let (p11_lo, p11_hi) = mul64_wide(a1, b1); + let (p12_lo, p12_hi) = mul64_wide(a1, b2); + + let r0 = p00_lo; + + let row1 = p00_hi as u128 + p01_lo as u128 + p10_lo as u128; + let r1 = row1 as u64; + let carry1 = row1 >> 64; + + let row2 = p01_hi as u128 + p02_lo as u128 + p10_hi as u128 + p11_lo as u128 + carry1; + let r2 = row2 as u64; + let carry2 = row2 >> 64; + + let row3 = p02_hi as u128 + p11_hi as u128 + p12_lo as u128 + carry2; + let r3 = row3 as u64; + let carry3 = row3 >> 64; + + let row4 = p12_hi as u128 + carry3; + let r4 = row4 as u64; + debug_assert_eq!(row4 >> 64, 0); + + let mut out = [0u64; OUT]; + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + out[4] = r4; + return out; + } + if M == 3 && OUT == 4 { + let b0 = other[0]; + let b1 = other[1]; + let b2 = other[2]; + + let (p00_lo, p00_hi) = mul64_wide(a0, b0); + let (p01_lo, p01_hi) = mul64_wide(a0, b1); + let (p02_lo, p02_hi) = mul64_wide(a0, b2); + let (p10_lo, p10_hi) = mul64_wide(a1, b0); + let (p11_lo, p11_hi) = mul64_wide(a1, b1); + let p12_lo = a1.wrapping_mul(b2); + + let r0 = p00_lo; + + let row1 = p00_hi as u128 + p01_lo as u128 + p10_lo as u128; + let r1 = row1 as u64; + let carry1 = row1 >> 64; + + let row2 = p01_hi as u128 + p02_lo as u128 + p10_hi as u128 + p11_lo as u128 + carry1; + let r2 = row2 as u64; + let carry2 = row2 >> 64; + + let row3 = p02_hi as u128 + p11_hi as u128 + p12_lo as u128 + carry2; + let r3 = row3 as u64; + + let mut out = [0u64; OUT]; + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + return out; + } + if M == 4 && OUT == 6 { + let b0 = other[0]; + let b1 = other[1]; + let b2 = other[2]; + let b3 = other[3]; + + let (p00_lo, p00_hi) = mul64_wide(a0, b0); + let (p01_lo, p01_hi) = mul64_wide(a0, b1); + let (p02_lo, p02_hi) = mul64_wide(a0, b2); + let (p03_lo, p03_hi) = mul64_wide(a0, b3); + let (p10_lo, p10_hi) = mul64_wide(a1, b0); + let (p11_lo, p11_hi) = mul64_wide(a1, b1); + let (p12_lo, p12_hi) = mul64_wide(a1, b2); + let (p13_lo, p13_hi) = mul64_wide(a1, b3); + + let r0 = p00_lo; + + let row1 = p00_hi as u128 + p01_lo as u128 + p10_lo as u128; + let r1 = row1 as u64; + let carry1 = row1 >> 64; + + let row2 = p01_hi as u128 + p02_lo as u128 + p10_hi as u128 + p11_lo as u128 + carry1; + let r2 = row2 as u64; + let carry2 = row2 >> 64; + + let row3 = p02_hi as u128 + p03_lo as u128 + p11_hi as u128 + p12_lo as u128 + carry2; + let r3 = row3 as u64; + let carry3 = row3 >> 64; + + let row4 = p03_hi as u128 + p12_hi as u128 + p13_lo as u128 + carry3; + let r4 = row4 as u64; + let carry4 = row4 >> 64; + + let row5 = p13_hi as u128 + carry4; + let r5 = row5 as u64; + debug_assert_eq!(row5 >> 64, 0); + + let mut out = [0u64; OUT]; + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + out[4] = r4; + out[5] = r5; + return out; + } + if M == 4 && OUT == 5 { + let b0 = other[0]; + let b1 = other[1]; + let b2 = other[2]; + let b3 = other[3]; + + let (p00_lo, p00_hi) = mul64_wide(a0, b0); + let (p01_lo, p01_hi) = mul64_wide(a0, b1); + let (p02_lo, p02_hi) = mul64_wide(a0, b2); + let (p03_lo, p03_hi) = mul64_wide(a0, b3); + let (p10_lo, p10_hi) = mul64_wide(a1, b0); + let (p11_lo, p11_hi) = mul64_wide(a1, b1); + let (p12_lo, p12_hi) = mul64_wide(a1, b2); + let p13_lo = a1.wrapping_mul(b3); + + let r0 = p00_lo; + + let row1 = p00_hi as u128 + p01_lo as u128 + p10_lo as u128; + let r1 = row1 as u64; + let carry1 = row1 >> 64; + + let row2 = p01_hi as u128 + p02_lo as u128 + p10_hi as u128 + p11_lo as u128 + carry1; + let r2 = row2 as u64; + let carry2 = row2 >> 64; + + let row3 = p02_hi as u128 + p03_lo as u128 + p11_hi as u128 + p12_lo as u128 + carry2; + let r3 = row3 as u64; + let carry3 = row3 >> 64; + + let row4 = p03_hi as u128 + p12_hi as u128 + p13_lo as u128 + carry3; + let r4 = row4 as u64; + + let mut out = [0u64; OUT]; + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + out[4] = r4; + return out; + } + if M == 4 && OUT == 4 { + let b0 = other[0]; + let b1 = other[1]; + let b2 = other[2]; + let b3 = other[3]; + + let (p00_lo, p00_hi) = mul64_wide(a0, b0); + let (p01_lo, p01_hi) = mul64_wide(a0, b1); + let (p02_lo, p02_hi) = mul64_wide(a0, b2); + let p03_lo = a0.wrapping_mul(b3); + let (p10_lo, p10_hi) = mul64_wide(a1, b0); + let (p11_lo, p11_hi) = mul64_wide(a1, b1); + let p12_lo = a1.wrapping_mul(b2); + + let r0 = p00_lo; + + let row1 = p00_hi as u128 + p01_lo as u128 + p10_lo as u128; + let r1 = row1 as u64; + let carry1 = row1 >> 64; + + let row2 = p01_hi as u128 + p02_lo as u128 + p10_hi as u128 + p11_lo as u128 + carry1; + let r2 = row2 as u64; + let carry2 = row2 >> 64; + + let row3 = p02_hi as u128 + p03_lo as u128 + p11_hi as u128 + p12_lo as u128 + carry2; + let r3 = row3 as u64; + + let mut out = [0u64; OUT]; + out[0] = r0; + out[1] = r1; + out[2] = r2; + out[3] = r3; + return out; + } + + let mut out = [0u64; OUT]; + + for (i, &b) in other.iter().enumerate() { + if i >= OUT { + break; + } + + let (p0_lo, p0_hi) = mul64_wide(a0, b); + let (p1_lo, p1_hi) = mul64_wide(a1, b); + + let s0 = out[i] as u128 + p0_lo as u128; + out[i] = s0 as u64; + let mut carry = s0 >> 64; + + if i + 1 >= OUT { + continue; + } + let s1 = out[i + 1] as u128 + p0_hi as u128 + p1_lo as u128 + carry; + out[i + 1] = s1 as u64; + carry = s1 >> 64; + + if i + 2 >= OUT { + continue; + } + let s2 = out[i + 2] as u128 + p1_hi as u128 + carry; + out[i + 2] = s2 as u64; + + let mut carry_hi = s2 >> 64; + let mut j = i + 3; + while carry_hi != 0 && j < OUT { + let sj = out[j] as u128 + carry_hi; + out[j] = sj as u64; + carry_hi = sj >> 64; + j += 1; + } + } + + out + } + + /// Reduce an arbitrary-width little-endian limb array to a canonical + /// field element via iterated Solinas folding. + /// + /// Each fold splits at the 128-bit boundary and replaces + /// `hi · 2^128` with `hi · C`, reducing width by one limb per + /// iteration. Supports 0–10 input limbs (up to 640 bits). + /// + /// # Panics + /// + /// Panics if `limbs.len() > 10`. + #[inline(always)] + pub fn solinas_reduce(limbs: &[u64]) -> Self { + match limbs.len() { + 0 => Self::zero(), + 1 => Self(pack(limbs[0], 0)), + 2 => Self::from_canonical_u128_reduced(to_u128([limbs[0], limbs[1]])), + 3 => Self(Self::fold2_canonicalize(limbs[0], limbs[1], limbs[2])), + 4 => Self(Self::reduce_4(limbs[0], limbs[1], limbs[2], limbs[3])), + 5 => { + let (l0, l1, l2, l3, l4) = (limbs[0], limbs[1], limbs[2], limbs[3], limbs[4]); + let (c2_lo, c2_hi) = Self::mul_c_wide(l2); + let (c3_lo, c3_hi) = Self::mul_c_wide(l3); + let (c4_lo, c4_hi) = Self::mul_c_wide(l4); + + let s0 = l0 as u128 + c2_lo as u128; + let s1 = l1 as u128 + c2_hi as u128 + c3_lo as u128 + (s0 >> 64); + let s2 = c3_hi as u128 + c4_lo as u128 + (s1 >> 64); + let s3 = c4_hi as u128 + (s2 >> 64); + debug_assert_eq!(s3 >> 64, 0); + + Self(Self::reduce_4(s0 as u64, s1 as u64, s2 as u64, s3 as u64)) + } + n => { + assert!(n <= 10, "solinas_reduce supports at most 10 limbs"); + let mut buf = [0u64; 11]; + buf[..n].copy_from_slice(limbs); + let mut len = n; + let c = Self::C_LO; + + while len > 5 { + let high_len = len - 2; + let mut next = [0u64; 11]; + + let mut carry: u64 = 0; + for i in 0..high_len { + let wide = c as u128 * buf[i + 2] as u128 + carry as u128; + next[i] = wide as u64; + carry = (wide >> 64) as u64; + } + next[high_len] = carry; + + let s0 = next[0] as u128 + buf[0] as u128; + next[0] = s0 as u64; + let s1 = next[1] as u128 + buf[1] as u128 + (s0 >> 64); + next[1] = s1 as u64; + let mut c_out = (s1 >> 64) as u64; + for limb in &mut next[2..=high_len] { + if c_out == 0 { + break; + } + let s = *limb as u128 + c_out as u128; + *limb = s as u64; + c_out = (s >> 64) as u64; + } + debug_assert_eq!(c_out, 0); + + buf = next; + len -= 1; + while len > 5 && buf[len - 1] == 0 { + len -= 1; + } + } + + Self::solinas_reduce(&buf[..len]) + } + } + } +} + +impl Add for Fp128

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self::Output { + Self(Self::add_raw(self.0, rhs.0)) + } +} + +impl Sub for Fp128

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self::Output { + Self(Self::sub_raw(self.0, rhs.0)) + } +} + +impl Mul for Fp128

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self::Output { + Self(Self::mul_raw(self.0, rhs.0)) + } +} + +impl Neg for Fp128

{ + type Output = Self; + #[inline] + fn neg(self) -> Self::Output { + Self(Self::sub_raw(pack(0, 0), self.0)) + } +} + +impl<'a, const P: u128> Add<&'a Self> for Fp128

{ + type Output = Self; + #[inline] + fn add(self, rhs: &'a Self) -> Self::Output { + self + *rhs + } +} + +impl<'a, const P: u128> Sub<&'a Self> for Fp128

{ + type Output = Self; + #[inline] + fn sub(self, rhs: &'a Self) -> Self::Output { + self - *rhs + } +} + +impl<'a, const P: u128> Mul<&'a Self> for Fp128

{ + type Output = Self; + #[inline] + fn mul(self, rhs: &'a Self) -> Self::Output { + self * *rhs + } +} + +impl Valid for Fp128

{ + fn check(&self) -> Result<(), SerializationError> { + if to_u128(self.0) < P { + Ok(()) + } else { + Err(SerializationError::InvalidData("Fp128 out of range".into())) + } + } +} + +impl HachiSerialize for Fp128

{ + fn serialize_with_mode( + &self, + mut writer: W, + _compress: Compress, + ) -> Result<(), SerializationError> { + to_u128(self.0).serialize_with_mode(&mut writer, Compress::No)?; + Ok(()) + } + + fn serialized_size(&self, _compress: Compress) -> usize { + 16 + } +} + +impl HachiDeserialize for Fp128

{ + fn deserialize_with_mode( + mut reader: R, + _compress: Compress, + validate: Validate, + ) -> Result { + let x = u128::deserialize_with_mode(&mut reader, Compress::No, validate)?; + if matches!(validate, Validate::Yes) && x >= P { + return Err(SerializationError::InvalidData( + "Fp128 out of range".to_string(), + )); + } + + // Without validation, reduce without division. + // For `p = 2^128 − c` with `c < 2^64` we have `p > 2^127`, + // so any `u128` is in `[0, 2p)` and one conditional subtract suffices. + let out = if matches!(validate, Validate::Yes) { + x + } else { + let (sub, borrow) = x.overflowing_sub(P); + if borrow { + x + } else { + sub + } + }; + Ok(Self(from_u128(out))) + } +} + +impl FieldCore for Fp128

{ + fn zero() -> Self { + Self(pack(0, 0)) + } + + fn one() -> Self { + Self(pack(1, 0)) + } + + fn is_zero(&self) -> bool { + self.0 == [0, 0] + } + + fn add(&self, rhs: &Self) -> Self { + *self + *rhs + } + + fn sub(&self, rhs: &Self) -> Self { + *self - *rhs + } + + fn mul(&self, rhs: &Self) -> Self { + *self * *rhs + } + + fn inv(self) -> Option { + let inv = self.inv_or_zero(); + if self.is_zero() { + None + } else { + Some(inv) + } + } +} + +impl Invertible for Fp128

{ + fn inv_or_zero(self) -> Self { + let candidate = self.pow_u128(P.wrapping_sub(2)); + let v = to_u128(self.0); + let nz = ((v | v.wrapping_neg()) >> 127) & 1; + let mask = 0u128.wrapping_sub(nz); + let masked = to_u128(candidate.0) & mask; + Self(from_u128(masked)) + } +} + +impl FieldSampling for Fp128

{ + fn sample(rng: &mut R) -> Self { + loop { + let lo = rng.next_u64(); + let hi = rng.next_u64(); + let x = lo as u128 | (hi as u128) << 64; + if x < P { + return Self(pack(lo, hi)); + } + } + } +} + +impl CanonicalField for Fp128

{ + fn from_u64(val: u64) -> Self { + // For Fp128 pseudo-Mersenne primes, p = 2^128 - c with c < 2^64. + // Therefore any u64 is always canonical (< p), so this can be a + // direct limb construction with no reduction path. + Self(from_u128(val as u128)) + } + + fn from_i64(val: i64) -> Self { + if val >= 0 { + Self::from_u64(val as u64) + } else { + // unsigned_abs avoids overflow for i64::MIN. + -Self::from_u64(val.unsigned_abs()) + } + } + + fn to_canonical_u128(self) -> u128 { + to_u128(self.0) + } + + fn from_canonical_u128_checked(val: u128) -> Option { + if val < P { + Some(Self(from_u128(val))) + } else { + None + } + } + + fn from_canonical_u128_reduced(val: u128) -> Self { + let (sub, borrow) = val.overflowing_sub(P); + Self(from_u128(if borrow { val } else { sub })) + } +} + +impl PseudoMersenneField for Fp128

{ + const MODULUS_BITS: u32 = 128; + const MODULUS_OFFSET: u128 = Self::C; +} + +/// `p = 2^128 − 2^13 − 2^4 + 2^0` (C = 8207). +pub type Prime128M13M4P0 = Fp128<0xffffffffffffffffffffffffffffdff1>; +/// `p = 2^128 − 2^37 + 2^3 + 2^0` (C = 137438953463). +pub type Prime128M37P3P0 = Fp128<0xffffffffffffffffffffffe000000009>; +/// `p = 2^128 − 2^52 − 2^3 + 2^0` (C = 4503599627370487). +pub type Prime128M52M3P0 = Fp128<0xffffffffffffffffffeffffffffffff9>; +/// `p = 2^128 − 2^54 + 2^4 + 2^0` (C = 18014398509481967). +pub type Prime128M54P4P0 = Fp128<0xffffffffffffffffffc0000000000011>; +/// `p = 2^128 − 2^8 − 2^4 − 2^1 − 2^0` (C = 275). +pub type Prime128M8M4M1M0 = Fp128<0xfffffffffffffffffffffffffffffeed>; +/// `p = 2^128 − 2^18 − 2^0` (C = 2^18 + 1). +pub type Prime128M18M0 = Fp128<0xfffffffffffffffffffffffffffbffff>; +/// `p = 2^128 − 2^54 + 2^0` (C = 2^54 − 1). +pub type Prime128M54P0 = Fp128<0xffffffffffffffffffc0000000000001>; + +#[cfg(test)] +mod tests { + use super::*; + use crate::{FieldSampling, PseudoMersenneField}; + use rand::rngs::StdRng; + use rand::SeedableRng; + use rand_core::RngCore; + + type F = Prime128M8M4M1M0; + + #[test] + fn to_limbs_roundtrip() { + let mut rng = StdRng::seed_from_u64(0xdead_beef_cafe_1234); + for _ in 0..1000 { + let a: F = FieldSampling::sample(&mut rng); + assert_eq!(Fp128(a.to_limbs()), a); + } + } + + #[test] + fn mul_wide_u64_matches_full_mul() { + let mut rng = StdRng::seed_from_u64(0x1122_3344_5566_7788); + for _ in 0..1000 { + let a: F = FieldSampling::sample(&mut rng); + let b = rng.next_u64(); + let expected = a * F::from_u64(b); + let reduced = F::solinas_reduce(&a.mul_wide_u64(b)); + assert_eq!(reduced, expected); + } + } + + #[test] + fn mul_wide_matches_full_mul() { + let mut rng = StdRng::seed_from_u64(0xaabb_ccdd_eeff_0011); + for _ in 0..1000 { + let a: F = FieldSampling::sample(&mut rng); + let b: F = FieldSampling::sample(&mut rng); + let expected = a * b; + let reduced = F::solinas_reduce(&a.mul_wide(b)); + assert_eq!(reduced, expected); + } + } + + #[test] + fn mul_wide_u128_matches_full_mul() { + let mut rng = StdRng::seed_from_u64(0x9988_7766_5544_3322); + for _ in 0..1000 { + let a: F = FieldSampling::sample(&mut rng); + let b = rng.next_u64() as u128 | ((rng.next_u64() as u128) << 64); + let expected = a * F::from_canonical_u128_reduced(b); + let reduced = F::solinas_reduce(&a.mul_wide_u128(b)); + assert_eq!(reduced, expected); + } + } + + #[test] + fn mul_wide_limbs_roundtrips_through_reduction() { + let mut rng = StdRng::seed_from_u64(0x1bad_f00d_0ddc_afe1); + for _ in 0..1000 { + let a: F = FieldSampling::sample(&mut rng); + let b3 = [rng.next_u64(), rng.next_u64(), rng.next_u64()]; + let b4 = [ + rng.next_u64(), + rng.next_u64(), + rng.next_u64(), + rng.next_u64(), + ]; + + let got3_full = a.mul_wide_limbs::<3, 5>(b3); + let got3_trunc = a.mul_wide_limbs::<3, 4>(b3); + assert_eq!( + got3_trunc, + [got3_full[0], got3_full[1], got3_full[2], got3_full[3]] + ); + let exp3 = a * F::solinas_reduce(&b3); + assert_eq!(F::solinas_reduce(&got3_full), exp3); + + let got4_full = a.mul_wide_limbs::<4, 6>(b4); + let got4_trunc = a.mul_wide_limbs::<4, 4>(b4); + assert_eq!( + got4_trunc, + [got4_full[0], got4_full[1], got4_full[2], got4_full[3]] + ); + let exp4 = a * F::solinas_reduce(&b4); + assert_eq!(F::solinas_reduce(&got4_full), exp4); + } + } + + #[test] + fn solinas_reduce_small_inputs() { + assert_eq!(F::solinas_reduce(&[]), F::zero()); + assert_eq!(F::solinas_reduce(&[42]), F::from_u64(42)); + let one_shifted = F::from_canonical_u128_reduced(1u128 << 64); + assert_eq!(F::solinas_reduce(&[0, 1]), one_shifted); + } + + #[test] + fn solinas_reduce_4_limbs_max() { + // 2^256 - 1 ≡ C² - 1 (mod P), since 2^128 ≡ C + let c = F::from_canonical_u128_reduced(::MODULUS_OFFSET); + let expected = c * c - F::one(); + assert_eq!(F::solinas_reduce(&[u64::MAX; 4]), expected); + } + + #[test] + fn solinas_reduce_9_limbs() { + // 1 + 2^512 = 1 + (2^128)^4 ≡ 1 + C^4 + let c = F::from_canonical_u128_reduced(::MODULUS_OFFSET); + let expected = F::one() + c * c * c * c; + assert_eq!(F::solinas_reduce(&[1, 0, 0, 0, 0, 0, 0, 0, 1]), expected); + } + + #[test] + fn solinas_reduce_accumulated_products() { + let mut rng = StdRng::seed_from_u64(0xfeed_face_0bad_c0de); + let mut acc = [0u64; 5]; + let mut expected = F::zero(); + + for _ in 0..200 { + let a: F = FieldSampling::sample(&mut rng); + let b = rng.next_u64(); + let wide = a.mul_wide_u64(b); + + let mut carry: u64 = 0; + for j in 0..5 { + let addend = if j < 3 { wide[j] } else { 0 }; + let sum = acc[j] as u128 + addend as u128 + carry as u128; + acc[j] = sum as u64; + carry = (sum >> 64) as u64; + } + assert_eq!(carry, 0); + expected = expected + a * F::from_u64(b); + } + + assert_eq!(F::solinas_reduce(&acc), expected); + } + + #[test] + fn solinas_reduce_cross_prime() { + // Verify with Prime128M18M0 (C = 2^18 + 1, shift+add path) + type G = Prime128M18M0; + let c = G::from_canonical_u128_reduced(::MODULUS_OFFSET); + let expected = c * c - G::one(); + assert_eq!(G::solinas_reduce(&[u64::MAX; 4]), expected); + + // Verify with Prime128M54P0 (C = 2^54 - 1, shift-sub path) + type H = Prime128M54P0; + let c = H::from_canonical_u128_reduced(::MODULUS_OFFSET); + let expected = c * c - H::one(); + assert_eq!(H::solinas_reduce(&[u64::MAX; 4]), expected); + } + + #[test] + fn from_i64_handles_min_without_overflow() { + let x = F::from_i64(i64::MIN); + let y = F::from_u64(i64::MIN.unsigned_abs()); + assert_eq!(x + y, F::zero()); + } +} diff --git a/src/algebra/fields/fp32.rs b/src/algebra/fields/fp32.rs new file mode 100644 index 00000000..0a834698 --- /dev/null +++ b/src/algebra/fields/fp32.rs @@ -0,0 +1,455 @@ +//! Prime field for primes of the form `p = 2^k − c` with `c` small, backed +//! by `u32` storage. +//! +//! Uses Solinas-style two-fold reduction: the offset `c` and fold point `k` +//! are computed at compile time from the const-generic modulus `P`. + +use std::ops::{Add, Mul, Neg, Sub}; + +use rand_core::RngCore; + +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; +use crate::{CanonicalField, FieldCore, FieldSampling, Invertible, PseudoMersenneField}; +use std::io::{Read, Write}; + +/// Prime field element for primes `p = 2^k − c` stored as `u32`. +/// +/// The fold point `k` and offset `c = 2^k − p` are computed at compile time +/// from the const-generic `P`. Instantiating with a modulus that does not +/// satisfy the Solinas conditions is a compile-time error. +#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)] +pub struct Fp32(pub(crate) u32); + +impl Fp32

{ + /// Fold point: smallest `k` such that `P ≤ 2^k`. + const BITS: u32 = 32 - P.leading_zeros(); + + /// Offset `c = 2^k − P`. + const C: u32 = { + let c = if Self::BITS == 32 { + 0u32.wrapping_sub(P) + } else { + (1u32 << Self::BITS) - P + }; + assert!(P != 0, "modulus must be nonzero"); + assert!(P & 1 == 1, "modulus must be odd"); + assert!( + (c as u64) * (c as u64 + 1) < P as u64, + "C(C+1) < P required for fused canonicalize" + ); + c + }; + + /// Mask for extracting the low `BITS` bits from a u64. + const MASK: u64 = if Self::BITS == 32 { + u32::MAX as u64 + } else { + (1u64 << Self::BITS) - 1 + }; + + /// Create from a canonical representative in `[0, P)`. + #[inline] + pub fn from_canonical_u32(x: u32) -> Self { + debug_assert!(x < P); + Self(x) + } + + /// Return the canonical representative in `[0, P)`. + #[inline] + pub fn to_canonical_u32(self) -> u32 { + self.0 + } + + /// Solinas reduction: fold a u64 at bit `BITS` until the value fits, + /// then conditionally subtract `P`. + /// + /// For multiplication products (< 2^{2·BITS}) exactly 2 folds suffice; + /// for arbitrary u64 inputs (e.g. `from_u64`) the loop runs at most + /// `ceil(64 / BITS)` iterations. + #[inline(always)] + fn reduce_u64(x: u64) -> u32 { + let c = Self::C as u64; + let mut v = x; + while v >> Self::BITS != 0 { + v = (v & Self::MASK) + c * (v >> Self::BITS); + } + let reduced = v.wrapping_sub(P as u64); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & (P as u64)) as u32 + } + + /// Reduce a `u128` to canonical form (for `from_canonical_u128_reduced`). + #[inline(always)] + fn reduce_u128(x: u128) -> u32 { + let c = Self::C as u128; + let bits = Self::BITS; + let mask = if bits == 32 { + u32::MAX as u128 + } else { + (1u128 << bits) - 1 + }; + let mut v = x; + while v >> bits != 0 { + v = (v & mask) + c * (v >> bits); + } + let f = v as u64; + let reduced = f.wrapping_sub(P as u64); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & (P as u64)) as u32 + } + + /// Two-fold Solinas reduction for multiplication products. + /// + /// Input must be < 2^{2·BITS} (guaranteed for `a*b` where `a,b < P`). + /// Exactly 2 folds + conditional subtract, no loop. + #[inline(always)] + fn reduce_product(x: u64) -> u32 { + let c = Self::C as u64; + let f1 = (x & Self::MASK) + c * (x >> Self::BITS); + let f2 = (f1 & Self::MASK) + c * (f1 >> Self::BITS); + let reduced = f2.wrapping_sub(P as u64); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & (P as u64)) as u32 + } + + #[inline(always)] + fn add_raw(a: u32, b: u32) -> u32 { + let s = (a as u64) + (b as u64); + let reduced = s.wrapping_sub(P as u64); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & (P as u64)) as u32 + } + + #[inline(always)] + fn sub_raw(a: u32, b: u32) -> u32 { + let diff = (a as u64).wrapping_sub(b as u64); + let borrow = diff >> 63; + diff.wrapping_add(borrow.wrapping_neg() & (P as u64)) as u32 + } + + #[inline(always)] + fn mul_raw(a: u32, b: u32) -> u32 { + Self::reduce_product((a as u64) * (b as u64)) + } + + #[inline(always)] + fn sqr_raw(a: u32) -> u32 { + Self::mul_raw(a, a) + } + + /// Squaring, equivalent to `self * self`. + #[inline(always)] + pub fn square(self) -> Self { + Self(Self::sqr_raw(self.0)) + } + + fn pow(self, mut exp: u64) -> Self { + let mut base = self; + let mut acc = Self::one(); + while exp > 0 { + if (exp & 1) == 1 { + acc = acc * base; + } + base = base.square(); + exp >>= 1; + } + acc + } + + /// Extract the canonical value. + #[inline(always)] + pub fn to_limbs(self) -> u32 { + self.0 + } + + /// 32×32 → 64-bit widening multiply, **no reduction**. + #[inline(always)] + pub fn mul_wide(self, other: Self) -> u64 { + (self.0 as u64) * (other.0 as u64) + } + + /// 32×32 → 64-bit widening multiply with a raw `u32` operand, + /// **no reduction**. + #[inline(always)] + pub fn mul_wide_u32(self, other: u32) -> u64 { + (self.0 as u64) * (other as u64) + } + + /// Reduce a u64 value via Solinas folding to a canonical field element. + #[inline(always)] + pub fn solinas_reduce(x: u64) -> Self { + Self(Self::reduce_u64(x)) + } +} + +impl Add for Fp32

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self::Output { + Self(Self::add_raw(self.0, rhs.0)) + } +} + +impl Sub for Fp32

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self::Output { + Self(Self::sub_raw(self.0, rhs.0)) + } +} + +impl Mul for Fp32

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self::Output { + Self(Self::mul_raw(self.0, rhs.0)) + } +} + +impl Neg for Fp32

{ + type Output = Self; + #[inline] + fn neg(self) -> Self::Output { + Self(Self::sub_raw(0, self.0)) + } +} + +impl<'a, const P: u32> Add<&'a Self> for Fp32

{ + type Output = Self; + #[inline] + fn add(self, rhs: &'a Self) -> Self::Output { + self + *rhs + } +} + +impl<'a, const P: u32> Sub<&'a Self> for Fp32

{ + type Output = Self; + #[inline] + fn sub(self, rhs: &'a Self) -> Self::Output { + self - *rhs + } +} + +impl<'a, const P: u32> Mul<&'a Self> for Fp32

{ + type Output = Self; + #[inline] + fn mul(self, rhs: &'a Self) -> Self::Output { + self * *rhs + } +} + +impl Valid for Fp32

{ + fn check(&self) -> Result<(), SerializationError> { + if self.0 < P { + Ok(()) + } else { + Err(SerializationError::InvalidData("Fp32 out of range".into())) + } + } +} + +impl HachiSerialize for Fp32

{ + fn serialize_with_mode( + &self, + mut writer: W, + _compress: Compress, + ) -> Result<(), SerializationError> { + self.0.serialize_with_mode(&mut writer, Compress::No)?; + Ok(()) + } + + fn serialized_size(&self, _compress: Compress) -> usize { + 4 + } +} + +impl HachiDeserialize for Fp32

{ + fn deserialize_with_mode( + mut reader: R, + _compress: Compress, + validate: Validate, + ) -> Result { + let x = u32::deserialize_with_mode(&mut reader, Compress::No, validate)?; + if matches!(validate, Validate::Yes) && x >= P { + return Err(SerializationError::InvalidData( + "Fp32 out of range".to_string(), + )); + } + let out = if matches!(validate, Validate::Yes) { + Self(x) + } else { + Self(Self::reduce_u64(x as u64)) + }; + Ok(out) + } +} + +impl FieldCore for Fp32

{ + fn zero() -> Self { + Self(0) + } + + fn one() -> Self { + Self(if P > 1 { 1 } else { 0 }) + } + + fn is_zero(&self) -> bool { + self.0 == 0 + } + + fn add(&self, rhs: &Self) -> Self { + *self + *rhs + } + + fn sub(&self, rhs: &Self) -> Self { + *self - *rhs + } + + fn mul(&self, rhs: &Self) -> Self { + *self * *rhs + } + + fn inv(self) -> Option { + let inv = self.inv_or_zero(); + if self.is_zero() { + None + } else { + Some(inv) + } + } +} + +impl Invertible for Fp32

{ + fn inv_or_zero(self) -> Self { + let candidate = self.pow((P as u64).wrapping_sub(2)); + let nz = ((self.0 | self.0.wrapping_neg()) >> 31) & 1; + let mask = 0u32.wrapping_sub(nz); + Self(candidate.0 & mask) + } +} + +impl FieldSampling for Fp32

{ + fn sample(rng: &mut R) -> Self { + Self(Self::reduce_u64(rng.next_u64())) + } +} + +impl CanonicalField for Fp32

{ + fn from_u64(val: u64) -> Self { + Self(Self::reduce_u64(val)) + } + + fn from_i64(val: i64) -> Self { + if val >= 0 { + Self::from_u64(val as u64) + } else { + -Self::from_u64((-val) as u64) + } + } + + fn to_canonical_u128(self) -> u128 { + self.0 as u128 + } + + fn from_canonical_u128_checked(val: u128) -> Option { + if val < P as u128 { + Some(Self(val as u32)) + } else { + None + } + } + + fn from_canonical_u128_reduced(val: u128) -> Self { + Self(Self::reduce_u128(val)) + } +} + +impl PseudoMersenneField for Fp32

{ + const MODULUS_BITS: u32 = Self::BITS; + const MODULUS_OFFSET: u128 = Self::C as u128; +} + +#[cfg(test)] +mod tests { + use super::*; + use rand::rngs::StdRng; + use rand::SeedableRng; + + type F = Fp32<251>; // 2^8 - 5 + + #[test] + fn solinas_constants() { + assert_eq!(F::BITS, 8); + assert_eq!(F::C, 5); + assert_eq!(F::MASK, 255); + + type G = Fp32<{ (1u32 << 24) - 3 }>; // 2^24 - 3 + assert_eq!(G::BITS, 24); + assert_eq!(G::C, 3); + } + + #[test] + fn basic_arithmetic() { + let a = F::from_u64(100); + let b = F::from_u64(200); + assert_eq!((a + b).to_canonical_u32(), (100 + 200) % 251); + assert_eq!((a * b).to_canonical_u32(), (100 * 200) % 251); + assert_eq!((b - a).to_canonical_u32(), 100); + assert_eq!((-a).to_canonical_u32(), 251 - 100); + } + + #[test] + fn mul_wide_matches_full_mul() { + let mut rng = StdRng::seed_from_u64(0x1234_5678); + for _ in 0..1000 { + let a: F = FieldSampling::sample(&mut rng); + let b: F = FieldSampling::sample(&mut rng); + let expected = a * b; + let reduced = F::solinas_reduce(a.mul_wide(b)); + assert_eq!(reduced, expected); + } + } + + #[test] + fn mul_wide_u32_matches() { + let mut rng = StdRng::seed_from_u64(0xabcd_ef01); + for _ in 0..1000 { + let a: F = FieldSampling::sample(&mut rng); + let b = rng.next_u32() % 251; + let expected = a * F::from_canonical_u32(b); + let reduced = F::solinas_reduce(a.mul_wide_u32(b)); + assert_eq!(reduced, expected); + } + } + + #[test] + fn reduce_large_values() { + assert_eq!( + F::from_u64(u64::MAX).to_canonical_u32(), + (u64::MAX % 251) as u32 + ); + assert_eq!(F::from_u64(0).to_canonical_u32(), 0); + assert_eq!(F::from_u64(251).to_canonical_u32(), 0); + assert_eq!(F::from_u64(252).to_canonical_u32(), 1); + } + + #[test] + fn pseudo_mersenne_trait() { + assert_eq!(::MODULUS_BITS, 8); + assert_eq!(::MODULUS_OFFSET, 5); + } + + #[test] + fn cross_prime_32bit() { + type G = Fp32<{ u32::MAX - 98 }>; // 2^32 - 99 + assert_eq!(G::BITS, 32); + assert_eq!(G::C, 99); + + let a = G::from_u64(1_000_000); + let b = G::from_u64(2_000_000); + let product = (1_000_000u64 * 2_000_000u64) % ((1u64 << 32) - 99); + assert_eq!((a * b).to_canonical_u32(), product as u32); + } +} diff --git a/src/algebra/fields/fp64.rs b/src/algebra/fields/fp64.rs new file mode 100644 index 00000000..a56e3c1c --- /dev/null +++ b/src/algebra/fields/fp64.rs @@ -0,0 +1,604 @@ +//! Prime field for primes of the form `p = 2^k − c` with `c` small, backed +//! by `u64` storage. +//! +//! Uses Solinas-style two-fold reduction. For `c = 2^a ± 1` the fold +//! multiply is replaced by shift+add/sub, saving a u128 widening multiply. + +use std::ops::{Add, Mul, Neg, Sub}; + +use rand_core::RngCore; + +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; +use crate::{CanonicalField, FieldCore, FieldSampling, Invertible, PseudoMersenneField}; +use std::io::{Read, Write}; + +#[inline(always)] +const fn is_pow2_u64(x: u64) -> bool { + x != 0 && (x & (x - 1)) == 0 +} + +#[inline(always)] +const fn log2_pow2_u64(mut x: u64) -> u32 { + let mut k = 0u32; + while x > 1 { + x >>= 1; + k += 1; + } + k +} + +#[inline(always)] +fn mul64_wide(a: u64, b: u64) -> (u64, u64) { + #[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] + { + unsafe { mul64_wide_bmi2(a, b) } + } + #[cfg(not(all(target_arch = "x86_64", target_feature = "bmi2")))] + { + let prod = (a as u128) * (b as u128); + (prod as u64, (prod >> 64) as u64) + } +} + +#[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] +#[inline(always)] +unsafe fn mul64_wide_bmi2(a: u64, b: u64) -> (u64, u64) { + let mut hi = 0; + // Safety: caller guarantees CPU support via cfg-gated compilation. + let lo = unsafe { std::arch::x86_64::_mulx_u64(a, b, &mut hi) }; + (lo, hi) +} + +/// Prime field element for primes `p = 2^k − c` stored as `u64`. +/// +/// The fold point `k` and offset `c = 2^k − p` are computed at compile time +/// from the const-generic `P`. For `c = 2^a ± 1`, the fold multiply is +/// replaced by shift+add/sub. +#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)] +pub struct Fp64(pub(crate) u64); + +impl Fp64

{ + /// Fold point: smallest `k` such that `P ≤ 2^k`. + const BITS: u32 = 64 - P.leading_zeros(); + + /// Offset `c = 2^k − P`. + const C: u64 = { + let c = if Self::BITS == 64 { + 0u64.wrapping_sub(P) + } else { + (1u64 << Self::BITS) - P + }; + assert!(P != 0, "modulus must be nonzero"); + assert!(P & 1 == 1, "modulus must be odd"); + assert!( + (c as u128) * (c as u128 + 1) < P as u128, + "C(C+1) < P required for fused canonicalize" + ); + c + }; + + /// +1 means `C = 2^a + 1`, -1 means `C = 2^a - 1`, 0 means generic. + const C_SHIFT_KIND: i8 = { + let c = Self::C; + if c > 1 && is_pow2_u64(c - 1) { + 1 + } else if c == u64::MAX || is_pow2_u64(c + 1) { + -1 + } else { + 0 + } + }; + + const C_SHIFT: u32 = { + let c = Self::C; + if Self::C_SHIFT_KIND == 1 { + log2_pow2_u64(c - 1) + } else if Self::C_SHIFT_KIND == -1 { + if c == u64::MAX { + 64 + } else { + log2_pow2_u64(c + 1) + } + } else { + 0 + } + }; + + /// Mask for extracting the low `BITS` bits from a u128. + const MASK: u128 = if Self::BITS == 64 { + u64::MAX as u128 + } else { + (1u128 << Self::BITS) - 1 + }; + + /// u64-width mask (only valid when BITS < 64). + const MASK64: u64 = if Self::BITS < 64 { + (1u64 << Self::BITS) - 1 + } else { + u64::MAX + }; + + /// Whether Solinas folding of a multiplication product can stay + /// entirely in u64. True when BITS < 64 and C·2^BITS < 2^64. + const FOLD_IN_U64: bool = Self::BITS < 64 && (Self::C as u128) < (1u128 << (64 - Self::BITS)); + + /// u64 multiply by C, split into u32-wide halves so LLVM emits + /// `umull` (32×32→64) instead of promoting to u128. + /// Only valid when C fits in u32 (always true: C < sqrt(P) < 2^32). + #[inline(always)] + fn mul_c_narrow(x: u64) -> u64 { + #[cfg(target_arch = "x86_64")] + { + // x86_64 has fast scalar 64-bit multiply; use one multiply instead + // of two widened 32-bit multiplies in the fold hot path. + Self::C.wrapping_mul(x) + } + #[cfg(not(target_arch = "x86_64"))] + { + let c = Self::C as u32; + let x_lo = x as u32; + let x_hi = (x >> 32) as u32; + (c as u64 * x_lo as u64).wrapping_add((c as u64 * x_hi as u64) << 32) + } + } + + /// Multiply `x` by `C`. For `C = 2^a ± 1` uses shift+add/sub. + #[inline(always)] + fn mul_c(x: u64) -> u128 { + if Self::C_SHIFT_KIND == 1 { + ((x as u128) << Self::C_SHIFT) + x as u128 + } else if Self::C_SHIFT_KIND == -1 { + ((x as u128) << Self::C_SHIFT) - x as u128 + } else { + (Self::C as u128) * (x as u128) + } + } + + /// Create from a canonical representative in `[0, P)`. + #[inline] + pub fn from_canonical_u64(x: u64) -> Self { + debug_assert!(x < P); + Self(x) + } + + /// Return the canonical representative in `[0, P)`. + #[inline] + pub fn to_canonical_u64(self) -> u64 { + self.0 + } + + /// Solinas reduction: fold a u128 at bit `BITS` until the value fits, + /// then conditionally subtract `P`. + /// + /// For multiplication products (< 2^{2·BITS}) exactly 2 folds suffice; + /// for arbitrary u128 inputs the loop runs at most `ceil(128 / BITS)` + /// iterations. + #[inline(always)] + fn reduce_u128(x: u128) -> u64 { + let mut v = x; + while v >> Self::BITS != 0 { + v = (v & Self::MASK) + Self::mul_c((v >> Self::BITS) as u64); + } + let reduced = v.wrapping_sub(P as u128); + let borrow = reduced >> 127; + reduced.wrapping_add(borrow.wrapping_neg() & (P as u128)) as u64 + } + + /// Two-fold Solinas reduction for multiplication products. + /// + /// Input must be < 2^{2·BITS} (guaranteed for `a*b` where `a,b < P`). + /// Exactly 2 folds + conditional subtract, no loop. + /// + /// When `FOLD_IN_U64` is true the entire reduction stays in u64, + /// avoiding expensive u128 mask/shift on sub-word primes. + #[inline(always)] + fn reduce_product(x: u128) -> u64 { + if Self::FOLD_IN_U64 { + let lo = x as u64; + let hi = (x >> 64) as u64; + let high = (lo >> Self::BITS) | (hi << (64 - Self::BITS)); + let f1 = (lo & Self::MASK64) + Self::mul_c_narrow(high); + let f2 = (f1 & Self::MASK64) + Self::mul_c_narrow(f1 >> Self::BITS); + let reduced = f2.wrapping_sub(P); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & P) + } else { + let f1 = (x & Self::MASK) + Self::mul_c((x >> Self::BITS) as u64); + let f2 = (f1 & Self::MASK) + Self::mul_c((f1 >> Self::BITS) as u64); + let reduced = f2.wrapping_sub(P as u128); + let borrow = reduced >> 127; + reduced.wrapping_add(borrow.wrapping_neg() & (P as u128)) as u64 + } + } + + /// BMI2 fast path: avoid re-materializing `u128` product in the common + /// sub-word configuration where reduction stays in `u64`. + #[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] + #[inline(always)] + fn reduce_product_wide(lo: u64, hi: u64) -> u64 { + if Self::FOLD_IN_U64 { + let high = (lo >> Self::BITS) | (hi << (64 - Self::BITS)); + let f1 = (lo & Self::MASK64) + Self::mul_c_narrow(high); + let f2 = (f1 & Self::MASK64) + Self::mul_c_narrow(f1 >> Self::BITS); + let reduced = f2.wrapping_sub(P); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & P) + } else { + Self::reduce_product(lo as u128 | ((hi as u128) << 64)) + } + } + + #[inline(always)] + fn add_raw(a: u64, b: u64) -> u64 { + if Self::BITS <= 62 { + let s = a + b; + let reduced = s.wrapping_sub(P); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & P) + } else { + let s = (a as u128) + (b as u128); + let reduced = s.wrapping_sub(P as u128); + let borrow = reduced >> 127; + reduced.wrapping_add(borrow.wrapping_neg() & (P as u128)) as u64 + } + } + + #[inline(always)] + fn sub_raw(a: u64, b: u64) -> u64 { + if Self::BITS <= 62 { + let diff = a.wrapping_sub(b); + let borrow = diff >> 63; + diff.wrapping_add(borrow.wrapping_neg() & P) + } else { + let diff = (a as u128).wrapping_sub(b as u128); + let borrow = diff >> 127; + diff.wrapping_add(borrow.wrapping_neg() & (P as u128)) as u64 + } + } + + #[inline(always)] + fn mul_raw(a: u64, b: u64) -> u64 { + #[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] + { + let (lo, hi) = mul64_wide(a, b); + Self::reduce_product_wide(lo, hi) + } + #[cfg(not(all(target_arch = "x86_64", target_feature = "bmi2")))] + { + Self::reduce_product((a as u128) * (b as u128)) + } + } + + #[inline(always)] + fn sqr_raw(a: u64) -> u64 { + Self::mul_raw(a, a) + } + + /// Squaring, equivalent to `self * self`. + #[inline(always)] + pub fn square(self) -> Self { + Self(Self::sqr_raw(self.0)) + } + + fn pow(self, mut exp: u64) -> Self { + let mut base = self; + let mut acc = Self::one(); + while exp > 0 { + if (exp & 1) == 1 { + acc = acc * base; + } + base = base.square(); + exp >>= 1; + } + acc + } + + /// Extract the canonical value. + #[inline(always)] + pub fn to_limbs(self) -> u64 { + self.0 + } + + /// 64×64 → 128-bit widening multiply, **no reduction**. + #[inline(always)] + pub fn mul_wide(self, other: Self) -> u128 { + let (lo, hi) = mul64_wide(self.0, other.0); + lo as u128 | ((hi as u128) << 64) + } + + /// 64×64 → 128-bit widening multiply with a raw `u64` operand, + /// **no reduction**. + #[inline(always)] + pub fn mul_wide_u64(self, other: u64) -> u128 { + let (lo, hi) = mul64_wide(self.0, other); + lo as u128 | ((hi as u128) << 64) + } + + /// Reduce a u128 value via Solinas folding to a canonical field element. + #[inline(always)] + pub fn solinas_reduce(x: u128) -> Self { + Self(Self::reduce_u128(x)) + } +} + +impl Add for Fp64

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self::Output { + Self(Self::add_raw(self.0, rhs.0)) + } +} + +impl Sub for Fp64

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self::Output { + Self(Self::sub_raw(self.0, rhs.0)) + } +} + +impl Mul for Fp64

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self::Output { + Self(Self::mul_raw(self.0, rhs.0)) + } +} + +impl Neg for Fp64

{ + type Output = Self; + #[inline] + fn neg(self) -> Self::Output { + Self(Self::sub_raw(0, self.0)) + } +} + +impl<'a, const P: u64> Add<&'a Self> for Fp64

{ + type Output = Self; + #[inline] + fn add(self, rhs: &'a Self) -> Self::Output { + self + *rhs + } +} + +impl<'a, const P: u64> Sub<&'a Self> for Fp64

{ + type Output = Self; + #[inline] + fn sub(self, rhs: &'a Self) -> Self::Output { + self - *rhs + } +} + +impl<'a, const P: u64> Mul<&'a Self> for Fp64

{ + type Output = Self; + #[inline] + fn mul(self, rhs: &'a Self) -> Self::Output { + self * *rhs + } +} + +impl Valid for Fp64

{ + fn check(&self) -> Result<(), SerializationError> { + if self.0 < P { + Ok(()) + } else { + Err(SerializationError::InvalidData("Fp64 out of range".into())) + } + } +} + +impl HachiSerialize for Fp64

{ + fn serialize_with_mode( + &self, + mut writer: W, + _compress: Compress, + ) -> Result<(), SerializationError> { + self.0.serialize_with_mode(&mut writer, Compress::No)?; + Ok(()) + } + + fn serialized_size(&self, _compress: Compress) -> usize { + 8 + } +} + +impl HachiDeserialize for Fp64

{ + fn deserialize_with_mode( + mut reader: R, + _compress: Compress, + validate: Validate, + ) -> Result { + let x = u64::deserialize_with_mode(&mut reader, Compress::No, validate)?; + if matches!(validate, Validate::Yes) && x >= P { + return Err(SerializationError::InvalidData( + "Fp64 out of range".to_string(), + )); + } + let out = if matches!(validate, Validate::Yes) { + Self(x) + } else { + Self(Self::reduce_u128(x as u128)) + }; + Ok(out) + } +} + +impl FieldCore for Fp64

{ + fn zero() -> Self { + Self(0) + } + + fn one() -> Self { + Self(if P > 1 { 1 } else { 0 }) + } + + fn is_zero(&self) -> bool { + self.0 == 0 + } + + fn add(&self, rhs: &Self) -> Self { + *self + *rhs + } + + fn sub(&self, rhs: &Self) -> Self { + *self - *rhs + } + + fn mul(&self, rhs: &Self) -> Self { + *self * *rhs + } + + fn inv(self) -> Option { + let inv = self.inv_or_zero(); + if self.is_zero() { + None + } else { + Some(inv) + } + } +} + +impl Invertible for Fp64

{ + fn inv_or_zero(self) -> Self { + let candidate = self.pow(P.wrapping_sub(2)); + let nz = ((self.0 | self.0.wrapping_neg()) >> 63) & 1; + let mask = 0u64.wrapping_sub(nz); + Self(candidate.0 & mask) + } +} + +impl FieldSampling for Fp64

{ + fn sample(rng: &mut R) -> Self { + let lo = rng.next_u64() as u128; + let hi = rng.next_u64() as u128; + Self(Self::reduce_u128(lo | (hi << 64))) + } +} + +impl CanonicalField for Fp64

{ + fn from_u64(val: u64) -> Self { + Self(Self::reduce_u128(val as u128)) + } + + fn from_i64(val: i64) -> Self { + if val >= 0 { + Self::from_u64(val as u64) + } else { + -Self::from_u64((-val) as u64) + } + } + + fn to_canonical_u128(self) -> u128 { + self.0 as u128 + } + + fn from_canonical_u128_checked(val: u128) -> Option { + if val < P as u128 { + Some(Self(val as u64)) + } else { + None + } + } + + fn from_canonical_u128_reduced(val: u128) -> Self { + Self(Self::reduce_u128(val)) + } +} + +impl PseudoMersenneField for Fp64

{ + const MODULUS_BITS: u32 = Self::BITS; + const MODULUS_OFFSET: u128 = Self::C as u128; +} + +#[cfg(test)] +mod tests { + use super::*; + use rand::rngs::StdRng; + use rand::SeedableRng; + + type F40 = Fp64<{ (1u64 << 40) - 195 }>; // 2^40 - 195 + type F64 = Fp64<{ u64::MAX - 58 }>; // 2^64 - 59 + + #[test] + fn solinas_constants() { + assert_eq!(F40::BITS, 40); + assert_eq!(F40::C, 195); + + assert_eq!(F64::BITS, 64); + assert_eq!(F64::C, 59); + } + + #[test] + fn basic_arithmetic_sub_word() { + let a = F40::from_u64(1_000_000); + let b = F40::from_u64(2_000_000); + let p = (1u64 << 40) - 195; + assert_eq!((a + b).to_canonical_u64(), 3_000_000); + assert_eq!( + (a * b).to_canonical_u64(), + (1_000_000u128 * 2_000_000u128 % p as u128) as u64 + ); + } + + #[test] + fn basic_arithmetic_full_word() { + let a = F64::from_u64(1_000_000_000); + let b = F64::from_u64(2_000_000_000); + let p = u64::MAX - 58; + assert_eq!( + (a * b).to_canonical_u64(), + (1_000_000_000u128 * 2_000_000_000u128 % p as u128) as u64 + ); + } + + #[test] + fn mul_wide_matches_full_mul() { + let mut rng = StdRng::seed_from_u64(0xdead_beef); + for _ in 0..1000 { + let a: F40 = FieldSampling::sample(&mut rng); + let b: F40 = FieldSampling::sample(&mut rng); + let expected = a * b; + let reduced = F40::solinas_reduce(a.mul_wide(b)); + assert_eq!(reduced, expected); + } + } + + #[test] + fn mul_wide_u64_matches() { + let mut rng = StdRng::seed_from_u64(0xcafe_d00d); + for _ in 0..1000 { + let a: F40 = FieldSampling::sample(&mut rng); + let b = rng.next_u64() % ((1u64 << 40) - 195); + let expected = a * F40::from_canonical_u64(b); + let reduced = F40::solinas_reduce(a.mul_wide_u64(b)); + assert_eq!(reduced, expected); + } + } + + #[test] + fn pseudo_mersenne_trait() { + assert_eq!(::MODULUS_BITS, 40); + assert_eq!(::MODULUS_OFFSET, 195); + assert_eq!(::MODULUS_BITS, 64); + assert_eq!(::MODULUS_OFFSET, 59); + } + + #[test] + fn shift_optimization_detected() { + type G = Fp64<{ (1u64 << 56) - 27 }>; // C = 27, not 2^a±1 + assert_eq!(G::C_SHIFT_KIND, 0); + + type H = Fp64<{ u64::MAX - 58 }>; // C = 59, not 2^a±1 + assert_eq!(H::C_SHIFT_KIND, 0); + } + + #[test] + fn reduce_u128_large() { + assert_eq!(F64::from_canonical_u128_reduced(u128::MAX), { + let p = u64::MAX as u128 - 58; + F64::from_canonical_u64((u128::MAX % p) as u64) + }); + } +} diff --git a/src/algebra/fields/lift.rs b/src/algebra/fields/lift.rs new file mode 100644 index 00000000..5e243c9c --- /dev/null +++ b/src/algebra/fields/lift.rs @@ -0,0 +1,43 @@ +//! Helpers for embedding base fields into extension fields. + +use crate::algebra::fields::ext::{Fp2, Fp2Config, Fp4, Fp4Config}; +use crate::primitives::serialization::Valid; +use crate::FieldCore; + +/// Lift a base-field element into an extension field. +/// +/// This is intentionally small: for extension towers we embed into the constant term. +pub trait LiftBase: FieldCore { + /// Embed `x ∈ F` as a constant in `Self`. + fn lift_base(x: F) -> Self; +} + +impl LiftBase for F { + #[inline] + fn lift_base(x: F) -> Self { + x + } +} + +impl LiftBase for Fp2 +where + F: FieldCore + Valid, + C: Fp2Config, +{ + #[inline] + fn lift_base(x: F) -> Self { + Self::new(x, F::zero()) + } +} + +impl LiftBase for Fp4 +where + F: FieldCore + Valid, + C2: Fp2Config, + C4: Fp4Config, +{ + #[inline] + fn lift_base(x: F) -> Self { + Self::new(Fp2::new(x, F::zero()), Fp2::new(F::zero(), F::zero())) + } +} diff --git a/src/algebra/fields/mod.rs b/src/algebra/fields/mod.rs new file mode 100644 index 00000000..d255852a --- /dev/null +++ b/src/algebra/fields/mod.rs @@ -0,0 +1,40 @@ +//! Prime fields and extension field towers. + +pub mod ext; +pub mod fp128; +pub mod fp32; +pub mod fp64; +pub mod lift; +pub mod packed; +#[cfg(all( + target_arch = "x86_64", + target_feature = "avx2", + not(all(target_feature = "avx512f", target_feature = "avx512dq")) +))] +pub mod packed_avx2; +#[cfg(all( + target_arch = "x86_64", + target_feature = "avx512f", + target_feature = "avx512dq" +))] +pub mod packed_avx512; +#[cfg(all(target_arch = "aarch64", target_feature = "neon"))] +pub mod packed_neon; +pub mod pseudo_mersenne; + +pub use ext::{Fp2, Fp2Config, Fp4, Fp4Config}; +pub use fp128::{ + Fp128, Prime128M13M4P0, Prime128M37P3P0, Prime128M52M3P0, Prime128M54P4P0, Prime128M8M4M1M0, +}; +pub use fp32::Fp32; +pub use fp64::Fp64; +pub use lift::LiftBase; +pub use packed::{ + Fp128Packing, Fp32Packing, Fp64Packing, HasPacking, NoPacking, PackedField, PackedValue, +}; +pub use pseudo_mersenne::{ + is_pow2_offset, pow2_offset, pseudo_mersenne_modulus, Pow2Offset128Field, Pow2Offset24Field, + Pow2Offset30Field, Pow2Offset31Field, Pow2Offset32Field, Pow2Offset40Field, Pow2Offset48Field, + Pow2Offset56Field, Pow2Offset64Field, Pow2OffsetPrimeSpec, POW2_OFFSET_IMPLEMENTED_MAX_BITS, + POW2_OFFSET_MAX, POW2_OFFSET_PRIMES, POW2_OFFSET_TABLE, +}; diff --git a/src/algebra/fields/packed.rs b/src/algebra/fields/packed.rs new file mode 100644 index 00000000..e66063a9 --- /dev/null +++ b/src/algebra/fields/packed.rs @@ -0,0 +1,434 @@ +//! Packed field abstractions and architecture-specific SIMD backends. + +use crate::algebra::fields::{Fp128, Fp32, Fp64}; +use crate::FieldCore; +use core::ops::{Add, Mul, Sub}; + +/// Array-like packed values over a scalar type. +pub trait PackedValue: 'static + Copy + Send + Sync { + /// Scalar value type carried by each lane. + type Value: 'static + Copy + Send + Sync; + + /// Number of scalar lanes. + const WIDTH: usize; + + /// Build from a lane generator. + fn from_fn(f: F) -> Self + where + F: FnMut(usize) -> Self::Value; + + /// Extract one lane. + fn extract(&self, lane: usize) -> Self::Value; + + /// Pack a scalar slice into packed values. + /// + /// # Panics + /// + /// Panics if the length is not divisible by `WIDTH`. + #[inline] + fn pack_slice(buf: &[Self::Value]) -> Vec { + assert!( + buf.len() % Self::WIDTH == 0, + "slice length {} must be divisible by WIDTH {}", + buf.len(), + Self::WIDTH + ); + buf.chunks_exact(Self::WIDTH) + .map(|chunk| Self::from_fn(|i| chunk[i])) + .collect() + } + + /// Packed prefix + scalar suffix split. + #[inline] + fn pack_slice_with_suffix(buf: &[Self::Value]) -> (Vec, &[Self::Value]) { + let split = buf.len() - (buf.len() % Self::WIDTH); + let (packed, suffix) = buf.split_at(split); + (Self::pack_slice(packed), suffix) + } + + /// Unpack packed values into a flat scalar vector. + #[inline] + fn unpack_slice(buf: &[Self]) -> Vec { + let mut out = Vec::with_capacity(buf.len() * Self::WIDTH); + for packed in buf { + for lane in 0..Self::WIDTH { + out.push(packed.extract(lane)); + } + } + out + } +} + +/// Packed arithmetic over a scalar field. +pub trait PackedField: + PackedValue + Add + Sub + Mul +{ + /// Scalar field type. + type Scalar: FieldCore; + + /// Broadcast one scalar across all lanes. + fn broadcast(value: Self::Scalar) -> Self; +} + +/// Scalar fallback packed type with one lane. +#[derive(Clone, Copy, Debug, Default, PartialEq, Eq)] +#[repr(transparent)] +pub struct NoPacking(pub [T; 1]); + +impl PackedValue for NoPacking +where + T: 'static + Copy + Send + Sync, +{ + type Value = T; + const WIDTH: usize = 1; + + #[inline] + fn from_fn(mut f: F) -> Self + where + F: FnMut(usize) -> Self::Value, + { + Self([f(0)]) + } + + #[inline] + fn extract(&self, lane: usize) -> Self::Value { + debug_assert_eq!(lane, 0); + self.0[0] + } +} + +impl Add for NoPacking { + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + Self([self.0[0] + rhs.0[0]]) + } +} + +impl Sub for NoPacking { + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + Self([self.0[0] - rhs.0[0]]) + } +} + +impl Mul for NoPacking { + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + Self([self.0[0] * rhs.0[0]]) + } +} + +impl PackedField for NoPacking { + type Scalar = T; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self([value]) + } +} + +/// Scalar field -> packed field association. +pub trait HasPacking: FieldCore { + /// Packed representation for this scalar field. + type Packing: PackedField; +} + +/// Selected packed backend for `Fp128`. +#[cfg(all(target_arch = "aarch64", target_feature = "neon"))] +pub type Fp128Packing = super::packed_neon::PackedFp128Neon

; + +/// Selected packed backend for `Fp128`. +#[cfg(all( + target_arch = "x86_64", + target_feature = "avx512f", + target_feature = "avx512dq" +))] +pub type Fp128Packing = super::packed_avx512::PackedFp128Avx512

; + +/// Selected packed backend for `Fp128`. +#[cfg(all( + target_arch = "x86_64", + target_feature = "avx2", + not(all(target_feature = "avx512f", target_feature = "avx512dq")) +))] +pub type Fp128Packing = super::packed_avx2::PackedFp128Avx2

; + +/// Selected packed backend for `Fp128`. +#[cfg(not(any( + all(target_arch = "aarch64", target_feature = "neon"), + all(target_arch = "x86_64", target_feature = "avx2") +)))] +pub type Fp128Packing = NoPacking>; + +impl HasPacking for Fp128

{ + type Packing = Fp128Packing

; +} + +/// Selected packed backend for `Fp32`. +#[cfg(all(target_arch = "aarch64", target_feature = "neon"))] +pub type Fp32Packing = super::packed_neon::PackedFp32Neon

; + +/// Selected packed backend for `Fp32`. +#[cfg(all( + target_arch = "x86_64", + target_feature = "avx512f", + target_feature = "avx512dq" +))] +pub type Fp32Packing = super::packed_avx512::PackedFp32Avx512

; + +/// Selected packed backend for `Fp32`. +#[cfg(all( + target_arch = "x86_64", + target_feature = "avx2", + not(all(target_feature = "avx512f", target_feature = "avx512dq")) +))] +pub type Fp32Packing = super::packed_avx2::PackedFp32Avx2

; + +/// Selected packed backend for `Fp32`. +#[cfg(not(any( + all(target_arch = "aarch64", target_feature = "neon"), + all(target_arch = "x86_64", target_feature = "avx2") +)))] +pub type Fp32Packing = NoPacking>; + +impl HasPacking for Fp32

{ + type Packing = Fp32Packing

; +} + +/// Selected packed backend for `Fp64`. +#[cfg(all(target_arch = "aarch64", target_feature = "neon"))] +pub type Fp64Packing = super::packed_neon::PackedFp64Neon

; + +/// Selected packed backend for `Fp64`. +#[cfg(all( + target_arch = "x86_64", + target_feature = "avx512f", + target_feature = "avx512dq" +))] +pub type Fp64Packing = super::packed_avx512::PackedFp64Avx512

; + +/// Selected packed backend for `Fp64`. +#[cfg(all( + target_arch = "x86_64", + target_feature = "avx2", + not(all(target_feature = "avx512f", target_feature = "avx512dq")) +))] +pub type Fp64Packing = super::packed_avx2::PackedFp64Avx2

; + +/// Selected packed backend for `Fp64`. +#[cfg(not(any( + all(target_arch = "aarch64", target_feature = "neon"), + all(target_arch = "x86_64", target_feature = "avx2") +)))] +pub type Fp64Packing = NoPacking>; + +impl HasPacking for Fp64

{ + type Packing = Fp64Packing

; +} + +#[cfg(test)] +mod tests { + use super::{HasPacking, PackedField, PackedValue}; + use crate::algebra::fields::{ + Pow2Offset24Field, Pow2Offset31Field, Pow2Offset32Field, Pow2Offset40Field, + Pow2Offset64Field, Prime128M13M4P0, + }; + use crate::{CanonicalField, FieldCore, FieldSampling}; + use rand::{rngs::StdRng, RngCore, SeedableRng}; + + fn rand_u128(rng: &mut R) -> u128 { + let lo = rng.next_u64() as u128; + let hi = rng.next_u64() as u128; + lo | (hi << 64) + } + + fn check_packed_add_sub_mul(seed: u64) + where + F: FieldCore + FieldSampling + PartialEq + std::fmt::Debug, + PF: PackedField + PackedValue, + { + let mut rng = StdRng::seed_from_u64(seed); + let len = PF::WIDTH * 17 + 3; + let lhs: Vec = (0..len).map(|_| FieldSampling::sample(&mut rng)).collect(); + let rhs: Vec = (0..len).map(|_| FieldSampling::sample(&mut rng)).collect(); + + let (lhs_p, lhs_s) = PF::pack_slice_with_suffix(&lhs); + let (rhs_p, rhs_s) = PF::pack_slice_with_suffix(&rhs); + + let add_p: Vec = lhs_p + .iter() + .zip(rhs_p.iter()) + .map(|(&a, &b)| a + b) + .collect(); + let sub_p: Vec = lhs_p + .iter() + .zip(rhs_p.iter()) + .map(|(&a, &b)| a - b) + .collect(); + let mul_p: Vec = lhs_p + .iter() + .zip(rhs_p.iter()) + .map(|(&a, &b)| a * b) + .collect(); + + let mut add_out = PF::unpack_slice(&add_p); + let mut sub_out = PF::unpack_slice(&sub_p); + let mut mul_out = PF::unpack_slice(&mul_p); + + for (&a, &b) in lhs_s.iter().zip(rhs_s.iter()) { + add_out.push(a + b); + sub_out.push(a - b); + mul_out.push(a * b); + } + + for i in 0..len { + assert_eq!( + add_out[i], + lhs[i] + rhs[i], + "packed add mismatch at lane {i}" + ); + assert_eq!( + sub_out[i], + lhs[i] - rhs[i], + "packed sub mismatch at lane {i}" + ); + assert_eq!( + mul_out[i], + lhs[i] * rhs[i], + "packed mul mismatch at lane {i}" + ); + } + } + + fn check_broadcast_roundtrip(val: F) + where + F: FieldCore + PartialEq + std::fmt::Debug, + PF: PackedField + PackedValue, + { + let p = PF::broadcast(val); + for lane in 0..PF::WIDTH { + assert_eq!(p.extract(lane), val); + } + } + + #[test] + fn packed_fp128_add_sub_mul_match_scalar() { + type F = Prime128M13M4P0; + type PF = ::Packing; + + let mut rng = StdRng::seed_from_u64(0x55aa_4422_1177_0033); + let len = PF::WIDTH * 17 + 3; + let lhs: Vec = (0..len) + .map(|_| F::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + let rhs: Vec = (0..len) + .map(|_| F::from_canonical_u128_reduced(rand_u128(&mut rng))) + .collect(); + + let (lhs_p, lhs_s) = PF::pack_slice_with_suffix(&lhs); + let (rhs_p, rhs_s) = PF::pack_slice_with_suffix(&rhs); + + let add_p: Vec = lhs_p + .iter() + .zip(rhs_p.iter()) + .map(|(&a, &b)| a + b) + .collect(); + let sub_p: Vec = lhs_p + .iter() + .zip(rhs_p.iter()) + .map(|(&a, &b)| a - b) + .collect(); + let mul_p: Vec = lhs_p + .iter() + .zip(rhs_p.iter()) + .map(|(&a, &b)| a * b) + .collect(); + + let mut add_out = PF::unpack_slice(&add_p); + let mut sub_out = PF::unpack_slice(&sub_p); + let mut mul_out = PF::unpack_slice(&mul_p); + + for (&a, &b) in lhs_s.iter().zip(rhs_s.iter()) { + add_out.push(a + b); + sub_out.push(a - b); + mul_out.push(a * b); + } + + for i in 0..len { + assert_eq!( + add_out[i], + lhs[i] + rhs[i], + "packed add mismatch at lane {i}" + ); + assert_eq!( + sub_out[i], + lhs[i] - rhs[i], + "packed sub mismatch at lane {i}" + ); + assert_eq!( + mul_out[i], + lhs[i] * rhs[i], + "packed mul mismatch at lane {i}" + ); + } + } + + #[test] + fn fp128_broadcast_and_extract_roundtrip() { + type F = Prime128M13M4P0; + type PF = ::Packing; + check_broadcast_roundtrip::(F::from_u64(42)); + } + + #[test] + fn packed_fp32_24b_add_sub_mul() { + type F = Pow2Offset24Field; + type PF = ::Packing; + check_packed_add_sub_mul::(0xaa24_bb24_cc24_dd24); + } + + #[test] + fn packed_fp32_31b_add_sub_mul() { + type F = Pow2Offset31Field; + type PF = ::Packing; + check_packed_add_sub_mul::(0xaa31_bb31_cc31_dd31); + } + + #[test] + fn packed_fp32_32b_add_sub_mul() { + type F = Pow2Offset32Field; + type PF = ::Packing; + check_packed_add_sub_mul::(0xaa32_bb32_cc32_dd32); + } + + #[test] + fn fp32_broadcast_and_extract_roundtrip() { + type F = Pow2Offset24Field; + type PF = ::Packing; + check_broadcast_roundtrip::(F::from_u64(42)); + } + + #[test] + fn packed_fp64_40b_add_sub_mul() { + type F = Pow2Offset40Field; + type PF = ::Packing; + check_packed_add_sub_mul::(0xaa40_bb40_cc40_dd40); + } + + #[test] + fn packed_fp64_64b_add_sub_mul() { + type F = Pow2Offset64Field; + type PF = ::Packing; + check_packed_add_sub_mul::(0xaa64_bb64_cc64_dd64); + } + + #[test] + fn fp64_broadcast_and_extract_roundtrip() { + type F = Pow2Offset40Field; + type PF = ::Packing; + check_broadcast_roundtrip::(F::from_u64(42)); + } +} diff --git a/src/algebra/fields/packed_avx2.rs b/src/algebra/fields/packed_avx2.rs new file mode 100644 index 00000000..95468959 --- /dev/null +++ b/src/algebra/fields/packed_avx2.rs @@ -0,0 +1,704 @@ +//! AVX2 packed backends for Fp32, Fp64, Fp128. +//! +//! Techniques adapted from plonky2 (Goldilocks) and plonky3 (Mersenne-31). + +use super::packed::{PackedField, PackedValue}; +use crate::algebra::fields::{Fp128, Fp32, Fp64}; +use core::arch::x86_64::*; +use core::fmt; +use core::mem::transmute; +use core::ops::{Add, Mul, Sub}; + +/// Duplicate high 32 bits of each 64-bit lane into the low 32 bits. +/// Uses the float `movehdup` instruction which runs on port 5 (doesn't compete +/// with multiply on ports 0/1). +#[inline(always)] +unsafe fn movehdup_epi32(x: __m256i) -> __m256i { + _mm256_castps_si256(_mm256_movehdup_ps(_mm256_castsi256_ps(x))) +} + +#[inline(always)] +unsafe fn moveldup_epi32(x: __m256i) -> __m256i { + _mm256_castps_si256(_mm256_moveldup_ps(_mm256_castsi256_ps(x))) +} + +/// 64×64→128 schoolbook multiply using 32×32→64 partial products. +/// Returns (hi, lo) representing the 128-bit product. +#[inline] +unsafe fn mul64_64_256(x: __m256i, y: __m256i) -> (__m256i, __m256i) { + let x_hi = movehdup_epi32(x); + let y_hi = movehdup_epi32(y); + + let mul_ll = _mm256_mul_epu32(x, y); + let mul_lh = _mm256_mul_epu32(x, y_hi); + let mul_hl = _mm256_mul_epu32(x_hi, y); + let mul_hh = _mm256_mul_epu32(x_hi, y_hi); + + let mul_ll_hi = _mm256_srli_epi64::<32>(mul_ll); + let t0 = _mm256_add_epi64(mul_hl, mul_ll_hi); + let mask32 = _mm256_set1_epi64x(0xFFFF_FFFF_i64); + let t0_lo = _mm256_and_si256(t0, mask32); + let t0_hi = _mm256_srli_epi64::<32>(t0); + let t1 = _mm256_add_epi64(mul_lh, t0_lo); + let t2 = _mm256_add_epi64(mul_hh, t0_hi); + let t1_hi = _mm256_srli_epi64::<32>(t1); + let res_hi = _mm256_add_epi64(t2, t1_hi); + + let t1_lo = moveldup_epi32(t1); + let res_lo = _mm256_blend_epi32::<0b10101010>(mul_ll, t1_lo); + + (res_hi, res_lo) +} + +/// Number of `Fp32` lanes in an AVX2 packed vector. +pub const FP32_WIDTH: usize = 8; + +/// AVX2 packed arithmetic for `Fp32

`, processing 8 lanes. +#[derive(Clone, Copy)] +#[repr(transparent)] +pub struct PackedFp32Avx2(pub [Fp32

; FP32_WIDTH]); + +impl PackedFp32Avx2

{ + const BITS: u32 = 32 - P.leading_zeros(); + + const C: u32 = { + let c = if Self::BITS == 32 { + 0u32.wrapping_sub(P) + } else { + (1u32 << Self::BITS) - P + }; + assert!(P != 0, "modulus must be nonzero"); + assert!(P & 1 == 1, "modulus must be odd"); + assert!( + (c as u64) * (c as u64 + 1) < P as u64, + "C(C+1) < P required for fused canonicalize" + ); + c + }; + + const MASK_U64: u64 = if Self::BITS == 32 { + u32::MAX as u64 + } else { + (1u64 << Self::BITS) - 1 + }; + + #[inline(always)] + fn to_vec(self) -> __m256i { + unsafe { transmute(self) } + } + + #[inline(always)] + unsafe fn from_vec(v: __m256i) -> Self { + unsafe { transmute(v) } + } +} + +impl Default for PackedFp32Avx2

{ + #[inline] + fn default() -> Self { + Self([Fp32(0); FP32_WIDTH]) + } +} + +impl fmt::Debug for PackedFp32Avx2

{ + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + f.debug_tuple("PackedFp32Avx2").field(&self.0).finish() + } +} + +impl PartialEq for PackedFp32Avx2

{ + #[inline] + fn eq(&self, other: &Self) -> bool { + self.0 == other.0 + } +} + +impl Eq for PackedFp32Avx2

{} + +impl Add for PackedFp32Avx2

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + unsafe { + let a = self.to_vec(); + let b = rhs.to_vec(); + let p = _mm256_set1_epi32(P as i32); + + let result = if Self::BITS <= 31 { + let t = _mm256_add_epi32(a, b); + let u = _mm256_sub_epi32(t, p); + _mm256_min_epu32(t, u) + } else { + let c = _mm256_set1_epi32(Self::C as i32); + let t = _mm256_add_epi32(a, b); + // Emulate unsigned compare: XOR with 0x80000000 converts u32 compare to i32 + let sign32 = _mm256_set1_epi32(i32::MIN); + let overflow = + _mm256_cmpgt_epi32(_mm256_xor_si256(a, sign32), _mm256_xor_si256(t, sign32)); + // Step 1: correct overflow (2^32 ≡ C mod P) + let t2 = _mm256_add_epi32(t, _mm256_and_si256(overflow, c)); + // Step 2: subtract P if t2 >= P + let r = _mm256_sub_epi32(t2, p); + _mm256_min_epu32(t2, r) + }; + + Self::from_vec(result) + } + } +} + +impl Sub for PackedFp32Avx2

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + unsafe { + let a = self.to_vec(); + let b = rhs.to_vec(); + let p = _mm256_set1_epi32(P as i32); + + let result = if Self::BITS <= 31 { + let t = _mm256_sub_epi32(a, b); + let u = _mm256_add_epi32(t, p); + _mm256_min_epu32(t, u) + } else { + let t = _mm256_sub_epi32(a, b); + let sign32 = _mm256_set1_epi32(i32::MIN); + let underflow = + _mm256_cmpgt_epi32(_mm256_xor_si256(b, sign32), _mm256_xor_si256(a, sign32)); + let corrected = _mm256_add_epi32(t, p); + _mm256_blendv_epi8(t, corrected, underflow) + }; + + Self::from_vec(result) + } + } +} + +impl Mul for PackedFp32Avx2

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + unsafe { + let a = self.to_vec(); + let b = rhs.to_vec(); + + let prod_evn = _mm256_mul_epu32(a, b); + let a_odd = movehdup_epi32(a); + let b_odd = movehdup_epi32(b); + let prod_odd = _mm256_mul_epu32(a_odd, b_odd); + + let mask = _mm256_set1_epi64x(Self::MASK_U64 as i64); + let c_vec = _mm256_set1_epi64x(Self::C as i64); + let shift = _mm_set_epi64x(0, Self::BITS as i64); + + // Fold 1 + let evn_lo = _mm256_and_si256(prod_evn, mask); + let evn_hi = _mm256_srl_epi64(prod_evn, shift); + let evn_f1 = _mm256_add_epi64(evn_lo, _mm256_mul_epu32(evn_hi, c_vec)); + + let odd_lo = _mm256_and_si256(prod_odd, mask); + let odd_hi = _mm256_srl_epi64(prod_odd, shift); + let odd_f1 = _mm256_add_epi64(odd_lo, _mm256_mul_epu32(odd_hi, c_vec)); + + // Fold 2 + let evn_f1_lo = _mm256_and_si256(evn_f1, mask); + let evn_f1_hi = _mm256_srl_epi64(evn_f1, shift); + let evn_f2 = _mm256_add_epi64(evn_f1_lo, _mm256_mul_epu32(evn_f1_hi, c_vec)); + + let odd_f1_lo = _mm256_and_si256(odd_f1, mask); + let odd_f1_hi = _mm256_srl_epi64(odd_f1, shift); + let odd_f2 = _mm256_add_epi64(odd_f1_lo, _mm256_mul_epu32(odd_f1_hi, c_vec)); + + // Recombine even/odd: shift odd results into high 32-bit positions, blend. + let odd_shifted = _mm256_slli_epi64::<32>(odd_f2); + let combined = _mm256_blend_epi32::<0b10101010>(evn_f2, odd_shifted); + + // Conditional subtract P + let p_vec = _mm256_set1_epi32(P as i32); + let reduced = _mm256_sub_epi32(combined, p_vec); + Self::from_vec(_mm256_min_epu32(combined, reduced)) + } + } +} + +impl PackedValue for PackedFp32Avx2

{ + type Value = Fp32

; + const WIDTH: usize = FP32_WIDTH; + + #[inline] + fn from_fn(mut f: F) -> Self + where + F: FnMut(usize) -> Self::Value, + { + Self([f(0), f(1), f(2), f(3), f(4), f(5), f(6), f(7)]) + } + + #[inline] + fn extract(&self, lane: usize) -> Self::Value { + debug_assert!(lane < FP32_WIDTH); + self.0[lane] + } +} + +impl PackedField for PackedFp32Avx2

{ + type Scalar = Fp32

; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self([value; FP32_WIDTH]) + } +} + +/// Number of `Fp64` lanes in an AVX2 packed vector. +pub const FP64_WIDTH: usize = 4; + +/// AVX2 packed arithmetic for `Fp64

`, processing 4 lanes. +#[derive(Clone, Copy)] +#[repr(transparent)] +pub struct PackedFp64Avx2(pub [Fp64

; FP64_WIDTH]); + +impl PackedFp64Avx2

{ + const BITS: u32 = 64 - P.leading_zeros(); + + const C_LO: u64 = { + let c = if Self::BITS == 64 { + 0u64.wrapping_sub(P) + } else { + (1u64 << Self::BITS) - P + }; + assert!(P != 0, "modulus must be nonzero"); + assert!(P & 1 == 1, "modulus must be odd"); + c + }; + + const MASK64: u64 = if Self::BITS < 64 { + (1u64 << Self::BITS) - 1 + } else { + u64::MAX + }; + + #[inline(always)] + fn to_vec(self) -> __m256i { + unsafe { transmute(self) } + } + + #[inline(always)] + unsafe fn from_vec(v: __m256i) -> Self { + unsafe { transmute(v) } + } + + #[inline] + unsafe fn reduce128_vec(hi: __m256i, lo: __m256i) -> __m256i { + if Self::BITS < 64 { + Self::reduce128_small_k(hi, lo) + } else { + Self::reduce128_full_k(hi, lo) + } + } + + /// Reduction for BITS < 64. All intermediates fit in u64 — no overflow. + #[inline] + unsafe fn reduce128_small_k(hi: __m256i, lo: __m256i) -> __m256i { + let mask_k = _mm256_set1_epi64x(Self::MASK64 as i64); + let c_vec = _mm256_set1_epi64x(Self::C_LO as i64); + let p_vec = _mm256_set1_epi64x(P as i64); + let shift_k = _mm_set_epi64x(0, Self::BITS as i64); + let shift_64mk = _mm_set_epi64x(0, (64 - Self::BITS) as i64); + + let lo_k = _mm256_and_si256(lo, mask_k); + let lo_upper = _mm256_srl_epi64(lo, shift_k); + let hi_shifted = _mm256_sll_epi64(hi, shift_64mk); + let hi_k = _mm256_or_si256(lo_upper, hi_shifted); + + let c_hi_lo = _mm256_mul_epu32(c_vec, hi_k); + let hi_k_top = _mm256_srli_epi64::<32>(hi_k); + let c_hi_top = _mm256_mul_epu32(c_vec, hi_k_top); + let c_hi_top_shifted = _mm256_slli_epi64::<32>(c_hi_top); + let c_hi_full = _mm256_add_epi64(c_hi_lo, c_hi_top_shifted); + + let fold1 = _mm256_add_epi64(lo_k, c_hi_full); + + let fold1_lo_k = _mm256_and_si256(fold1, mask_k); + let fold1_hi = _mm256_srl_epi64(fold1, shift_k); + let c_fold1_hi = _mm256_mul_epu32(c_vec, fold1_hi); + let fold2 = _mm256_add_epi64(fold1_lo_k, c_fold1_hi); + + let reduced = _mm256_sub_epi64(fold2, p_vec); + let sign = _mm256_set1_epi64x(i64::MIN); + let fold2_s = _mm256_xor_si256(fold2, sign); + let reduced_s = _mm256_xor_si256(reduced, sign); + let fold2_lt = _mm256_cmpgt_epi64(reduced_s, fold2_s); + _mm256_blendv_epi8(reduced, fold2, fold2_lt) + } + + /// Reduction for BITS == 64. Uses XOR-with-SIGN_BIT trick for unsigned + /// overflow detection. + #[inline] + unsafe fn reduce128_full_k(hi: __m256i, lo: __m256i) -> __m256i { + let c_vec = _mm256_set1_epi64x(Self::C_LO as i64); + let p_vec = _mm256_set1_epi64x(P as i64); + let sign = _mm256_set1_epi64x(i64::MIN); + let c_hi_lo = _mm256_mul_epu32(c_vec, hi); + let hi_hi = _mm256_srli_epi64::<32>(hi); + let c_hi_hi = _mm256_mul_epu32(c_vec, hi_hi); + + let c_hi_hi_lo32 = _mm256_slli_epi64::<32>(c_hi_hi); + let c_hi_carry = _mm256_srli_epi64::<32>(c_hi_hi); + + let sum_lo = _mm256_add_epi64(c_hi_lo, c_hi_hi_lo32); + let c_hi_lo_s = _mm256_xor_si256(c_hi_lo, sign); + let sum_lo_s = _mm256_xor_si256(sum_lo, sign); + let carry0 = _mm256_cmpgt_epi64(c_hi_lo_s, sum_lo_s); + let overflow = _mm256_sub_epi64(c_hi_carry, carry0); + + let s = _mm256_add_epi64(lo, sum_lo); + let lo_s = _mm256_xor_si256(lo, sign); + let s_s = _mm256_xor_si256(s, sign); + let carry1 = _mm256_cmpgt_epi64(lo_s, s_s); + let total_overflow = _mm256_sub_epi64(overflow, carry1); + + let final_corr = _mm256_mul_epu32(c_vec, total_overflow); + let result = _mm256_add_epi64(s, final_corr); + let s2_s = _mm256_xor_si256(s, sign); + let result_s = _mm256_xor_si256(result, sign); + let carry_f = _mm256_cmpgt_epi64(s2_s, result_s); + let corr_f = _mm256_and_si256(carry_f, c_vec); + let result = _mm256_add_epi64(result, corr_f); + + let result_s2 = _mm256_xor_si256(result, sign); + let p_s = _mm256_xor_si256(p_vec, sign); + let lt_p = _mm256_cmpgt_epi64(p_s, result_s2); + let sub_amt = _mm256_andnot_si256(lt_p, p_vec); + _mm256_sub_epi64(result, sub_amt) + } +} + +impl Default for PackedFp64Avx2

{ + #[inline] + fn default() -> Self { + Self([Fp64(0); FP64_WIDTH]) + } +} + +impl fmt::Debug for PackedFp64Avx2

{ + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + f.debug_tuple("PackedFp64Avx2").field(&self.0).finish() + } +} + +impl PartialEq for PackedFp64Avx2

{ + #[inline] + fn eq(&self, other: &Self) -> bool { + self.0 == other.0 + } +} + +impl Eq for PackedFp64Avx2

{} + +impl Add for PackedFp64Avx2

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + unsafe { + let a = self.to_vec(); + let b = rhs.to_vec(); + let p = _mm256_set1_epi64x(P as i64); + + let result = if Self::BITS <= 62 { + // a + b < 2P < 2^63: no overflow. + let s = _mm256_add_epi64(a, b); + let r = _mm256_sub_epi64(s, p); + // s < P? Use signed compare after shift trick. + let sign = _mm256_set1_epi64x(i64::MIN); + let s_s = _mm256_xor_si256(s, sign); + let p_s = _mm256_xor_si256(p, sign); + let borrow = _mm256_cmpgt_epi64(p_s, s_s); + _mm256_blendv_epi8(r, s, borrow) + } else { + // a + b can overflow u64. + let s = _mm256_add_epi64(a, b); + let sign = _mm256_set1_epi64x(i64::MIN); + let a_s = _mm256_xor_si256(a, sign); + let s_s = _mm256_xor_si256(s, sign); + let overflow = _mm256_cmpgt_epi64(a_s, s_s); + let c = _mm256_set1_epi64x(Self::C_LO as i64); + let s_plus_c = _mm256_add_epi64(s, c); + let s_minus_p = _mm256_sub_epi64(s, p); + let p_s = _mm256_xor_si256(p, sign); + let lt_p = _mm256_cmpgt_epi64(p_s, s_s); + let no_of = _mm256_blendv_epi8(s_minus_p, s, lt_p); + _mm256_blendv_epi8(no_of, s_plus_c, overflow) + }; + + Self::from_vec(result) + } + } +} + +impl Sub for PackedFp64Avx2

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + unsafe { + let a = self.to_vec(); + let b = rhs.to_vec(); + let p = _mm256_set1_epi64x(P as i64); + let d = _mm256_sub_epi64(a, b); + + let sign = _mm256_set1_epi64x(i64::MIN); + let a_s = _mm256_xor_si256(a, sign); + let b_s = _mm256_xor_si256(b, sign); + let underflow = _mm256_cmpgt_epi64(b_s, a_s); + let corrected = _mm256_add_epi64(d, p); + Self::from_vec(_mm256_blendv_epi8(d, corrected, underflow)) + } + } +} + +impl Mul for PackedFp64Avx2

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + unsafe { + let (hi, lo) = mul64_64_256(self.to_vec(), rhs.to_vec()); + Self::from_vec(Self::reduce128_vec(hi, lo)) + } + } +} + +impl PackedValue for PackedFp64Avx2

{ + type Value = Fp64

; + const WIDTH: usize = FP64_WIDTH; + + #[inline] + fn from_fn(mut f: F) -> Self + where + F: FnMut(usize) -> Self::Value, + { + Self([f(0), f(1), f(2), f(3)]) + } + + #[inline] + fn extract(&self, lane: usize) -> Self::Value { + debug_assert!(lane < FP64_WIDTH); + self.0[lane] + } +} + +impl PackedField for PackedFp64Avx2

{ + type Scalar = Fp64

; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self([value; FP64_WIDTH]) + } +} + +/// Number of `Fp128` lanes in an AVX2 packed vector. +pub const FP128_WIDTH: usize = 4; + +/// AVX2 packed arithmetic for `Fp128

`, 4 lanes in SoA layout. +/// +/// Stores 4 elements as separate `lo` and `hi` `u64` arrays, enabling +/// vectorized add/sub via `__m256i`. Mul remains scalar per-lane. +#[derive(Clone, Copy)] +pub struct PackedFp128Avx2 { + lo: [u64; FP128_WIDTH], + hi: [u64; FP128_WIDTH], +} + +impl PackedFp128Avx2

{ + const P_LO: u64 = P as u64; + const P_HI: u64 = (P >> 64) as u64; +} + +impl Default for PackedFp128Avx2

{ + #[inline] + fn default() -> Self { + Self { + lo: [0; FP128_WIDTH], + hi: [0; FP128_WIDTH], + } + } +} + +impl fmt::Debug for PackedFp128Avx2

{ + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + let elems: Vec<_> = (0..FP128_WIDTH).map(|i| self.extract(i)).collect(); + f.debug_tuple("PackedFp128Avx2").field(&elems).finish() + } +} + +impl PartialEq for PackedFp128Avx2

{ + #[inline] + fn eq(&self, other: &Self) -> bool { + self.lo == other.lo && self.hi == other.hi + } +} + +impl Eq for PackedFp128Avx2

{} + +impl Add for PackedFp128Avx2

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + unsafe { + let a_lo = _mm256_loadu_si256(self.lo.as_ptr().cast()); + let a_hi = _mm256_loadu_si256(self.hi.as_ptr().cast()); + let b_lo = _mm256_loadu_si256(rhs.lo.as_ptr().cast()); + let b_hi = _mm256_loadu_si256(rhs.hi.as_ptr().cast()); + let p_lo = _mm256_set1_epi64x(Self::P_LO as i64); + let p_hi = _mm256_set1_epi64x(Self::P_HI as i64); + let sign = _mm256_set1_epi64x(i64::MIN); + let one = _mm256_set1_epi64x(1); + + // 128-bit add with unsigned compare emulation (XOR sign bit) + let sum_lo = _mm256_add_epi64(a_lo, b_lo); + let carry_lo = + _mm256_cmpgt_epi64(_mm256_xor_si256(a_lo, sign), _mm256_xor_si256(sum_lo, sign)); + let carry_lo_bit = _mm256_and_si256(carry_lo, one); + + let hi_tmp = _mm256_add_epi64(a_hi, b_hi); + let ov1 = + _mm256_cmpgt_epi64(_mm256_xor_si256(a_hi, sign), _mm256_xor_si256(hi_tmp, sign)); + let sum_hi = _mm256_add_epi64(hi_tmp, carry_lo_bit); + let ov2 = _mm256_cmpgt_epi64( + _mm256_xor_si256(hi_tmp, sign), + _mm256_xor_si256(sum_hi, sign), + ); + let carry_128 = _mm256_or_si256(ov1, ov2); + + // 128-bit subtract P + let red_lo = _mm256_sub_epi64(sum_lo, p_lo); + let borrow_lo = + _mm256_cmpgt_epi64(_mm256_xor_si256(p_lo, sign), _mm256_xor_si256(sum_lo, sign)); + let borrow_lo_bit = _mm256_and_si256(borrow_lo, one); + + let red_hi_tmp = _mm256_sub_epi64(sum_hi, p_hi); + let bw1 = + _mm256_cmpgt_epi64(_mm256_xor_si256(p_hi, sign), _mm256_xor_si256(sum_hi, sign)); + let red_hi = _mm256_sub_epi64(red_hi_tmp, borrow_lo_bit); + let bw2 = _mm256_cmpgt_epi64( + _mm256_xor_si256(borrow_lo_bit, sign), + _mm256_xor_si256(red_hi_tmp, sign), + ); + let borrow = _mm256_or_si256(bw1, bw2); + + // use_reduced = carry_128 | !borrow + let not_borrow = _mm256_xor_si256(borrow, _mm256_set1_epi64x(-1)); + let use_reduced = _mm256_or_si256(carry_128, not_borrow); + let out_lo = _mm256_blendv_epi8(sum_lo, red_lo, use_reduced); + let out_hi = _mm256_blendv_epi8(sum_hi, red_hi, use_reduced); + + let mut result = Self::default(); + _mm256_storeu_si256(result.lo.as_mut_ptr().cast(), out_lo); + _mm256_storeu_si256(result.hi.as_mut_ptr().cast(), out_hi); + result + } + } +} + +impl Sub for PackedFp128Avx2

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + unsafe { + let a_lo = _mm256_loadu_si256(self.lo.as_ptr().cast()); + let a_hi = _mm256_loadu_si256(self.hi.as_ptr().cast()); + let b_lo = _mm256_loadu_si256(rhs.lo.as_ptr().cast()); + let b_hi = _mm256_loadu_si256(rhs.hi.as_ptr().cast()); + let p_lo = _mm256_set1_epi64x(Self::P_LO as i64); + let p_hi = _mm256_set1_epi64x(Self::P_HI as i64); + let sign = _mm256_set1_epi64x(i64::MIN); + let one = _mm256_set1_epi64x(1); + + // 128-bit sub + let diff_lo = _mm256_sub_epi64(a_lo, b_lo); + let borrow_lo = + _mm256_cmpgt_epi64(_mm256_xor_si256(b_lo, sign), _mm256_xor_si256(a_lo, sign)); + let borrow_lo_bit = _mm256_and_si256(borrow_lo, one); + + let hi_tmp = _mm256_sub_epi64(a_hi, b_hi); + let bw1 = + _mm256_cmpgt_epi64(_mm256_xor_si256(b_hi, sign), _mm256_xor_si256(a_hi, sign)); + let diff_hi = _mm256_sub_epi64(hi_tmp, borrow_lo_bit); + let bw2 = _mm256_cmpgt_epi64( + _mm256_xor_si256(borrow_lo_bit, sign), + _mm256_xor_si256(hi_tmp, sign), + ); + let borrow_128 = _mm256_or_si256(bw1, bw2); + + // Correction: add P back where underflow occurred + let corr_lo = _mm256_add_epi64(diff_lo, p_lo); + let carry_lo = _mm256_cmpgt_epi64( + _mm256_xor_si256(diff_lo, sign), + _mm256_xor_si256(corr_lo, sign), + ); + let carry_lo_bit = _mm256_and_si256(carry_lo, one); + let corr_hi = _mm256_add_epi64(diff_hi, p_hi); + let corr_hi = _mm256_add_epi64(corr_hi, carry_lo_bit); + + let out_lo = _mm256_blendv_epi8(diff_lo, corr_lo, borrow_128); + let out_hi = _mm256_blendv_epi8(diff_hi, corr_hi, borrow_128); + + let mut result = Self::default(); + _mm256_storeu_si256(result.lo.as_mut_ptr().cast(), out_lo); + _mm256_storeu_si256(result.hi.as_mut_ptr().cast(), out_hi); + result + } + } +} + +impl Mul for PackedFp128Avx2

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + let mut out = Self::default(); + for i in 0..FP128_WIDTH { + let a = Fp128::

([self.lo[i], self.hi[i]]); + let b = Fp128::

([rhs.lo[i], rhs.hi[i]]); + let r = a * b; + out.lo[i] = r.0[0]; + out.hi[i] = r.0[1]; + } + out + } +} + +impl PackedValue for PackedFp128Avx2

{ + type Value = Fp128

; + const WIDTH: usize = FP128_WIDTH; + + #[inline] + fn from_fn(mut f: F) -> Self + where + F: FnMut(usize) -> Self::Value, + { + let mut lo = [0u64; FP128_WIDTH]; + let mut hi = [0u64; FP128_WIDTH]; + for i in 0..FP128_WIDTH { + let v = f(i); + lo[i] = v.0[0]; + hi[i] = v.0[1]; + } + Self { lo, hi } + } + + #[inline] + fn extract(&self, lane: usize) -> Self::Value { + debug_assert!(lane < FP128_WIDTH); + Fp128([self.lo[lane], self.hi[lane]]) + } +} + +impl PackedField for PackedFp128Avx2

{ + type Scalar = Fp128

; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self { + lo: [value.0[0]; FP128_WIDTH], + hi: [value.0[1]; FP128_WIDTH], + } + } +} diff --git a/src/algebra/fields/packed_avx512.rs b/src/algebra/fields/packed_avx512.rs new file mode 100644 index 00000000..1102ac95 --- /dev/null +++ b/src/algebra/fields/packed_avx512.rs @@ -0,0 +1,666 @@ +//! AVX-512 packed backends for Fp32, Fp64, Fp128. +//! +//! Requires AVX-512F + AVX-512DQ. Uses native unsigned comparisons and mask +//! registers for branchless conditionals. + +use super::packed::{PackedField, PackedValue}; +use crate::algebra::fields::{Fp128, Fp32, Fp64}; +use crate::FieldCore; +use core::arch::x86_64::*; +use core::fmt; +use core::mem::transmute; +use core::ops::{Add, Mul, Sub}; + +#[inline(always)] +unsafe fn movehdup_epi32_512(x: __m512i) -> __m512i { + _mm512_castps_si512(_mm512_movehdup_ps(_mm512_castsi512_ps(x))) +} + +#[inline(always)] +unsafe fn moveldup_epi32_512(x: __m512i) -> __m512i { + _mm512_castps_si512(_mm512_moveldup_ps(_mm512_castsi512_ps(x))) +} + +/// 64×64→128 schoolbook multiply using 32×32→64 partial products. +/// Returns (hi, lo) representing the 128-bit product. +/// Adapted from plonky3's Goldilocks AVX-512 backend. +#[inline] +unsafe fn mul64_64_512(x: __m512i, y: __m512i) -> (__m512i, __m512i) { + let x_hi = movehdup_epi32_512(x); + let y_hi = movehdup_epi32_512(y); + + let mul_ll = _mm512_mul_epu32(x, y); + let mul_lh = _mm512_mul_epu32(x, y_hi); + let mul_hl = _mm512_mul_epu32(x_hi, y); + let mul_hh = _mm512_mul_epu32(x_hi, y_hi); + + let mul_ll_hi = _mm512_srli_epi64::<32>(mul_ll); + let t0 = _mm512_add_epi64(mul_hl, mul_ll_hi); + let mask32 = _mm512_set1_epi64(0xFFFF_FFFF_i64); + let t0_lo = _mm512_and_si512(t0, mask32); + let t0_hi = _mm512_srli_epi64::<32>(t0); + let t1 = _mm512_add_epi64(mul_lh, t0_lo); + let t2 = _mm512_add_epi64(mul_hh, t0_hi); + let t1_hi = _mm512_srli_epi64::<32>(t1); + let res_hi = _mm512_add_epi64(t2, t1_hi); + + let t1_lo = moveldup_epi32_512(t1); + let res_lo = _mm512_mask_blend_epi32(0b0101_0101_0101_0101, t1_lo, mul_ll); + + (res_hi, res_lo) +} + +/// Number of `Fp32` lanes in an AVX-512 packed vector. +pub const FP32_WIDTH: usize = 16; + +/// AVX-512 packed arithmetic for `Fp32

`, processing 16 lanes. +#[derive(Clone, Copy)] +#[repr(transparent)] +pub struct PackedFp32Avx512(pub [Fp32

; FP32_WIDTH]); + +impl PackedFp32Avx512

{ + const BITS: u32 = 32 - P.leading_zeros(); + + const C: u32 = { + let c = if Self::BITS == 32 { + 0u32.wrapping_sub(P) + } else { + (1u32 << Self::BITS) - P + }; + assert!(P != 0, "modulus must be nonzero"); + assert!(P & 1 == 1, "modulus must be odd"); + assert!( + (c as u64) * (c as u64 + 1) < P as u64, + "C(C+1) < P required for fused canonicalize" + ); + c + }; + + const MASK_U64: u64 = if Self::BITS == 32 { + u32::MAX as u64 + } else { + (1u64 << Self::BITS) - 1 + }; + + #[inline(always)] + fn to_vec(self) -> __m512i { + unsafe { transmute(self) } + } + + #[inline(always)] + unsafe fn from_vec(v: __m512i) -> Self { + unsafe { transmute(v) } + } +} + +impl Default for PackedFp32Avx512

{ + #[inline] + fn default() -> Self { + Self([Fp32(0); FP32_WIDTH]) + } +} + +impl fmt::Debug for PackedFp32Avx512

{ + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + f.debug_tuple("PackedFp32Avx512").field(&self.0).finish() + } +} + +impl PartialEq for PackedFp32Avx512

{ + #[inline] + fn eq(&self, other: &Self) -> bool { + self.0 == other.0 + } +} + +impl Eq for PackedFp32Avx512

{} + +impl Add for PackedFp32Avx512

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + unsafe { + let a = self.to_vec(); + let b = rhs.to_vec(); + let p = _mm512_set1_epi32(P as i32); + + let result = if Self::BITS <= 31 { + let t = _mm512_add_epi32(a, b); + let u = _mm512_sub_epi32(t, p); + _mm512_min_epu32(t, u) + } else { + let c = _mm512_set1_epi32(Self::C as i32); + let t = _mm512_add_epi32(a, b); + // Step 1: correct overflow (2^32 ≡ C mod P) + let overflow = _mm512_cmplt_epu32_mask(t, a); + let t2 = _mm512_mask_add_epi32(t, overflow, t, c); + // Step 2: subtract P if t2 >= P + let geq_p = _mm512_cmpge_epu32_mask(t2, p); + _mm512_mask_sub_epi32(t2, geq_p, t2, p) + }; + + Self::from_vec(result) + } + } +} + +impl Sub for PackedFp32Avx512

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + unsafe { + let a = self.to_vec(); + let b = rhs.to_vec(); + let p = _mm512_set1_epi32(P as i32); + + let result = if Self::BITS <= 31 { + let t = _mm512_sub_epi32(a, b); + let u = _mm512_add_epi32(t, p); + _mm512_min_epu32(t, u) + } else { + let t = _mm512_sub_epi32(a, b); + let underflow = _mm512_cmplt_epu32_mask(a, b); + _mm512_mask_add_epi32(t, underflow, t, p) + }; + + Self::from_vec(result) + } + } +} + +impl Mul for PackedFp32Avx512

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + unsafe { + let a = self.to_vec(); + let b = rhs.to_vec(); + + let prod_evn = _mm512_mul_epu32(a, b); + let a_odd = movehdup_epi32_512(a); + let b_odd = movehdup_epi32_512(b); + let prod_odd = _mm512_mul_epu32(a_odd, b_odd); + + let mask = _mm512_set1_epi64(Self::MASK_U64 as i64); + let c_vec = _mm512_set1_epi64(Self::C as i64); + let shift = _mm_set_epi64x(0, Self::BITS as i64); + + // Fold 1 + let evn_lo = _mm512_and_si512(prod_evn, mask); + let evn_hi = _mm512_srl_epi64(prod_evn, shift); + let evn_f1 = _mm512_add_epi64(evn_lo, _mm512_mul_epu32(evn_hi, c_vec)); + + let odd_lo = _mm512_and_si512(prod_odd, mask); + let odd_hi = _mm512_srl_epi64(prod_odd, shift); + let odd_f1 = _mm512_add_epi64(odd_lo, _mm512_mul_epu32(odd_hi, c_vec)); + + // Fold 2 + let evn_f1_lo = _mm512_and_si512(evn_f1, mask); + let evn_f1_hi = _mm512_srl_epi64(evn_f1, shift); + let evn_f2 = _mm512_add_epi64(evn_f1_lo, _mm512_mul_epu32(evn_f1_hi, c_vec)); + + let odd_f1_lo = _mm512_and_si512(odd_f1, mask); + let odd_f1_hi = _mm512_srl_epi64(odd_f1, shift); + let odd_f2 = _mm512_add_epi64(odd_f1_lo, _mm512_mul_epu32(odd_f1_hi, c_vec)); + + // Recombine even/odd + let odd_shifted = _mm512_slli_epi64::<32>(odd_f2); + let combined = _mm512_mask_blend_epi32(0b1010101010101010, evn_f2, odd_shifted); + + // Conditional subtract P + let p_vec = _mm512_set1_epi32(P as i32); + let reduced = _mm512_sub_epi32(combined, p_vec); + Self::from_vec(_mm512_min_epu32(combined, reduced)) + } + } +} + +impl PackedValue for PackedFp32Avx512

{ + type Value = Fp32

; + const WIDTH: usize = FP32_WIDTH; + + #[inline] + fn from_fn(mut f: F) -> Self + where + F: FnMut(usize) -> Self::Value, + { + Self([ + f(0), + f(1), + f(2), + f(3), + f(4), + f(5), + f(6), + f(7), + f(8), + f(9), + f(10), + f(11), + f(12), + f(13), + f(14), + f(15), + ]) + } + + #[inline] + fn extract(&self, lane: usize) -> Self::Value { + debug_assert!(lane < FP32_WIDTH); + self.0[lane] + } +} + +impl PackedField for PackedFp32Avx512

{ + type Scalar = Fp32

; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self([value; FP32_WIDTH]) + } +} + +/// Number of `Fp64` lanes in an AVX-512 packed vector. +pub const FP64_WIDTH: usize = 8; + +/// AVX-512 packed arithmetic for `Fp64

`, processing 8 lanes. +#[derive(Clone, Copy)] +#[repr(transparent)] +pub struct PackedFp64Avx512(pub [Fp64

; FP64_WIDTH]); + +impl PackedFp64Avx512

{ + const BITS: u32 = 64 - P.leading_zeros(); + + const C_LO: u64 = { + let c = if Self::BITS == 64 { + 0u64.wrapping_sub(P) + } else { + (1u64 << Self::BITS) - P + }; + assert!(P != 0, "modulus must be nonzero"); + assert!(P & 1 == 1, "modulus must be odd"); + c + }; + + const MASK64: u64 = if Self::BITS < 64 { + (1u64 << Self::BITS) - 1 + } else { + u64::MAX + }; + + #[inline(always)] + fn to_vec(self) -> __m512i { + unsafe { transmute(self) } + } + + #[inline(always)] + unsafe fn from_vec(v: __m512i) -> Self { + unsafe { transmute(v) } + } + + /// Vectorized 128-bit Solinas reduction for p = 2^BITS - C. + /// Given (hi, lo) = 128-bit product, computes result ≡ (hi*2^64 + lo) mod p. + #[inline] + unsafe fn reduce128_vec(hi: __m512i, lo: __m512i) -> __m512i { + if Self::BITS < 64 { + Self::reduce128_small_k(hi, lo) + } else { + Self::reduce128_full_k(hi, lo) + } + } + + /// Reduction for BITS < 64 (e.g. 40-bit prime). No overflow issues: all + /// intermediates fit in u64. + #[inline] + unsafe fn reduce128_small_k(hi: __m512i, lo: __m512i) -> __m512i { + let mask_k = _mm512_set1_epi64(Self::MASK64 as i64); + let c_vec = _mm512_set1_epi64(Self::C_LO as i64); + let p_vec = _mm512_set1_epi64(P as i64); + let shift_k = _mm_set_epi64x(0, Self::BITS as i64); + let shift_64mk = _mm_set_epi64x(0, (64 - Self::BITS) as i64); + + let lo_k = _mm512_and_si512(lo, mask_k); + let lo_upper = _mm512_srl_epi64(lo, shift_k); + let hi_shifted = _mm512_sll_epi64(hi, shift_64mk); + let hi_k = _mm512_or_si512(lo_upper, hi_shifted); + + // c * hi_k: hi_k may exceed 32 bits, split into lo32 and top + let c_hi_lo = _mm512_mul_epu32(c_vec, hi_k); + let hi_k_top = _mm512_srli_epi64::<32>(hi_k); + let c_hi_top = _mm512_mul_epu32(c_vec, hi_k_top); + let c_hi_top_shifted = _mm512_slli_epi64::<32>(c_hi_top); + let c_hi_full = _mm512_add_epi64(c_hi_lo, c_hi_top_shifted); + + let fold1 = _mm512_add_epi64(lo_k, c_hi_full); + + let fold1_lo_k = _mm512_and_si512(fold1, mask_k); + let fold1_hi = _mm512_srl_epi64(fold1, shift_k); + let c_fold1_hi = _mm512_mul_epu32(c_vec, fold1_hi); + let fold2 = _mm512_add_epi64(fold1_lo_k, c_fold1_hi); + + let reduced = _mm512_sub_epi64(fold2, p_vec); + _mm512_min_epu64(fold2, reduced) + } + + /// Reduction for BITS == 64 (e.g. p = 2^64 - 87). Tracks overflow from + /// c*hi exceeding 64 bits, using native unsigned comparisons. + #[inline] + unsafe fn reduce128_full_k(hi: __m512i, lo: __m512i) -> __m512i { + let c_vec = _mm512_set1_epi64(Self::C_LO as i64); + let p_vec = _mm512_set1_epi64(P as i64); + let one = _mm512_set1_epi64(1); + + // c * hi_lo32 + let c_hi_lo = _mm512_mul_epu32(c_vec, hi); + // c * hi_hi32 + let hi_hi = _mm512_srli_epi64::<32>(hi); + let c_hi_hi = _mm512_mul_epu32(c_vec, hi_hi); + + let c_hi_hi_lo32 = _mm512_slli_epi64::<32>(c_hi_hi); + let c_hi_carry = _mm512_srli_epi64::<32>(c_hi_hi); + + // Lower 64 bits of c * hi + let sum_lo = _mm512_add_epi64(c_hi_lo, c_hi_hi_lo32); + let carry0 = _mm512_cmplt_epu64_mask(sum_lo, c_hi_lo); + let overflow = _mm512_mask_add_epi64(c_hi_carry, carry0, c_hi_carry, one); + + // lo + sum_lo + let s = _mm512_add_epi64(lo, sum_lo); + let carry1 = _mm512_cmplt_epu64_mask(s, lo); + let total_overflow = _mm512_mask_add_epi64(overflow, carry1, overflow, one); + + // Fold overflow: total_overflow * c (at most ~2^15) + let final_corr = _mm512_mul_epu32(c_vec, total_overflow); + let result = _mm512_add_epi64(s, final_corr); + let carry_f = _mm512_cmplt_epu64_mask(result, s); + let result = _mm512_mask_add_epi64(result, carry_f, result, c_vec); + + let ge_mask = _mm512_cmpge_epu64_mask(result, p_vec); + _mm512_mask_sub_epi64(result, ge_mask, result, p_vec) + } +} + +impl Default for PackedFp64Avx512

{ + #[inline] + fn default() -> Self { + Self([Fp64(0); FP64_WIDTH]) + } +} + +impl fmt::Debug for PackedFp64Avx512

{ + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + f.debug_tuple("PackedFp64Avx512").field(&self.0).finish() + } +} + +impl PartialEq for PackedFp64Avx512

{ + #[inline] + fn eq(&self, other: &Self) -> bool { + self.0 == other.0 + } +} + +impl Eq for PackedFp64Avx512

{} + +impl Add for PackedFp64Avx512

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + unsafe { + let a = self.to_vec(); + let b = rhs.to_vec(); + let p = _mm512_set1_epi64(P as i64); + + let result = if Self::BITS <= 62 { + let s = _mm512_add_epi64(a, b); + let geq_p = _mm512_cmpge_epu64_mask(s, p); + _mm512_mask_sub_epi64(s, geq_p, s, p) + } else { + let s = _mm512_add_epi64(a, b); + let overflow = _mm512_cmplt_epu64_mask(s, a); + let c = _mm512_set1_epi64(Self::C_LO as i64); + let geq_p = _mm512_cmpge_epu64_mask(s, p); + let no_of = _mm512_mask_sub_epi64(s, geq_p, s, p); + let s_plus_c = _mm512_add_epi64(s, c); + _mm512_mask_blend_epi64(overflow, no_of, s_plus_c) + }; + + Self::from_vec(result) + } + } +} + +impl Sub for PackedFp64Avx512

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + unsafe { + let a = self.to_vec(); + let b = rhs.to_vec(); + let p = _mm512_set1_epi64(P as i64); + let d = _mm512_sub_epi64(a, b); + let underflow = _mm512_cmplt_epu64_mask(a, b); + Self::from_vec(_mm512_mask_add_epi64(d, underflow, d, p)) + } + } +} + +impl Mul for PackedFp64Avx512

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + unsafe { + let (hi, lo) = mul64_64_512(self.to_vec(), rhs.to_vec()); + Self::from_vec(Self::reduce128_vec(hi, lo)) + } + } +} + +impl PackedValue for PackedFp64Avx512

{ + type Value = Fp64

; + const WIDTH: usize = FP64_WIDTH; + + #[inline] + fn from_fn(mut f: F) -> Self + where + F: FnMut(usize) -> Self::Value, + { + Self([f(0), f(1), f(2), f(3), f(4), f(5), f(6), f(7)]) + } + + #[inline] + fn extract(&self, lane: usize) -> Self::Value { + debug_assert!(lane < FP64_WIDTH); + self.0[lane] + } +} + +impl PackedField for PackedFp64Avx512

{ + type Scalar = Fp64

; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self([value; FP64_WIDTH]) + } +} + +/// Number of `Fp128` lanes in an AVX-512 packed vector. +pub const FP128_WIDTH: usize = 8; + +/// AVX-512 packed arithmetic for `Fp128

`, 8 lanes in SoA layout. +/// +/// Stores 8 elements as separate `lo` and `hi` `u64` arrays, enabling +/// vectorized add/sub via `__m512i`. Mul remains scalar per-lane. +#[derive(Clone, Copy)] +pub struct PackedFp128Avx512 { + lo: [u64; FP128_WIDTH], + hi: [u64; FP128_WIDTH], +} + +impl PackedFp128Avx512

{ + const P_LO: u64 = P as u64; + const P_HI: u64 = (P >> 64) as u64; +} + +impl Default for PackedFp128Avx512

{ + #[inline] + fn default() -> Self { + Self { + lo: [0; FP128_WIDTH], + hi: [0; FP128_WIDTH], + } + } +} + +impl fmt::Debug for PackedFp128Avx512

{ + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + let elems: Vec<_> = (0..FP128_WIDTH).map(|i| self.extract(i)).collect(); + f.debug_tuple("PackedFp128Avx512").field(&elems).finish() + } +} + +impl PartialEq for PackedFp128Avx512

{ + #[inline] + fn eq(&self, other: &Self) -> bool { + self.lo == other.lo && self.hi == other.hi + } +} + +impl Eq for PackedFp128Avx512

{} + +impl Add for PackedFp128Avx512

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + unsafe { + let a_lo = _mm512_loadu_si512(self.lo.as_ptr().cast()); + let a_hi = _mm512_loadu_si512(self.hi.as_ptr().cast()); + let b_lo = _mm512_loadu_si512(rhs.lo.as_ptr().cast()); + let b_hi = _mm512_loadu_si512(rhs.hi.as_ptr().cast()); + let p_lo = _mm512_set1_epi64(Self::P_LO as i64); + let p_hi = _mm512_set1_epi64(Self::P_HI as i64); + let one = _mm512_set1_epi64(1); + + // 128-bit add: (sum_hi, sum_lo) = (a_hi, a_lo) + (b_hi, b_lo) + let sum_lo = _mm512_add_epi64(a_lo, b_lo); + let carry_lo = _mm512_cmplt_epu64_mask(sum_lo, a_lo); + let hi_tmp = _mm512_add_epi64(a_hi, b_hi); + let ov1 = _mm512_cmplt_epu64_mask(hi_tmp, a_hi); + let sum_hi = _mm512_mask_add_epi64(hi_tmp, carry_lo, hi_tmp, one); + let ov2 = _mm512_cmplt_epu64_mask(sum_hi, hi_tmp); + let carry_128 = ov1 | ov2; + + // 128-bit subtract P: (red_hi, red_lo) = (sum_hi, sum_lo) - P + let red_lo = _mm512_sub_epi64(sum_lo, p_lo); + let borrow_lo = _mm512_cmplt_epu64_mask(sum_lo, p_lo); + let red_hi_tmp = _mm512_sub_epi64(sum_hi, p_hi); + let bw1 = _mm512_cmplt_epu64_mask(sum_hi, p_hi); + let red_hi = _mm512_mask_sub_epi64(red_hi_tmp, borrow_lo, red_hi_tmp, one); + let bw2 = _mm512_cmplt_epu64_mask(red_hi_tmp, _mm512_maskz_mov_epi64(borrow_lo, one)); + let borrow = bw1 | bw2; + + // Use reduced if: overflow happened OR subtraction didn't borrow + let use_reduced = carry_128 | !borrow; + let out_lo = _mm512_mask_blend_epi64(use_reduced, sum_lo, red_lo); + let out_hi = _mm512_mask_blend_epi64(use_reduced, sum_hi, red_hi); + + let mut result = Self::default(); + _mm512_storeu_si512(result.lo.as_mut_ptr().cast(), out_lo); + _mm512_storeu_si512(result.hi.as_mut_ptr().cast(), out_hi); + result + } + } +} + +impl Sub for PackedFp128Avx512

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + unsafe { + let a_lo = _mm512_loadu_si512(self.lo.as_ptr().cast()); + let a_hi = _mm512_loadu_si512(self.hi.as_ptr().cast()); + let b_lo = _mm512_loadu_si512(rhs.lo.as_ptr().cast()); + let b_hi = _mm512_loadu_si512(rhs.hi.as_ptr().cast()); + let p_lo = _mm512_set1_epi64(Self::P_LO as i64); + let p_hi = _mm512_set1_epi64(Self::P_HI as i64); + let one = _mm512_set1_epi64(1); + + // 128-bit sub: (diff_hi, diff_lo) = (a_hi, a_lo) - (b_hi, b_lo) + let diff_lo = _mm512_sub_epi64(a_lo, b_lo); + let borrow_lo = _mm512_cmplt_epu64_mask(a_lo, b_lo); + let hi_tmp = _mm512_sub_epi64(a_hi, b_hi); + let bw1 = _mm512_cmplt_epu64_mask(a_hi, b_hi); + let diff_hi = _mm512_mask_sub_epi64(hi_tmp, borrow_lo, hi_tmp, one); + let bw2 = _mm512_cmplt_epu64_mask(hi_tmp, _mm512_maskz_mov_epi64(borrow_lo, one)); + let borrow_128 = bw1 | bw2; + + // Correction: add P back where underflow occurred + let corr_lo = _mm512_add_epi64(diff_lo, p_lo); + let carry_lo = _mm512_cmplt_epu64_mask(corr_lo, diff_lo); + let corr_hi = _mm512_add_epi64(diff_hi, p_hi); + let corr_hi = _mm512_mask_add_epi64(corr_hi, carry_lo, corr_hi, one); + + let out_lo = _mm512_mask_blend_epi64(borrow_128, diff_lo, corr_lo); + let out_hi = _mm512_mask_blend_epi64(borrow_128, diff_hi, corr_hi); + + let mut result = Self::default(); + _mm512_storeu_si512(result.lo.as_mut_ptr().cast(), out_lo); + _mm512_storeu_si512(result.hi.as_mut_ptr().cast(), out_hi); + result + } + } +} + +impl Mul for PackedFp128Avx512

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + let mut out = Self::default(); + for i in 0..FP128_WIDTH { + let a = Fp128::

([self.lo[i], self.hi[i]]); + let b = Fp128::

([rhs.lo[i], rhs.hi[i]]); + let r = a * b; + out.lo[i] = r.0[0]; + out.hi[i] = r.0[1]; + } + out + } +} + +impl PackedValue for PackedFp128Avx512

{ + type Value = Fp128

; + const WIDTH: usize = FP128_WIDTH; + + #[inline] + fn from_fn(mut f: F) -> Self + where + F: FnMut(usize) -> Self::Value, + { + let mut lo = [0u64; FP128_WIDTH]; + let mut hi = [0u64; FP128_WIDTH]; + for i in 0..FP128_WIDTH { + let v = f(i); + lo[i] = v.0[0]; + hi[i] = v.0[1]; + } + Self { lo, hi } + } + + #[inline] + fn extract(&self, lane: usize) -> Self::Value { + debug_assert!(lane < FP128_WIDTH); + Fp128([self.lo[lane], self.hi[lane]]) + } +} + +impl PackedField for PackedFp128Avx512

{ + type Scalar = Fp128

; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self { + lo: [value.0[0]; FP128_WIDTH], + hi: [value.0[1]; FP128_WIDTH], + } + } +} diff --git a/src/algebra/fields/packed_neon.rs b/src/algebra/fields/packed_neon.rs new file mode 100644 index 00000000..aeeea0ef --- /dev/null +++ b/src/algebra/fields/packed_neon.rs @@ -0,0 +1,731 @@ +//! AArch64 NEON packed backends for Fp32, Fp64, Fp128. + +use super::packed::{PackedField, PackedValue}; +use crate::algebra::fields::{Fp128, Fp32, Fp64}; +use crate::FieldCore; +use core::arch::aarch64::{ + uint32x2_t, uint32x4_t, uint64x2_t, vaddq_u32, vaddq_u64, vandq_u64, vbslq_u32, vbslq_u64, + vcgtq_u64, vcltq_u32, vcltq_u64, vcombine_u32, vdup_n_u32, vdupq_n_s64, vdupq_n_u32, + vdupq_n_u64, veorq_u64, vget_low_u32, vminq_u32, vmovn_u64, vmull_high_u32, vmull_u32, + vorrq_u64, vshlq_u64, vsubq_u32, vsubq_u64, +}; +use core::fmt; +use core::mem::transmute; +use core::ops::{Add, Mul, Sub}; + +/// Number of packed `Fp128` lanes in this backend. +pub const WIDTH: usize = 2; + +/// True SoA layout for two packed `Fp128` lanes. +/// +/// `lo = [lane0.lo, lane1.lo]` +/// `hi = [lane0.hi, lane1.hi]` +#[derive(Clone, Copy)] +pub struct PackedFp128Neon { + lo: [u64; 2], + hi: [u64; 2], +} + +#[inline(always)] +fn to_vec(x: [u64; 2]) -> uint64x2_t { + unsafe { transmute::<[u64; 2], uint64x2_t>(x) } +} + +#[inline(always)] +fn from_vec(v: uint64x2_t) -> [u64; 2] { + unsafe { transmute::(v) } +} + +#[inline(always)] +fn mask_to_bit(mask: uint64x2_t) -> uint64x2_t { + // SAFETY: NEON intrinsics are available under this cfg. + unsafe { vandq_u64(mask, vdupq_n_u64(1)) } +} + +#[inline(always)] +const fn modulus_lo() -> u64 { + P as u64 +} + +#[inline(always)] +const fn modulus_hi() -> u64 { + (P >> 64) as u64 +} + +#[inline(always)] +const fn is_pow2_u64(x: u64) -> bool { + x != 0 && (x & (x - 1)) == 0 +} + +#[inline(always)] +const fn log2_pow2_u64(mut x: u64) -> u32 { + let mut k = 0u32; + while x > 1 { + x >>= 1; + k += 1; + } + k +} + +impl PackedFp128Neon

{ + const C: u128 = { + let c = 0u128.wrapping_sub(P); + assert!(P != 0, "modulus must be nonzero"); + assert!(P & 1 == 1, "modulus must be odd"); + assert!(c < (1u128 << 64), "P must be 2^128 - c with c < 2^64"); + assert!( + c * (c + 1) < P, + "C(C+1) < P required for fused canonicalize" + ); + c + }; + const C_LO: u64 = Self::C as u64; + const C_SHIFT_KIND: i8 = { + let c = Self::C_LO; + if c > 1 && is_pow2_u64(c - 1) { + 1 + } else if c == u64::MAX || is_pow2_u64(c + 1) { + -1 + } else { + 0 + } + }; + const C_SHIFT: u32 = { + let c = Self::C_LO; + if Self::C_SHIFT_KIND == 1 { + log2_pow2_u64(c - 1) + } else if Self::C_SHIFT_KIND == -1 { + if c == u64::MAX { + 64 + } else { + log2_pow2_u64(c + 1) + } + } else { + 0 + } + }; + + #[inline(always)] + fn mul_wide_u64(a: u64, b: u64) -> (u64, u64) { + let prod = (a as u128) * (b as u128); + (prod as u64, (prod >> 64) as u64) + } + + #[inline(always)] + fn mul_c_wide(x: u64) -> (u64, u64) { + if Self::C_SHIFT_KIND == 1 { + let v = ((x as u128) << Self::C_SHIFT) + x as u128; + (v as u64, (v >> 64) as u64) + } else if Self::C_SHIFT_KIND == -1 { + let v = ((x as u128) << Self::C_SHIFT) - x as u128; + (v as u64, (v >> 64) as u64) + } else { + Self::mul_wide_u64(Self::C_LO, x) + } + } + + #[inline(always)] + fn fold2_canonicalize(t0: u64, t1: u64, t2: u64) -> (u64, u64) { + let (ct2_lo, ct2_hi) = Self::mul_c_wide(t2); + + let (s0, carry0) = t0.overflowing_add(ct2_lo); + let (s1a, carry1a) = t1.overflowing_add(ct2_hi); + let (s1, carry1b) = s1a.overflowing_add(carry0 as u64); + let overflow = carry1a | carry1b; + + let (r0, carry2) = s0.overflowing_add(Self::C_LO); + let (r1, carry3) = s1.overflowing_add(carry2 as u64); + + if overflow | carry3 { + (r0, r1) + } else { + (s0, s1) + } + } + + #[inline(always)] + fn mul_raw_lane(a0: u64, a1: u64, b0: u64, b1: u64) -> (u64, u64) { + let (p00_lo, p00_hi) = Self::mul_wide_u64(a0, b0); + let (p01_lo, p01_hi) = Self::mul_wide_u64(a0, b1); + let (p10_lo, p10_hi) = Self::mul_wide_u64(a1, b0); + let (p11_lo, p11_hi) = Self::mul_wide_u64(a1, b1); + + let row1 = p00_hi as u128 + p01_lo as u128 + p10_lo as u128; + let r0 = p00_lo; + let r1 = row1 as u64; + let carry1 = (row1 >> 64) as u64; + + let row2 = p01_hi as u128 + p10_hi as u128 + p11_lo as u128 + carry1 as u128; + let r2 = row2 as u64; + let carry2 = (row2 >> 64) as u64; + + let row3 = p11_hi as u128 + carry2 as u128; + let r3 = row3 as u64; + debug_assert_eq!(row3 >> 64, 0); + + let (cr2_lo, cr2_hi) = Self::mul_c_wide(r2); + let (cr3_lo, cr3_hi) = Self::mul_c_wide(r3); + + let t0_sum = r0 as u128 + cr2_lo as u128; + let t0 = t0_sum as u64; + let carryf = (t0_sum >> 64) as u64; + + let t1_sum = r1 as u128 + cr2_hi as u128 + cr3_lo as u128 + carryf as u128; + let t1 = t1_sum as u64; + + let t2_sum = cr3_hi as u128 + (t1_sum >> 64); + let t2 = t2_sum as u64; + debug_assert_eq!(t2_sum >> 64, 0); + + Self::fold2_canonicalize(t0, t1, t2) + } +} + +impl Default for PackedFp128Neon

{ + #[inline] + fn default() -> Self { + Self::broadcast(Fp128::zero()) + } +} + +impl fmt::Debug for PackedFp128Neon

{ + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + f.debug_tuple("PackedFp128Neon") + .field(&[self.extract(0), self.extract(1)]) + .finish() + } +} + +impl PartialEq for PackedFp128Neon

{ + #[inline] + fn eq(&self, other: &Self) -> bool { + self.extract(0) == other.extract(0) && self.extract(1) == other.extract(1) + } +} + +impl Eq for PackedFp128Neon

{} + +impl PackedValue for PackedFp128Neon

{ + type Value = Fp128

; + const WIDTH: usize = WIDTH; + + #[inline] + fn from_fn(mut f: F) -> Self + where + F: FnMut(usize) -> Self::Value, + { + let x0 = f(0); + let x1 = f(1); + Self { + lo: [x0.0[0], x1.0[0]], + hi: [x0.0[1], x1.0[1]], + } + } + + #[inline] + fn extract(&self, lane: usize) -> Self::Value { + debug_assert!(lane < WIDTH); + Fp128([self.lo[lane], self.hi[lane]]) + } +} + +impl Add for PackedFp128Neon

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + let lo_a = to_vec(self.lo); + let hi_a = to_vec(self.hi); + let lo_b = to_vec(rhs.lo); + let hi_b = to_vec(rhs.hi); + + let (out_lo, out_hi) = unsafe { + let p_lo = vdupq_n_u64(modulus_lo::

()); + let p_hi = vdupq_n_u64(modulus_hi::

()); + + let sum_lo = vaddq_u64(lo_a, lo_b); + let carry_lo = mask_to_bit(vcltq_u64(sum_lo, lo_a)); + + let hi_tmp = vaddq_u64(hi_a, hi_b); + let carry_hi1 = vcltq_u64(hi_tmp, hi_a); + let sum_hi = vaddq_u64(hi_tmp, carry_lo); + let carry_hi2 = vcltq_u64(sum_hi, hi_tmp); + let carry_128 = vorrq_u64(carry_hi1, carry_hi2); + + let red_lo = vsubq_u64(sum_lo, p_lo); + let borrow_lo = mask_to_bit(vcgtq_u64(p_lo, sum_lo)); + + let red_hi_tmp = vsubq_u64(sum_hi, p_hi); + let borrow_hi1 = vcgtq_u64(p_hi, sum_hi); + let red_hi = vsubq_u64(red_hi_tmp, borrow_lo); + let borrow_hi2 = vcltq_u64(red_hi_tmp, borrow_lo); + let borrow = vorrq_u64(borrow_hi1, borrow_hi2); + + let not_borrow = veorq_u64(borrow, vdupq_n_u64(u64::MAX)); + let use_reduced = vorrq_u64(carry_128, not_borrow); + let out_lo = vbslq_u64(use_reduced, red_lo, sum_lo); + let out_hi = vbslq_u64(use_reduced, red_hi, sum_hi); + (out_lo, out_hi) + }; + + Self { + lo: from_vec(out_lo), + hi: from_vec(out_hi), + } + } +} + +impl Sub for PackedFp128Neon

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + let lo_a = to_vec(self.lo); + let hi_a = to_vec(self.hi); + let lo_b = to_vec(rhs.lo); + let hi_b = to_vec(rhs.hi); + + let (out_lo, out_hi) = unsafe { + let p_lo = vdupq_n_u64(modulus_lo::

()); + let p_hi = vdupq_n_u64(modulus_hi::

()); + + let diff_lo = vsubq_u64(lo_a, lo_b); + let borrow_lo = mask_to_bit(vcltq_u64(lo_a, lo_b)); + + let diff_hi_tmp = vsubq_u64(hi_a, hi_b); + let borrow_hi1 = vcltq_u64(hi_a, hi_b); + let diff_hi = vsubq_u64(diff_hi_tmp, borrow_lo); + let borrow_hi2 = vcltq_u64(diff_hi_tmp, borrow_lo); + let borrow_128 = vorrq_u64(borrow_hi1, borrow_hi2); + + let corr_lo = vaddq_u64(diff_lo, p_lo); + let carry_lo = mask_to_bit(vcltq_u64(corr_lo, diff_lo)); + + let corr_hi_tmp = vaddq_u64(diff_hi, p_hi); + let corr_hi = vaddq_u64(corr_hi_tmp, carry_lo); + + let out_lo = vbslq_u64(borrow_128, corr_lo, diff_lo); + let out_hi = vbslq_u64(borrow_128, corr_hi, diff_hi); + (out_lo, out_hi) + }; + + Self { + lo: from_vec(out_lo), + hi: from_vec(out_hi), + } + } +} + +impl Mul for PackedFp128Neon

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + let (o0_lo, o0_hi) = Self::mul_raw_lane(self.lo[0], self.hi[0], rhs.lo[0], rhs.hi[0]); + let (o1_lo, o1_hi) = Self::mul_raw_lane(self.lo[1], self.hi[1], rhs.lo[1], rhs.hi[1]); + + Self { + lo: [o0_lo, o1_lo], + hi: [o0_hi, o1_hi], + } + } +} + +impl PackedField for PackedFp128Neon

{ + type Scalar = Fp128

; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self::from_fn(|_| value) + } +} + +/// Number of packed `Fp32` lanes. +pub const FP32_WIDTH: usize = 4; + +/// NEON packed `Fp32` backend: 4 lanes in `uint32x4_t`. +#[derive(Clone, Copy)] +pub struct PackedFp32Neon { + vals: [u32; 4], +} + +#[inline(always)] +fn to_vec32(x: [u32; 4]) -> uint32x4_t { + unsafe { transmute::<[u32; 4], uint32x4_t>(x) } +} + +#[inline(always)] +fn from_vec32(v: uint32x4_t) -> [u32; 4] { + unsafe { transmute::(v) } +} + +impl PackedFp32Neon

{ + const BITS: u32 = 32 - P.leading_zeros(); + + const C: u32 = { + let c = if Self::BITS == 32 { + 0u32.wrapping_sub(P) + } else { + (1u32 << Self::BITS) - P + }; + assert!(P != 0, "modulus must be nonzero"); + assert!(P & 1 == 1, "modulus must be odd"); + assert!( + (c as u64) * (c as u64 + 1) < P as u64, + "C(C+1) < P required for fused canonicalize" + ); + c + }; + + const MASK_U64: u64 = if Self::BITS == 32 { + u32::MAX as u64 + } else { + (1u64 << Self::BITS) - 1 + }; + + #[inline(always)] + fn mul_c_u64(hi: uint64x2_t, c: uint32x2_t) -> uint64x2_t { + unsafe { + let hi_narrow = vmovn_u64(hi); + vmull_u32(hi_narrow, c) + } + } + + #[inline(always)] + fn solinas_reduce(prod_lo: uint64x2_t, prod_hi: uint64x2_t) -> uint32x4_t { + unsafe { + let mask = vdupq_n_u64(Self::MASK_U64); + let neg_bits = vdupq_n_s64(-(Self::BITS as i64)); + let c = vdup_n_u32(Self::C); + + let f1_lo = vaddq_u64( + vandq_u64(prod_lo, mask), + Self::mul_c_u64(vshlq_u64(prod_lo, neg_bits), c), + ); + let f1_hi = vaddq_u64( + vandq_u64(prod_hi, mask), + Self::mul_c_u64(vshlq_u64(prod_hi, neg_bits), c), + ); + + let f2_lo = vaddq_u64( + vandq_u64(f1_lo, mask), + Self::mul_c_u64(vshlq_u64(f1_lo, neg_bits), c), + ); + let f2_hi = vaddq_u64( + vandq_u64(f1_hi, mask), + Self::mul_c_u64(vshlq_u64(f1_hi, neg_bits), c), + ); + + if Self::BITS < 32 { + let result = vcombine_u32(vmovn_u64(f2_lo), vmovn_u64(f2_hi)); + let p = vdupq_n_u32(P); + vminq_u32(result, vsubq_u32(result, p)) + } else { + let p_u64 = vdupq_n_u64(P as u64); + + let red_lo = vsubq_u64(f2_lo, p_u64); + let keep_lo = vcltq_u64(f2_lo, p_u64); + let out_lo = vbslq_u64(keep_lo, f2_lo, red_lo); + + let red_hi = vsubq_u64(f2_hi, p_u64); + let keep_hi = vcltq_u64(f2_hi, p_u64); + let out_hi = vbslq_u64(keep_hi, f2_hi, red_hi); + + vcombine_u32(vmovn_u64(out_lo), vmovn_u64(out_hi)) + } + } + } +} + +impl Default for PackedFp32Neon

{ + #[inline] + fn default() -> Self { + Self { vals: [0; 4] } + } +} + +impl fmt::Debug for PackedFp32Neon

{ + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + f.debug_tuple("PackedFp32Neon").field(&self.vals).finish() + } +} + +impl PartialEq for PackedFp32Neon

{ + #[inline] + fn eq(&self, other: &Self) -> bool { + self.vals == other.vals + } +} + +impl Eq for PackedFp32Neon

{} + +impl Add for PackedFp32Neon

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + let a = to_vec32(self.vals); + let b = to_vec32(rhs.vals); + let result = unsafe { + let p = vdupq_n_u32(P); + if Self::BITS <= 31 { + let t = vaddq_u32(a, b); + vminq_u32(t, vsubq_u32(t, p)) + } else { + let c = vdupq_n_u32(Self::C); + let t = vaddq_u32(a, b); + let overflow = vcltq_u32(t, a); + let t_plus_c = vaddq_u32(t, c); + let no_of = vminq_u32(t, vsubq_u32(t, p)); + vbslq_u32(overflow, t_plus_c, no_of) + } + }; + Self { + vals: from_vec32(result), + } + } +} + +impl Sub for PackedFp32Neon

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + let a = to_vec32(self.vals); + let b = to_vec32(rhs.vals); + let result = unsafe { + let p = vdupq_n_u32(P); + if Self::BITS <= 31 { + let t = vsubq_u32(a, b); + vminq_u32(t, vaddq_u32(t, p)) + } else { + let t = vsubq_u32(a, b); + let underflow = vcltq_u32(a, b); + vbslq_u32(underflow, vaddq_u32(t, p), t) + } + }; + Self { + vals: from_vec32(result), + } + } +} + +impl Mul for PackedFp32Neon

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + let a = to_vec32(self.vals); + let b = to_vec32(rhs.vals); + let result = unsafe { + let prod_lo = vmull_u32(vget_low_u32(a), vget_low_u32(b)); + let prod_hi = vmull_high_u32(a, b); + Self::solinas_reduce(prod_lo, prod_hi) + }; + Self { + vals: from_vec32(result), + } + } +} + +impl PackedValue for PackedFp32Neon

{ + type Value = Fp32

; + const WIDTH: usize = FP32_WIDTH; + + #[inline] + fn from_fn(mut f: F) -> Self + where + F: FnMut(usize) -> Self::Value, + { + Self { + vals: [f(0).0, f(1).0, f(2).0, f(3).0], + } + } + + #[inline] + fn extract(&self, lane: usize) -> Self::Value { + debug_assert!(lane < FP32_WIDTH); + Fp32(self.vals[lane]) + } +} + +impl PackedField for PackedFp32Neon

{ + type Scalar = Fp32

; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self { vals: [value.0; 4] } + } +} + +/// Number of packed `Fp64` lanes. +pub const FP64_WIDTH: usize = 2; + +/// NEON packed `Fp64` backend: 2 lanes in `uint64x2_t`. +#[derive(Clone, Copy)] +pub struct PackedFp64Neon { + vals: [u64; 2], +} + +impl PackedFp64Neon

{ + const BITS: u32 = 64 - P.leading_zeros(); + + const C_LO: u64 = { + let c = if Self::BITS == 64 { + 0u64.wrapping_sub(P) + } else { + (1u64 << Self::BITS) - P + }; + assert!(P != 0, "modulus must be nonzero"); + assert!(P & 1 == 1, "modulus must be odd"); + c + }; + + const MASK64: u64 = if Self::BITS < 64 { + (1u64 << Self::BITS) - 1 + } else { + u64::MAX + }; + + const MASK_U128: u128 = if Self::BITS == 64 { + u64::MAX as u128 + } else { + (1u128 << Self::BITS) - 1 + }; + + const FOLD_IN_U64: bool = + Self::BITS < 64 && (Self::C_LO as u128) < (1u128 << (64 - Self::BITS)); + + #[inline(always)] + fn mul_c_narrow(x: u64) -> u64 { + Self::C_LO.wrapping_mul(x) + } + + #[inline(always)] + fn reduce_product(x: u128) -> u64 { + if Self::FOLD_IN_U64 { + let lo = x as u64; + let hi = (x >> 64) as u64; + let high = (lo >> Self::BITS) | (hi << (64 - Self::BITS)); + let f1 = (lo & Self::MASK64).wrapping_add(Self::mul_c_narrow(high)); + let f2 = (f1 & Self::MASK64).wrapping_add(Self::mul_c_narrow(f1 >> Self::BITS)); + let reduced = f2.wrapping_sub(P); + let borrow = reduced >> 63; + reduced.wrapping_add(borrow.wrapping_neg() & P) + } else { + let f1 = + (x & Self::MASK_U128) + (Self::C_LO as u128) * ((x >> Self::BITS) as u64 as u128); + let f2 = + (f1 & Self::MASK_U128) + (Self::C_LO as u128) * ((f1 >> Self::BITS) as u64 as u128); + let reduced = f2.wrapping_sub(P as u128); + let borrow = reduced >> 127; + reduced.wrapping_add(borrow.wrapping_neg() & (P as u128)) as u64 + } + } +} + +impl Default for PackedFp64Neon

{ + #[inline] + fn default() -> Self { + Self { vals: [0; 2] } + } +} + +impl fmt::Debug for PackedFp64Neon

{ + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + f.debug_tuple("PackedFp64Neon").field(&self.vals).finish() + } +} + +impl PartialEq for PackedFp64Neon

{ + #[inline] + fn eq(&self, other: &Self) -> bool { + self.vals == other.vals + } +} + +impl Eq for PackedFp64Neon

{} + +impl Add for PackedFp64Neon

{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + let a = to_vec(self.vals); + let b = to_vec(rhs.vals); + let result = unsafe { + let p = vdupq_n_u64(P); + if Self::BITS <= 62 { + let s = vaddq_u64(a, b); + let r = vsubq_u64(s, p); + let borrow = vcltq_u64(s, p); + vbslq_u64(borrow, s, r) + } else { + let s = vaddq_u64(a, b); + let overflow = vcltq_u64(s, a); + let c = vdupq_n_u64(Self::C_LO); + let s_plus_c = vaddq_u64(s, c); + let s_minus_p = vsubq_u64(s, p); + let borrow = vcltq_u64(s, p); + let no_of = vbslq_u64(borrow, s, s_minus_p); + vbslq_u64(overflow, s_plus_c, no_of) + } + }; + Self { + vals: from_vec(result), + } + } +} + +impl Sub for PackedFp64Neon

{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + let a = to_vec(self.vals); + let b = to_vec(rhs.vals); + let result = unsafe { + let p = vdupq_n_u64(P); + let d = vsubq_u64(a, b); + let underflow = vcltq_u64(a, b); + vbslq_u64(underflow, vaddq_u64(d, p), d) + }; + Self { + vals: from_vec(result), + } + } +} + +impl Mul for PackedFp64Neon

{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + let x0 = (self.vals[0] as u128) * (rhs.vals[0] as u128); + let x1 = (self.vals[1] as u128) * (rhs.vals[1] as u128); + let r0 = Self::reduce_product(x0); + let r1 = Self::reduce_product(x1); + Self { vals: [r0, r1] } + } +} + +impl PackedValue for PackedFp64Neon

{ + type Value = Fp64

; + const WIDTH: usize = FP64_WIDTH; + + #[inline] + fn from_fn(mut f: F) -> Self + where + F: FnMut(usize) -> Self::Value, + { + Self { + vals: [f(0).0, f(1).0], + } + } + + #[inline] + fn extract(&self, lane: usize) -> Self::Value { + debug_assert!(lane < FP64_WIDTH); + Fp64(self.vals[lane]) + } +} + +impl PackedField for PackedFp64Neon

{ + type Scalar = Fp64

; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self { vals: [value.0; 2] } + } +} diff --git a/src/algebra/fields/pseudo_mersenne.rs b/src/algebra/fields/pseudo_mersenne.rs new file mode 100644 index 00000000..17920899 --- /dev/null +++ b/src/algebra/fields/pseudo_mersenne.rs @@ -0,0 +1,177 @@ +//! `2^k - offset` pseudo-Mersenne registry and field aliases. +//! +//! This module models the specific flavor where each modulus is the smallest +//! prime below `2^k` with `q % 8 == 5`, written as `q = 2^k - offset`. + +use super::{Fp128, Fp32, Fp64}; + +/// Offset table (`q = 2^k - offset[k]`) imported from `labrador/data.py`. +pub const POW2_OFFSET_TABLE: [i16; 256] = [ + -1, -1, -1, 3, 3, 3, 3, 19, 27, 3, 3, 19, 3, 75, 3, 19, 99, 91, 11, 19, 3, 19, 3, 27, 3, 91, + 27, 115, 299, 3, 35, 19, 99, 355, 131, 451, 243, 123, 107, 19, 195, 75, 11, 67, 539, 139, 635, + 115, 59, 123, 27, 139, 395, 315, 131, 67, 27, 195, 27, 99, 107, 259, 171, 259, 59, 115, 203, + 19, 83, 19, 35, 411, 107, 475, 35, 427, 123, 43, 11, 67, 1307, 51, 315, 139, 35, 19, 35, 67, + 299, 99, 75, 315, 83, 51, 3, 211, 147, 595, 51, 115, 99, 99, 483, 339, 395, 139, 1187, 171, 59, + 91, 195, 835, 75, 211, 11, 67, 3, 451, 563, 867, 395, 531, 3, 67, 59, 579, 203, 507, 275, 315, + 27, 315, 347, 99, 603, 795, 243, 339, 203, 187, 27, 171, 1491, 355, 83, 355, 1371, 387, 347, + 99, 3, 195, 539, 171, 243, 499, 195, 19, 155, 91, 75, 1011, 627, 867, 155, 115, 1811, 771, + 1467, 643, 195, 19, 155, 531, 3, 267, 563, 339, 563, 507, 107, 283, 267, 147, 59, 339, 371, + 1411, 363, 819, 11, 19, 915, 123, 75, 915, 459, 75, 627, 459, 75, 1035, 195, 187, 1515, 1219, + 1443, 91, 299, 451, 171, 1099, 99, 3, 395, 1147, 683, 675, 243, 355, 395, 3, 875, 235, 363, + 1131, 155, 835, 723, 91, 27, 235, 875, 3, 83, 259, 875, 1515, 731, 531, 467, 819, 267, 475, + 1923, 163, 107, 411, 387, 75, 2331, 355, 1515, 1723, 1427, 19, +]; + +/// Maximum supported offset in this `2^k - offset` specialization. +pub const POW2_OFFSET_MAX: u128 = 1u128 << 16; + +/// Current active bit-size bound for concrete field aliases in this phase. +pub const POW2_OFFSET_IMPLEMENTED_MAX_BITS: u32 = 128; + +/// Metadata describing a `2^k - offset` pseudo-Mersenne modulus. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct Pow2OffsetPrimeSpec { + /// `k` in `2^k - offset`. + pub bits: u32, + /// `offset` in `2^k - offset`. + pub offset: u16, + /// Modulus value. + pub modulus: u128, +} + +/// Return table offset for `q = 2^k - offset` when available and positive. +pub const fn pow2_offset(bits: u32) -> Option { + if bits as usize >= POW2_OFFSET_TABLE.len() { + return None; + } + let offset = POW2_OFFSET_TABLE[bits as usize]; + if offset <= 0 { + None + } else { + Some(offset as u16) + } +} + +/// Compute `2^k - offset` for `k <= 128`. +pub const fn pseudo_mersenne_modulus(bits: u32, offset: u128) -> Option { + if bits == 0 || bits > 128 || offset == 0 { + return None; + } + if bits == 128 { + Some(u128::MAX - (offset - 1)) + } else { + Some((1u128 << bits) - offset) + } +} + +/// Check whether `(k, offset)` is accepted by the `2^k - offset` policy. +pub const fn is_pow2_offset(bits: u32, offset: u128) -> bool { + if bits > POW2_OFFSET_IMPLEMENTED_MAX_BITS || offset > POW2_OFFSET_MAX { + return false; + } + match pow2_offset(bits) { + Some(qoff) => (qoff as u128) == offset, + None => false, + } +} + +/// `offset` for `k = 24`. +pub const POW2_OFFSET_24: u16 = 3; +/// `offset` for `k = 30`. +pub const POW2_OFFSET_30: u16 = 35; +/// `offset` for `k = 31`. +pub const POW2_OFFSET_31: u16 = 19; +/// `offset` for `k = 32`. +pub const POW2_OFFSET_32: u16 = 99; +/// `offset` for `k = 40`. +pub const POW2_OFFSET_40: u16 = 195; +/// `offset` for `k = 48`. +pub const POW2_OFFSET_48: u16 = 59; +/// `offset` for `k = 56`. +pub const POW2_OFFSET_56: u16 = 27; +/// `offset` for `k = 64`. +pub const POW2_OFFSET_64: u16 = 59; +/// `offset` for `k = 128`. +pub const POW2_OFFSET_128: u16 = 275; + +/// `2^24 - 3`. +pub const POW2_OFFSET_MODULUS_24: u32 = ((1u128 << 24) - (POW2_OFFSET_24 as u128)) as u32; +/// `2^30 - 35`. +pub const POW2_OFFSET_MODULUS_30: u32 = ((1u128 << 30) - (POW2_OFFSET_30 as u128)) as u32; +/// `2^31 - 19`. +pub const POW2_OFFSET_MODULUS_31: u32 = ((1u128 << 31) - (POW2_OFFSET_31 as u128)) as u32; +/// `2^32 - 99`. +pub const POW2_OFFSET_MODULUS_32: u32 = ((1u128 << 32) - (POW2_OFFSET_32 as u128)) as u32; +/// `2^40 - 195`. +pub const POW2_OFFSET_MODULUS_40: u64 = ((1u128 << 40) - (POW2_OFFSET_40 as u128)) as u64; +/// `2^48 - 59`. +pub const POW2_OFFSET_MODULUS_48: u64 = ((1u128 << 48) - (POW2_OFFSET_48 as u128)) as u64; +/// `2^56 - 27`. +pub const POW2_OFFSET_MODULUS_56: u64 = ((1u128 << 56) - (POW2_OFFSET_56 as u128)) as u64; +/// `2^64 - 59`. +pub const POW2_OFFSET_MODULUS_64: u64 = u64::MAX - ((POW2_OFFSET_64 as u64) - 1); +/// `2^128 - 275`. +pub const POW2_OFFSET_MODULUS_128: u128 = u128::MAX - (POW2_OFFSET_128 as u128 - 1); + +/// Alias for `2^24 - offset`. +pub type Pow2Offset24Field = Fp32; +/// Alias for `2^30 - offset`. +pub type Pow2Offset30Field = Fp32; +/// Alias for `2^31 - offset`. +pub type Pow2Offset31Field = Fp32; +/// Alias for `2^32 - offset`. +pub type Pow2Offset32Field = Fp32; +/// Alias for `2^40 - offset`. +pub type Pow2Offset40Field = Fp64; +/// Alias for `2^48 - offset`. +pub type Pow2Offset48Field = Fp64; +/// Alias for `2^56 - offset`. +pub type Pow2Offset56Field = Fp64; +/// Alias for `2^64 - offset`. +pub type Pow2Offset64Field = Fp64; +/// Alias for `2^128 - offset`. +pub type Pow2Offset128Field = Fp128; + +/// `2^k - offset` profiles currently enabled in-code. +/// +/// Each listed modulus satisfies `q % 8 == 5`. +pub const POW2_OFFSET_PRIMES: [Pow2OffsetPrimeSpec; 7] = [ + Pow2OffsetPrimeSpec { + bits: 24, + offset: POW2_OFFSET_24, + modulus: POW2_OFFSET_MODULUS_24 as u128, + }, + Pow2OffsetPrimeSpec { + bits: 32, + offset: POW2_OFFSET_32, + modulus: POW2_OFFSET_MODULUS_32 as u128, + }, + Pow2OffsetPrimeSpec { + bits: 40, + offset: POW2_OFFSET_40, + modulus: POW2_OFFSET_MODULUS_40 as u128, + }, + Pow2OffsetPrimeSpec { + bits: 48, + offset: POW2_OFFSET_48, + modulus: POW2_OFFSET_MODULUS_48 as u128, + }, + Pow2OffsetPrimeSpec { + bits: 56, + offset: POW2_OFFSET_56, + modulus: POW2_OFFSET_MODULUS_56 as u128, + }, + Pow2OffsetPrimeSpec { + bits: 64, + offset: POW2_OFFSET_64, + modulus: POW2_OFFSET_MODULUS_64 as u128, + }, + Pow2OffsetPrimeSpec { + bits: 128, + offset: POW2_OFFSET_128, + modulus: POW2_OFFSET_MODULUS_128, + }, +]; + +// All PseudoMersenneField impls for Fp32/Fp64/Fp128 are blanket impls in +// their respective modules (fp32.rs, fp64.rs, fp128.rs). diff --git a/src/algebra/mod.rs b/src/algebra/mod.rs new file mode 100644 index 00000000..8a5cc194 --- /dev/null +++ b/src/algebra/mod.rs @@ -0,0 +1,34 @@ +//! Concrete algebra backends and arithmetic building blocks. +//! +//! This module includes: +//! - Generic prime fields and extensions (`fields`) +//! - Module and polynomial containers (`module`, `poly`) +//! - Low-level NTT and CRT+NTT arithmetic scaffolding (`ntt`) + +pub mod backend; +pub mod domains; +pub mod fields; +pub mod module; +pub mod ntt; +pub mod poly; +pub mod ring; + +// Flat re-exports for convenience. +pub use backend::{CrtReconstruct, NttPrimeOps, NttTransform, RingBackend, ScalarBackend}; +pub use domains::{CoeffDomain, CrtNttDomain}; +pub use fields::{ + is_pow2_offset, pow2_offset, pseudo_mersenne_modulus, Fp128, Fp128Packing, Fp2, Fp2Config, + Fp32, Fp32Packing, Fp4, Fp4Config, Fp64, Fp64Packing, HasPacking, NoPacking, PackedField, + PackedValue, Pow2Offset128Field, Pow2Offset24Field, Pow2Offset30Field, Pow2Offset31Field, + Pow2Offset32Field, Pow2Offset40Field, Pow2Offset48Field, Pow2Offset56Field, Pow2Offset64Field, + Pow2OffsetPrimeSpec, Prime128M13M4P0, Prime128M37P3P0, Prime128M52M3P0, Prime128M54P4P0, + Prime128M8M4M1M0, POW2_OFFSET_IMPLEMENTED_MAX_BITS, POW2_OFFSET_MAX, POW2_OFFSET_PRIMES, + POW2_OFFSET_TABLE, +}; +pub use module::VectorModule; +pub use ntt::tables; +pub use ntt::{LimbQ, MontCoeff, NttPrime, QData, RADIX_BITS}; +pub use ring::{ + CrtNttConvertibleField, CyclotomicCrtNtt, CyclotomicRing, SparseChallenge, + SparseChallengeConfig, +}; diff --git a/src/algebra/module.rs b/src/algebra/module.rs new file mode 100644 index 00000000..6cfdb554 --- /dev/null +++ b/src/algebra/module.rs @@ -0,0 +1,202 @@ +//! Simple module implementations. + +use super::fields::{Fp128, Fp32, Fp64}; +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; +use crate::{CanonicalField, FieldCore, FieldSampling, Module}; +use rand_core::RngCore; +use std::io::{Read, Write}; +use std::ops::{Add, Mul, Neg, Sub}; + +/// Fixed-length vector module over a scalar type `F`. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct VectorModule(pub [F; N]); + +impl VectorModule { + /// Construct the zero vector. + #[inline] + pub fn zero_vec() -> Self { + Self([F::zero(); N]) + } +} + +impl Add for VectorModule { + type Output = Self; + fn add(self, rhs: Self) -> Self::Output { + let mut out = self.0; + for (dst, src) in out.iter_mut().zip(rhs.0.iter()) { + *dst = *dst + *src; + } + Self(out) + } +} + +impl Sub for VectorModule { + type Output = Self; + fn sub(self, rhs: Self) -> Self::Output { + let mut out = self.0; + for (dst, src) in out.iter_mut().zip(rhs.0.iter()) { + *dst = *dst - *src; + } + Self(out) + } +} + +impl Neg for VectorModule { + type Output = Self; + fn neg(self) -> Self::Output { + let mut out = self.0; + for coeff in &mut out { + *coeff = -*coeff; + } + Self(out) + } +} + +impl<'a, F: FieldCore, const N: usize> Add<&'a Self> for VectorModule { + type Output = Self; + fn add(self, rhs: &'a Self) -> Self::Output { + self + *rhs + } +} + +impl<'a, F: FieldCore, const N: usize> Sub<&'a Self> for VectorModule { + type Output = Self; + fn sub(self, rhs: &'a Self) -> Self::Output { + self - *rhs + } +} + +impl Valid for VectorModule { + fn check(&self) -> Result<(), SerializationError> { + for x in self.0.iter() { + x.check()?; + } + Ok(()) + } +} + +impl HachiSerialize for VectorModule { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + for x in self.0.iter() { + x.serialize_with_mode(&mut writer, compress)?; + } + Ok(()) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.0.iter().map(|x| x.serialized_size(compress)).sum() + } +} + +impl HachiDeserialize for VectorModule { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let mut arr = [F::zero(); N]; + for coeff in &mut arr { + *coeff = F::deserialize_with_mode(&mut reader, compress, validate)?; + } + let out = Self(arr); + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +impl Module for VectorModule +where + F: FieldCore + + CanonicalField + + FieldSampling + + Valid + + Mul, Output = VectorModule> + + for<'a> Mul<&'a VectorModule, Output = VectorModule>, +{ + type Scalar = F; + + fn zero() -> Self { + Self::zero_vec() + } + + fn add(&self, rhs: &Self) -> Self { + *self + *rhs + } + + fn neg(&self) -> Self { + -*self + } + + fn scale(&self, k: &Self::Scalar) -> Self { + // Delegate to Scalar * VectorModule to satisfy the Module trait’s scalar bounds. + *k * *self + } + + fn random(rng: &mut R) -> Self { + Self(std::array::from_fn(|_| F::sample(rng))) + } +} + +// Scalar * VectorModule impls for our local prime field types. + +impl Mul, N>> for Fp32

{ + type Output = VectorModule, N>; + fn mul(self, rhs: VectorModule, N>) -> Self::Output { + let mut out = rhs.0; + for coeff in &mut out { + *coeff = self * *coeff; + } + VectorModule(out) + } +} + +impl<'a, const P: u32, const N: usize> Mul<&'a VectorModule, N>> for Fp32

{ + type Output = VectorModule, N>; + fn mul(self, rhs: &'a VectorModule, N>) -> Self::Output { + self * *rhs + } +} + +impl Mul, N>> for Fp64

{ + type Output = VectorModule, N>; + fn mul(self, rhs: VectorModule, N>) -> Self::Output { + let mut out = rhs.0; + for coeff in &mut out { + *coeff = self * *coeff; + } + VectorModule(out) + } +} + +impl<'a, const P: u64, const N: usize> Mul<&'a VectorModule, N>> for Fp64

{ + type Output = VectorModule, N>; + fn mul(self, rhs: &'a VectorModule, N>) -> Self::Output { + self * *rhs + } +} + +impl Mul, N>> for Fp128

{ + type Output = VectorModule, N>; + fn mul(self, rhs: VectorModule, N>) -> Self::Output { + let mut out = rhs.0; + for coeff in &mut out { + *coeff = self * *coeff; + } + VectorModule(out) + } +} + +impl<'a, const P: u128, const N: usize> Mul<&'a VectorModule, N>> for Fp128

{ + type Output = VectorModule, N>; + fn mul(self, rhs: &'a VectorModule, N>) -> Self::Output { + self * *rhs + } +} diff --git a/src/algebra/ntt/butterfly.rs b/src/algebra/ntt/butterfly.rs new file mode 100644 index 00000000..9f58da94 --- /dev/null +++ b/src/algebra/ntt/butterfly.rs @@ -0,0 +1,155 @@ +//! NTT butterfly transforms for negacyclic rings `Z_p[X]/(X^D + 1)`. +//! +//! Uses a merged negacyclic Cooley-Tukey / Gentleman-Sande butterfly where +//! the twist factors for `X^D + 1` are folded directly into the twiddles. +//! Twiddle factors are powers of `psi`, a primitive `2D`-th root of unity +//! (`psi^D = -1 mod p`), rather than a `D`-th root. +//! +//! TODO(perf): migrate twiddle tables to compile-time `const` arrays once +//! parameter sets are finalized. + +use super::prime::{MontCoeff, NttPrime}; + +/// Precomputed twiddle factors for a specific prime and degree `D`. +/// +/// `D` must be a power of two. +pub struct NttTwiddles { + /// Twiddle factors in Montgomery form, indexed by bit-reversed position. + /// `zetas[i] = from_canonical(psi^{brv(i)})` for `i = 0..D`. + /// Index 0 is unused by the forward NTT but set to the Montgomery form of 1. + pub(crate) zetas: [MontCoeff; D], + /// `D^{-1} mod p` in Montgomery form, used for inverse NTT final scaling. + pub(crate) d_inv: MontCoeff, +} + +impl NttTwiddles { + /// Compute twiddle factors for the given prime. + /// + /// Finds a primitive `2D`-th root of unity mod `p`, then fills the + /// twiddle table in bit-reversed order. All values are stored in + /// Montgomery form. + /// + /// # Panics + /// + /// Panics if `D` is not a power of two, or if `2D` does not divide `p - 1`. + pub fn compute(prime: NttPrime) -> Self { + assert!(D.is_power_of_two(), "D must be a power of two"); + let p = prime.p as i64; + assert!( + (p - 1) % (2 * D as i64) == 0, + "2D must divide p - 1 for NTT roots to exist" + ); + + let n = D.trailing_zeros(); + let psi = find_primitive_root_2d(p, D); + + let mut zetas = [MontCoeff::from_raw(0); D]; + for (i, z) in zetas.iter_mut().enumerate() { + let brv_i = bit_reverse(i, n); + let power = pow_mod(psi, brv_i as i64, p) as i16; + *z = prime.from_canonical(power); + } + + let d_inv_canonical = pow_mod(D as i64, p - 2, p) as i16; + let d_inv = prime.from_canonical(d_inv_canonical); + + Self { zetas, d_inv } + } +} + +/// Forward negacyclic NTT (Cooley-Tukey, decimation-in-time). +/// +/// Transforms `D` coefficients in-place from coefficient form to NTT +/// evaluation form. Both outputs of each butterfly are Barrett-reduced +/// to prevent overflow. +/// +/// After this call, the coefficients represent evaluations at +/// `psi^{2*brv(i)+1}` for `i = 0..D-1`. +pub fn forward_ntt(a: &mut [MontCoeff; D], prime: NttPrime, tw: &NttTwiddles) { + let mut k = 1usize; + let mut len = D / 2; + while len >= 1 { + let mut start = 0; + while start < D { + let zeta = tw.zetas[k]; + k += 1; + for j in start..(start + len) { + let t = prime.mul(a[j + len], zeta); + let diff = a[j].raw().wrapping_sub(t.raw()); + let sum = a[j].raw().wrapping_add(t.raw()); + a[j + len] = prime.reduce(MontCoeff::from_raw(diff)); + a[j] = prime.reduce(MontCoeff::from_raw(sum)); + } + start += 2 * len; + } + len /= 2; + } +} + +/// Inverse negacyclic NTT (Gentleman-Sande, decimation-in-frequency). +/// +/// Transforms `D` evaluations in-place back to coefficient form. +/// Includes the final `D^{-1}` scaling. +pub fn inverse_ntt(a: &mut [MontCoeff; D], prime: NttPrime, tw: &NttTwiddles) { + let mut k = D - 1; + let mut len = 1; + while len <= D / 2 { + let mut start = 0; + while start < D { + let zeta = tw.zetas[k]; + k = k.wrapping_sub(1); + for j in start..(start + len) { + let t = a[j]; + let sum = t.raw().wrapping_add(a[j + len].raw()); + let diff = t.raw().wrapping_sub(a[j + len].raw()); + a[j] = prime.reduce(MontCoeff::from_raw(sum)); + // Multiply difference by negative twiddle: negate zeta. + let neg_zeta = MontCoeff::from_raw(zeta.raw().wrapping_neg()); + a[j + len] = prime.mul(MontCoeff::from_raw(diff), neg_zeta); + } + start += 2 * len; + } + len *= 2; + } + + // Scale by D^{-1}. + for c in a.iter_mut() { + *c = prime.mul(*c, tw.d_inv); + } +} + +/// Bit-reverse an `n`-bit integer. +fn bit_reverse(x: usize, n: u32) -> usize { + x.reverse_bits() >> (usize::BITS - n) +} + +/// Find a primitive `2D`-th root of unity mod `p`. +/// +/// Returns `psi` in `[0, p)` such that `psi^D = -1 mod p`. +fn find_primitive_root_2d(p: i64, d: usize) -> i64 { + // Find the smallest quadratic non-residue a (i.e., a^{(p-1)/2} = -1 mod p). + let half = (p - 1) / 2; + let exp = (p - 1) / (2 * d as i64); + for a in 2..p { + if pow_mod(a, half, p) == p - 1 { + let psi = pow_mod(a, exp, p); + debug_assert_eq!(pow_mod(psi, d as i64, p), p - 1, "psi^D != -1"); + return psi; + } + } + panic!("no primitive root found for p={p}"); +} + +/// Modular exponentiation: `base^exp mod modulus`. +fn pow_mod(mut base: i64, mut exp: i64, modulus: i64) -> i64 { + let mut result = 1i64; + base %= modulus; + while exp > 0 { + if exp & 1 == 1 { + result = result * base % modulus; + } + base = base * base % modulus; + exp >>= 1; + } + result +} diff --git a/src/algebra/ntt/crt.rs b/src/algebra/ntt/crt.rs new file mode 100644 index 00000000..7df39710 --- /dev/null +++ b/src/algebra/ntt/crt.rs @@ -0,0 +1,189 @@ +//! Limb-based helpers for `q = 2^k - c` style moduli. +//! +//! Big-`q` coefficients are stored in radix `2^14` limbs. +//! This module provides a portable scalar representation with the same limb layout. + +use std::cmp::Ordering; +use std::fmt; +use std::ops::{Add, Sub}; + +/// Limb radix bit-width (`2^14`). +pub const RADIX_BITS: u32 = 14; +const RADIX: i32 = 1 << RADIX_BITS; +const RADIX_MASK: i32 = RADIX - 1; + +/// Fixed-width radix-`2^14` integer. +/// +/// Limbs are little-endian: `limbs[0]` is least significant. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct LimbQ { + /// Little-endian limbs. + pub limbs: [u16; L], +} + +impl Default for LimbQ { + #[inline] + fn default() -> Self { + Self::zero() + } +} + +impl LimbQ { + /// Zero value. + #[inline] + pub const fn zero() -> Self { + Self { limbs: [0; L] } + } + + /// Construct directly from limbs. + #[inline] + pub const fn from_limbs(limbs: [u16; L]) -> Self { + Self { limbs } + } + + /// Conditional subtraction: if `self >= modulus`, return `self - modulus` (branchless). + #[inline] + pub fn csub_mod(self, modulus: Self) -> Self { + // Compute self - modulus, tracking the final borrow. + let mut diff = [0u16; L]; + let mut borrow = 0i32; + for (i, df) in diff.iter_mut().enumerate() { + let d = self.limbs[i] as i32 - modulus.limbs[i] as i32 + borrow; + borrow = d >> 31; + if i + 1 < L { + *df = (d - borrow * RADIX) as u16; + } else { + *df = d as u16; + } + } + // borrow = -1 if self < modulus (underflowed), 0 otherwise. + // Branchless select: mask = 0xFFFF if underflow (keep self), 0 if not (keep diff). + let mask = borrow as u16; + let mut result = [0u16; L]; + for (i, r) in result.iter_mut().enumerate() { + *r = (self.limbs[i] & mask) | (diff[i] & !mask); + } + Self { limbs: result } + } +} + +impl From for LimbQ { + fn from(mut x: u128) -> Self { + let mut out = [0u16; L]; + for (i, limb) in out.iter_mut().enumerate() { + if i + 1 < L { + *limb = (x & (RADIX_MASK as u128)) as u16; + x >>= RADIX_BITS; + } else { + *limb = x as u16; + } + } + Self { limbs: out } + } +} + +impl TryFrom> for u128 { + type Error = &'static str; + + fn try_from(limb: LimbQ) -> Result { + if (L as u32) * RADIX_BITS > 128 { + return Err("LimbQ too wide for u128"); + } + let mut acc = 0u128; + for i in (0..L).rev() { + acc <<= RADIX_BITS; + acc |= limb.limbs[i] as u128; + } + Ok(acc) + } +} + +impl PartialOrd for LimbQ { + #[inline] + fn partial_cmp(&self, other: &Self) -> Option { + Some(self.cmp(other)) + } +} + +impl Ord for LimbQ { + fn cmp(&self, other: &Self) -> Ordering { + for i in (0..L).rev() { + match self.limbs[i].cmp(&other.limbs[i]) { + Ordering::Equal => continue, + ord => return ord, + } + } + Ordering::Equal + } +} + +impl Add for LimbQ { + type Output = Self; + + fn add(self, rhs: Self) -> Self { + let mut out = [0u16; L]; + let mut carry = 0i32; + for (i, out_limb) in out.iter_mut().enumerate() { + let s = self.limbs[i] as i32 + rhs.limbs[i] as i32 + carry; + if i + 1 < L { + carry = s >> RADIX_BITS; + *out_limb = (s & RADIX_MASK) as u16; + } else { + *out_limb = s as u16; + } + } + Self { limbs: out } + } +} + +impl Sub for LimbQ { + type Output = Self; + + fn sub(self, rhs: Self) -> Self { + let mut out = [0u16; L]; + let mut borrow = 0i32; + for (i, out_limb) in out.iter_mut().enumerate() { + let d = self.limbs[i] as i32 - rhs.limbs[i] as i32 + borrow; + if i + 1 < L { + borrow = d >> 31; + *out_limb = (d - borrow * RADIX) as u16; + } else { + *out_limb = d as u16; + } + } + Self { limbs: out } + } +} + +impl fmt::Display for LimbQ { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + if let Ok(val) = u128::try_from(*self) { + write!(f, "{val}") + } else { + write!(f, "LimbQ{:?}", self.limbs) + } + } +} + +/// CRT/q constants for a given parameter set. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct QData { + /// The modulus `q` in radix-`2^14` limbs. + pub q: LimbQ, + /// `-P mod q` in limbs (where `P = prod p_i`). + pub pmq: LimbQ, + /// `P/p_i mod q` in limbs. + pub xvec: [LimbQ; K], + /// `k` in `q = 2^k - c`. + pub logq: u32, + /// `c` in `q = 2^k - c`. + pub qoff: u16, +} + +impl QData { + /// `q` as `u128` when representable. + #[inline] + pub fn q_u128(self) -> Option { + u128::try_from(self.q).ok() + } +} diff --git a/src/algebra/ntt/mod.rs b/src/algebra/ntt/mod.rs new file mode 100644 index 00000000..fffbf284 --- /dev/null +++ b/src/algebra/ntt/mod.rs @@ -0,0 +1,10 @@ +//! NTT-friendly small-prime arithmetic and CRT helpers. + +pub mod butterfly; +pub mod crt; +pub mod prime; +pub mod tables; + +pub use butterfly::NttTwiddles; +pub use crt::{LimbQ, QData, RADIX_BITS}; +pub use prime::{MontCoeff, NttPrime}; diff --git a/src/algebra/ntt/prime.rs b/src/algebra/ntt/prime.rs new file mode 100644 index 00000000..9b19cf22 --- /dev/null +++ b/src/algebra/ntt/prime.rs @@ -0,0 +1,180 @@ +//! Small-prime arithmetic kernels for NTT-friendly parameter sets. +//! +//! Per-prime scalar operations: +//! - Montgomery multiplication ([`NttPrime::mul`]) +//! - Barrett-style reduction ([`NttPrime::reduce`]) +//! - Branchless conditional add/sub +//! +//! Coefficients in Montgomery domain are wrapped in [`MontCoeff`] to prevent +//! accidental mixing with canonical `i16` values. + +use std::fmt; + +/// A coefficient in Montgomery domain for an NTT prime. +/// +/// Wraps an `i16` representing `a * R mod p` (where `R = 2^16`). +/// Use [`NttPrime::from_canonical`] to enter and [`NttPrime::to_canonical`] +/// to leave Montgomery domain. +#[derive(Clone, Copy, PartialEq, Eq, Default)] +#[repr(transparent)] +pub struct MontCoeff(i16); + +impl MontCoeff { + /// Wrap a raw Montgomery-domain value. + /// + /// The caller must ensure `val` is a valid Montgomery-domain representative + /// for the intended prime. + #[inline] + pub const fn from_raw(val: i16) -> Self { + Self(val) + } + + /// Extract the raw `i16` (still in Montgomery domain). + #[inline] + pub const fn raw(self) -> i16 { + self.0 + } +} + +impl fmt::Debug for MontCoeff { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + write!(f, "Mont({})", self.0) + } +} + +/// Per-prime constants for NTT arithmetic over a small prime `p < 2^14`. +/// +/// All scalar operations use Montgomery representation internally. Constants +/// are stored as raw `i16` in centered signed form. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct NttPrime { + /// Prime modulus. + pub p: i16, + /// `p^{-1} mod 2^{16}` (centered signed). Used in Montgomery reduction. + pub pinv: i16, + /// `round(2^{27} / p)` for Barrett-style range reduction. + pub v: i16, + /// `R mod p` where `R = 2^{16}` (centered signed). Montgomery form of 1. + pub mont: i16, + /// `R^2 mod p` (centered signed). Used for canonical → Montgomery conversion. + pub montsq: i16, + /// NTT injection scale factor (centered signed). + pub s: i16, + /// Inverse-NTT post-scale factor (centered signed). + pub f: i16, + /// CRT reconstruction factor (centered signed). + pub t: i16, +} + +impl NttPrime { + /// Montgomery product: `a * b * R^{-1} mod p` where `R = 2^{16}`. + #[inline] + pub fn mul(self, a: MontCoeff, b: MontCoeff) -> MontCoeff { + MontCoeff(self.mont_mul_raw(a.0, b.0)) + } + + /// Raw Montgomery multiply on bare `i16` values. + /// + /// Computes `(a*b - ((a*b mod R) * p_inv mod R) * p) / R`. + #[inline] + pub(crate) fn mont_mul_raw(self, a: i16, b: i16) -> i16 { + let c = (a as i32) * (b as i32); + let t = (c as i16).wrapping_mul(self.pinv) as i32; + ((c - t * (self.p as i32)) >> 16) as i16 + } + + /// Barrett-style reduction: tighten a Montgomery coefficient's range + /// toward `[0, p)` without full normalization. + #[inline] + pub fn reduce(self, a: MontCoeff) -> MontCoeff { + let val = a.0; + let mut t = (((self.v as i32) * (val as i32) + (1 << 26)) >> 27) as i16; + t = t.wrapping_mul(self.p); + MontCoeff(val.wrapping_sub(t)) + } + + /// Conditionally subtract `p` if `a >= p` (branchless). + #[inline] + pub fn csubp(self, a: MontCoeff) -> MontCoeff { + let diff = a.0.wrapping_sub(self.p); + let mask = diff >> 15; + MontCoeff(diff.wrapping_add(mask & self.p)) + } + + /// Conditionally add `p` if `a < 0` (branchless). + #[inline] + pub fn caddp(self, a: MontCoeff) -> MontCoeff { + let mask = a.0 >> 15; + MontCoeff(a.0.wrapping_add(mask & self.p)) + } + + /// Fully normalize a Montgomery coefficient to `[0, p)`. + #[inline] + pub fn normalize(self, a: MontCoeff) -> MontCoeff { + self.csubp(self.caddp(self.reduce(a))) + } + + /// Convert a canonical `i16` into Montgomery domain: `a ↦ a * R mod p`. + #[inline] + pub fn from_canonical(self, a: i16) -> MontCoeff { + MontCoeff(self.mont_mul_raw(a, self.montsq)) + } + + /// Convert from Montgomery domain to canonical `[0, p)`. + #[inline] + pub fn to_canonical(self, a: MontCoeff) -> i16 { + let raw = MontCoeff(self.mont_mul_raw(a.0, 1)); + self.normalize(raw).0 + } + + /// Center a canonical value from approximately `(-p, p)` into `[-p/2, p/2)`. + /// + /// First conditionally adds `p` (if negative), then subtracts `p` (if > p/2). + /// Both steps are branchless. + #[inline] + pub fn center(self, a: i16) -> i16 { + let mask_neg = a >> 15; + let canonical = a.wrapping_add(mask_neg & self.p); + let half = self.p / 2; + let needs_sub = half.wrapping_sub(canonical) >> 15; + canonical.wrapping_add(needs_sub & self.p.wrapping_neg()) + } + + /// Pointwise Montgomery multiplication of two coefficient slices. + /// + /// # Panics + /// + /// Panics if slices have different lengths. + #[inline] + pub fn pointwise_mul(self, out: &mut [MontCoeff], lhs: &[MontCoeff], rhs: &[MontCoeff]) { + assert_eq!(out.len(), lhs.len()); + assert_eq!(lhs.len(), rhs.len()); + for ((o, a), b) in out.iter_mut().zip(lhs.iter()).zip(rhs.iter()) { + *o = self.mul(*a, *b); + } + } + + /// In-place Montgomery scaling by a constant. + #[inline] + pub fn scale_in_place(self, coeffs: &mut [MontCoeff], scalar: MontCoeff) { + for c in coeffs { + *c = self.mul(*c, scalar); + } + } + + /// In-place Barrett reduction on a coefficient slice. + #[inline] + pub fn reduce_in_place(self, coeffs: &mut [MontCoeff]) { + for c in coeffs { + *c = self.reduce(*c); + } + } + + /// In-place centering of canonical values to `[-p/2, p/2)`. + #[inline] + pub fn center_slice(self, coeffs: &mut [i16]) { + for c in coeffs { + *c = self.center(*c); + } + } +} diff --git a/src/algebra/ntt/tables.rs b/src/algebra/ntt/tables.rs new file mode 100644 index 00000000..613ccc95 --- /dev/null +++ b/src/algebra/ntt/tables.rs @@ -0,0 +1,149 @@ +//! Deterministic parameter presets for small-prime CRT arithmetic. +//! +//! Initial scope: `logq = 32` preset with six NTT-friendly primes. + +use super::crt::{LimbQ, QData}; +use super::prime::NttPrime; + +/// Polynomial degree for the base ring `Z_q[X]/(X^d + 1)`. +pub const RING_DEGREE: usize = 64; + +/// Number of CRT primes for the `logq = 32` parameter set. +pub const Q32_NUM_PRIMES: usize = 6; + +/// Number of radix-`2^14` limbs for `logq = 32`. +pub const Q32_NUM_LIMBS: usize = 3; + +/// Offset `c` in `q = 2^32 - c`. +pub const Q32_OFFSET: u16 = 99; + +/// `log2(q)` for the `logq = 32` parameter set. +pub const Q32_LOG_MODULUS: u32 = 32; + +/// The modulus `q = 2^32 - 99`. +pub const Q32_MODULUS: u64 = (1u64 << 32) - (Q32_OFFSET as u64); + +/// CRT primes and per-prime Montgomery constants for `logq = 32`. +pub const Q32_PRIMES: [NttPrime; Q32_NUM_PRIMES] = [ + NttPrime { + p: 13697, + pinv: 2689, + v: 9799, + mont: -2949, + montsq: -994, + s: 4705, + f: 3540, + t: -5758, + }, + NttPrime { + p: 13441, + pinv: 2945, + v: 9986, + mont: -1669, + montsq: 3274, + s: 3777, + f: -5468, + t: -1680, + }, + NttPrime { + p: 13313, + pinv: -13311, + v: 10082, + mont: -1029, + montsq: -6199, + s: 3325, + f: 4553, + t: -948, + }, + NttPrime { + p: 12289, + pinv: -12287, + v: 10922, + mont: 4091, + montsq: -1337, + s: -3, + f: 354, + t: 4472, + }, + NttPrime { + p: 12161, + pinv: 4225, + v: 11037, + mont: 4731, + montsq: -6040, + s: -383, + f: 5993, + t: 1653, + }, + NttPrime { + p: 11777, + pinv: -11775, + v: 11397, + mont: -5126, + montsq: 1389, + s: -1475, + f: -3812, + t: 1191, + }, +]; + +/// CRT limb constants for the `logq = 32` parameter set. +pub const Q32_DATA: QData = QData { + q: LimbQ::from_limbs([16285, 16383, 15]), + pmq: LimbQ::from_limbs([8747, 999, 12]), + xvec: [ + LimbQ::from_limbs([9406, 14930, 2]), + LimbQ::from_limbs([9295, 15936, 2]), + LimbQ::from_limbs([16336, 1061, 5]), + LimbQ::from_limbs([1006, 14584, 9]), + LimbQ::from_limbs([1315, 5273, 10]), + LimbQ::from_limbs([7927, 10169, 6]), + ], + logq: Q32_LOG_MODULUS, + qoff: Q32_OFFSET, +}; + +#[cfg(test)] +mod tests { + use super::*; + + /// Verify that derived constants (`pinv`, `v`, `mont`, `montsq`) are + /// consistent with the prime `p`. Turns the magic numbers into auditable + /// values. + #[test] + fn verify_prime_derived_constants() { + for prime in &Q32_PRIMES { + let p = prime.p; + + // pinv: p * pinv ≡ 1 (mod 2^16) + assert_eq!(p.wrapping_mul(prime.pinv), 1, "pinv failed for p={p}"); + + // v: round(2^27 / p) + let expected_v = ((1i64 << 27) + (p as i64 / 2)) / (p as i64); + assert_eq!(prime.v as i64, expected_v, "v failed for p={p}"); + + // mont: 2^16 mod p, centered to [-p/2, p/2) + let raw_mont = ((1i32 << 16) % (p as i32)) as i16; + let centered_mont = if raw_mont > p / 2 { + raw_mont - p + } else { + raw_mont + }; + assert_eq!(prime.mont, centered_mont, "mont failed for p={p}"); + + // montsq: 2^32 mod p, centered to [-p/2, p/2) + let raw_montsq = ((1i64 << 32) % (p as i64)) as i16; + let centered_montsq = if raw_montsq > p / 2 { + raw_montsq - p + } else { + raw_montsq + }; + assert_eq!(prime.montsq, centered_montsq, "montsq failed for p={p}"); + } + } + + #[test] + fn verify_q_value() { + assert_eq!(Q32_DATA.q_u128().unwrap(), Q32_MODULUS as u128); + } +} diff --git a/src/algebra/poly.rs b/src/algebra/poly.rs new file mode 100644 index 00000000..684aa7d8 --- /dev/null +++ b/src/algebra/poly.rs @@ -0,0 +1,95 @@ +//! Fixed-size polynomial container. + +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; +use crate::FieldCore; +use std::io::{Read, Write}; + +/// A degree-(pub [F; D]); + +impl Poly { + /// Construct the zero polynomial. + pub fn zero() -> Self { + Self([F::zero(); D]) + } +} + +impl std::ops::Add for Poly { + type Output = Self; + fn add(self, rhs: Self) -> Self::Output { + let mut out = self.0; + for (dst, src) in out.iter_mut().zip(rhs.0.iter()) { + *dst = *dst + *src; + } + Self(out) + } +} + +impl std::ops::Sub for Poly { + type Output = Self; + fn sub(self, rhs: Self) -> Self::Output { + let mut out = self.0; + for (dst, src) in out.iter_mut().zip(rhs.0.iter()) { + *dst = *dst - *src; + } + Self(out) + } +} + +impl std::ops::Neg for Poly { + type Output = Self; + fn neg(self) -> Self::Output { + let mut out = self.0; + for coeff in &mut out { + *coeff = -*coeff; + } + Self(out) + } +} + +impl Valid for Poly { + fn check(&self) -> Result<(), SerializationError> { + for x in self.0.iter() { + x.check()?; + } + Ok(()) + } +} + +impl HachiSerialize for Poly { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + for x in self.0.iter() { + x.serialize_with_mode(&mut writer, compress)?; + } + Ok(()) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.0.iter().map(|x| x.serialized_size(compress)).sum() + } +} + +impl HachiDeserialize for Poly { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let mut arr = [F::zero(); D]; + for coeff in &mut arr { + *coeff = F::deserialize_with_mode(&mut reader, compress, validate)?; + } + let out = Self(arr); + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} diff --git a/src/algebra/ring/crt_ntt_repr.rs b/src/algebra/ring/crt_ntt_repr.rs new file mode 100644 index 00000000..18e4772a --- /dev/null +++ b/src/algebra/ring/crt_ntt_repr.rs @@ -0,0 +1,246 @@ +//! CRT+NTT-domain representation of cyclotomic ring elements. + +use crate::algebra::backend::{CrtReconstruct, NttPrimeOps, NttTransform, ScalarBackend}; +use crate::algebra::fields::{Fp128, Fp32, Fp64}; +use crate::algebra::ntt::butterfly::NttTwiddles; +use crate::algebra::ntt::crt::QData; +use crate::algebra::ntt::prime::{MontCoeff, NttPrime}; +use crate::{CanonicalField, FieldCore}; + +use super::cyclotomic::CyclotomicRing; + +/// CRT+NTT-domain representation of a cyclotomic ring element. +/// +/// Stores `K` arrays of `D` [`MontCoeff`] values, one per CRT prime. +/// Multiplication is pointwise per prime - O(K*D) vs O(D^2) for coefficient form. +/// +/// Use [`CyclotomicCrtNtt::from_ring`] and [`CyclotomicCrtNtt::to_ring`] to convert +/// between coefficient and CRT+NTT domains. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct CyclotomicCrtNtt { + pub(crate) limbs: [[MontCoeff; D]; K], +} + +/// Field types that can safely convert to and from the CRT+NTT representation. +pub trait CrtNttConvertibleField: FieldCore + CanonicalField { + /// Reduce this field element modulo a small prime `p`. + fn mod_small_prime(self, p: i16) -> i16; + + /// Reconstruct from a residue in `[0, q)` after CRT combination. + fn from_q_residue_u128(x: u128) -> Self; +} + +impl CrtNttConvertibleField for Fp32

{ + #[inline] + fn mod_small_prime(self, p: i16) -> i16 { + (self.to_canonical_u32() % (p as u32)) as i16 + } + + #[inline] + fn from_q_residue_u128(x: u128) -> Self { + let narrowed = u32::try_from(x).expect("CRT residue does not fit in u32"); + Self::from_u64(narrowed as u64) + } +} + +impl CrtNttConvertibleField for Fp64

{ + #[inline] + fn mod_small_prime(self, p: i16) -> i16 { + (self.to_canonical_u64() % (p as u64)) as i16 + } + + #[inline] + fn from_q_residue_u128(x: u128) -> Self { + let narrowed = u64::try_from(x).expect("CRT residue does not fit in u64"); + Self::from_u64(narrowed) + } +} + +impl CrtNttConvertibleField for Fp128

{ + #[inline] + fn mod_small_prime(self, p: i16) -> i16 { + (self.to_canonical_u128() % (p as u128)) as i16 + } + + #[inline] + fn from_q_residue_u128(x: u128) -> Self { + Self::from_canonical_u128_reduced(x) + } +} + +impl CyclotomicCrtNtt { + /// The additive identity (all zeros in every CRT limb). + pub fn zero() -> Self { + Self { + limbs: [[MontCoeff::from_raw(0); D]; K], + } + } + + /// Convert a coefficient-form ring element into CRT+NTT domain + /// using the default scalar backend. + pub fn from_ring( + ring: &CyclotomicRing, + primes: &[NttPrime; K], + twiddles: &[NttTwiddles; K], + ) -> Self { + Self::from_ring_with_backend::(ring, primes, twiddles) + } + + /// Convert a coefficient-form ring element into CRT+NTT domain + /// through an explicit backend implementation. + pub fn from_ring_with_backend< + F: CrtNttConvertibleField, + B: NttPrimeOps + NttTransform, + >( + ring: &CyclotomicRing, + primes: &[NttPrime; K], + twiddles: &[NttTwiddles; K], + ) -> Self { + let mut limbs = [[MontCoeff::from_raw(0); D]; K]; + for ((limb, prime), tw) in limbs.iter_mut().zip(primes.iter()).zip(twiddles.iter()) { + // Reduce each coefficient mod p and convert to Montgomery form. + for (dst, src) in limb.iter_mut().zip(ring.coeffs.iter()) { + let val = src.mod_small_prime(prime.p); + *dst = B::from_canonical(*prime, val); + } + B::forward_ntt(limb, *prime, tw); + } + Self { limbs } + } + + /// Convert from CRT+NTT domain back to coefficient form + /// using the default scalar backend. + pub fn to_ring( + &self, + primes: &[NttPrime; K], + twiddles: &[NttTwiddles; K], + qdata: &QData, + ) -> CyclotomicRing { + self.to_ring_with_backend::(primes, twiddles, qdata) + } + + /// Convert from CRT+NTT domain back to coefficient form + /// through an explicit backend implementation. + pub fn to_ring_with_backend< + F: CrtNttConvertibleField, + B: NttPrimeOps + NttTransform + CrtReconstruct, + const L: usize, + >( + &self, + primes: &[NttPrime; K], + twiddles: &[NttTwiddles; K], + qdata: &QData, + ) -> CyclotomicRing { + let mut canonical = [[0i16; D]; K]; + for (k, ((can, prime), tw)) in canonical + .iter_mut() + .zip(primes.iter()) + .zip(twiddles.iter()) + .enumerate() + { + let mut limb = self.limbs[k]; + B::inverse_ntt(&mut limb, *prime, tw); + for (dst, src) in can.iter_mut().zip(limb.iter()) { + *dst = B::to_canonical(*prime, *src); + } + } + + let coeffs = B::reconstruct::(primes, &canonical, qdata); + + CyclotomicRing::from_coefficients(coeffs) + } + + /// Add another CRT+NTT element and reduce each coefficient with the matching + /// prime to maintain valid Montgomery ranges using the scalar backend. + pub fn add_reduced(&self, rhs: &Self, primes: &[NttPrime; K]) -> Self { + self.add_reduced_with_backend::(rhs, primes) + } + + /// Add another CRT+NTT element and reduce each coefficient with the matching + /// prime through an explicit backend implementation. + pub fn add_reduced_with_backend>( + &self, + rhs: &Self, + primes: &[NttPrime; K], + ) -> Self { + let mut out = self.clone(); + for (k, (limb, rhs_limb)) in out.limbs.iter_mut().zip(rhs.limbs.iter()).enumerate() { + let prime = primes[k]; + for (a, b) in limb.iter_mut().zip(rhs_limb.iter()) { + let sum = MontCoeff::from_raw(a.raw().wrapping_add(b.raw())); + *a = B::reduce(prime, sum); + } + } + out + } + + /// Subtract another CRT+NTT element and reduce each coefficient with the + /// matching prime to maintain valid Montgomery ranges using the scalar backend. + pub fn sub_reduced(&self, rhs: &Self, primes: &[NttPrime; K]) -> Self { + self.sub_reduced_with_backend::(rhs, primes) + } + + /// Subtract another CRT+NTT element and reduce each coefficient with the + /// matching prime through an explicit backend implementation. + pub fn sub_reduced_with_backend>( + &self, + rhs: &Self, + primes: &[NttPrime; K], + ) -> Self { + let mut out = self.clone(); + for (k, (limb, rhs_limb)) in out.limbs.iter_mut().zip(rhs.limbs.iter()).enumerate() { + let prime = primes[k]; + for (a, b) in limb.iter_mut().zip(rhs_limb.iter()) { + let diff = MontCoeff::from_raw(a.raw().wrapping_sub(b.raw())); + *a = B::reduce(prime, diff); + } + } + out + } + + /// Negate each CRT+NTT coefficient and reduce with the matching prime + /// using the scalar backend. + pub fn neg_reduced(&self, primes: &[NttPrime; K]) -> Self { + self.neg_reduced_with_backend::(primes) + } + + /// Negate each CRT+NTT coefficient and reduce with the matching prime + /// through an explicit backend implementation. + pub fn neg_reduced_with_backend>(&self, primes: &[NttPrime; K]) -> Self { + let mut out = self.clone(); + for (k, limb) in out.limbs.iter_mut().enumerate() { + let prime = primes[k]; + for a in limb.iter_mut() { + let neg = MontCoeff::from_raw(a.raw().wrapping_neg()); + *a = B::reduce(prime, neg); + } + } + out + } + + /// Pointwise multiplication in CRT+NTT domain. + /// + /// Each limb is multiplied pointwise using the corresponding prime's + /// Montgomery multiplication. + pub fn pointwise_mul(&self, rhs: &Self, primes: &[NttPrime; K]) -> Self { + self.pointwise_mul_with_backend::(rhs, primes) + } + + /// Pointwise multiplication in CRT+NTT domain through an explicit backend implementation. + pub fn pointwise_mul_with_backend>( + &self, + rhs: &Self, + primes: &[NttPrime; K], + ) -> Self { + let mut out = [[MontCoeff::from_raw(0); D]; K]; + for (k, ((o, a), b)) in out + .iter_mut() + .zip(self.limbs.iter()) + .zip(rhs.limbs.iter()) + .enumerate() + { + B::pointwise_mul(primes[k], o, a, b); + } + Self { limbs: out } + } +} diff --git a/src/algebra/ring/cyclotomic.rs b/src/algebra/ring/cyclotomic.rs new file mode 100644 index 00000000..5dd2f0fc --- /dev/null +++ b/src/algebra/ring/cyclotomic.rs @@ -0,0 +1,439 @@ +//! Cyclotomic ring `Z_q[X]/(X^D + 1)` in coefficient form. + +use super::sparse_challenge::SparseChallenge; +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; +use crate::{CanonicalField, FieldCore, FieldSampling}; +use rand_core::RngCore; +use std::io::{Read, Write}; +use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign}; + +/// Element of the cyclotomic ring `Z_q[X]/(X^D + 1)`. +/// +/// Stored as `D` coefficients in the base field `F`, representing +/// `a_0 + a_1*X + ... + a_{D-1}*X^{D-1}`. +/// +/// Multiplication is negacyclic convolution: `X^D = -1`, so a product +/// term at index `i + j >= D` wraps to index `(i + j) - D` with a sign flip. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct CyclotomicRing { + pub(crate) coeffs: [F; D], +} + +impl CyclotomicRing { + /// Construct from a coefficient array. + #[inline] + pub fn from_coefficients(coeffs: [F; D]) -> Self { + Self { coeffs } + } + + /// Borrow the coefficient array. + #[inline] + pub fn coefficients(&self) -> &[F; D] { + &self.coeffs + } + + /// The additive identity (all-zero polynomial). + #[inline] + pub fn zero() -> Self { + Self { + coeffs: [F::zero(); D], + } + } + + /// The multiplicative identity (`1 + 0*X + ... + 0*X^{D-1}`). + #[inline] + pub fn one() -> Self { + let mut coeffs = [F::zero(); D]; + coeffs[0] = F::one(); + Self { coeffs } + } + + /// The monomial `X` (i.e., `[0, 1, 0, ..., 0]`). + /// + /// # Panics + /// + /// Panics if `D < 2`. + #[inline] + pub fn x() -> Self { + assert!(D >= 2, "ring degree must be at least 2"); + let mut coeffs = [F::zero(); D]; + coeffs[1] = F::one(); + Self { coeffs } + } + + /// Scalar multiplication: multiply every coefficient by `k`. + #[inline] + pub fn scale(&self, k: &F) -> Self { + let mut out = self.coeffs; + for c in &mut out { + *c = *c * *k; + } + Self { coeffs: out } + } + + /// Apply the cyclotomic automorphism `sigma_k: X -> X^k` for odd `k`. + /// + /// In `Z_q[X]/(X^D + 1)`, this permutes/sign-flips coefficients using + /// exponent reduction modulo `2D`. + /// + /// # Panics + /// + /// Panics if `D == 0` or `k` is not odd modulo `2D`. + pub fn sigma(&self, k: usize) -> Self { + assert!(D > 0, "ring degree must be non-zero"); + let two_d = 2 * D; + let k_mod = k % two_d; + assert!(k_mod % 2 == 1, "sigma_k requires odd k in Z_q[X]/(X^D + 1)"); + + let mut out = [F::zero(); D]; + for (j, coeff) in self.coeffs.iter().copied().enumerate() { + let idx = (j * k_mod) % two_d; + if idx < D { + out[idx] = out[idx] + coeff; + } else { + out[idx - D] = out[idx - D] - coeff; + } + } + Self { coeffs: out } + } + + /// Apply `sigma_{-1}` (`X -> X^{-1} = X^{2D-1}` in this ring). + /// + /// # Panics + /// + /// Panics if `D == 0`. + pub fn sigma_m1(&self) -> Self { + assert!(D > 0, "ring degree must be non-zero"); + self.sigma(2 * D - 1) + } + + /// Multiply by `X^k` in `Z_q[X]/(X^D + 1)` via O(D) coefficient rotation. + /// + /// Since `X^D = -1`, coefficients that wrap past index `D` get negated. + #[inline] + pub fn negacyclic_shift(&self, k: usize) -> Self { + let k = k % D; + if k == 0 { + return *self; + } + let mut out = [F::zero(); D]; + for i in 0..D { + let target = i + k; + if target < D { + out[target] = self.coeffs[i]; + } else { + out[target - D] = -self.coeffs[i]; + } + } + Self { coeffs: out } + } + + /// Multiply `self` by a sum of monomials `X^{k_1} + X^{k_2} + ...` + /// + /// Each term is a negacyclic shift, so the total cost is + /// `O(positions.len() * D)` field additions with zero multiplications. + pub fn mul_by_monomial_sum(&self, nonzero_positions: &[usize]) -> Self { + let mut result = Self::zero(); + for &k in nonzero_positions { + result += self.negacyclic_shift(k); + } + result + } + + /// Multiply `self` by a sparse challenge element. + /// + /// Cost: `O(omega * D)` field additions instead of `O(D^2)` multiplications. + /// For `omega=23, D=256` this is 5,888 adds vs 65,536 muls. + pub fn mul_by_sparse(&self, challenge: &SparseChallenge) -> Self + where + F: CanonicalField, + { + let mut result = Self::zero(); + for (&pos, &coeff) in challenge.positions.iter().zip(challenge.coeffs.iter()) { + let shifted = self.negacyclic_shift(pos as usize); + match coeff { + 1 => result += shifted, + -1 => result -= shifted, + c => result += shifted.scale(&F::from_i64(c as i64)), + } + } + result + } + + /// Check whether all coefficients are zero. + #[inline] + pub fn is_zero(&self) -> bool { + self.coeffs.iter().all(|c| c.is_zero()) + } + + /// Count non-zero coefficients. + #[inline] + pub fn hamming_weight(&self) -> usize { + self.coeffs.iter().filter(|c| !c.is_zero()).count() + } + + /// Sample a sparse challenge with exactly `omega` non-zeros in `{+1, -1}`. + /// + /// # Panics + /// + /// Panics if `omega > D` or `D == 0` with non-zero `omega`. + pub fn sample_sparse_pm1(rng: &mut R, omega: usize) -> Self { + assert!(omega <= D, "omega must be <= ring degree"); + assert!(D > 0 || omega == 0, "ring degree must be non-zero"); + + let mut coeffs = [F::zero(); D]; + let mut placed = 0usize; + while placed < omega { + let idx = (rng.next_u64() % (D as u64)) as usize; + if coeffs[idx].is_zero() { + coeffs[idx] = if (rng.next_u32() & 1) == 0 { + F::one() + } else { + -F::one() + }; + placed += 1; + } + } + Self { coeffs } + } +} + +impl CyclotomicRing { + /// Functional gadget recomposition (`G * digits`) for base `2^log_basis`. + /// + /// Coefficients from each part are interpreted as one digit plane and + /// recombined back into canonical integers (then reduced into the field). + /// + /// # Panics + /// + /// Panics if `log_basis == 0`, `log_basis >= 128`, or `parts.len() * log_basis > 128`. + pub fn gadget_recompose_pow2(parts: &[Self], log_basis: u32) -> Self { + if parts.is_empty() { + return Self::zero(); + } + + assert!(log_basis > 0 && log_basis < 128, "invalid log_basis"); + + let b = F::from_canonical_u128_reduced(1u128 << log_basis); + let coeffs = std::array::from_fn(|i| { + let mut acc = F::zero(); + let mut power = F::one(); + for part in parts.iter() { + acc = acc + part.coeffs[i] * power; + power = power * b; + } + acc + }); + Self { coeffs } + } + + /// Balanced (centered) base-`2^log_basis` gadget decomposition: `G^{-1}`. + /// + /// Each coefficient `c` (centered into `(-q/2, q/2]`) is decomposed into + /// `levels` balanced digits `d_k ∈ [-b/2, b/2)` satisfying + /// `c ≡ Σ_k d_k · b^k (mod q)`. + /// + /// Negative digits are stored as their field representation (`q + d`). + /// + /// # Panics + /// + /// Panics if `log_basis == 0`, `log_basis >= 128`, or `levels * log_basis > 128`. + pub fn balanced_decompose_pow2(&self, levels: usize, log_basis: u32) -> Vec { + assert!(log_basis > 0 && log_basis < 128, "invalid log_basis"); + assert!( + (levels as u32).saturating_mul(log_basis) <= 128, + "levels * log_basis must be <= 128" + ); + + let b = 1i128 << log_basis; + let half_b = b / 2; + let q = (-F::one()).to_canonical_u128() as i128 + 1; + let half_q = q / 2; + + let mut digit_planes: Vec<[F; D]> = (0..levels).map(|_| [F::zero(); D]).collect(); + + for i in 0..D { + let canonical = self.coeffs[i].to_canonical_u128() as i128; + let mut c = if canonical > half_q { + canonical - q + } else { + canonical + }; + + for plane in digit_planes.iter_mut() { + let d = c.rem_euclid(b); + let balanced = if d >= half_b { d - b } else { d }; + c = (c - balanced) / b; + + plane[i] = if balanced >= 0 { + F::from_canonical_u128_reduced(balanced as u128) + } else { + F::from_canonical_u128_reduced((q + balanced) as u128) + }; + } + } + + digit_planes + .into_iter() + .map(Self::from_coefficients) + .collect() + } +} + +impl CyclotomicRing { + /// Generate a random ring element. + pub fn random(rng: &mut R) -> Self { + Self { + coeffs: std::array::from_fn(|_| F::sample(rng)), + } + } +} + +impl AddAssign for CyclotomicRing { + fn add_assign(&mut self, rhs: Self) { + for (dst, src) in self.coeffs.iter_mut().zip(rhs.coeffs.iter()) { + *dst = *dst + *src; + } + } +} + +impl SubAssign for CyclotomicRing { + fn sub_assign(&mut self, rhs: Self) { + for (dst, src) in self.coeffs.iter_mut().zip(rhs.coeffs.iter()) { + *dst = *dst - *src; + } + } +} + +impl Add for CyclotomicRing { + type Output = Self; + fn add(mut self, rhs: Self) -> Self { + self += rhs; + self + } +} + +impl Sub for CyclotomicRing { + type Output = Self; + fn sub(mut self, rhs: Self) -> Self { + self -= rhs; + self + } +} + +impl Neg for CyclotomicRing { + type Output = Self; + fn neg(self) -> Self { + let mut out = self.coeffs; + for c in &mut out { + *c = -*c; + } + Self { coeffs: out } + } +} + +impl MulAssign for CyclotomicRing { + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + +impl<'a, F: FieldCore, const D: usize> Add<&'a Self> for CyclotomicRing { + type Output = Self; + fn add(self, rhs: &'a Self) -> Self { + self + *rhs + } +} + +impl<'a, F: FieldCore, const D: usize> Sub<&'a Self> for CyclotomicRing { + type Output = Self; + fn sub(self, rhs: &'a Self) -> Self { + self - *rhs + } +} + +impl<'a, F: FieldCore, const D: usize> Mul<&'a Self> for CyclotomicRing { + type Output = Self; + fn mul(self, rhs: &'a Self) -> Self { + self * *rhs + } +} + +/// Schoolbook negacyclic convolution: O(D^2). +/// +/// For each pair `(i, j)`: +/// - If `i + j < D`: accumulate `a_i * b_j` at index `i + j`. +/// - If `i + j >= D`: accumulate `-(a_i * b_j)` at index `(i + j) - D`. +impl Mul for CyclotomicRing { + type Output = Self; + fn mul(self, rhs: Self) -> Self { + let mut out = [F::zero(); D]; + for i in 0..D { + for j in 0..D { + let product = self.coeffs[i] * rhs.coeffs[j]; + let idx = i + j; + if idx < D { + out[idx] = out[idx] + product; + } else { + out[idx - D] = out[idx - D] - product; + } + } + } + Self { coeffs: out } + } +} + +impl Valid for CyclotomicRing { + fn check(&self) -> Result<(), SerializationError> { + for x in self.coeffs.iter() { + x.check()?; + } + Ok(()) + } +} + +impl HachiSerialize for CyclotomicRing { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + for x in self.coeffs.iter() { + x.serialize_with_mode(&mut writer, compress)?; + } + Ok(()) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.coeffs + .iter() + .map(|x| x.serialized_size(compress)) + .sum() + } +} + +impl HachiDeserialize for CyclotomicRing { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let mut coeffs = [F::zero(); D]; + for c in &mut coeffs { + *c = F::deserialize_with_mode(&mut reader, compress, validate)?; + } + let out = Self { coeffs }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +impl Default for CyclotomicRing { + fn default() -> Self { + Self::zero() + } +} diff --git a/src/algebra/ring/mod.rs b/src/algebra/ring/mod.rs new file mode 100644 index 00000000..1b64555e --- /dev/null +++ b/src/algebra/ring/mod.rs @@ -0,0 +1,9 @@ +//! Cyclotomic ring types and NTT representations. + +pub mod crt_ntt_repr; +pub mod cyclotomic; +pub mod sparse_challenge; + +pub use crt_ntt_repr::{CrtNttConvertibleField, CyclotomicCrtNtt}; +pub use cyclotomic::CyclotomicRing; +pub use sparse_challenge::{SparseChallenge, SparseChallengeConfig}; diff --git a/src/algebra/ring/sparse_challenge.rs b/src/algebra/ring/sparse_challenge.rs new file mode 100644 index 00000000..4f55b06a --- /dev/null +++ b/src/algebra/ring/sparse_challenge.rs @@ -0,0 +1,164 @@ +//! Sparse ring challenges for cyclotomic protocols. +//! +//! Many lattice protocols sample "short/sparse" ring challenges whose coefficients +//! are mostly zero and whose non-zero coefficients come from a tiny integer alphabet +//! (e.g. `{±1}` or `{±1,±2}`), with a fixed Hamming weight `ω`. +//! +//! This module provides a minimal representation that is: +//! - independent of any specific protocol (Hachi/Greyhound/SuperNeo, etc.), +//! - easy to sample deterministically from Fiat–Shamir at the protocol layer, +//! - and efficient to evaluate at a point `α` using precomputed powers. + +use super::CyclotomicRing; +use crate::{CanonicalField, FieldCore}; + +/// Configuration for sampling a sparse challenge. +/// +/// This intentionally avoids redundant knobs: the distribution is determined by: +/// - exact `weight` (Hamming weight), +/// - and a list of allowed **non-zero** integer coefficients. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct SparseChallengeConfig { + /// Exact Hamming weight ω. + pub weight: usize, + /// Allowed non-zero coefficients (small signed integers). + /// + /// Examples: + /// - `{±1}`: `vec![-1, 1]` + /// - `{±1,±2}`: `vec![-2, -1, 1, 2]` + pub nonzero_coeffs: Vec, +} + +impl SparseChallengeConfig { + /// Validate basic invariants for a given ring degree `D`. + /// + /// # Errors + /// + /// Returns an error if `weight > D`, if `nonzero_coeffs` is empty, or if it + /// contains `0`. + pub fn validate(&self) -> Result<(), &'static str> { + if self.weight > D { + return Err("weight must be <= ring degree D"); + } + if self.nonzero_coeffs.is_empty() { + return Err("nonzero_coeffs must be non-empty"); + } + if self.nonzero_coeffs.contains(&0) { + return Err("nonzero_coeffs must not contain 0"); + } + Ok(()) + } +} + +/// Sparse polynomial in `F[X]/(X^D+1)` represented by its non-zero terms. +/// +/// Invariants: +/// - `positions.len() == coeffs.len()` +/// - all positions are `< D` +/// - positions are unique +/// - all coeffs are non-zero +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct SparseChallenge { + /// Coefficient indices (powers of `X`) where the polynomial is non-zero. + pub positions: Vec, + /// Small integer coefficients at the corresponding positions. + pub coeffs: Vec, +} + +impl SparseChallenge { + /// Construct an empty (all-zero) challenge. + #[inline] + pub fn zero() -> Self { + Self { + positions: Vec::new(), + coeffs: Vec::new(), + } + } + + /// Number of non-zero coefficients (Hamming weight). + #[inline] + pub fn hamming_weight(&self) -> usize { + debug_assert_eq!(self.positions.len(), self.coeffs.len()); + self.positions.len() + } + + /// ℓ₁ norm over integers: `Σ |coeff_i|`. + #[inline] + pub fn l1_norm(&self) -> u64 { + self.coeffs + .iter() + .map(|&c| (c as i32).unsigned_abs() as u64) + .sum() + } + + /// Validate structural invariants for a ring degree `D`. + /// + /// # Errors + /// + /// Returns an error if lengths mismatch, if any coefficient is zero, if any + /// position is out of range, or if positions contain duplicates. + pub fn validate(&self) -> Result<(), &'static str> { + if self.positions.len() != self.coeffs.len() { + return Err("positions and coeffs must have same length"); + } + // Check coeffs are non-zero and positions are in range + unique. + let mut seen = vec![false; D]; + for (&pos, &c) in self.positions.iter().zip(self.coeffs.iter()) { + if c == 0 { + return Err("coeffs must not contain 0"); + } + let p = pos as usize; + if p >= D { + return Err("position out of range"); + } + if seen[p] { + return Err("positions must be unique"); + } + seen[p] = true; + } + Ok(()) + } + + /// Convert to a dense ring element by placing coefficients in the canonical + /// coefficient basis. + /// + /// # Errors + /// + /// Returns an error if the sparse representation violates structural invariants. + pub fn to_dense( + &self, + ) -> Result, &'static str> { + self.validate::()?; + let mut out = [F::zero(); D]; + for (&pos, &c) in self.positions.iter().zip(self.coeffs.iter()) { + out[pos as usize] = out[pos as usize] + F::from_i64(c as i64); + } + Ok(CyclotomicRing::from_coefficients(out)) + } + + /// Evaluate this sparse polynomial at `α` in `E`, given precomputed powers + /// `[α^0, α^1, ..., α^{D-1}]`. + /// + /// This is `O(weight)` and is intended to be used for verifier-side oracles + /// where `D` may be large but `weight` is small. + /// + /// # Errors + /// + /// Returns an error if structural invariants fail or if `alpha_pows.len() != D`. + pub fn eval_at_alpha(&self, alpha_pows: &[E]) -> Result + where + F: FieldCore + CanonicalField, + E: FieldCore + crate::algebra::fields::LiftBase, + { + self.validate::()?; + if alpha_pows.len() != D { + return Err("alpha_pows length mismatch"); + } + let mut acc = E::zero(); + for (&pos, &c) in self.positions.iter().zip(self.coeffs.iter()) { + let coeff_f = F::from_i64(c as i64); + acc = acc + (E::lift_base(coeff_f) * alpha_pows[pos as usize]); + } + Ok(acc) + } +} diff --git a/src/lib.rs b/src/lib.rs index e3859c54..eb5ac81c 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -1,3 +1,7 @@ +#![cfg_attr( + all(target_arch = "x86_64", target_feature = "avx512f"), + feature(stdarch_x86_avx512) +)] //! # hachi //! //! A high performance and modular implementation of the Hachi polynomial commitment scheme. @@ -35,7 +39,21 @@ pub mod error; /// Primitive traits and operations pub mod primitives; +/// Concrete algebra backends (prime fields, extensions, rings) +pub mod algebra; + +/// Protocol-layer transcript and commitment abstractions +pub mod protocol; + +#[doc(hidden)] +#[allow(missing_docs)] +pub mod test_utils; + pub use error::HachiError; -pub use primitives::arithmetic::{Field, HachiRoutines, Module}; +pub use primitives::arithmetic::{ + CanonicalField, FieldCore, FieldSampling, HachiRoutines, Invertible, Module, + PseudoMersenneField, +}; pub use primitives::poly::{MultilinearLagrange, Polynomial}; pub use primitives::serialization::{HachiDeserialize, HachiSerialize}; +pub use protocol::{CommitmentScheme, StreamingCommitmentScheme, Transcript}; diff --git a/src/primitives/arithmetic.rs b/src/primitives/arithmetic.rs index ccaaa4ae..903b3a17 100644 --- a/src/primitives/arithmetic.rs +++ b/src/primitives/arithmetic.rs @@ -3,8 +3,8 @@ use super::{HachiDeserialize, HachiSerialize}; use rand_core::RngCore; -/// Field trait for lattice-based arithmetic -pub trait Field: +/// Core field operations required across algebra backends. +pub trait FieldCore: Sized + Clone + Copy @@ -39,17 +39,55 @@ pub trait Field: /// Field multiplication fn mul(&self, rhs: &Self) -> Self; - /// Field inversion + /// Field inversion. + /// + /// This API may branch on zero-check and is intended for public/non-secret + /// values. For secret-bearing paths, use [`Invertible::inv_or_zero`]. fn inv(self) -> Option; +} - /// Generate random field element - fn random(rng: &mut R) -> Self; +/// Constant-time inversion helper for secret-bearing code paths. +/// +/// Implementations return `0` when the input is `0`, and `x^{-1}` otherwise, +/// without branching on the input value. +pub trait Invertible: FieldCore { + /// Constant-time inversion with zero-mapping behavior. + fn inv_or_zero(self) -> Self; +} - /// Convert from u64 +/// Canonical conversion operations for field elements. +pub trait CanonicalField: FieldCore { + /// Convert from `u64`. fn from_u64(val: u64) -> Self; - /// Convert from i64 + /// Convert from `i64`. fn from_i64(val: i64) -> Self; + + /// Return canonical integer representation as `u128`. + fn to_canonical_u128(self) -> u128; + + /// Construct from canonical value if it is in range. + fn from_canonical_u128_checked(val: u128) -> Option; + + /// Construct from canonical value reduced modulo the field modulus. + fn from_canonical_u128_reduced(val: u128) -> Self; +} + +/// Optional sampling support for field elements. +/// +/// This is intentionally separate from core field algebra and may evolve. +pub trait FieldSampling: FieldCore { + /// Generate a sampled field element. + fn sample(rng: &mut R) -> Self; +} + +/// Metadata for pseudo-Mersenne style moduli (`2^k - c`). +pub trait PseudoMersenneField: CanonicalField { + /// Exponent `k` in `2^k - c`. + const MODULUS_BITS: u32; + + /// Offset `c` in `2^k - c`. + const MODULUS_OFFSET: u128; } /// Module trait for lattice-based algebraic structures @@ -73,7 +111,9 @@ pub trait Module: + for<'a> std::ops::Sub<&'a Self, Output = Self> { /// Scalar type (field/ring elements) - type Scalar: Field + type Scalar: FieldCore + + CanonicalField + + FieldSampling + std::ops::Mul + for<'a> std::ops::Mul<&'a Self, Output = Self>; diff --git a/src/primitives/mod.rs b/src/primitives/mod.rs index 9f53c2f1..21376422 100644 --- a/src/primitives/mod.rs +++ b/src/primitives/mod.rs @@ -2,6 +2,7 @@ //! This submodule defines the basic lattice arithmetic and cryptographic tools that Hachi is built upon pub mod arithmetic; +pub mod multilinear_evals; pub mod poly; pub mod serialization; pub mod transcript; diff --git a/src/primitives/multilinear_evals.rs b/src/primitives/multilinear_evals.rs new file mode 100644 index 00000000..2ba3b95a --- /dev/null +++ b/src/primitives/multilinear_evals.rs @@ -0,0 +1,155 @@ +//! Dense multilinear polynomials in evaluation form. +//! +//! This module intentionally follows the same high-level representation style as +//! Jolt's `DensePolynomial` for multilinear extensions (MLEs): store the values +//! of the multilinear polynomial on the Boolean hypercube `{0,1}^n` and provide +//! binding/evaluation by iterative folding. +//! +//! The key convention for this repo (used by the ring-switch witness table) is: +//! +//! - An evaluation index `idx` is interpreted in binary. +//! - The **lowest** index bit is the **first** variable bound under +//! [`BindingOrder::LowToHigh`]. +//! +//! This matches the row-major flattening `idx = row * d + col` when `d` is a +//! power of two: the low `log2(d)` bits correspond to the `col` coordinate. + +use crate::primitives::arithmetic::FieldCore; +use crate::primitives::poly::Polynomial; + +/// The order in which variables are bound/evaluated. +#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)] +pub enum BindingOrder { + /// Bind the lowest index bit first (LSB → MSB). + #[default] + LowToHigh, + /// Bind the highest index bit first (MSB → LSB). + HighToLow, +} + +/// Dense multilinear polynomial in evaluation form over `{0,1}^num_vars`. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct DenseMultilinearEvals { + /// Number of variables in the multilinear extension. + pub num_vars: usize, + /// Active length (decreases as variables are bound). + pub len: usize, + /// Evaluations on the hypercube, length is a power of two. + pub evals: Vec, +} + +impl Default for DenseMultilinearEvals { + fn default() -> Self { + Self { + num_vars: 0, + len: 1, + evals: vec![F::zero()], + } + } +} + +impl DenseMultilinearEvals { + /// Construct from evaluations, padding with zeros to a power of two. + /// + /// The variable count is derived from the padded length. + pub fn new_padded(mut evals: Vec) -> Self { + if evals.is_empty() { + evals.push(F::zero()); + } + while !evals.len().is_power_of_two() { + evals.push(F::zero()); + } + let num_vars = evals.len().trailing_zeros() as usize; + let len = evals.len(); + Self { + num_vars, + len, + evals, + } + } + + /// Return the original (backing) evaluation length. + pub fn original_len(&self) -> usize { + self.evals.len() + } + + /// Bind one variable in-place, reducing `len` by a factor of 2. + /// + /// After binding, the polynomial has one fewer variable. + /// + /// # Panics + /// + /// Panics if the current backing length is not a power of two, or if attempting + /// to bind a constant (length-1) polynomial. + pub fn bind_in_place(&mut self, r: F, order: BindingOrder) { + assert!(self.len.is_power_of_two()); + assert!(self.len >= 2, "cannot bind variable of constant polynomial"); + match order { + BindingOrder::LowToHigh => self.bind_lsb_in_place(r), + BindingOrder::HighToLow => self.bind_msb_in_place(r), + } + } + + #[inline] + fn bind_lsb_in_place(&mut self, r: F) { + let next_len = self.len / 2; + for i in 0..next_len { + let v0 = self.evals[i << 1]; + let v1 = self.evals[(i << 1) | 1]; + // (1-r)*v0 + r*v1 = v0 + r*(v1-v0) + self.evals[i] = v0 + r * (v1 - v0); + } + self.len = next_len; + self.num_vars = self.num_vars.saturating_sub(1); + } + + #[inline] + fn bind_msb_in_place(&mut self, r: F) { + let next_len = self.len / 2; + let (left, right) = self.evals.split_at_mut(next_len); + for i in 0..next_len { + let v0 = left[i]; + let v1 = right[i]; + left[i] = v0 + r * (v1 - v0); + } + self.len = next_len; + self.num_vars = self.num_vars.saturating_sub(1); + } + + /// Evaluate without mutating `self`. + /// + /// # Panics + /// + /// Panics if `point.len() != self.num_vars`. + pub fn evaluate_with_order(&self, point: &[F], order: BindingOrder) -> F { + if point.is_empty() { + return self.evals[0]; + } + assert_eq!( + point.len(), + self.num_vars, + "point dimension mismatch: expected {}, got {}", + self.num_vars, + point.len() + ); + let mut tmp = self.clone(); + for r in point.iter().copied() { + tmp.bind_in_place(r, order); + } + tmp.evals[0] + } +} + +impl Polynomial for DenseMultilinearEvals { + fn num_vars(&self) -> usize { + self.num_vars + } + + fn evaluate(&self, point: &[F]) -> F { + self.evaluate_with_order(point, BindingOrder::LowToHigh) + } + + fn coeffs(&self) -> Vec { + self.evals[..self.len].to_vec() + } +} diff --git a/src/primitives/poly.rs b/src/primitives/poly.rs index 1e9a8b63..16f034cd 100644 --- a/src/primitives/poly.rs +++ b/src/primitives/poly.rs @@ -1,9 +1,9 @@ -//! Polynomial trait for multilinear polynomials +//! Polynomial trait for multilinear polynomials. -use super::arithmetic::Field; +use super::arithmetic::FieldCore; /// Trait for multilinear Lagrange polynomial operations -pub trait MultilinearLagrange: Polynomial { +pub trait MultilinearLagrange: Polynomial { /// Compute multilinear Lagrange basis evaluations at a point /// /// For variables (r₀, r₁, ..., r_{n-1}), computes all 2^n basis polynomial evaluations. @@ -30,7 +30,7 @@ pub trait MultilinearLagrange: Polynomial { /// Trait for multilinear polynomials /// /// Represents a polynomial in evaluation form (coefficients at hypercube points). -pub trait Polynomial { +pub trait Polynomial { /// Number of variables fn num_vars(&self) -> usize; @@ -52,6 +52,9 @@ pub trait Polynomial { /// # Returns /// Polynomial evaluation result fn evaluate(&self, point: &[F]) -> F; + + /// Return the coefficient/evaluation table on `{0,1}^n` in LSB-first order. + fn coeffs(&self) -> Vec; } /// Compute multilinear Lagrange basis evaluations at a point @@ -62,7 +65,7 @@ pub trait Polynomial { /// Uses an iterative doubling approach: /// - Start with [1-r₀, r₀] /// - For each variable rᵢ, split each value v into [v*(1-rᵢ), v*rᵢ] -pub(crate) fn multilinear_lagrange_basis(output: &mut [F], point: &[F]) { +pub(crate) fn multilinear_lagrange_basis(output: &mut [F], point: &[F]) { assert!( output.len() <= (1 << point.len()), "Output length must be at most 2^point.len()" @@ -115,7 +118,7 @@ pub(crate) fn multilinear_lagrange_basis(output: &mut [F], point: &[F] /// polynomial_evaluation(point) = L^T × M × R /// /// Splits variables between rows and columns based on sigma and nu. -pub fn compute_left_right_vectors( +pub fn compute_left_right_vectors( point: &[F], nu: usize, sigma: usize, diff --git a/src/primitives/serialization.rs b/src/primitives/serialization.rs index f4a0bf1e..eaca5481 100644 --- a/src/primitives/serialization.rs +++ b/src/primitives/serialization.rs @@ -182,11 +182,13 @@ mod primitive_impls { impl_primitive_serialization!(u16, 2); impl_primitive_serialization!(u32, 4); impl_primitive_serialization!(u64, 8); + impl_primitive_serialization!(u128, 16); impl_primitive_serialization!(usize, std::mem::size_of::()); impl_primitive_serialization!(i8, 1); impl_primitive_serialization!(i16, 2); impl_primitive_serialization!(i32, 4); impl_primitive_serialization!(i64, 8); + impl_primitive_serialization!(i128, 16); impl Valid for bool { fn check(&self) -> Result<(), SerializationError> { diff --git a/src/primitives/transcript.rs b/src/primitives/transcript.rs index 89ebc29a..ce2e8f53 100644 --- a/src/primitives/transcript.rs +++ b/src/primitives/transcript.rs @@ -2,13 +2,13 @@ #![allow(missing_docs)] -use crate::primitives::arithmetic::{Field, Module}; +use crate::primitives::arithmetic::{CanonicalField, FieldCore, Module}; use crate::primitives::HachiSerialize; /// Transcript for Fiat-Shamir transformations pub trait Transcript { /// Field type for challenges - type Field: Field; + type Field: FieldCore + CanonicalField; /// Append raw bytes to the transcript fn append_bytes(&mut self, label: &[u8], bytes: &[u8]); diff --git a/src/protocol/challenges/mod.rs b/src/protocol/challenges/mod.rs new file mode 100644 index 00000000..524941ed --- /dev/null +++ b/src/protocol/challenges/mod.rs @@ -0,0 +1,6 @@ +//! Protocol-level Fiat–Shamir challenge samplers. +//! +//! These utilities derive structured challenges (e.g. sparse ring elements) from +//! the transcript while keeping the low-level representations in the algebra layer. + +pub mod sparse; diff --git a/src/protocol/challenges/sparse.rs b/src/protocol/challenges/sparse.rs new file mode 100644 index 00000000..aca54aaf --- /dev/null +++ b/src/protocol/challenges/sparse.rs @@ -0,0 +1,121 @@ +//! Sparse challenge sampling via Fiat–Shamir. + +use crate::algebra::ring::{CyclotomicRing, SparseChallenge, SparseChallengeConfig}; +use crate::error::HachiError; +use crate::protocol::transcript::labels::{ABSORB_SPARSE_CHALLENGE, CHALLENGE_SPARSE_CHALLENGE}; +use crate::protocol::transcript::Transcript; +use crate::{CanonicalField, FieldCore}; + +/// Sample a sparse ring challenge (exact weight ω) from a transcript. +/// +/// This is intentionally deterministic and label-aware: +/// - first we absorb the sampling context under `ABSORB_SPARSE_CHALLENGE`, +/// - then we derive as many `CHALLENGE_SPARSE_CHALLENGE` scalars as needed. +/// +/// Notes: +/// - Indices are sampled with a simple `mod D` reduction. For the intended +/// regimes (small `D`, cryptographic transcript), any bias is negligible. +/// - Duplicate indices are rejected to enforce exact Hamming weight. +/// +/// # Errors +/// +/// Returns an error if the provided config is invalid for degree `D`. +pub fn sparse_challenge_from_transcript( + transcript: &mut T, + label: &[u8], + instance_idx: u64, + cfg: &SparseChallengeConfig, +) -> Result +where + F: FieldCore + CanonicalField, + T: Transcript, +{ + cfg.validate::() + .map_err(|e| HachiError::InvalidInput(format!("invalid sparse challenge config: {e}")))?; + + // Absorb domain-separating context so different call sites can't collide. + transcript.append_bytes(ABSORB_SPARSE_CHALLENGE, label); + transcript.append_bytes(ABSORB_SPARSE_CHALLENGE, &instance_idx.to_le_bytes()); + transcript.append_bytes(ABSORB_SPARSE_CHALLENGE, &(D as u64).to_le_bytes()); + transcript.append_bytes(ABSORB_SPARSE_CHALLENGE, &(cfg.weight as u64).to_le_bytes()); + // Include the coefficient alphabet (as little-endian i16 stream). + let mut coeff_bytes = Vec::with_capacity(cfg.nonzero_coeffs.len() * 2); + for &c in cfg.nonzero_coeffs.iter() { + coeff_bytes.extend_from_slice(&c.to_le_bytes()); + } + transcript.append_bytes(ABSORB_SPARSE_CHALLENGE, &coeff_bytes); + + let mut seen = vec![false; D]; + let mut positions = Vec::with_capacity(cfg.weight); + let mut coeffs = Vec::with_capacity(cfg.weight); + + while positions.len() < cfg.weight { + let r = transcript + .challenge_scalar(CHALLENGE_SPARSE_CHALLENGE) + .to_canonical_u128(); + let lo = r as u64; + let hi = (r >> 64) as u64; + + let pos = (lo % (D as u64)) as usize; + if seen[pos] { + continue; + } + seen[pos] = true; + positions.push(pos as u32); + + let coeff_idx = (hi % (cfg.nonzero_coeffs.len() as u64)) as usize; + let c = cfg.nonzero_coeffs[coeff_idx]; + debug_assert_ne!(c, 0); + coeffs.push(c); + } + + Ok(SparseChallenge { positions, coeffs }) +} + +/// Sample `n` sparse challenges from a transcript, returning the sparse +/// representation directly. +/// +/// # Errors +/// +/// Returns an error if challenge sampling fails. +pub fn sample_sparse_challenges( + transcript: &mut T, + label: &[u8], + n: usize, + cfg: &SparseChallengeConfig, +) -> Result, HachiError> +where + F: FieldCore + CanonicalField, + T: Transcript, +{ + (0..n) + .map(|i| sparse_challenge_from_transcript::(transcript, label, i as u64, cfg)) + .collect() +} + +/// Sample `n` sparse challenges from a transcript and convert them to dense +/// `CyclotomicRing` elements. +/// +/// # Errors +/// +/// Returns an error if challenge sampling or dense conversion fails. +pub fn sample_dense_challenges( + transcript: &mut T, + label: &[u8], + n: usize, + cfg: &SparseChallengeConfig, +) -> Result>, HachiError> +where + F: FieldCore + CanonicalField, + T: Transcript, +{ + (0..n) + .map(|i| { + let sparse = + sparse_challenge_from_transcript::(transcript, label, i as u64, cfg)?; + sparse + .to_dense::() + .map_err(|e| HachiError::InvalidInput(e.to_string())) + }) + .collect() +} diff --git a/src/protocol/commitment/commit.rs b/src/protocol/commitment/commit.rs new file mode 100644 index 00000000..485a5570 --- /dev/null +++ b/src/protocol/commitment/commit.rs @@ -0,0 +1,146 @@ +//! Ring-native §4.1 commitment core implementation. + +use super::config::{ + ensure_block_layout, ensure_matrix_shape, ensure_supported_num_vars, validate_and_derive_layout, +}; +use super::onehot::{inner_ajtai_onehot, map_onehot_to_sparse_blocks}; +use super::scheme::RingCommitmentScheme; +use super::types::RingCommitment; +use super::utils::linear::{decompose_block, decompose_rows, mat_vec_mul_unchecked}; +use super::utils::matrix::{derive_public_matrix, sample_public_matrix_seed, PublicMatrixSeed}; +use super::CommitmentConfig; +use crate::algebra::ring::CyclotomicRing; +use crate::error::HachiError; +use crate::{CanonicalField, FieldCore, FieldSampling}; + +/// Unified setup for the ring-native commitment (§4.1) and prover (§4.2). +#[allow(non_snake_case)] +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct RingCommitmentSetup { + /// Maximum supported variable count. + pub max_num_vars: usize, + /// Public seed used to derive commitment matrices. + pub public_matrix_seed: PublicMatrixSeed, + /// Inner matrix `A`. + pub A: Vec>>, + /// Outer matrix `B`. + pub B: Vec>>, + /// Prover matrix `D ∈ R_q^{n_D × δ·2^R}` (§4.2). + pub D: Vec>>, +} + +/// Concrete §4.1 commitment core. +#[derive(Clone, Copy, Default)] +pub struct HachiCommitmentCore; + +impl RingCommitmentScheme for HachiCommitmentCore +where + F: FieldCore + CanonicalField + FieldSampling, + Cfg: CommitmentConfig, +{ + type ProverSetup = RingCommitmentSetup; + type VerifierSetup = RingCommitmentSetup; + type Commitment = RingCommitment; + + fn setup(max_num_vars: usize) -> Result<(Self::ProverSetup, Self::VerifierSetup), HachiError> { + let layout = validate_and_derive_layout::()?; + ensure_supported_num_vars(max_num_vars, layout.required_vars)?; + let public_matrix_seed = sample_public_matrix_seed(); + let a_matrix = + derive_public_matrix::(Cfg::N_A, layout.inner_width, &public_matrix_seed, b"A"); + let b_matrix = + derive_public_matrix::(Cfg::N_B, layout.outer_width, &public_matrix_seed, b"B"); + let d_matrix = derive_public_matrix::( + Cfg::N_D, + layout.d_matrix_width, + &public_matrix_seed, + b"D", + ); + + let setup = RingCommitmentSetup { + max_num_vars, + public_matrix_seed, + A: a_matrix, + B: b_matrix, + D: d_matrix, + }; + ensure_matrix_shape(&setup.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape(&setup.B, Cfg::N_B, layout.outer_width, "B")?; + ensure_matrix_shape(&setup.D, Cfg::N_D, layout.d_matrix_width, "D")?; + Ok((setup.clone(), setup)) + } + + #[allow(clippy::type_complexity)] + fn commit_ring_blocks( + f_blocks: &[Vec>], + setup: &Self::ProverSetup, + ) -> Result< + ( + Self::Commitment, + Vec>>, + Vec>>, + ), + HachiError, + > { + let layout = validate_and_derive_layout::()?; + ensure_supported_num_vars(setup.max_num_vars, layout.required_vars)?; + ensure_block_layout(f_blocks, layout)?; + ensure_matrix_shape(&setup.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape(&setup.B, Cfg::N_B, layout.outer_width, "B")?; + + let mut s_all: Vec>> = Vec::with_capacity(layout.num_blocks); + let mut t_hat_all: Vec>> = Vec::with_capacity(layout.num_blocks); + let mut t_hat_flat: Vec> = Vec::with_capacity(layout.outer_width); + for block in f_blocks { + let s_i = decompose_block(block, Cfg::DELTA, Cfg::LOG_BASIS); + + let t_i = mat_vec_mul_unchecked(&setup.A, &s_i); + let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); + t_hat_flat.extend(t_hat_i.iter().copied()); + + s_all.push(s_i); + t_hat_all.push(t_hat_i); + } + + let u = mat_vec_mul_unchecked(&setup.B, &t_hat_flat); + Ok((RingCommitment { u }, s_all, t_hat_all)) + } + + #[allow(clippy::type_complexity)] + fn commit_onehot( + onehot_k: usize, + indices: &[usize], + setup: &Self::ProverSetup, + ) -> Result< + ( + Self::Commitment, + Vec>>, + Vec>>, + ), + HachiError, + > { + let layout = validate_and_derive_layout::()?; + ensure_supported_num_vars(setup.max_num_vars, layout.required_vars)?; + ensure_matrix_shape(&setup.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape(&setup.B, Cfg::N_B, layout.outer_width, "B")?; + + let sparse_blocks = map_onehot_to_sparse_blocks(onehot_k, indices, Cfg::R, Cfg::M, D)?; + + let mut s_all: Vec>> = Vec::with_capacity(layout.num_blocks); + let mut t_hat_all: Vec>> = Vec::with_capacity(layout.num_blocks); + let mut t_hat_flat: Vec> = Vec::with_capacity(layout.outer_width); + + for block_entries in &sparse_blocks { + let (t_i, s_i) = + inner_ajtai_onehot(&setup.A, block_entries, layout.block_len, Cfg::DELTA); + let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); + t_hat_flat.extend(t_hat_i.iter().copied()); + + s_all.push(s_i); + t_hat_all.push(t_hat_i); + } + + let u = mat_vec_mul_unchecked(&setup.B, &t_hat_flat); + Ok((RingCommitment { u }, s_all, t_hat_all)) + } +} diff --git a/src/protocol/commitment/config.rs b/src/protocol/commitment/config.rs new file mode 100644 index 00000000..3150554e --- /dev/null +++ b/src/protocol/commitment/config.rs @@ -0,0 +1,186 @@ +//! Configuration presets for ring-native commitment construction. + +use super::utils::math::checked_pow2; +use crate::algebra::ring::CyclotomicRing; +use crate::error::HachiError; +use crate::FieldCore; + +/// Parameter bundle for the ring-native commitment core (§4.1–§4.2). +pub trait CommitmentConfig: Clone + Send + Sync + 'static { + /// Ring degree used by `CyclotomicRing`. + const D: usize; + /// Number of variables inside each committed block (`2^M` entries). + const M: usize; + /// Number of block-select variables (`2^R` blocks). + const R: usize; + /// Inner Ajtai matrix row count. + const N_A: usize; + /// Outer commitment matrix row count. + const N_B: usize; + /// Prover commitment matrix `D` row count (§4.2). + const N_D: usize; + /// Base-2 logarithm of gadget decomposition base. + const LOG_BASIS: u32; + /// Decomposition levels `delta`. + const DELTA: usize; + /// Decomposition levels for the folded witness `z` (`τ` in the paper). + const TAU: usize; + /// L∞ norm bound for `z` (`β` in the paper). Prover aborts if exceeded. + const BETA: u128; + /// Hamming weight of sparse challenges (`ω` in the paper). + const CHALLENGE_WEIGHT: usize; +} + +/// Runtime-derived dimensions from a `CommitmentConfig`. +#[derive(Debug, Clone, Copy)] +pub(super) struct CommitmentLayout { + /// Number of committed blocks (`2^R`). + pub(super) num_blocks: usize, + /// Number of ring elements per block (`2^M`). + pub(super) block_len: usize, + /// Width of inner matrix `A`. + pub(super) inner_width: usize, + /// Width of outer matrix `B`. + pub(super) outer_width: usize, + /// Width of prover matrix `D` (`δ · 2^R`). + pub(super) d_matrix_width: usize, + /// Minimum variable count supported by this config. + pub(super) required_vars: usize, +} + +/// Validate static config invariants and derive runtime dimensions. +/// +/// # Errors +/// +/// Returns an error when config constants are inconsistent or overflow. +pub(super) fn validate_and_derive_layout( +) -> Result { + if D != Cfg::D { + return Err(HachiError::InvalidSetup(format!( + "const D={D} mismatches config D={}", + Cfg::D + ))); + } + if Cfg::LOG_BASIS == 0 || Cfg::LOG_BASIS >= 128 { + return Err(HachiError::InvalidSetup("invalid LOG_BASIS".to_string())); + } + if (Cfg::DELTA as u32).saturating_mul(Cfg::LOG_BASIS) > 128 { + return Err(HachiError::InvalidSetup( + "DELTA * LOG_BASIS must be <= 128".to_string(), + )); + } + + let num_blocks = checked_pow2(Cfg::R)?; + let block_len = checked_pow2(Cfg::M)?; + let inner_width = block_len + .checked_mul(Cfg::DELTA) + .ok_or_else(|| HachiError::InvalidSetup("inner width overflow".to_string()))?; + let outer_width = Cfg::N_A + .checked_mul(Cfg::DELTA) + .and_then(|x| x.checked_mul(num_blocks)) + .ok_or_else(|| HachiError::InvalidSetup("outer width overflow".to_string()))?; + let d_matrix_width = Cfg::DELTA + .checked_mul(num_blocks) + .ok_or_else(|| HachiError::InvalidSetup("D-matrix width overflow".to_string()))?; + let required_vars = Cfg::M + .checked_add(Cfg::R) + .ok_or_else(|| HachiError::InvalidSetup("variable count overflow".to_string()))?; + + Ok(CommitmentLayout { + num_blocks, + block_len, + inner_width, + outer_width, + d_matrix_width, + required_vars, + }) +} + +/// Ensure `max_num_vars` is sufficient for config dimensions. +/// +/// # Errors +/// +/// Returns an error when `max_num_vars < required_vars`. +pub(super) fn ensure_supported_num_vars( + max_num_vars: usize, + required_vars: usize, +) -> Result<(), HachiError> { + if max_num_vars < required_vars { + return Err(HachiError::InvalidSetup(format!( + "max_num_vars {max_num_vars} is smaller than required {required_vars}" + ))); + } + Ok(()) +} + +/// Ensure input blocks match the expected config-derived layout. +/// +/// # Errors +/// +/// Returns an error when block count or per-block size mismatch. +pub(super) fn ensure_block_layout( + f_blocks: &[Vec>], + layout: CommitmentLayout, +) -> Result<(), HachiError> { + if f_blocks.len() != layout.num_blocks { + return Err(HachiError::InvalidSize { + expected: layout.num_blocks, + actual: f_blocks.len(), + }); + } + for block in f_blocks { + if block.len() != layout.block_len { + return Err(HachiError::InvalidSize { + expected: layout.block_len, + actual: block.len(), + }); + } + } + Ok(()) +} + +/// Ensure matrix shape matches expected dimensions. +/// +/// # Errors +/// +/// Returns an error if row count or row width mismatch. +pub(super) fn ensure_matrix_shape( + mat: &[Vec], + expected_rows: usize, + expected_cols: usize, + name: &str, +) -> Result<(), HachiError> { + if mat.len() != expected_rows { + return Err(HachiError::InvalidSize { + expected: expected_rows, + actual: mat.len(), + }); + } + for (row_idx, row) in mat.iter().enumerate() { + if row.len() != expected_cols { + return Err(HachiError::InvalidSetup(format!( + "{name} row {row_idx} has width {}, expected {expected_cols}", + row.len() + ))); + } + } + Ok(()) +} + +/// Default correctness-first config for early protocol integration. +#[derive(Clone, Copy, Debug, Default)] +pub struct DefaultCommitmentConfig; + +impl CommitmentConfig for DefaultCommitmentConfig { + const D: usize = 16; + const M: usize = 4; + const R: usize = 2; + const N_A: usize = 8; + const N_B: usize = 4; + const N_D: usize = 4; + const LOG_BASIS: u32 = 4; + const DELTA: usize = 9; + const TAU: usize = 4; + const BETA: u128 = 1_000_000; + const CHALLENGE_WEIGHT: usize = 3; +} diff --git a/src/protocol/commitment/mod.rs b/src/protocol/commitment/mod.rs new file mode 100644 index 00000000..3a3b7170 --- /dev/null +++ b/src/protocol/commitment/mod.rs @@ -0,0 +1,17 @@ +//! Protocol commitment abstraction layer. + +mod commit; +mod config; +pub(crate) mod onehot; +mod scheme; +mod transcript_append; +mod types; +pub(crate) mod utils; + +pub use commit::{HachiCommitmentCore, RingCommitmentSetup}; +pub use config::{CommitmentConfig, DefaultCommitmentConfig}; +pub use scheme::{CommitmentScheme, RingCommitmentScheme, StreamingCommitmentScheme}; +pub use transcript_append::AppendToTranscript; +pub use types::{ + DummyProof, HachiCommitment, HachiOpeningClaim, HachiOpeningPoint, RingCommitment, +}; diff --git a/src/protocol/commitment/onehot.rs b/src/protocol/commitment/onehot.rs new file mode 100644 index 00000000..ccf5998d --- /dev/null +++ b/src/protocol/commitment/onehot.rs @@ -0,0 +1,268 @@ +//! One-hot commitment path for regular one-hot ring elements. +//! +//! Exploits the sparsity of one-hot witnesses (coefficients in {0,1}) to +//! eliminate all inner ring multiplications. The inner Ajtai `t = A * s` +//! reduces to summing selected columns of `A` with negacyclic rotations. + +use std::collections::BTreeMap; + +use crate::algebra::ring::CyclotomicRing; +use crate::error::HachiError; +use crate::{CanonicalField, FieldCore}; + +/// Describes a nonzero ring element within one block of the commitment layout. +#[derive(Debug, Clone)] +pub(crate) struct SparseBlockEntry { + /// Position within the block (0..2^M). + pub pos_in_block: usize, + /// Coefficient indices that are 1 within this ring element. + pub nonzero_coeffs: Vec, +} + +/// Map a regular one-hot witness to sparse ring block entries. +/// +/// - `onehot_k`: chunk size K. The witness has T chunks of K field elements, +/// each chunk containing exactly one 1. +/// - `indices`: length-T slice where `indices[c]` is the hot position in +/// chunk `c` (must be in `[0, K)`). +/// - `r`, `m`: commitment config parameters (2^R blocks of 2^M ring elements). +/// - `D`: ring degree (const generic on caller side, passed as runtime here). +/// +/// Returns one `Vec` per block (outer len = 2^R). +/// +/// # Errors +/// +/// Returns an error if K and D are not "nicely matched" (one must divide +/// the other), if any index is out of range, or if the dimensions don't +/// fill the commitment layout. +pub(crate) fn map_onehot_to_sparse_blocks( + onehot_k: usize, + indices: &[usize], + r: usize, + m: usize, + d: usize, +) -> Result>, HachiError> { + if onehot_k == 0 || d == 0 { + return Err(HachiError::InvalidInput( + "onehot_k and D must be nonzero".into(), + )); + } + if !(onehot_k % d == 0 || d % onehot_k == 0) { + return Err(HachiError::InvalidInput(format!( + "K={onehot_k} and D={d} must be nicely matched (one divides the other)" + ))); + } + + let num_chunks = indices.len(); + let total_field_elems = num_chunks + .checked_mul(onehot_k) + .ok_or_else(|| HachiError::InvalidInput("T*K overflow".into()))?; + if total_field_elems % d != 0 { + return Err(HachiError::InvalidInput(format!( + "T*K={total_field_elems} is not divisible by D={d}" + ))); + } + let total_ring_elems = total_field_elems / d; + let num_blocks = 1usize << r; + let block_len = 1usize << m; + if total_ring_elems != num_blocks * block_len { + return Err(HachiError::InvalidSize { + expected: num_blocks * block_len, + actual: total_ring_elems, + }); + } + + // Accumulate nonzero coefficients per ring element index. + let mut ring_elem_map: BTreeMap> = BTreeMap::new(); + for (c, &idx) in indices.iter().enumerate() { + if idx >= onehot_k { + return Err(HachiError::InvalidInput(format!( + "index {idx} out of range for chunk size K={onehot_k} at position {c}" + ))); + } + let field_pos = c * onehot_k + idx; + let ring_elem_idx = field_pos / d; + let coeff_idx = field_pos % d; + ring_elem_map + .entry(ring_elem_idx) + .or_default() + .push(coeff_idx); + } + + // Distribute into blocks using the same interleaved layout as commit_coeffs: + // block_idx = ring_elem_idx % num_blocks + // pos_in_block = ring_elem_idx / num_blocks + // (equivalently: flat_idx = (pos_in_block << R) + block_idx) + let mut blocks: Vec> = vec![Vec::new(); num_blocks]; + for (ring_elem_idx, nonzero_coeffs) in ring_elem_map { + let block_idx = ring_elem_idx & (num_blocks - 1); + let pos_in_block = ring_elem_idx >> r; + blocks[block_idx].push(SparseBlockEntry { + pos_in_block, + nonzero_coeffs, + }); + } + + Ok(blocks) +} + +/// Sparse inner Ajtai: compute `t = A * s` for a one-hot block. +/// +/// Instead of materializing the full decomposed vector `s` and doing a dense +/// matvec, we accumulate only the nonzero contributions: +/// +/// ```text +/// t[a] = sum_{entry} A[a][entry.pos * delta].mul_by_monomial_sum(entry.nonzero_coeffs) +/// ``` +/// +/// Also returns `s` (densely materialized) for the opening proof hint. +#[allow(non_snake_case)] +pub(crate) fn inner_ajtai_onehot( + A: &[Vec>], + sparse_entries: &[SparseBlockEntry], + block_len: usize, + delta: usize, +) -> (Vec>, Vec>) { + let n_a = A.len(); + let inner_width = block_len * delta; + + // Build s: mostly zeros, with level-0 entries for nonzero ring elements. + let mut s = vec![CyclotomicRing::::zero(); inner_width]; + for entry in sparse_entries { + let mut coeffs = [F::zero(); D]; + for &ci in &entry.nonzero_coeffs { + coeffs[ci] = F::one(); + } + s[entry.pos_in_block * delta] = CyclotomicRing::from_coefficients(coeffs); + } + + // Compute t[a] = sum over nonzero entries of A[a][pos*delta] * f_j, + // where f_j is the monomial sum at that position. + let mut t = vec![CyclotomicRing::::zero(); n_a]; + for entry in sparse_entries { + let col = entry.pos_in_block * delta; + for a in 0..n_a { + t[a] += A[a][col].mul_by_monomial_sum(&entry.nonzero_coeffs); + } + } + + (t, s) +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::test_utils::F; + + #[test] + fn map_onehot_k_gt_d() { + // K=16, D=4, T=2 chunks => 32 field elements => 8 ring elements + // R=1 (2 blocks), M=2 (4 per block) => 8 ring elements total + let k = 16; + let d = 4; + let indices = vec![3, 10]; + let blocks = map_onehot_to_sparse_blocks(k, &indices, 1, 2, d).unwrap(); + + assert_eq!(blocks.len(), 2); + let total_entries: usize = blocks.iter().map(|b| b.len()).sum(); + assert_eq!(total_entries, 2, "T=2 nonzero ring elements"); + + for block in &blocks { + for entry in block { + assert_eq!(entry.nonzero_coeffs.len(), 1, "K>D => single monomial"); + } + } + } + + #[test] + fn map_onehot_k_eq_d() { + // K=4, D=4, T=4 chunks => 16 field elements => 4 ring elements + // R=1 (2 blocks), M=1 (2 per block) + let k = 4; + let d = 4; + let indices = vec![0, 2, 3, 1]; + let blocks = map_onehot_to_sparse_blocks(k, &indices, 1, 1, d).unwrap(); + + assert_eq!(blocks.len(), 2); + let total_entries: usize = blocks.iter().map(|b| b.len()).sum(); + assert_eq!(total_entries, 4, "K=D => every ring element is nonzero"); + + for block in &blocks { + for entry in block { + assert_eq!(entry.nonzero_coeffs.len(), 1, "K=D => single monomial"); + } + } + } + + #[test] + fn map_onehot_k_lt_d() { + // K=4, D=8, T=8 chunks => 32 field elements => 4 ring elements + // R=1 (2 blocks), M=1 (2 per block) + let k = 4; + let d = 8; + let indices = vec![0, 2, 3, 1, 0, 0, 3, 3]; + let blocks = map_onehot_to_sparse_blocks(k, &indices, 1, 1, d).unwrap(); + + assert_eq!(blocks.len(), 2); + let total_entries: usize = blocks.iter().map(|b| b.len()).sum(); + assert_eq!(total_entries, 4, "D>K => all ring elements nonzero"); + + for block in &blocks { + for entry in block { + assert_eq!( + entry.nonzero_coeffs.len(), + 2, + "D=2K => 2 nonzero coeffs per ring element" + ); + } + } + } + + #[test] + fn map_onehot_rejects_non_divisible() { + let result = map_onehot_to_sparse_blocks(3, &[0, 1], 0, 1, 4); + assert!(result.is_err()); + } + + #[test] + fn inner_ajtai_onehot_single_monomial() { + const D: usize = 4; + type R = CyclotomicRing; + + // A is 2x4 (N_A=2, inner_width = block_len * delta = 2 * 2 = 4) + let a: Vec> = vec![ + vec![ + R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 1) as u64))), + R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 10) as u64))), + R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 20) as u64))), + R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 30) as u64))), + ], + vec![ + R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 5) as u64))), + R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 15) as u64))), + R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 25) as u64))), + R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 35) as u64))), + ], + ]; + + // One nonzero entry at pos=1, coefficient index 2 => monomial X^2 + let entries = vec![SparseBlockEntry { + pos_in_block: 1, + nonzero_coeffs: vec![2], + }]; + + let (t, s) = inner_ajtai_onehot(&a, &entries, 2, 2); + + // t[row] should equal A[row][1*2] * X^2 = A[row][2].negacyclic_shift(2) + for row in 0..2 { + let expected = a[row][2].negacyclic_shift(2); + assert_eq!(t[row], expected); + } + + // s should have a nonzero entry at position 1*2 = 2 + assert_eq!(s[2].coefficients()[2], F::one()); + assert!(s[0] == R::zero()); + assert!(s[1] == R::zero()); + assert!(s[3] == R::zero()); + } +} diff --git a/src/protocol/commitment/scheme.rs b/src/protocol/commitment/scheme.rs new file mode 100644 index 00000000..df0c4301 --- /dev/null +++ b/src/protocol/commitment/scheme.rs @@ -0,0 +1,277 @@ +//! Commitment-scheme trait surface for Hachi protocol code. + +use super::config::CommitmentConfig; +use super::transcript_append::AppendToTranscript; +use super::utils::math::checked_pow2; +use crate::algebra::ring::CyclotomicRing; +use crate::error::HachiError; +use crate::protocol::transcript::Transcript; +use crate::{CanonicalField, FieldCore, Polynomial}; + +/// Output type for batched commitments. +pub(crate) type BatchCommitOutput = Result, HachiError>; + +/// Generic commitment-scheme interface used by Hachi protocol code. +pub trait CommitmentScheme: Clone + Send + Sync + 'static +where + F: FieldCore + CanonicalField, +{ + /// Prover setup parameters. + type ProverSetup: Clone + Send + Sync; + /// Verifier setup parameters. + type VerifierSetup: Clone + Send + Sync; + /// Commitment object. + type Commitment: Clone + PartialEq + Send + Sync + AppendToTranscript; + /// Evaluation/opening proof object. + type Proof: Clone + Send + Sync; + /// Optional prover-side hint produced at commitment time. + type OpeningProofHint: Clone + Send + Sync; + + /// Build prover setup for maximum polynomial dimension. + fn setup_prover(max_num_vars: usize) -> Self::ProverSetup; + + /// Derive verifier setup from prover setup. + fn setup_verifier(setup: &Self::ProverSetup) -> Self::VerifierSetup; + + /// Commit to one polynomial. + /// + /// # Errors + /// + /// Returns an error when setup/parameter constraints are not satisfied. + fn commit>( + poly: &P, + setup: &Self::ProverSetup, + ) -> Result<(Self::Commitment, Self::OpeningProofHint), HachiError>; + + /// Commit to many polynomials. + /// + /// # Errors + /// + /// Returns an error if any per-polynomial commitment fails. + fn batch_commit>( + polys: &[P], + setup: &Self::ProverSetup, + ) -> BatchCommitOutput { + polys.iter().map(|p| Self::commit(p, setup)).collect() + } + + /// Produce an opening proof at `opening_point`. + /// + /// # Errors + /// + /// Returns an error if the opening point is invalid or proof generation fails. + fn prove, P: Polynomial>( + setup: &Self::ProverSetup, + poly: &P, + opening_point: &[F], + hint: Option, + transcript: &mut T, + commitment: &Self::Commitment, + ) -> Result; + + /// Verify an opening proof. + /// + /// # Errors + /// + /// Returns an error when verification fails. + fn verify>( + proof: &Self::Proof, + setup: &Self::VerifierSetup, + transcript: &mut T, + opening_point: &[F], + opening: &F, + commitment: &Self::Commitment, + ) -> Result<(), HachiError>; + + /// Homomorphic commitment combination. + fn combine_commitments(commitments: &[Self::Commitment], coeffs: &[F]) -> Self::Commitment; + + /// Homomorphic hint combination. + fn combine_hints(hints: Vec, coeffs: &[F]) -> Self::OpeningProofHint; + + /// Protocol identifier. + fn protocol_name() -> &'static [u8]; +} + +/// Streaming extension for chunked commitment workflows. +pub trait StreamingCommitmentScheme: CommitmentScheme +where + F: FieldCore + CanonicalField, +{ + /// Intermediate chunk state. + type ChunkState: Clone + Send + Sync + PartialEq + std::fmt::Debug; + + /// Process one chunk of field elements. + fn process_chunk(setup: &Self::ProverSetup, chunk: &[F]) -> Self::ChunkState; + + /// Process one chunk of one-hot values. + fn process_chunk_onehot( + setup: &Self::ProverSetup, + onehot_k: usize, + chunk: &[Option], + ) -> Self::ChunkState; + + /// Aggregate chunk states into one commitment + hint. + fn aggregate_chunks( + setup: &Self::ProverSetup, + onehot_k: Option, + chunks: &[Self::ChunkState], + ) -> (Self::Commitment, Self::OpeningProofHint); +} + +/// Ring-native commitment interface for §4.1 implementation work. +pub trait RingCommitmentScheme: Clone + Send + Sync + 'static +where + F: FieldCore + CanonicalField, + Cfg: CommitmentConfig, +{ + /// Prover setup parameters. + type ProverSetup: Clone + Send + Sync; + /// Verifier setup parameters. + type VerifierSetup: Clone + Send + Sync; + /// Ring-native commitment type. + type Commitment: Clone + PartialEq + Send + Sync; + + /// Construct commitment setup for at most `max_num_vars` variables. + /// + /// # Errors + /// + /// Returns an error if dimensions are inconsistent with `Cfg`. + fn setup(max_num_vars: usize) -> Result<(Self::ProverSetup, Self::VerifierSetup), HachiError>; + + /// Commit to ring blocks arranged as `2^R` vectors of length `2^M`. + /// + /// Returns `(commitment, s, t_hat)` where `s` and `t_hat` are the + /// decomposed witness vectors from §4.1. + /// + /// # Errors + /// + /// Returns an error if block layout mismatches config or commitment fails. + #[allow(clippy::type_complexity)] + fn commit_ring_blocks( + f_blocks: &[Vec>], + setup: &Self::ProverSetup, + ) -> Result< + ( + Self::Commitment, + Vec>>, + Vec>>, + ), + HachiError, + >; + + /// Commit to a flat coefficient table `(f_i)_{i∈{0,1}^ℓ}` in ring form. + /// + /// The input is indexed in LSB-first order (same convention as + /// `DenseMultilinearEvals`). We split the variables as: + /// + /// - outer index `i` for the first `R` variables, + /// - inner index `j` for the last `M` variables, + /// + /// We then form blocks `f_i = (f_{i||j})_{j}` (Eq. (12) in the paper). + /// + /// This prepares `f_blocks` and delegates to `commit_ring_blocks`. + /// + /// # Errors + /// + /// Returns an error if `f_coeffs.len()` does not match the configured block + /// layout, if internal index computations overflow, or if the underlying + /// commitment routine fails. + #[allow(clippy::type_complexity)] + fn commit_coeffs( + f_coeffs: &[CyclotomicRing], + setup: &Self::ProverSetup, + ) -> Result< + ( + Self::Commitment, + Vec>>, + Vec>>, + ), + HachiError, + > { + let num_blocks = checked_pow2(Cfg::R)?; + let block_len = checked_pow2(Cfg::M)?; + let expected_len = num_blocks + .checked_mul(block_len) + .ok_or_else(|| HachiError::InvalidSetup("coefficient length overflow".to_string()))?; + if f_coeffs.len() != expected_len { + return Err(HachiError::InvalidSize { + expected: expected_len, + actual: f_coeffs.len(), + }); + } + + let mut blocks = Vec::with_capacity(num_blocks); + for i in 0..num_blocks { + let mut block = Vec::with_capacity(block_len); + for j in 0..block_len { + let idx = (j << Cfg::R) + .checked_add(i) + .ok_or_else(|| HachiError::InvalidSetup("index overflow".to_string()))?; + block.push(f_coeffs[idx]); + } + blocks.push(block); + } + + Self::commit_ring_blocks(&blocks, setup) + } + + /// Commit to a regular one-hot witness. + /// + /// The witness represents `T` chunks of `onehot_k` field elements, each + /// chunk containing exactly one 1 and all other entries 0. `indices[c]` + /// gives the hot position in chunk `c` (must be in `[0, onehot_k)`). + /// + /// Requires `D` and `onehot_k` to be "nicely matched": one must divide + /// the other. + /// + /// The default implementation materializes the full one-hot field vector, + /// packs it into ring elements via coefficient embedding, and delegates + /// to `commit_coeffs`. Implementations may override this with a + /// sparse-aware path that avoids all inner ring multiplications. + /// + /// # Errors + /// + /// Returns an error if dimensions are inconsistent or any index is out + /// of range. + #[allow(clippy::type_complexity)] + fn commit_onehot( + onehot_k: usize, + indices: &[usize], + setup: &Self::ProverSetup, + ) -> Result< + ( + Self::Commitment, + Vec>>, + Vec>>, + ), + HachiError, + > { + let num_chunks = indices.len(); + let total_field_elems = num_chunks + .checked_mul(onehot_k) + .ok_or_else(|| HachiError::InvalidInput("T*K overflow".into()))?; + if total_field_elems % D != 0 { + return Err(HachiError::InvalidInput(format!( + "T*K={total_field_elems} is not divisible by D={D}" + ))); + } + + // Materialize the full one-hot vector as ring elements. + let total_ring_elems = total_field_elems / D; + let mut ring_coeffs = vec![CyclotomicRing::::zero(); total_ring_elems]; + for (c, &idx) in indices.iter().enumerate() { + if idx >= onehot_k { + return Err(HachiError::InvalidInput(format!( + "index {idx} out of range for chunk size K={onehot_k} at position {c}" + ))); + } + let field_pos = c * onehot_k + idx; + let ring_idx = field_pos / D; + let coeff_idx = field_pos % D; + ring_coeffs[ring_idx].coeffs[coeff_idx] = F::one(); + } + + Self::commit_coeffs(&ring_coeffs, setup) + } +} diff --git a/src/protocol/commitment/transcript_append.rs b/src/protocol/commitment/transcript_append.rs new file mode 100644 index 00000000..6510ccb5 --- /dev/null +++ b/src/protocol/commitment/transcript_append.rs @@ -0,0 +1,13 @@ +//! Traits for appending commitment objects to protocol transcripts. + +use crate::protocol::transcript::Transcript; +use crate::{CanonicalField, FieldCore}; + +/// Protocol object that can be absorbed into a transcript. +pub trait AppendToTranscript +where + F: FieldCore + CanonicalField, +{ + /// Append this object to a transcript using the provided event label. + fn append_to_transcript>(&self, label: &[u8], transcript: &mut T); +} diff --git a/src/protocol/commitment/types.rs b/src/protocol/commitment/types.rs new file mode 100644 index 00000000..339a1a03 --- /dev/null +++ b/src/protocol/commitment/types.rs @@ -0,0 +1,157 @@ +//! Protocol commitment/opening wrapper types. + +use super::transcript_append::AppendToTranscript; +use crate::algebra::ring::CyclotomicRing; +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; +use crate::protocol::transcript::Transcript; +use crate::{CanonicalField, FieldCore}; +use std::io::{Read, Write}; + +/// A Hachi opening point represented as field coordinates. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct HachiOpeningPoint { + /// Point coordinates used for multilinear opening. + pub r: Vec, +} + +/// A Hachi opening claim `(point, value)`. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct HachiOpeningClaim { + /// Opening point. + pub point: HachiOpeningPoint, + /// Claimed value at `point`. + pub value: F, +} + +/// Minimal commitment wrapper used by protocol traits/tests. +#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)] +pub struct HachiCommitment(pub u128); + +/// Minimal proof wrapper used by protocol trait stubs and tests. +#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)] +pub struct DummyProof(pub u128); + +impl Valid for HachiCommitment { + fn check(&self) -> Result<(), SerializationError> { + Ok(()) + } +} + +impl HachiSerialize for HachiCommitment { + fn serialize_with_mode( + &self, + mut writer: W, + _compress: Compress, + ) -> Result<(), SerializationError> { + self.0.serialize_with_mode(&mut writer, Compress::No) + } + + fn serialized_size(&self, _compress: Compress) -> usize { + 16 + } +} + +impl HachiDeserialize for HachiCommitment { + fn deserialize_with_mode( + mut reader: R, + _compress: Compress, + validate: Validate, + ) -> Result { + let value = u128::deserialize_with_mode(&mut reader, Compress::No, validate)?; + Ok(Self(value)) + } +} + +impl Valid for DummyProof { + fn check(&self) -> Result<(), SerializationError> { + Ok(()) + } +} + +impl HachiSerialize for DummyProof { + fn serialize_with_mode( + &self, + mut writer: W, + _compress: Compress, + ) -> Result<(), SerializationError> { + self.0.serialize_with_mode(&mut writer, Compress::No) + } + + fn serialized_size(&self, _compress: Compress) -> usize { + 16 + } +} + +impl HachiDeserialize for DummyProof { + fn deserialize_with_mode( + mut reader: R, + _compress: Compress, + validate: Validate, + ) -> Result { + let value = u128::deserialize_with_mode(&mut reader, Compress::No, validate)?; + Ok(Self(value)) + } +} + +impl AppendToTranscript for HachiCommitment +where + F: FieldCore + CanonicalField, +{ + fn append_to_transcript>(&self, label: &[u8], transcript: &mut T) { + transcript.append_serde(label, self); + } +} + +/// Ring-native commitment object `u in R_q^{n_B}` used by §4.1. +#[derive(Debug, Clone, PartialEq, Eq, Default)] +pub struct RingCommitment { + /// Outer commitment vector. + pub u: Vec>, +} + +impl Valid for RingCommitment { + fn check(&self) -> Result<(), SerializationError> { + self.u.check() + } +} + +impl HachiSerialize for RingCommitment { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.u.serialize_with_mode(&mut writer, compress) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.u.serialized_size(compress) + } +} + +impl HachiDeserialize for RingCommitment { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let u = + Vec::>::deserialize_with_mode(&mut reader, compress, validate)?; + let out = Self { u }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +impl AppendToTranscript for RingCommitment +where + F: FieldCore + CanonicalField, +{ + fn append_to_transcript>(&self, label: &[u8], transcript: &mut T) { + transcript.append_serde(label, self); + } +} diff --git a/src/protocol/commitment/utils/linear.rs b/src/protocol/commitment/utils/linear.rs new file mode 100644 index 00000000..daca6d24 --- /dev/null +++ b/src/protocol/commitment/utils/linear.rs @@ -0,0 +1,44 @@ +//! Linear algebra helpers for ring commitment. + +use crate::algebra::ring::CyclotomicRing; +use crate::{CanonicalField, FieldCore}; + +pub(crate) fn mat_vec_mul_unchecked( + mat: &[Vec>], + vec: &[CyclotomicRing], +) -> Vec> { + let mut out = Vec::with_capacity(mat.len()); + for row in mat { + debug_assert_eq!(row.len(), vec.len()); + let mut acc = CyclotomicRing::::zero(); + for (a, x) in row.iter().zip(vec.iter()) { + acc += *a * *x; + } + out.push(acc); + } + out +} + +pub(crate) fn decompose_block( + block: &[CyclotomicRing], + delta: usize, + log_basis: u32, +) -> Vec> { + let mut out = Vec::with_capacity(block.len() * delta); + for coeff_vec in block { + out.extend(coeff_vec.balanced_decompose_pow2(delta, log_basis)); + } + out +} + +pub(crate) fn decompose_rows( + rows: &[CyclotomicRing], + delta: usize, + log_basis: u32, +) -> Vec> { + let mut out = Vec::with_capacity(rows.len() * delta); + for row in rows { + out.extend(row.balanced_decompose_pow2(delta, log_basis)); + } + out +} diff --git a/src/protocol/commitment/utils/math.rs b/src/protocol/commitment/utils/math.rs new file mode 100644 index 00000000..16cf8618 --- /dev/null +++ b/src/protocol/commitment/utils/math.rs @@ -0,0 +1,14 @@ +//! Small math helpers for commitment internals. + +use crate::error::HachiError; + +/// Compute `2^exp` with overflow checks. +/// +/// # Errors +/// +/// Returns `InvalidSetup` if `2^exp` does not fit in `usize`. +pub(in crate::protocol::commitment) fn checked_pow2(exp: usize) -> Result { + 1usize + .checked_shl(exp as u32) + .ok_or_else(|| HachiError::InvalidSetup(format!("2^{exp} does not fit usize"))) +} diff --git a/src/protocol/commitment/utils/matrix.rs b/src/protocol/commitment/utils/matrix.rs new file mode 100644 index 00000000..fa0b80ce --- /dev/null +++ b/src/protocol/commitment/utils/matrix.rs @@ -0,0 +1,131 @@ +//! Matrix sampling helpers for setup. + +use crate::algebra::ring::CyclotomicRing; +use crate::{FieldCore, FieldSampling}; +use rand_core::{CryptoRng, RngCore}; +use sha3::digest::{ExtendableOutput, Update, XofReader}; +use sha3::Shake256; + +/// Public seed used to derive commitment matrices. +pub(crate) type PublicMatrixSeed = [u8; 32]; + +const PUBLIC_MATRIX_DOMAIN: &[u8] = b"hachi/commitment/public-matrix"; + +/// Fixed public seed for deterministic, reproducible setup. +pub(crate) fn sample_public_matrix_seed() -> PublicMatrixSeed { + let mut seed = [0u8; 32]; + seed[..8].copy_from_slice(&0xDEAD_BEEF_CAFE_BABEu64.to_le_bytes()); + seed +} + +/// Derive a public matrix from a seed using domain-separated SHAKE expansion. +/// +/// This follows the same high-level pattern used in NIST lattice specs: +/// derive deterministic public structure from a seed + indices, then sample +/// coefficients via rejection-sampling at the field layer. +/// +/// NOTE: Potential future hardening: +/// move toward stricter ML-KEM/ML-DSA-style byte layout and parsing rules +/// (fixed-format seed/index encoding and scheme-specific expansion details) +/// if we decide to maximize standards-shape interoperability. +pub(crate) fn derive_public_matrix( + rows: usize, + cols: usize, + seed: &PublicMatrixSeed, + matrix_label: &[u8], +) -> Vec>> { + (0..rows) + .map(|r| { + (0..cols) + .map(|c| { + let mut entry_rng = ShakeXofRng::new(seed, matrix_label, rows, cols, r, c); + CyclotomicRing::random(&mut entry_rng) + }) + .collect() + }) + .collect() +} + +struct ShakeXofRng { + reader: Box, +} + +impl ShakeXofRng { + fn new( + seed: &PublicMatrixSeed, + matrix_label: &[u8], + rows: usize, + cols: usize, + row: usize, + col: usize, + ) -> Self { + let mut xof = Shake256::default(); + absorb_len_prefixed(&mut xof, b"domain", PUBLIC_MATRIX_DOMAIN); + absorb_len_prefixed(&mut xof, b"seed", seed); + absorb_len_prefixed(&mut xof, b"matrix", matrix_label); + absorb_len_prefixed(&mut xof, b"rows", &(rows as u64).to_le_bytes()); + absorb_len_prefixed(&mut xof, b"cols", &(cols as u64).to_le_bytes()); + absorb_len_prefixed(&mut xof, b"row", &(row as u64).to_le_bytes()); + absorb_len_prefixed(&mut xof, b"col", &(col as u64).to_le_bytes()); + Self { + reader: Box::new(xof.finalize_xof()), + } + } +} + +impl RngCore for ShakeXofRng { + fn next_u32(&mut self) -> u32 { + let mut buf = [0u8; 4]; + self.fill_bytes(&mut buf); + u32::from_le_bytes(buf) + } + + fn next_u64(&mut self) -> u64 { + let mut buf = [0u8; 8]; + self.fill_bytes(&mut buf); + u64::from_le_bytes(buf) + } + + fn fill_bytes(&mut self, dest: &mut [u8]) { + self.reader.read(dest); + } + + fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), rand_core::Error> { + self.fill_bytes(dest); + Ok(()) + } +} + +impl CryptoRng for ShakeXofRng {} + +fn absorb_len_prefixed(xof: &mut Shake256, label: &[u8], data: &[u8]) { + xof.update(&(label.len() as u64).to_le_bytes()); + xof.update(label); + xof.update(&(data.len() as u64).to_le_bytes()); + xof.update(data); +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::algebra::Fp64; + + type F = Fp64<4294967197>; + const D: usize = 64; + + #[test] + fn matrix_derivation_is_deterministic_for_same_seed() { + let seed = [42u8; 32]; + let m1 = derive_public_matrix::(3, 5, &seed, b"A"); + let m2 = derive_public_matrix::(3, 5, &seed, b"A"); + assert_eq!(m1, m2); + } + + #[test] + fn matrix_derivation_domain_separates_labels() { + let seed = [7u8; 32]; + let a = derive_public_matrix::(2, 3, &seed, b"A"); + let b = derive_public_matrix::(2, 3, &seed, b"B"); + assert_ne!(a, b); + } +} diff --git a/src/protocol/commitment/utils/mod.rs b/src/protocol/commitment/utils/mod.rs new file mode 100644 index 00000000..39f38327 --- /dev/null +++ b/src/protocol/commitment/utils/mod.rs @@ -0,0 +1,6 @@ +//! Utility helpers for commitment internals. + +pub(crate) mod linear; +pub(crate) mod math; +pub(crate) mod matrix; +pub(crate) mod norm; diff --git a/src/protocol/commitment/utils/norm.rs b/src/protocol/commitment/utils/norm.rs new file mode 100644 index 00000000..cc01f9a7 --- /dev/null +++ b/src/protocol/commitment/utils/norm.rs @@ -0,0 +1,48 @@ +//! Infinity norm utilities for ring elements over Z_q. + +use crate::algebra::ring::CyclotomicRing; +use crate::CanonicalField; + +/// Detect the field modulus from the canonical representation. +/// +/// Uses the identity: the canonical form of `−1` in `Z_q` is `q − 1`. +pub(crate) fn detect_field_modulus() -> u128 { + (-F::one()).to_canonical_u128() + 1 +} + +/// Centered absolute value of a field element. +/// +/// Maps canonical representation `v ∈ [0, q)` to `min(v, q − v)`. +#[inline] +pub(crate) fn centered_abs(x: F, modulus: u128) -> u128 { + let v = x.to_canonical_u128(); + let half = modulus / 2; + if v <= half { + v + } else { + modulus - v + } +} + +/// L∞ norm of a single ring element (maximum centered coefficient magnitude). +pub(crate) fn ring_inf_norm( + r: &CyclotomicRing, + modulus: u128, +) -> u128 { + r.coefficients() + .iter() + .map(|c| centered_abs(*c, modulus)) + .max() + .unwrap_or(0) +} + +/// L∞ norm of a vector of ring elements. +pub(crate) fn vec_inf_norm( + v: &[CyclotomicRing], + modulus: u128, +) -> u128 { + v.iter() + .map(|r| ring_inf_norm(r, modulus)) + .max() + .unwrap_or(0) +} diff --git a/src/protocol/commitment_scheme.rs b/src/protocol/commitment_scheme.rs new file mode 100644 index 00000000..6da64c79 --- /dev/null +++ b/src/protocol/commitment_scheme.rs @@ -0,0 +1,425 @@ +//! Commitment scheme trait implementation. + +use crate::algebra::ring::CyclotomicRing; +use crate::error::HachiError; +use crate::primitives::poly::multilinear_lagrange_basis; +use crate::protocol::commitment::{ + CommitmentConfig, CommitmentScheme, DefaultCommitmentConfig, HachiCommitmentCore, + RingCommitment, RingCommitmentScheme, RingCommitmentSetup, +}; +use crate::protocol::opening_point::RingOpeningPoint; +use crate::protocol::proof::{HachiCommitmentHint, HachiProof, SumcheckAux}; +use crate::protocol::quadratic_equation::QuadraticEquation; +use crate::protocol::ring_switch::{ring_switch_prover, ring_switch_verifier}; +use crate::protocol::sumcheck::norm_sumcheck::{NormSumcheckProver, NormSumcheckVerifier}; +use crate::protocol::sumcheck::relation_sumcheck::{ + RelationSumcheckProver, RelationSumcheckVerifier, +}; +use crate::protocol::sumcheck::{prove_sumcheck, verify_sumcheck}; +use crate::protocol::transcript::labels::CHALLENGE_SUMCHECK_ROUND; +use crate::protocol::transcript::Transcript; +use crate::{CanonicalField, FieldCore, FieldSampling, Polynomial}; + +#[cfg(test)] +use crate::protocol::ring_switch::{eval_ring_matrix_at, expand_m_a}; +#[cfg(test)] +use crate::protocol::transcript::labels::{ + ABSORB_SUMCHECK_W, CHALLENGE_RING_SWITCH, DOMAIN_HACHI_PROTOCOL, +}; +#[cfg(test)] +use crate::protocol::transcript::Blake2bTranscript; + +type Cfg = DefaultCommitmentConfig; +const D: usize = Cfg::D; + +/// Placeholder for the end-to-end PCS wrapper. +#[derive(Clone, Copy, Debug, Default)] +pub struct HachiCommitmentScheme; + +impl CommitmentScheme for HachiCommitmentScheme +where + F: FieldCore + CanonicalField + FieldSampling, +{ + type ProverSetup = RingCommitmentSetup; + type VerifierSetup = RingCommitmentSetup; + type Commitment = RingCommitment; + type Proof = HachiProof; + type OpeningProofHint = HachiCommitmentHint; + + fn setup_prover(max_num_vars: usize) -> Self::ProverSetup { + let (setup, _) = + >::setup(max_num_vars) + .expect("commitment setup failed"); + setup + } + + fn setup_verifier(setup: &Self::ProverSetup) -> Self::VerifierSetup { + setup.clone() + } + + fn commit>( + poly: &P, + setup: &Self::ProverSetup, + ) -> Result<(Self::Commitment, Self::OpeningProofHint), HachiError> { + let ring_coeffs = + reduce_coeffs_to_ring_elements::(poly.num_vars(), &poly.coeffs())?; + let (commitment, s, t_hat) = >::commit_coeffs(&ring_coeffs, setup)?; + let hint = HachiCommitmentHint { + s, + t_hat, + ring_coeffs, + }; + Ok((commitment, hint)) + } + + fn prove, P: Polynomial>( + setup: &Self::ProverSetup, + poly: &P, + opening_point: &[F], + hint: Option, + transcript: &mut T, + commitment: &Self::Commitment, + ) -> Result { + let hint = hint.ok_or_else(|| { + HachiError::InvalidInput("missing commitment hint for proving".to_string()) + })?; + let num_vars = poly.num_vars(); + let alpha = Cfg::D.trailing_zeros() as usize; + let reduced_len = num_vars + .checked_sub(alpha) + .ok_or_else(|| HachiError::InvalidSetup("reduction length underflow".to_string()))?; + if opening_point.len() < reduced_len { + return Err(HachiError::InvalidPointDimension { + expected: reduced_len, + actual: opening_point.len(), + }); + } + + let ring_opening_point = + ring_opening_point_from_field::(&opening_point[..reduced_len], Cfg::R, Cfg::M)?; + + let y_ring = + evaluate_packed_ring_poly::(&hint.ring_coeffs, &opening_point[..reduced_len]); + + // §4.2 Quadratic equation + let quad_eq = QuadraticEquation::::new_prover( + setup, + &ring_opening_point, + &hint, + transcript, + commitment, + &y_ring, + )?; + + // §4.3 Ring switch + let rs = ring_switch_prover::(&quad_eq, transcript)?; + + // Norm sumcheck (range check on w) + let mut norm_prover = NormSumcheckProver::new(&rs.tau0, rs.w_evals.clone(), rs.b); + let (norm_proof, ..) = + prove_sumcheck::(&mut norm_prover, transcript, |tr| { + tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND) + })?; + + // Relation sumcheck (evaluation relation) + let mut relation_prover = RelationSumcheckProver::new( + rs.w_evals, + &rs.alpha_evals_y, + &rs.m_evals_x, + rs.num_u, + rs.num_l, + ); + let (relation_proof, ..) = + prove_sumcheck::(&mut relation_prover, transcript, |tr| { + tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND) + })?; + + Ok(HachiProof { + v: quad_eq.v, + y_ring, + norm_proof, + relation_proof, + sumcheck_aux: SumcheckAux { w: rs.w }, + w_commitment: rs.w_commitment, + }) + } + + fn verify>( + proof: &Self::Proof, + setup: &Self::VerifierSetup, + transcript: &mut T, + opening_point: &[F], + opening: &F, + commitment: &Self::Commitment, + ) -> Result<(), HachiError> { + let alpha_bits = Cfg::D.trailing_zeros() as usize; + let reduced_len = opening_point.len().checked_sub(alpha_bits).ok_or_else(|| { + HachiError::InvalidSetup("opening point length underflow".to_string()) + })?; + let reduced_opening_point = &opening_point[..reduced_len]; + let inner_point = &opening_point[reduced_len..]; + + // §3.1 trace check + let v = reduce_inner_openings_to_ring_elements::(inner_point)?; + let d = F::from_u64(Cfg::D as u64); + let trace_lhs = trace::(&(proof.y_ring * v.sigma_m1())); + let trace_rhs = d * *opening; + if trace_lhs != trace_rhs { + return Err(HachiError::InvalidProof); + } + + // §4.2 Quadratic equation + let ring_opening_point = + ring_opening_point_from_field::(reduced_opening_point, Cfg::R, Cfg::M)?; + let quad_eq = QuadraticEquation::::new_verifier( + setup, + &ring_opening_point, + &proof.v, + transcript, + commitment, + &proof.y_ring, + )?; + + // §4.3 Ring switch (verifier side) + let rs = ring_switch_verifier::( + &quad_eq, + &proof.sumcheck_aux.w, + &proof.w_commitment, + transcript, + )?; + + // Norm sumcheck verification (range check) + let norm_verifier = NormSumcheckVerifier::new(rs.tau0, rs.w_evals.clone(), rs.b); + verify_sumcheck::(&proof.norm_proof, &norm_verifier, transcript, |tr| { + tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND) + })?; + + // Relation sumcheck verification (evaluation relation) + let relation_verifier = RelationSumcheckVerifier::new( + rs.w_evals, + rs.alpha_evals_y, + rs.m_evals_x, + rs.tau1, + proof.v.clone(), + commitment.u.clone(), + proof.y_ring, + rs.alpha, + rs.num_u, + rs.num_l, + ); + verify_sumcheck::( + &proof.relation_proof, + &relation_verifier, + transcript, + |tr| tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND), + )?; + + Ok(()) + } + + fn combine_commitments(_commitments: &[Self::Commitment], _coeffs: &[F]) -> Self::Commitment { + unimplemented!() + } + + fn combine_hints(_hints: Vec, _coeffs: &[F]) -> Self::OpeningProofHint { + unimplemented!() + } + + fn protocol_name() -> &'static [u8] { + unimplemented!() + } +} + +/// Re-derive the ring-switch challenge `alpha` and the expanded `M_a` vector +/// by replaying the transcript from the proof data and setup, exactly as the +/// verifier does. +#[cfg(test)] +pub(crate) fn rederive_alpha_and_m_a( + proof: &HachiProof, + setup: &>::ProverSetup, + opening_point: &[F], + commitment: &>::Commitment, +) -> Result<(F, Vec), HachiError> +where + F: FieldCore + CanonicalField + FieldSampling + 'static, +{ + let alpha_bits = Cfg::D.trailing_zeros() as usize; + let reduced_len = opening_point + .len() + .checked_sub(alpha_bits) + .ok_or_else(|| HachiError::InvalidSetup("opening point length underflow".to_string()))?; + let ring_opening_point = + ring_opening_point_from_field::(&opening_point[..reduced_len], Cfg::R, Cfg::M)?; + let mut transcript = Blake2bTranscript::::new(DOMAIN_HACHI_PROTOCOL); + let quad_eq = QuadraticEquation::::new_verifier( + setup, + &ring_opening_point, + &proof.v, + &mut transcript, + commitment, + &proof.y_ring, + )?; + transcript.append_serde(ABSORB_SUMCHECK_W, &proof.w_commitment); + let alpha: F = transcript.challenge_scalar(CHALLENGE_RING_SWITCH); + let m_a = eval_ring_matrix_at::(quad_eq.m(), &alpha); + let m_a_vec = expand_m_a::(&m_a, alpha)?; + Ok((alpha, m_a_vec)) +} + +fn lagrange_weights(point: &[F]) -> Vec { + let len = 1usize << point.len(); + let mut weights = vec![F::zero(); len]; + multilinear_lagrange_basis(&mut weights, point); + weights +} + +fn ring_opening_point_from_field( + opening_point: &[F], + r_vars: usize, + m_vars: usize, +) -> Result, HachiError> { + let expected_len = r_vars + .checked_add(m_vars) + .ok_or_else(|| HachiError::InvalidSetup("opening point length overflow".to_string()))?; + if opening_point.len() != expected_len { + return Err(HachiError::InvalidPointDimension { + expected: expected_len, + actual: opening_point.len(), + }); + } + + let b = lagrange_weights(&opening_point[..r_vars]); + let a = lagrange_weights(&opening_point[r_vars..]); + Ok(RingOpeningPoint { a, b }) +} + +fn reduce_coeffs_to_ring_elements( + num_vars: usize, + coeffs: &[F], +) -> Result>, HachiError> { + if D == 0 || !D.is_power_of_two() { + return Err(HachiError::InvalidInput(format!( + "ring degree D={D} is not a power of two" + ))); + } + let alpha = D.trailing_zeros() as usize; + if num_vars < alpha { + return Err(HachiError::InvalidInput(format!( + "num_vars {num_vars} is smaller than alpha {alpha}" + ))); + } + + let expected_len = 1usize + .checked_shl(num_vars as u32) + .ok_or_else(|| HachiError::InvalidInput(format!("2^{num_vars} does not fit usize")))?; + if coeffs.len() != expected_len { + return Err(HachiError::InvalidSize { + expected: expected_len, + actual: coeffs.len(), + }); + } + + let outer_vars = num_vars - alpha; + let outer_len = 1usize + .checked_shl(outer_vars as u32) + .ok_or_else(|| HachiError::InvalidInput(format!("2^{outer_vars} does not fit usize")))?; + + let mut out = Vec::with_capacity(outer_len); + for i in 0..outer_len { + let coeffs = std::array::from_fn(|j| { + let idx = i + (j << outer_vars); + coeffs[idx] + }); + out.push(CyclotomicRing::from_coefficients(coeffs)); + } + Ok(out) +} + +fn reduce_inner_openings_to_ring_elements( + inner_point: &[F], +) -> Result, HachiError> { + let weights = lagrange_weights(inner_point); + if weights.len() != D { + return Err(HachiError::InvalidInput(format!( + "inner basis length {} does not match D={D}", + weights.len() + ))); + } + let coeffs = std::array::from_fn(|i| weights[i]); + Ok(CyclotomicRing::from_coefficients(coeffs)) +} + +fn evaluate_packed_ring_poly( + packed_coeffs: &[CyclotomicRing], + outer_point: &[F], +) -> CyclotomicRing { + let weights = lagrange_weights(outer_point); + debug_assert_eq!(weights.len(), packed_coeffs.len()); + packed_coeffs + .iter() + .zip(weights.iter()) + .fold(CyclotomicRing::::zero(), |acc, (f_i, w_i)| { + acc + f_i.scale(w_i) + }) +} + +fn trace(u: &CyclotomicRing) -> F { + let d = F::from_u64(D as u64); + u.coefficients()[0] * d +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::primitives::multilinear_evals::DenseMultilinearEvals; + use crate::protocol::commitment::CommitmentConfig; + use crate::protocol::transcript::Blake2bTranscript; + use crate::test_utils::F; + use crate::{CommitmentScheme, Polynomial}; + + #[test] + fn verify_passes_for_consistent_opening() { + let alpha = Cfg::D.trailing_zeros() as usize; + let num_vars = Cfg::R + Cfg::M + alpha; + let len = 1usize << num_vars; + + let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); + let poly = DenseMultilinearEvals::new_padded(evals); + + let setup = >::setup_prover(num_vars); + let verifier_setup = >::setup_verifier(&setup); + + let (commitment, hint) = + >::commit(&poly, &setup).unwrap(); + + let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); + let opening = poly.evaluate(&opening_point); + + let mut prover_transcript = Blake2bTranscript::::new(b"test/prove"); + let proof = >::prove( + &setup, + &poly, + &opening_point, + Some(hint), + &mut prover_transcript, + &commitment, + ) + .unwrap(); + + let mut verifier_transcript = Blake2bTranscript::::new(b"test/prove"); + let result = >::verify( + &proof, + &verifier_setup, + &mut verifier_transcript, + &opening_point, + &opening, + &commitment, + ); + + assert!(result.is_ok()); + } +} diff --git a/src/protocol/mod.rs b/src/protocol/mod.rs new file mode 100644 index 00000000..49997845 --- /dev/null +++ b/src/protocol/mod.rs @@ -0,0 +1,30 @@ +//! Protocol-layer transcript and commitment abstractions. +//! +//! This module defines the Hachi-native protocol interfaces used by higher-level +//! proof logic. It intentionally stays independent from external integration +//! details (for example, Jolt wiring). + +pub mod challenges; +pub mod commitment; +pub mod commitment_scheme; +pub mod opening_point; +pub mod proof; +pub mod quadratic_equation; +pub mod ring_switch; +pub mod sumcheck; +pub mod transcript; + +pub use commitment::{ + AppendToTranscript, CommitmentConfig, CommitmentScheme, DefaultCommitmentConfig, DummyProof, + HachiCommitment, HachiCommitmentCore, HachiOpeningClaim, HachiOpeningPoint, RingCommitment, + RingCommitmentScheme, RingCommitmentSetup, StreamingCommitmentScheme, +}; +pub use commitment_scheme::HachiCommitmentScheme; +pub use opening_point::RingOpeningPoint; +pub use proof::{HachiProof, SumcheckAux}; +pub use quadratic_equation::QuadraticEquation; +pub use sumcheck::{ + prove_sumcheck, verify_sumcheck, CompressedUniPoly, SumcheckInstanceProver, + SumcheckInstanceVerifier, SumcheckProof, UniPoly, +}; +pub use transcript::{Blake2bTranscript, KeccakTranscript, Transcript}; diff --git a/src/protocol/opening_point.rs b/src/protocol/opening_point.rs new file mode 100644 index 00000000..154402a9 --- /dev/null +++ b/src/protocol/opening_point.rs @@ -0,0 +1,20 @@ +//! Ring-native opening point for the Hachi protocol. + +use crate::FieldCore; + +/// Ring-native opening point storing field scalars (Lagrange weights). +/// +/// Contains the two vectors used by the §4.2 prover: +/// - `a`: evaluation vector of length `2^m` (inner-block coordinates). +/// - `b`: block-select vector of length `2^r` (outer coordinates). +/// +/// These are raw field scalars, not ring elements — they originate from +/// multilinear Lagrange basis evaluations and are always constant (scalar) +/// ring elements when embedded into the ring. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct RingOpeningPoint { + /// Evaluation vector of length `2^m` (field scalars). + pub a: Vec, + /// Block-select vector of length `2^r` (field scalars). + pub b: Vec, +} diff --git a/src/protocol/proof.rs b/src/protocol/proof.rs new file mode 100644 index 00000000..9a8c07e3 --- /dev/null +++ b/src/protocol/proof.rs @@ -0,0 +1,59 @@ +//! Proof structures for the Hachi protocol. + +use crate::algebra::ring::CyclotomicRing; +use crate::primitives::serialization::Compress; +use crate::protocol::commitment::RingCommitment; +use crate::protocol::sumcheck::SumcheckProof; +use crate::{FieldCore, HachiSerialize}; + +/// Prover-side hint produced at commitment time. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct HachiCommitmentHint { + /// Decomposed `s_i` blocks from the commitment phase. + pub s: Vec>>, + /// Decomposed `t̂_i` blocks from the commitment phase. + pub t_hat: Vec>>, + /// Ring coefficients from the §3.1 reduction (evaluation table). + pub ring_coeffs: Vec>, +} + +/// Temporary auxiliary data the verifier needs for sumcheck output verification. +/// +/// Will be removed once recursive PCS evaluation proofs replace the direct +/// oracle check at the end of each sumcheck instance. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct SumcheckAux { + /// `w` coefficients (z and r coefficients, concatenated). The verifier + /// reshapes this into sumcheck evaluation form to compute the expected + /// output claims for F_0 and F_alpha. + pub w: Vec, +} + +/// Hachi Proof for One Iteration. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct HachiProof { + /// `y_ring` from the §3.1 reduction. + pub y_ring: CyclotomicRing, + /// `v = D · ŵ`. + pub v: Vec>, + /// Range-check (norm) sumcheck proof (§4.3, F_0). + pub norm_proof: SumcheckProof, + /// Evaluation-relation sumcheck proof (§4.3, F_α). + pub relation_proof: SumcheckProof, + /// Temporary verifier auxiliary (will be removed with recursive PCS). + pub sumcheck_aux: SumcheckAux, + /// Commitment to the sumcheck witness `w`. + pub w_commitment: RingCommitment, +} + +impl HachiProof { + /// Returns the proof size in bytes (uncompressed). + pub fn size(&self) -> usize { + self.v.serialized_size(Compress::No) + + self.y_ring.serialized_size(Compress::No) + + self.sumcheck_aux.w.serialized_size(Compress::No) + + self.norm_proof.serialized_size(Compress::No) + + self.relation_proof.serialized_size(Compress::No) + + self.w_commitment.serialized_size(Compress::No) + } +} diff --git a/src/protocol/quadratic_equation.rs b/src/protocol/quadratic_equation.rs new file mode 100644 index 00000000..16114ffa --- /dev/null +++ b/src/protocol/quadratic_equation.rs @@ -0,0 +1,744 @@ +//! Quadratic equation builder for the Hachi PCS (§4.2). +//! +//! This module encapsulates the stage-1 prover logic and the generation of +//! the quadratic equation components M, y, z, and v. + +use crate::algebra::ring::{CyclotomicRing, SparseChallenge, SparseChallengeConfig}; +use crate::error::HachiError; +use crate::protocol::challenges::sparse::sample_sparse_challenges; +use crate::protocol::commitment::utils::linear::mat_vec_mul_unchecked; +use crate::protocol::commitment::utils::norm::{detect_field_modulus, vec_inf_norm}; +use crate::protocol::commitment::{CommitmentConfig, RingCommitment, RingCommitmentSetup}; +use crate::protocol::opening_point::RingOpeningPoint; +use crate::protocol::proof::HachiCommitmentHint; +use crate::protocol::transcript::labels::{ABSORB_PROVER_V, CHALLENGE_STAGE1_FOLD}; +use crate::protocol::transcript::Transcript; +use crate::{CanonicalField, FieldCore}; + +/// **Steps 1–3.** Compute `w_i = a^T G_{2^m} s_i` and decompose: `ŵ_i = G_1^{-1}(w_i)`. +fn compute_w_hat( + opening_point: &RingOpeningPoint, + s: &[Vec>], +) -> Vec>> +where + F: FieldCore + CanonicalField, + Cfg: CommitmentConfig, +{ + let a = &opening_point.a; + let block_len = 1usize << Cfg::M; + let delta = Cfg::DELTA; + let log_basis = Cfg::LOG_BASIS; + + debug_assert_eq!(a.len(), block_len); + + s.iter() + .map(|s_i| { + let mut w_i = CyclotomicRing::::zero(); + for (j, a_j) in a.iter().enumerate().take(block_len) { + let start = j * delta; + let end = start + delta; + let recomp_j = CyclotomicRing::gadget_recompose_pow2(&s_i[start..end], log_basis); + w_i += recomp_j.scale(a_j); + } + w_i.balanced_decompose_pow2(delta, log_basis) + }) + .collect() +} + +/// **Step 4.** Compute `v = D · ŵ` (first prover message). +#[allow(non_snake_case)] +fn compute_v( + d: &[Vec>], + w_hat: &[Vec>], +) -> Vec> { + let w_hat_flat: Vec> = + w_hat.iter().flat_map(|v| v.iter().copied()).collect(); + mat_vec_mul_unchecked(d, &w_hat_flat) +} + +/// **Steps 7–9.** Fold `z = Σ c_i · s_i`, check `‖z‖_∞ ≤ β`, and decompose `ẑ = J^{-1}(z)`. +fn compute_z_hat( + s: &[Vec>], + challenges: &[SparseChallenge], +) -> Result>, HachiError> +where + F: FieldCore + CanonicalField, + Cfg: CommitmentConfig, +{ + debug_assert_eq!(challenges.len(), s.len()); + let len = s[0].len(); + let mut z = vec![CyclotomicRing::::zero(); len]; + for (c_i, s_i) in challenges.iter().zip(s.iter()) { + for (z_j, s_ij) in z.iter_mut().zip(s_i.iter()) { + *z_j += s_ij.mul_by_sparse(c_i); + } + } + + let modulus = detect_field_modulus::(); + let norm = vec_inf_norm(&z, modulus); + if norm > Cfg::BETA { + return Err(HachiError::InvalidInput(format!( + "prover abort: ||z||_inf = {norm} > beta = {}", + Cfg::BETA + ))); + } + + Ok(z.iter() + .flat_map(|z_j| z_j.balanced_decompose_pow2(Cfg::TAU, Cfg::LOG_BASIS)) + .collect()) +} + +/// Stage-1 quadratic equation state for the Hachi protocol. +/// +/// Encapsulates the relation $M(x) \cdot z = y(x) + (X^D + 1) \cdot r(x)$ +/// along with intermediate prover witness data (`w_hat`, `z_hat`, `hint`). +pub struct QuadraticEquation { + /// Stage-1 proof vector `v = D · ŵ`. + pub v: Vec>, + /// Stage-1 folding challenges (sparse representation). + pub challenges: Vec, + /// Matrix `M`. + m: Vec>>, + /// Vector `y`. + y: Vec>, + /// Vector `z` (prover only). + z: Option>>, + /// Decomposed `ŵ_i = G_1^{-1}(w_i)` (prover only). + w_hat: Option>>>, + /// Decomposed `ẑ = J^{-1}(z)` (prover only). + z_hat: Option>>, + /// Commitment hint (prover only). + hint: Option>, + + _marker: std::marker::PhantomData, +} + +impl QuadraticEquation +where + F: FieldCore + CanonicalField, + Cfg: CommitmentConfig, +{ + /// Prover constructor: runs §4.2 stage 1 and builds all equation components. + /// + /// # Errors + /// + /// Returns an error if the norm check, challenge sampling, or matrix + /// generation fails. + pub fn new_prover>( + setup: &RingCommitmentSetup, + ring_opening_point: &RingOpeningPoint, + hint: &HachiCommitmentHint, + transcript: &mut T, + commitment: &RingCommitment, + y_ring: &CyclotomicRing, + ) -> Result { + // Steps 1–3: w_i = a^T G_{2^m} s_i, then ŵ_i = G_1^{-1}(w_i) + let w_hat = compute_w_hat::(ring_opening_point, &hint.s); + + // Step 4: v = D · ŵ + let v = compute_v(&setup.D, &w_hat); + + // Step 5: append v to transcript + transcript.append_serde(ABSORB_PROVER_V, &v); + + // Step 6: sample sparse folding challenges + let challenge_cfg = SparseChallengeConfig { + weight: Cfg::CHALLENGE_WEIGHT, + nonzero_coeffs: vec![-1, 1], + }; + let challenges = sample_sparse_challenges::( + transcript, + CHALLENGE_STAGE1_FOLD, + 1usize << Cfg::R, + &challenge_cfg, + )?; + + // Steps 7–9: z = Σ c_i · s_i, check ‖z‖_∞ ≤ β, then ẑ = J^{-1}(z) + let z_hat = compute_z_hat::(&hint.s, &challenges)?; + + let m = generate_m::(setup, ring_opening_point, &challenges)?; + let y = generate_y::(&v, &commitment.u, y_ring)?; + let z = generate_z(&w_hat, &hint.t_hat, &z_hat); + + Ok(Self { + v, + challenges, + m, + y, + z: Some(z), + w_hat: Some(w_hat), + z_hat: Some(z_hat), + hint: Some(hint.clone()), + _marker: std::marker::PhantomData, + }) + } + + /// Verifier constructor: Derives challenges and computes M and y. + /// + /// # Errors + /// + /// Returns an error if challenge derivation fails. + pub fn new_verifier>( + setup: &RingCommitmentSetup, + ring_opening_point: &RingOpeningPoint, + v: &Vec>, + transcript: &mut T, + commitment: &RingCommitment, + y_ring: &CyclotomicRing, + ) -> Result { + let challenges = derive_stage1_challenges::(transcript, v)?; + let m = generate_m::(setup, ring_opening_point, &challenges)?; + let y = generate_y::(v, &commitment.u, y_ring)?; + + Ok(Self { + v: v.to_vec(), + challenges, + m, + y, + z: None, + w_hat: None, + z_hat: None, + hint: None, + _marker: std::marker::PhantomData, + }) + } + + /// Get the matrix M. + pub fn m(&self) -> &[Vec>] { + &self.m + } + + /// Get the vector y. + pub fn y(&self) -> &[CyclotomicRing] { + &self.y + } + + /// Get the vector z (returns None if constructed by verifier). + pub fn z(&self) -> Option<&[CyclotomicRing]> { + self.z.as_deref() + } + + /// Get the vector v. + pub fn v(&self) -> &[CyclotomicRing] { + &self.v + } + + /// Get the decomposed witness `ŵ` (prover only). + pub fn w_hat(&self) -> Option<&[Vec>]> { + self.w_hat.as_deref() + } + + /// Get the decomposed folded witness `ẑ` (prover only). + pub fn z_hat(&self) -> Option<&[CyclotomicRing]> { + self.z_hat.as_deref() + } + + /// Get the commitment hint (prover only). + pub fn hint(&self) -> Option<&HachiCommitmentHint> { + self.hint.as_ref() + } +} + +pub(crate) fn derive_stage1_challenges( + transcript: &mut T, + v: &Vec>, +) -> Result, HachiError> +where + F: FieldCore + CanonicalField, + T: Transcript, +{ + let challenge_cfg = SparseChallengeConfig { + weight: Cfg::CHALLENGE_WEIGHT, + nonzero_coeffs: vec![-1, 1], + }; + let num_blocks = 1usize + .checked_shl(Cfg::R as u32) + .ok_or_else(|| HachiError::InvalidSetup("2^R does not fit usize".to_string()))?; + transcript.append_serde(ABSORB_PROVER_V, v); + sample_sparse_challenges::( + transcript, + CHALLENGE_STAGE1_FOLD, + num_blocks, + &challenge_cfg, + ) +} + +fn constant_ring(value: F) -> CyclotomicRing { + let mut coeffs = [F::zero(); D]; + coeffs[0] = value; + CyclotomicRing::from_coefficients(coeffs) +} + +fn gadget_row_scalars(levels: usize, log_basis: u32) -> Vec { + let base = F::from_canonical_u128_reduced(1u128 << log_basis); + let mut out = Vec::with_capacity(levels); + let mut power = F::one(); + for _ in 0..levels { + out.push(power); + power = power * base; + } + out +} + +/// Kronecker product of two scalar vectors, producing constant ring elements. +/// Cost: O(1) per pair (just a field multiplication + ring construction). +fn kron_scalars( + left: &[F], + right: &[F], +) -> Vec> { + let mut out = Vec::with_capacity(left.len().saturating_mul(right.len())); + for &l in left { + for &r in right { + out.push(constant_ring(l * r)); + } + } + out +} + +/// Kronecker product where the right operand is field scalars. +/// Cost: O(D) per pair instead of O(D^2). +fn kron_row_scale( + left: &[CyclotomicRing], + right: &[F], +) -> Vec> { + let mut out = Vec::with_capacity(left.len().saturating_mul(right.len())); + for l in left { + for &r in right { + out.push(l.scale(&r)); + } + } + out +} + +/// Kronecker product of sparse challenges with scalar gadget entries. +/// Cost: O(omega + D) per pair instead of O(D^2). +fn kron_sparse_scale( + left: &[SparseChallenge], + right: &[F], +) -> Vec> { + let mut out = Vec::with_capacity(left.len().saturating_mul(right.len())); + for l in left { + let dense: CyclotomicRing = l.to_dense().expect("valid sparse challenge"); + for &r in right { + out.push(dense.scale(&r)); + } + } + out +} + +fn gadget_block_diag_scalars(blocks: usize, row: &[F]) -> Vec> { + let row_len = row.len(); + let mut rows = Vec::with_capacity(blocks); + for i in 0..blocks { + let mut out = vec![F::zero(); blocks * row_len]; + let start = i * row_len; + out[start..start + row_len].copy_from_slice(row); + rows.push(out); + } + rows +} + +pub(crate) fn generate_m( + setup: &RingCommitmentSetup, + opening_point: &RingOpeningPoint, + challenges: &[SparseChallenge], +) -> Result>>, HachiError> +where + F: FieldCore + CanonicalField, +{ + let num_blocks = 1usize + .checked_shl(Cfg::R as u32) + .ok_or_else(|| HachiError::InvalidSetup("2^R does not fit usize".to_string()))?; + let block_len = 1usize + .checked_shl(Cfg::M as u32) + .ok_or_else(|| HachiError::InvalidSetup("2^M does not fit usize".to_string()))?; + let w_len = Cfg::DELTA + .checked_mul(num_blocks) + .ok_or_else(|| HachiError::InvalidSetup("w length overflow".to_string()))?; + let t_len = Cfg::DELTA + .checked_mul(Cfg::N_A) + .and_then(|v| v.checked_mul(num_blocks)) + .ok_or_else(|| HachiError::InvalidSetup("t length overflow".to_string()))?; + let z_len = Cfg::TAU + .checked_mul(Cfg::DELTA) + .and_then(|v| v.checked_mul(block_len)) + .ok_or_else(|| HachiError::InvalidSetup("z length overflow".to_string()))?; + let total_cols = w_len + .checked_add(t_len) + .and_then(|v| v.checked_add(z_len)) + .ok_or_else(|| HachiError::InvalidSetup("matrix width overflow".to_string()))?; + + if opening_point.b.len() != num_blocks { + return Err(HachiError::InvalidPointDimension { + expected: num_blocks, + actual: opening_point.b.len(), + }); + } + if opening_point.a.len() != block_len { + return Err(HachiError::InvalidPointDimension { + expected: block_len, + actual: opening_point.a.len(), + }); + } + if challenges.len() != num_blocks { + return Err(HachiError::InvalidSize { + expected: num_blocks, + actual: challenges.len(), + }); + } + if setup.D.len() != Cfg::N_D { + return Err(HachiError::InvalidSize { + expected: Cfg::N_D, + actual: setup.D.len(), + }); + } + if setup.B.len() != Cfg::N_B { + return Err(HachiError::InvalidSize { + expected: Cfg::N_B, + actual: setup.B.len(), + }); + } + if setup.A.len() != Cfg::N_A { + return Err(HachiError::InvalidSize { + expected: Cfg::N_A, + actual: setup.A.len(), + }); + } + if setup.A.first().map(|row| row.len()) != Some(block_len * Cfg::DELTA) { + return Err(HachiError::InvalidSetup("A row width mismatch".to_string())); + } + + let g1 = gadget_row_scalars::(Cfg::DELTA, Cfg::LOG_BASIS); + let j1 = gadget_row_scalars::(Cfg::TAU, Cfg::LOG_BASIS); + + let row3_w = kron_scalars::(&opening_point.b, &g1); + let row4_w = kron_sparse_scale::(challenges, &g1); + + let ag = kron_scalars::(&opening_point.a, &g1); + let ag_scalars: Vec = ag.iter().map(|r| r.coefficients()[0]).collect(); + let row4_z = kron_scalars::(&ag_scalars, &j1) + .into_iter() + .map(|x| -x) + .collect::>(); + + let g_na = gadget_block_diag_scalars::(Cfg::N_A, &g1); + let row5_mid = g_na + .iter() + .map(|row| kron_sparse_scale::(challenges, row)) + .collect::>(); + let row5_right = setup + .A + .iter() + .map(|row| kron_row_scale(row, &j1).into_iter().map(|x| -x).collect()) + .collect::>>(); + + let zero = CyclotomicRing::::zero(); + let mut rows = Vec::with_capacity(Cfg::N_D + Cfg::N_B + 1usize + 1usize + Cfg::N_A); + + for row in setup.D.iter() { + if row.len() != w_len { + return Err(HachiError::InvalidSetup("D row width mismatch".to_string())); + } + let mut full = vec![zero; total_cols]; + full[..w_len].copy_from_slice(row); + rows.push(full); + } + + for row in setup.B.iter() { + if row.len() != t_len { + return Err(HachiError::InvalidSetup("B row width mismatch".to_string())); + } + let mut full = vec![zero; total_cols]; + full[w_len..w_len + t_len].copy_from_slice(row); + rows.push(full); + } + + let mut row3 = vec![zero; total_cols]; + row3[..w_len].copy_from_slice(&row3_w); + rows.push(row3); + + let mut row4 = vec![zero; total_cols]; + row4[..w_len].copy_from_slice(&row4_w); + row4[w_len + t_len..].copy_from_slice(&row4_z); + rows.push(row4); + + for (mid, right) in row5_mid.into_iter().zip(row5_right.into_iter()) { + let mut row = vec![zero; total_cols]; + row[w_len..w_len + t_len].copy_from_slice(&mid); + row[w_len + t_len..].copy_from_slice(&right); + rows.push(row); + } + + Ok(rows) +} + +pub(crate) fn generate_z( + w_hat: &[Vec>], + t_hat: &[Vec>], + z_hat: &[CyclotomicRing], +) -> Vec> { + let mut out = Vec::with_capacity( + w_hat.len() + + t_hat.len() + + z_hat.len() + + w_hat.iter().map(|v| v.len()).sum::() + + t_hat.iter().map(|v| v.len()).sum::(), + ); + for w in w_hat { + out.extend(w.iter().copied()); + } + for t in t_hat { + out.extend(t.iter().copied()); + } + out.extend_from_slice(z_hat); + out +} + +pub(crate) fn generate_y( + v: &[CyclotomicRing], + u: &[CyclotomicRing], + u_eval: &CyclotomicRing, +) -> Result>, HachiError> +where + F: FieldCore, +{ + if v.len() != Cfg::N_D { + return Err(HachiError::InvalidSize { + expected: Cfg::N_D, + actual: v.len(), + }); + } + if u.len() != Cfg::N_B { + return Err(HachiError::InvalidSize { + expected: Cfg::N_B, + actual: u.len(), + }); + } + let mut out = Vec::with_capacity(Cfg::N_D + Cfg::N_B + 1 + 1 + Cfg::N_A); + out.extend_from_slice(v); + out.extend_from_slice(u); + out.push(*u_eval); + out.push(CyclotomicRing::::zero()); + out.extend(std::iter::repeat_n( + CyclotomicRing::::zero(), + Cfg::N_A, + )); + Ok(out) +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::algebra::ring::SparseChallengeConfig; + use crate::algebra::CyclotomicRing; + use crate::protocol::challenges::sparse::sample_sparse_challenges; + use crate::protocol::commitment::{HachiCommitmentCore, RingCommitmentScheme}; + use crate::protocol::proof::HachiCommitmentHint; + use crate::protocol::transcript::Blake2bTranscript; + use crate::test_utils::*; + use crate::Transcript; + + const TRANSCRIPT_SEED: &[u8] = b"test/prover-relation"; + + fn replay_challenges(v: &Vec>) -> Vec> { + let mut transcript = Blake2bTranscript::::new(TRANSCRIPT_SEED); + transcript.append_serde(ABSORB_PROVER_V, v); + + let challenge_cfg = SparseChallengeConfig { + weight: TinyConfig::CHALLENGE_WEIGHT, + nonzero_coeffs: vec![-1, 1], + }; + let sparse = sample_sparse_challenges::, D>( + &mut transcript, + CHALLENGE_STAGE1_FOLD, + NUM_BLOCKS, + &challenge_cfg, + ) + .unwrap(); + sparse + .iter() + .map(|c| c.to_dense::().unwrap()) + .collect() + } + + struct Fixture { + setup: RingCommitmentSetup, + commitment_u: Vec>, + point: RingOpeningPoint, + blocks: Vec>>, + quad_eq: QuadraticEquation, + /// Challenges re-derived via transcript replay (cross-check). + challenges: Vec>, + } + + fn build_fixture() -> Fixture { + let (setup, _) = + >::setup(16).unwrap(); + + let blocks = sample_blocks(); + let (commitment, s, t_hat) = + >::commit_ring_blocks( + &blocks, &setup, + ) + .unwrap(); + + let point = RingOpeningPoint { + a: sample_a(), + b: sample_b(), + }; + + let hint = HachiCommitmentHint { + s, + t_hat, + ring_coeffs: Vec::new(), + }; + let mut transcript = Blake2bTranscript::::new(TRANSCRIPT_SEED); + let y_ring = CyclotomicRing::::zero(); + let quad_eq = QuadraticEquation::::new_prover( + &setup, + &point, + &hint, + &mut transcript, + &commitment, + &y_ring, + ) + .unwrap(); + + let challenges = replay_challenges(&quad_eq.v); + + Fixture { + setup, + commitment_u: commitment.u.clone(), + point, + blocks, + quad_eq, + challenges, + } + } + + /// Row 1: D · ŵ = v + #[test] + fn row1_d_times_w_hat_equals_v() { + let f = build_fixture(); + + let w_hat = f.quad_eq.w_hat().unwrap(); + let w_hat_flat: Vec> = + w_hat.iter().flat_map(|v| v.iter().copied()).collect(); + let lhs = mat_vec_mul(&f.setup.D, &w_hat_flat); + + assert_eq!(lhs, f.quad_eq.v(), "Row 1 failed: D · ŵ ≠ v"); + } + + /// Row 2: B · t̂ = u (commitment vector) + #[test] + fn row2_b_times_t_hat_equals_u_commitment() { + let f = build_fixture(); + + let hint = f.quad_eq.hint().unwrap(); + let t_hat_flat: Vec> = + hint.t_hat.iter().flat_map(|v| v.iter().copied()).collect(); + let lhs = mat_vec_mul(&f.setup.B, &t_hat_flat); + + assert_eq!(lhs, f.commitment_u, "Row 2 failed: B · t̂ ≠ u"); + } + + /// Row 3: b^T · G_{2^r} · ŵ = u_eval + #[test] + fn row3_bt_gadget_w_hat_equals_u_eval() { + let f = build_fixture(); + + let w_hat = f.quad_eq.w_hat().unwrap(); + let w_recomposed: Vec> = w_hat + .iter() + .map(|w_hat_i| CyclotomicRing::gadget_recompose_pow2(w_hat_i, LOG_BASIS)) + .collect(); + + let u_eval = w_recomposed + .iter() + .zip(f.point.b.iter()) + .fold(CyclotomicRing::::zero(), |acc, (w_i, b_i)| { + acc + w_i.scale(b_i) + }); + + let u_eval_direct = f.blocks.iter().zip(f.point.b.iter()).fold( + CyclotomicRing::::zero(), + |acc, (block_i, b_i)| { + let inner: CyclotomicRing = block_i + .iter() + .zip(f.point.a.iter()) + .fold(CyclotomicRing::::zero(), |acc2, (f_ij, a_j)| { + acc2 + f_ij.scale(a_j) + }); + acc + inner.scale(b_i) + }, + ); + + assert_eq!( + u_eval, u_eval_direct, + "Row 3 failed: b^T G ŵ ≠ Σ b_i (a^T f_i)" + ); + } + + /// Row 4: (c^T ⊗ G_1) · ŵ = a^T · G_{2^m} · J · ẑ + #[test] + fn row4_challenge_fold_w_equals_a_gadget_j_z_hat() { + let f = build_fixture(); + + let w_hat = f.quad_eq.w_hat().unwrap(); + let w: Vec> = w_hat + .iter() + .map(|w_hat_i| CyclotomicRing::gadget_recompose_pow2(w_hat_i, LOG_BASIS)) + .collect(); + + let lhs = f + .challenges + .iter() + .zip(w.iter()) + .fold(CyclotomicRing::::zero(), |acc, (c_i, w_i)| { + acc + (*c_i * *w_i) + }); + + let z_recovered = recompose_z_hat(f.quad_eq.z_hat().unwrap()); + let rhs = a_transpose_gadget_times_vec(&f.point.a, &z_recovered); + + assert_eq!(lhs, rhs, "Row 4 failed: (c^T ⊗ G_1)ŵ ≠ a^T G J ẑ"); + } + + /// Row 5: (c^T ⊗ G_{n_A}) · t̂ = A · J · ẑ + #[test] + fn row5_challenge_fold_t_equals_a_j_z_hat() { + let f = build_fixture(); + + let hint = f.quad_eq.hint().unwrap(); + let mut lhs = vec![CyclotomicRing::::zero(); N_A]; + for (c_i, t_hat_i) in f.challenges.iter().zip(hint.t_hat.iter()) { + let t_i = gadget_recompose_vec(t_hat_i); + assert_eq!(t_i.len(), N_A); + for (lhs_j, t_ij) in lhs.iter_mut().zip(t_i.iter()) { + *lhs_j += *c_i * *t_ij; + } + } + + let z_recovered = recompose_z_hat(f.quad_eq.z_hat().unwrap()); + let rhs = mat_vec_mul(&f.setup.A, &z_recovered); + + assert_eq!(lhs, rhs, "Row 5 failed: (c^T ⊗ G_nA)t̂ ≠ A · J · ẑ"); + } + + #[test] + fn prove_output_shapes_are_correct() { + let f = build_fixture(); + + assert_eq!(f.quad_eq.v().len(), TinyConfig::N_D); + + let w_hat = f.quad_eq.w_hat().unwrap(); + assert_eq!(w_hat.len(), NUM_BLOCKS); + assert!(w_hat.iter().all(|v| v.len() == DELTA)); + + let hint = f.quad_eq.hint().unwrap(); + assert_eq!(hint.t_hat.len(), NUM_BLOCKS); + assert!(hint.t_hat.iter().all(|v| v.len() == N_A * DELTA)); + + assert_eq!(f.quad_eq.z_hat().unwrap().len(), BLOCK_LEN * DELTA * TAU); + } +} diff --git a/src/protocol/ring_switch.rs b/src/protocol/ring_switch.rs new file mode 100644 index 00000000..9a9d19a7 --- /dev/null +++ b/src/protocol/ring_switch.rs @@ -0,0 +1,453 @@ +//! Ring switching logic for the Hachi PCS (Section 4.3). +//! +//! Handles the transition from the ring-based quadratic equation to field-based +//! sumcheck instances by expanding the ring elements into their coefficient +//! vectors and setting up the evaluation tables. + +use crate::algebra::ring::CyclotomicRing; +use crate::error::HachiError; +use crate::protocol::commitment::utils::norm::detect_field_modulus; +use crate::protocol::commitment::{ + CommitmentConfig, DefaultCommitmentConfig, HachiCommitmentCore, RingCommitment, + RingCommitmentScheme, +}; +use crate::protocol::quadratic_equation::QuadraticEquation; +use crate::protocol::sumcheck::eq_evals; +use crate::protocol::transcript::labels::{ + ABSORB_SUMCHECK_W, CHALLENGE_RING_SWITCH, CHALLENGE_TAU0, CHALLENGE_TAU1, +}; +use crate::protocol::transcript::Transcript; +use crate::{CanonicalField, FieldCore, FieldSampling}; + +/// Output of the ring switch prover, containing everything needed for sumchecks. +pub struct RingSwitchOutput { + /// The witness vector w (concatenation of z and r coefficients). + pub w: Vec, + /// Commitment to w. + pub w_commitment: RingCommitment, + /// Evaluation table of w (reordered for sumcheck). + pub w_evals: Vec, + /// Evaluation table of M_alpha(x) (tau1-weighted). + pub m_evals_x: Vec, + /// Evaluation table of alpha powers (y dimension). + pub alpha_evals_y: Vec, + /// Number of upper variable bits in w_evals. + pub num_u: usize, + /// Number of lower variable bits in w_evals. + pub num_l: usize, + /// Challenge tau0 for F_0 sumcheck. + pub tau0: Vec, + /// Challenge tau1 for F_alpha sumcheck. + pub tau1: Vec, + /// Basis size b = 2^LOG_BASIS. + pub b: usize, + /// Ring-switch challenge alpha. + pub alpha: F, +} + +/// Execute the prover side of the ring switching protocol (Section 4.3). +/// +/// # Errors +/// +/// Returns an error if z is missing, commitment fails, or matrix expansion fails. +pub fn ring_switch_prover( + quad_eq: &QuadraticEquation, + transcript: &mut T, +) -> Result, HachiError> +where + F: FieldCore + CanonicalField + FieldSampling, + T: Transcript, + Cfg: CommitmentConfig, +{ + let z = quad_eq + .z() + .ok_or_else(|| HachiError::InvalidInput("missing z in prover".to_string()))?; + let r = compute_r_via_poly_division::(quad_eq.m(), z, quad_eq.y()); + let w = build_w_coeffs::(z, &r); + + let w_commitment = commit_w::(&w)?; + transcript.append_serde(ABSORB_SUMCHECK_W, &w_commitment); + + let alpha: F = transcript.challenge_scalar(CHALLENGE_RING_SWITCH); + + let m_a = eval_ring_matrix_at::(quad_eq.m(), &alpha); + let m_a_vec = expand_m_a::(&m_a, alpha)?; + let m_rows = m_row_count::(); + let m_cols = if m_a.is_empty() { + 0 + } else { + m_a_vec.len() / m_a.len() + }; + + let (w_evals, num_u, num_l) = build_w_evals(&w, D); + let alpha_evals_y = build_alpha_evals_y(alpha, D); + + let num_sc_vars = num_u + num_l; + let tau0 = sample_tau::(transcript, CHALLENGE_TAU0, num_sc_vars); + + let num_i = m_rows.next_power_of_two().trailing_zeros() as usize; + let tau1 = sample_tau::(transcript, CHALLENGE_TAU1, num_i); + + let m_evals_x = build_m_evals_x::(&m_a_vec, m_rows, m_cols, &tau1); + + Ok(RingSwitchOutput { + w, + w_commitment, + w_evals, + m_evals_x, + alpha_evals_y, + num_u, + num_l, + tau0, + tau1, + b: 1usize << Cfg::LOG_BASIS, + alpha, + }) +} + +/// Replay the verifier side of ring switching to reconstruct evaluation tables. +/// +/// # Errors +/// +/// Returns an error if matrix expansion fails. +pub fn ring_switch_verifier( + quad_eq: &QuadraticEquation, + w: &[F], + w_commitment: &RingCommitment, + transcript: &mut T, +) -> Result, HachiError> +where + F: FieldCore + CanonicalField + FieldSampling, + T: Transcript, + Cfg: CommitmentConfig, +{ + transcript.append_serde(ABSORB_SUMCHECK_W, w_commitment); + + let alpha: F = transcript.challenge_scalar(CHALLENGE_RING_SWITCH); + + let m_a = eval_ring_matrix_at::(quad_eq.m(), &alpha); + let m_a_vec = expand_m_a::(&m_a, alpha)?; + let m_rows = m_row_count::(); + let m_cols = if m_a.is_empty() { + 0 + } else { + m_a_vec.len() / m_a.len() + }; + + let (w_evals, num_u, num_l) = build_w_evals(w, D); + let alpha_evals_y = build_alpha_evals_y(alpha, D); + + let num_sc_vars = num_u + num_l; + let tau0 = sample_tau::(transcript, CHALLENGE_TAU0, num_sc_vars); + + let num_i = m_rows.next_power_of_two().trailing_zeros() as usize; + let tau1 = sample_tau::(transcript, CHALLENGE_TAU1, num_i); + + let m_evals_x = build_m_evals_x::(&m_a_vec, m_rows, m_cols, &tau1); + + Ok(RingSwitchOutput { + w: w.to_vec(), + w_commitment: w_commitment.clone(), + w_evals, + m_evals_x, + alpha_evals_y, + num_u, + num_l, + tau0, + tau1, + b: 1usize << Cfg::LOG_BASIS, + alpha, + }) +} + +pub(crate) fn compute_r_via_poly_division( + m: &[Vec>], + z: &[CyclotomicRing], + y: &[CyclotomicRing], +) -> Vec> { + let poly_len = 2 * D - 1; + m.iter() + .zip(y.iter()) + .map(|(row, y_i)| { + let mut poly = vec![F::zero(); poly_len]; + for (m_ij, z_j) in row.iter().zip(z.iter()) { + if m_ij.is_zero() { + continue; + } + let a = m_ij.coefficients(); + let b = z_j.coefficients(); + + // Detect constant (scalar) ring elements: only a[0] is non-zero. + let is_scalar = a[1..].iter().all(|c| c.is_zero()); + if is_scalar { + let scalar = a[0]; + for s in 0..D { + poly[s] = poly[s] + scalar * b[s]; + } + } else { + for t in 0..D { + for s in 0..D { + poly[t + s] = poly[t + s] + a[t] * b[s]; + } + } + } + } + let y_coeffs = y_i.coefficients(); + for k in 0..D { + poly[k] = poly[k] - y_coeffs[k]; + } + let mut quotient = vec![F::zero(); D]; + for k in (D..poly_len).rev() { + let q = poly[k]; + quotient[k - D] = q; + poly[k - D] = poly[k - D] - q; + } + let coeffs: [F; D] = std::array::from_fn(|k| quotient[k]); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect() +} + +#[derive(Clone, Copy, Debug)] +struct WCommitmentConfig; + +impl CommitmentConfig for WCommitmentConfig { + const D: usize = DefaultCommitmentConfig::D; + const M: usize = 11; + const R: usize = 0; + const N_A: usize = DefaultCommitmentConfig::N_A; + const N_B: usize = DefaultCommitmentConfig::N_B; + const N_D: usize = DefaultCommitmentConfig::N_D; + const LOG_BASIS: u32 = DefaultCommitmentConfig::LOG_BASIS; + const DELTA: usize = DefaultCommitmentConfig::DELTA; + const TAU: usize = DefaultCommitmentConfig::TAU; + const BETA: u128 = DefaultCommitmentConfig::BETA; + const CHALLENGE_WEIGHT: usize = DefaultCommitmentConfig::CHALLENGE_WEIGHT; +} + +fn commit_w(w: &[F]) -> Result, HachiError> +where + F: FieldCore + CanonicalField + FieldSampling, +{ + let d = DefaultCommitmentConfig::D; + let block_len = 1usize << WCommitmentConfig::M; + + let ring_elems: Vec> = w + .chunks(d) + .map(|chunk| { + let coeffs: [F; DefaultCommitmentConfig::D] = + std::array::from_fn(|i| if i < chunk.len() { chunk[i] } else { F::zero() }); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect(); + + let mut padded = ring_elems; + padded.resize( + block_len, + CyclotomicRing::::zero(), + ); + + let blocks = vec![padded]; + + let (w_setup, _) = >::setup(WCommitmentConfig::M)?; + + let (commitment, _, _) = >::commit_ring_blocks(&blocks, &w_setup)?; + + Ok(commitment) +} + +pub(crate) fn eval_ring_at(r: &CyclotomicRing, alpha: &F) -> F { + let mut acc = F::zero(); + let mut power = F::one(); + for coeff in r.coefficients() { + acc = acc + (*coeff * power); + power = power * *alpha; + } + acc +} + +pub(crate) fn eval_ring_vec_at( + v: &[CyclotomicRing], + alpha: &F, +) -> Vec { + v.iter().map(|r| eval_ring_at(r, alpha)).collect() +} + +pub(crate) fn eval_ring_matrix_at( + m: &[Vec>], + alpha: &F, +) -> Vec> { + m.iter().map(|row| eval_ring_vec_at(row, alpha)).collect() +} + +pub(crate) fn r_decomp_levels() -> usize { + let modulus = detect_field_modulus::(); + let bits = 128 - (modulus.saturating_sub(1)).leading_zeros() as usize; + let log_basis = Cfg::LOG_BASIS as usize; + let mut levels = (bits + log_basis.saturating_sub(1)) / log_basis.max(1); + if levels == 0 { + levels = 1; + } + + let b = 1u128 << Cfg::LOG_BASIS; + let half_q = modulus / 2; + let half_b_minus_1 = b / 2 - 1; + let b_minus_1 = b - 1; + let mut b_pow = 1u128; + for _ in 0..levels { + b_pow = b_pow.saturating_mul(b); + } + let max_positive = half_b_minus_1.saturating_mul((b_pow - 1) / b_minus_1); + if max_positive < half_q { + levels += 1; + } + + levels +} + +pub(crate) fn expand_m_a( + m_a: &[Vec], + alpha: F, +) -> Result, HachiError> { + if m_a.is_empty() { + return Ok(Vec::new()); + } + let rows = m_a.len(); + let cols = m_a[0].len(); + if cols == 0 { + return Ok(vec![F::zero(); rows]); + } + for row in m_a.iter() { + if row.len() != cols { + return Err(HachiError::InvalidSize { + expected: cols, + actual: row.len(), + }); + } + } + + let levels = r_decomp_levels::(); + let total_cols = cols + .checked_add( + rows.checked_mul(levels) + .ok_or_else(|| HachiError::InvalidSetup("expanded M width overflow".to_string()))?, + ) + .ok_or_else(|| HachiError::InvalidSetup("expanded M width overflow".to_string()))?; + + let base = F::from_canonical_u128_reduced(1u128 << Cfg::LOG_BASIS); + let mut gadget_row = Vec::with_capacity(levels); + let mut power = F::one(); + for _ in 0..levels { + gadget_row.push(power); + power = power * base; + } + + let mut alpha_pow = F::one(); + for _ in 0..D { + alpha_pow = alpha_pow * alpha; + } + let denom = alpha_pow + F::one(); + + let mut out = vec![F::zero(); rows * total_cols]; + for (i, m_a_row) in m_a.iter().enumerate() { + let row_start = i * total_cols; + out[row_start..row_start + cols].copy_from_slice(m_a_row); + let r_start = row_start + cols + i * levels; + for (j, g) in gadget_row.iter().enumerate() { + out[r_start + j] = -denom * *g; + } + } + Ok(out) +} + +pub(crate) fn build_w_evals(w: &[F], d: usize) -> (Vec, usize, usize) { + let num_l = d.trailing_zeros() as usize; + let num_ring_elems = w.len() / d.max(1); + let num_u = num_ring_elems.next_power_of_two().trailing_zeros() as usize; + let x_len = 1usize << num_u; + let y_len = 1usize << num_l; + let n = x_len * y_len; + + let mut evals = vec![F::zero(); n]; + for x in 0..x_len { + for y in 0..y_len { + let src = y + (x << num_l); + if src < w.len() { + let dst = x + (y << num_u); + evals[dst] = w[src]; + } + } + } + (evals, num_u, num_l) +} + +pub(crate) fn m_row_count() -> usize { + Cfg::N_D + Cfg::N_B + 1 + 1 + Cfg::N_A +} + +pub(crate) fn build_m_evals_x( + m_a_flat: &[F], + rows: usize, + cols: usize, + tau1: &[F], +) -> Vec { + let eq_tau1 = eq_evals(tau1); + let x_len = cols.next_power_of_two(); + let mut m_evals = vec![F::zero(); x_len]; + for x in 0..x_len { + let mut acc = F::zero(); + for i in 0..eq_tau1.len() { + let row_val = if i < rows && x < cols { + m_a_flat[i * cols + x] + } else { + F::zero() + }; + acc = acc + eq_tau1[i] * row_val; + } + m_evals[x] = acc; + } + m_evals +} + +pub(crate) fn build_alpha_evals_y(alpha: F, d: usize) -> Vec { + let mut out = vec![F::zero(); d]; + let mut power = F::one(); + for val in out.iter_mut() { + *val = power; + power = power * alpha; + } + out +} + +pub(crate) fn sample_tau>( + transcript: &mut T, + label: &[u8], + n: usize, +) -> Vec { + (0..n).map(|_| transcript.challenge_scalar(label)).collect() +} + +pub(crate) fn build_w_coeffs( + z: &[CyclotomicRing], + r: &[CyclotomicRing], +) -> Vec { + let levels = r_decomp_levels::(); + let r_hat: Vec> = r + .iter() + .flat_map(|ri| ri.balanced_decompose_pow2(levels, Cfg::LOG_BASIS)) + .collect(); + + let mut out = Vec::with_capacity((z.len() + r_hat.len()) * D); + for elem in z.iter().chain(r_hat.iter()) { + out.extend_from_slice(elem.coefficients()); + } + out +} diff --git a/src/protocol/sumcheck/mod.rs b/src/protocol/sumcheck/mod.rs new file mode 100644 index 00000000..2bba5ca0 --- /dev/null +++ b/src/protocol/sumcheck/mod.rs @@ -0,0 +1,641 @@ +//! Sumcheck core building blocks (univariate messages + proof transcript driver). +//! +//! This module provides: +//! - Univariate polynomials over a field `E` (`UniPoly`). +//! - A compressed univariate representation (`CompressedUniPoly`) that omits the +//! linear term and reconstructs it from the per-round sumcheck hint `g(0)+g(1)`. +//! - A minimal sumcheck proof container (`SumcheckProof`) with a verifier-side +//! transcript driver that returns the derived point and final claimed value. +//! +//! It intentionally does **not** implement a concrete sumcheck prover for any +//! particular oracle/table representation. Higher-level protocols (e.g. Hachi §4.3) +//! should implement the prover logic that constructs each round's univariate `g_i(X)`. +//! +//! ## Temporary duplication notice (Jolt integration) +//! +//! Jolt already has a mature, streaming-aware sumcheck implementation. Long-term, we +//! expect to extract the common sumcheck machinery into a dedicated crate and depend +//! on it from both Hachi and Jolt. Until that exists, this module intentionally +//! duplicates the essential sumcheck data types and transcript-driving logic as a +//! pragmatic workaround. + +pub mod norm_sumcheck; +pub mod relation_sumcheck; + +use crate::error::HachiError; +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; +use crate::protocol::transcript::labels; +use crate::protocol::transcript::Transcript; +use crate::CanonicalField; +use crate::FieldCore; +use std::io::{Read, Write}; + +/// Univariate polynomial in coefficient form: `p(X) = Σ_{i=0}^d coeffs[i] * X^i`. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct UniPoly { + /// Coefficients from low degree to high degree. + pub coeffs: Vec, +} + +impl UniPoly { + /// Construct from coefficients in increasing-degree order. + pub fn from_coeffs(coeffs: Vec) -> Self { + Self { coeffs } + } + + /// Degree of the polynomial. + /// + /// # Panics + /// + /// Panics if the polynomial has no coefficients. + pub fn degree(&self) -> usize { + self.coeffs + .len() + .checked_sub(1) + .expect("UniPoly must have at least one coefficient") + } + + /// Evaluate at `x` via Horner's method. + pub fn evaluate(&self, x: &E) -> E { + // Horner from highest degree. + let mut acc = E::zero(); + for c in self.coeffs.iter().rev() { + acc = acc * *x + *c; + } + acc + } + + /// Compress this polynomial by omitting the linear coefficient. + /// + /// The verifier can reconstruct/evaluate the missing linear coefficient using + /// the per-round hint `g(0)+g(1)` from the sumcheck protocol. + /// + /// This matches the technique used by Jolt's sumcheck (`CompressedUniPoly`). + pub fn compress(&self) -> CompressedUniPoly { + let coeffs = &self.coeffs; + if coeffs.is_empty() { + return CompressedUniPoly { + coeffs_except_linear_term: Vec::new(), + }; + } + if coeffs.len() == 1 { + return CompressedUniPoly { + coeffs_except_linear_term: vec![coeffs[0]], + }; + } + // Keep coeff[0], drop coeff[1], keep coeff[2..]. + let mut out = Vec::with_capacity(coeffs.len().saturating_sub(1)); + out.push(coeffs[0]); + out.extend_from_slice(&coeffs[2..]); + CompressedUniPoly { + coeffs_except_linear_term: out, + } + } +} + +impl UniPoly { + /// Interpolate from evaluations at equispaced integer points `x = 0, 1, ..., d`. + /// + /// Uses Newton forward-difference interpolation: compute divided differences, + /// then expand via Horner on the nested Newton form. + /// + /// # Panics + /// + /// Panics if any required factorial inverse does not exist (field characteristic + /// must exceed the number of evaluation points). + pub fn from_evals(evals: &[E]) -> Self { + let n = evals.len(); + if n == 0 { + return Self::from_coeffs(vec![]); + } + if n == 1 { + return Self::from_coeffs(vec![evals[0]]); + } + + // Forward differences: delta^k[0] + let mut table = evals.to_vec(); + let mut deltas = vec![table[0]]; + for _ in 1..n { + for j in 0..table.len() - 1 { + table[j] = table[j + 1] - table[j]; + } + table.pop(); + deltas.push(table[0]); + } + + // Divided differences: dd[k] = delta^k / k! + let mut factorial = E::one(); + let mut divided_diffs = vec![deltas[0]]; + for (k, delta_k) in deltas.iter().enumerate().skip(1) { + factorial = factorial * E::from_u64(k as u64); + divided_diffs.push( + *delta_k + * factorial + .inv() + .expect("field characteristic too small for interpolation"), + ); + } + + // Horner expansion of the Newton nested form: + // p(x) = dd[0] + (x-0)(dd[1] + (x-1)(dd[2] + ...)) + let mut coeffs = vec![divided_diffs[n - 1]]; + + for k in (0..n - 1).rev() { + let shift = E::from_u64(k as u64); + let old_len = coeffs.len(); + let mut new_coeffs = vec![E::zero(); old_len + 1]; + + new_coeffs[0] = divided_diffs[k]; + for i in 0..old_len { + new_coeffs[i + 1] = new_coeffs[i + 1] + coeffs[i]; + new_coeffs[i] = new_coeffs[i] - shift * coeffs[i]; + } + + coeffs = new_coeffs; + } + + while coeffs.len() > 1 && coeffs.last().is_some_and(|c| c.is_zero()) { + coeffs.pop(); + } + + Self::from_coeffs(coeffs) + } +} + +impl Valid for UniPoly { + fn check(&self) -> Result<(), SerializationError> { + self.coeffs.check() + } +} + +impl HachiSerialize for UniPoly { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.coeffs.serialize_with_mode(&mut writer, compress) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.coeffs.serialized_size(compress) + } +} + +impl HachiDeserialize for UniPoly { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let coeffs = Vec::::deserialize_with_mode(&mut reader, compress, validate)?; + let out = Self { coeffs }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +/// Compressed univariate polynomial representation omitting the linear term. +/// +/// We store `[c0, c2, c3, ..., cd]`. Given the sumcheck hint `hint = g(0)+g(1)`, +/// the missing linear coefficient is: +/// +/// `c1 = hint - 2*c0 - Σ_{i=2..d} ci`. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct CompressedUniPoly { + /// Coefficients excluding the linear term: `[c0, c2, c3, ..., cd]`. + pub coeffs_except_linear_term: Vec, +} + +impl CompressedUniPoly { + /// Degree of the underlying uncompressed polynomial. + /// + /// For degree `d`, this stores `d` coefficients (all except the linear term). + pub fn degree(&self) -> usize { + self.coeffs_except_linear_term.len().saturating_sub(1) + } + + fn recover_linear_term(&self, hint: &E) -> E { + if self.coeffs_except_linear_term.is_empty() { + // Treat empty as the zero polynomial. + return E::zero(); + } + + // linear = hint - 2*c0 - Σ_{i>=2} ci + let c0 = self.coeffs_except_linear_term[0]; + let mut linear = *hint - c0 - c0; + for c in self.coeffs_except_linear_term.iter().skip(1) { + linear = linear - *c; + } + linear + } + + /// Decompress using `hint = g(0)+g(1)`. + pub fn decompress(&self, hint: &E) -> UniPoly { + if self.coeffs_except_linear_term.is_empty() { + return UniPoly::from_coeffs(Vec::new()); + } + let linear = self.recover_linear_term(hint); + // Always materialize the missing linear coefficient. + // For truly-constant polynomials, the hint forces `linear = 0`, so this is harmless. + let mut coeffs = Vec::with_capacity(self.coeffs_except_linear_term.len() + 1); + coeffs.push(self.coeffs_except_linear_term[0]); + coeffs.push(linear); + coeffs.extend_from_slice(&self.coeffs_except_linear_term[1..]); + UniPoly::from_coeffs(coeffs) + } + + /// Evaluate the uncompressed polynomial at `x`, using `hint = g(0)+g(1)`. + /// + /// This avoids materializing the full coefficient list. + pub fn eval_from_hint(&self, hint: &E, x: &E) -> E { + if self.coeffs_except_linear_term.is_empty() { + return E::zero(); + } + + let linear = self.recover_linear_term(hint); + let mut acc = self.coeffs_except_linear_term[0] + (*x * linear); + + // Add Σ_{i=2..d} c_i * x^i, where stored slice is [c2, c3, ..., cd] + let mut pow = *x * *x; // x^2 + for c in self.coeffs_except_linear_term.iter().skip(1) { + acc = acc + (*c * pow); + pow = pow * *x; + } + acc + } +} + +impl Valid for CompressedUniPoly { + fn check(&self) -> Result<(), SerializationError> { + self.coeffs_except_linear_term.check() + } +} + +impl HachiSerialize for CompressedUniPoly { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.coeffs_except_linear_term + .serialize_with_mode(&mut writer, compress) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.coeffs_except_linear_term.serialized_size(compress) + } +} + +impl HachiDeserialize for CompressedUniPoly { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let coeffs_except_linear_term = + Vec::::deserialize_with_mode(&mut reader, compress, validate)?; + let out = Self { + coeffs_except_linear_term, + }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +/// Sumcheck proof containing one compressed univariate polynomial per round. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct SumcheckProof { + /// One compressed univariate polynomial per sumcheck round. + pub round_polys: Vec>, +} + +impl Valid for SumcheckProof { + fn check(&self) -> Result<(), SerializationError> { + self.round_polys.check() + } +} + +impl HachiSerialize for SumcheckProof { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.round_polys.serialize_with_mode(&mut writer, compress) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.round_polys.serialized_size(compress) + } +} + +impl HachiDeserialize for SumcheckProof { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let round_polys = + Vec::>::deserialize_with_mode(&mut reader, compress, validate)?; + let out = Self { round_polys }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +impl SumcheckProof { + /// Verifier-side sumcheck transcript driver. + /// + /// This method: + /// - absorbs the per-round prover message (compressed univariate), + /// - samples one challenge per round via `sample_challenge`, + /// - updates the running claim using `eval_from_hint`. + /// + /// It does **not** perform the final oracle check `final_claim == f(r*)`. + /// Callers (e.g. ring-switching) must compute `f(r*)` themselves and compare. + /// + /// # Errors + /// + /// Returns an error if the proof length does not match `num_rounds` or if any + /// per-round polynomial exceeds `degree_bound`. + pub fn verify( + &self, + mut claim: E, + num_rounds: usize, + degree_bound: usize, + transcript: &mut T, + mut sample_challenge: S, + ) -> Result<(E, Vec), HachiError> + where + F: crate::FieldCore + crate::CanonicalField, + T: Transcript, + S: FnMut(&mut T) -> E, + { + if self.round_polys.len() != num_rounds { + return Err(HachiError::InvalidSize { + expected: num_rounds, + actual: self.round_polys.len(), + }); + } + + let mut r = Vec::with_capacity(num_rounds); + for poly in &self.round_polys { + if poly.degree() > degree_bound { + return Err(HachiError::InvalidInput(format!( + "sumcheck round poly degree {} exceeds bound {}", + poly.degree(), + degree_bound + ))); + } + + transcript.append_serde(labels::ABSORB_SUMCHECK_ROUND, poly); + let r_i = sample_challenge(transcript); + r.push(r_i); + + claim = poly.eval_from_hint(&claim, &r_i); + } + + Ok((claim, r)) + } +} + +/// Prover-side sumcheck instance interface. +/// +/// This trait encapsulates the protocol-specific logic required to compute each +/// per-round univariate polynomial `g_j(X)` and to update (fold) internal state +/// after receiving the verifier challenge `r_j`. +/// +/// Hachi §4.3 will implement concrete instances for `H_0` and `H_α`. +pub trait SumcheckInstanceProver: Send + Sync { + /// Number of rounds (i.e. number of variables bound by sumcheck). + fn num_rounds(&self) -> usize; + + /// Maximum allowed degree for any round univariate polynomial. + fn degree_bound(&self) -> usize; + + /// The initial claimed sum that this sumcheck instance is proving. + fn input_claim(&self) -> E; + + /// Compute the prover message `g_round(X)` given the previous running claim. + /// + /// In standard sumcheck, `previous_claim` is the expected value of the + /// remaining sum after binding previous challenges, and must satisfy: + /// + /// `g_round(0) + g_round(1) == previous_claim`. + fn compute_round_univariate(&mut self, round: usize, previous_claim: E) -> UniPoly; + + /// Ingest the verifier challenge `r_round` to fold/bind the current variable. + fn ingest_challenge(&mut self, round: usize, r_round: E); + + /// Optional end-of-protocol hook after the last challenge has been ingested. + fn finalize(&mut self) {} +} + +/// Verifier-side sumcheck instance interface. +/// +/// Implementations provide the initial claim and the oracle evaluation at the +/// challenge point, enabling the verifier to perform the final consistency check. +pub trait SumcheckInstanceVerifier: Send + Sync { + /// Number of rounds (i.e. number of variables bound by sumcheck). + fn num_rounds(&self) -> usize; + + /// Maximum allowed degree for any round univariate polynomial. + fn degree_bound(&self) -> usize; + + /// The initial claimed sum that this sumcheck instance is proving. + fn input_claim(&self) -> E; + + /// Compute the expected final evaluation `f(r_0, ..., r_{n-1})` at the + /// challenge point derived during the protocol. + fn expected_output_claim(&self, challenges: &[E]) -> E; +} + +/// Produce a sumcheck proof for a single instance, driving the Fiat–Shamir transcript. +/// +/// This method: +/// - does **not** absorb the initial claim into the transcript (callers should do so), +/// - appends each round message under `labels::ABSORB_SUMCHECK_ROUND`, +/// - samples one challenge per round via `sample_challenge`, +/// - updates the running claim using the per-round hint (`g(0)+g(1)`). +/// +/// It returns the proof, the derived point `r`, and the final claimed value at `r`. +/// +/// # Errors +/// +/// Returns an error if any per-round polynomial exceeds the instance's degree bound. +pub fn prove_sumcheck( + instance: &mut Inst, + transcript: &mut T, + mut sample_challenge: S, +) -> Result<(SumcheckProof, Vec, E), HachiError> +where + F: crate::FieldCore + crate::CanonicalField, + T: Transcript, + E: FieldCore, + S: FnMut(&mut T) -> E, + Inst: SumcheckInstanceProver, +{ + let mut claim = instance.input_claim(); + transcript.append_serde(labels::ABSORB_SUMCHECK_CLAIM, &claim); + + let num_rounds = instance.num_rounds(); + let degree_bound = instance.degree_bound(); + + let mut round_polys = Vec::with_capacity(num_rounds); + let mut r = Vec::with_capacity(num_rounds); + + for round in 0..num_rounds { + let g = instance.compute_round_univariate(round, claim); + // Optional sanity: enforce hint relation in debug builds. + debug_assert!( + g.evaluate(&E::zero()) + g.evaluate(&E::one()) == claim, + "sumcheck round univariate does not match previous claim hint" + ); + + let compressed = g.compress(); + if compressed.degree() > degree_bound { + return Err(HachiError::InvalidInput(format!( + "sumcheck round poly degree {} exceeds bound {}", + compressed.degree(), + degree_bound + ))); + } + + transcript.append_serde(labels::ABSORB_SUMCHECK_ROUND, &compressed); + let r_i = sample_challenge(transcript); + r.push(r_i); + + // Update running claim (this is g(r_i)). + claim = compressed.eval_from_hint(&claim, &r_i); + + instance.ingest_challenge(round, r_i); + round_polys.push(compressed); + } + + instance.finalize(); + + let proof = SumcheckProof { round_polys }; + Ok((proof, r, claim)) +} + +/// Verify a single-instance sumcheck proof. +/// +/// This function: +/// - absorbs the initial claim into the transcript, +/// - delegates round-by-round verification to [`SumcheckProof::verify`], +/// - performs the final oracle check: `final_claim == verifier.expected_output_claim(r)`. +/// +/// Returns the challenge point `r` on success. +/// +/// # Errors +/// +/// Returns [`HachiError::InvalidProof`] if the final sumcheck claim does not +/// match the oracle evaluation, or propagates any error from the per-round +/// verification (e.g. degree-bound violation, round-count mismatch). +pub fn verify_sumcheck( + proof: &SumcheckProof, + verifier: &V, + transcript: &mut T, + sample_challenge: S, +) -> Result, HachiError> +where + F: crate::FieldCore + crate::CanonicalField, + T: Transcript, + E: FieldCore, + S: FnMut(&mut T) -> E, + V: SumcheckInstanceVerifier, +{ + let claim = verifier.input_claim(); + transcript.append_serde(labels::ABSORB_SUMCHECK_CLAIM, &claim); + let (final_claim, challenges) = proof.verify::( + claim, + verifier.num_rounds(), + verifier.degree_bound(), + transcript, + sample_challenge, + )?; + + let expected = verifier.expected_output_claim(&challenges); + if final_claim != expected { + return Err(HachiError::InvalidProof); + } + + Ok(challenges) +} + +/// Build the full eq polynomial evaluation table. +/// +/// Returns a vector of size `2^{tau.len()}` where entry `b` (interpreted as a +/// little-endian bit string, i.e. bit `k` of `b` corresponds to `τ[k]`) equals +/// `ẽq(τ, b) = Π_i (τ_i·b_i + (1−τ_i)(1−b_i))`. +pub fn eq_evals(tau: &[E]) -> Vec { + let size = 1usize << tau.len(); + let mut evals = vec![E::zero(); size]; + evals[0] = E::one(); + let mut len = 1usize; + for &t in tau.iter().rev() { + let one_minus_t = E::one() - t; + for j in (0..len).rev() { + evals[2 * j + 1] = evals[j] * t; + evals[2 * j] = evals[j] * one_minus_t; + } + len *= 2; + } + evals +} + +/// Evaluate ẽq(τ, r) at a single point. +pub fn eq_eval(tau: &[E], point: &[E]) -> E { + debug_assert_eq!(tau.len(), point.len()); + tau.iter().zip(point).fold(E::one(), |acc, (&t, &r)| { + acc * (t * r + (E::one() - t) * (E::one() - r)) + }) +} + +/// Evaluate the range-check polynomial `w · Π_{k=1}^{b−1} (w − k)(w + k)`. +/// +/// This polynomial vanishes exactly when `w ∈ {−(b−1), …, b−1}`. +/// Total degree in `w` is `2b − 1`. +pub fn range_check_eval(w: E, b: usize) -> E { + let mut acc = w; + for k in 1..b { + let k_e = E::from_u64(k as u64); + acc = acc * (w - k_e) * (w + k_e); + } + acc +} + +/// Evaluate a multilinear polynomial (given by boolean-hypercube evaluations in +/// little-endian bit order) at an arbitrary point via iterated folding. +pub fn multilinear_eval(evals: &[E], point: &[E]) -> E { + let mut current = evals.to_vec(); + for &r in point { + let half = current.len() / 2; + let mut next = Vec::with_capacity(half); + for i in 0..half { + next.push(current[2 * i] + r * (current[2 * i + 1] - current[2 * i])); + } + current = next; + } + current[0] +} + +/// Fold an evaluation table by binding its first variable to `r`, halving the +/// table size. +pub(crate) fn fold_evals(evals: &[E], r: E) -> Vec { + let half = evals.len() / 2; + let mut out = Vec::with_capacity(half); + for i in 0..half { + out.push(evals[2 * i] + r * (evals[2 * i + 1] - evals[2 * i])); + } + out +} diff --git a/src/protocol/sumcheck/norm_sumcheck.rs b/src/protocol/sumcheck/norm_sumcheck.rs new file mode 100644 index 00000000..e1b72490 --- /dev/null +++ b/src/protocol/sumcheck/norm_sumcheck.rs @@ -0,0 +1,255 @@ +//! Norm (range-check) sumcheck instance (F_0). +//! +//! **F_{0,τ₀}(x, y)** = ẽq(τ₀,(x,y)) · w̃(x,y) · (w̃−1)(w̃+1)···(w̃−b+1)(w̃+b−1) +//! +//! Proves that all entries of w̃ lie in {−(b−1), …, b−1}; the sum over the +//! boolean hypercube should equal zero when the range constraint holds. + +use super::{eq_eval, eq_evals, fold_evals, multilinear_eval, range_check_eval}; +use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, UniPoly}; +use crate::{CanonicalField, FieldCore}; + +/// Prover for `F_{0,τ₀}(x,y) = ẽq(τ₀,(x,y)) · w̃(x,y) · range_check(w̃(x,y), b)`. +/// +/// Stores `eq` and `w` evaluation tables separately so the composite can be +/// evaluated at the `2b + 1` points needed per round (degree `2b`). +pub struct NormSumcheckProver { + eq_table: Vec, + w_table: Vec, + num_vars: usize, + b: usize, +} + +impl NormSumcheckProver { + /// Create a new norm (range-check) sumcheck prover. + /// + /// # Panics + /// + /// Panics if `w_evals.len() != 2^tau.len()`. + pub fn new(tau: &[E], w_evals: Vec, b: usize) -> Self { + let num_vars = tau.len(); + assert_eq!(w_evals.len(), 1 << num_vars); + Self { + eq_table: eq_evals(tau), + w_table: w_evals, + num_vars, + b, + } + } +} + +impl SumcheckInstanceProver for NormSumcheckProver { + fn num_rounds(&self) -> usize { + self.num_vars + } + + fn degree_bound(&self) -> usize { + 2 * self.b + } + + fn input_claim(&self) -> E { + E::zero() + } + + fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { + let half = self.eq_table.len() / 2; + let degree = 2 * self.b; + let num_points = degree + 1; + let mut round_evals = vec![E::zero(); num_points]; + + for j in 0..half { + let eq_0 = self.eq_table[2 * j]; + let eq_1 = self.eq_table[2 * j + 1]; + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + + for (t, eval) in round_evals.iter_mut().enumerate() { + let t_e = E::from_u64(t as u64); + let eq_t = eq_0 + t_e * (eq_1 - eq_0); + let w_t = w_0 + t_e * (w_1 - w_0); + *eval = *eval + eq_t * range_check_eval(w_t, self.b); + } + } + + UniPoly::from_evals(&round_evals) + } + + fn ingest_challenge(&mut self, _round: usize, r: E) { + self.eq_table = fold_evals(&self.eq_table, r); + self.w_table = fold_evals(&self.w_table, r); + } +} + +/// Verifier for the norm (range-check) sumcheck `F_{0,τ₀}`. +pub struct NormSumcheckVerifier { + tau: Vec, + w_evals: Vec, + num_vars: usize, + b: usize, +} + +impl NormSumcheckVerifier { + /// Create a new norm (range-check) sumcheck verifier. + /// + /// # Panics + /// + /// Panics if `w_evals.len() != 2^tau.len()`. + pub fn new(tau: Vec, w_evals: Vec, b: usize) -> Self { + let num_vars = tau.len(); + assert_eq!(w_evals.len(), 1 << num_vars); + Self { + tau, + w_evals, + num_vars, + b, + } + } +} + +impl SumcheckInstanceVerifier for NormSumcheckVerifier { + fn num_rounds(&self) -> usize { + self.num_vars + } + + fn degree_bound(&self) -> usize { + 2 * self.b + } + + fn input_claim(&self) -> E { + E::zero() + } + + fn expected_output_claim(&self, challenges: &[E]) -> E { + let eq_val = eq_eval(&self.tau, challenges); + let w_val = multilinear_eval(&self.w_evals, challenges); + eq_val * range_check_eval(w_val, self.b) + } +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::algebra::ring::CyclotomicRing; + use crate::algebra::Fp64; + use crate::primitives::multilinear_evals::DenseMultilinearEvals; + use crate::protocol::ring_switch::build_w_coeffs; + use crate::protocol::sumcheck::eq_evals; + use crate::protocol::transcript::labels; + use crate::protocol::{ + prove_sumcheck, verify_sumcheck, Blake2bTranscript, CommitmentConfig, CommitmentScheme, + DefaultCommitmentConfig, HachiCommitmentScheme, Transcript, + }; + use crate::{CanonicalField, FieldCore}; + + type F = Fp64<4294967197>; + const D: usize = 8; + + fn ring_with_small_coeff(value: u64) -> CyclotomicRing { + let coeffs = std::array::from_fn(|_| F::from_u64(value)); + CyclotomicRing::from_coefficients(coeffs) + } + + #[test] + fn norm_sumcheck_uses_commitment_w_evals() { + let z = vec![ + ring_with_small_coeff(1), + ring_with_small_coeff(2), + ring_with_small_coeff(3), + ]; + let r = vec![ring_with_small_coeff(0), ring_with_small_coeff(1)]; + let mut w_evals = build_w_coeffs::(&z, &r); + + let target_len = w_evals.len().next_power_of_two(); + w_evals.resize(target_len, F::zero()); + let num_vars = target_len.trailing_zeros() as usize; + let tau: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); + let b = 1usize << DefaultCommitmentConfig::LOG_BASIS; + + let eq_table = eq_evals(&tau); + let _claim: F = (0..w_evals.len()) + .map(|i| eq_table[i] * range_check_eval(w_evals[i], b)) + .fold(F::zero(), |a, v| a + v); + + let mut prover = NormSumcheckProver::new(&tau, w_evals.clone(), b); + let mut pt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let (proof, prover_challenges, final_claim) = + prove_sumcheck::(&mut prover, &mut pt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + let oracle = eq_eval(&tau, &prover_challenges) + * range_check_eval(multilinear_eval(&w_evals, &prover_challenges), b); + assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); + + let verifier = NormSumcheckVerifier::new(tau, w_evals, b); + let mut vt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let verifier_challenges = + verify_sumcheck::(&proof, &verifier, &mut vt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + assert_eq!(prover_challenges, verifier_challenges); + } + + #[test] + fn norm_sumcheck_uses_prove_w_evals() { + let alpha = DefaultCommitmentConfig::D.trailing_zeros() as usize; + let num_vars = DefaultCommitmentConfig::R + DefaultCommitmentConfig::M + alpha; + let len = 1usize << num_vars; + let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); + let poly = DenseMultilinearEvals::new_padded(evals); + + let setup = HachiCommitmentScheme::setup_prover(num_vars); + let (commitment, hint) = HachiCommitmentScheme::commit(&poly, &setup).unwrap(); + + let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); + let mut prover_transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let proof = HachiCommitmentScheme::prove( + &setup, + &poly, + &opening_point, + Some(hint), + &mut prover_transcript, + &commitment, + ) + .unwrap(); + + let mut w_evals = proof.sumcheck_aux.w.clone(); + let target_len = w_evals.len().next_power_of_two(); + w_evals.resize(target_len, F::zero()); + let num_sumcheck_vars = target_len.trailing_zeros() as usize; + let tau: Vec = (0..num_sumcheck_vars) + .map(|i| F::from_u64((i + 3) as u64)) + .collect(); + let b = 1usize << DefaultCommitmentConfig::LOG_BASIS; + + let eq_table = eq_evals(&tau); + let _claim: F = (0..w_evals.len()) + .map(|i| eq_table[i] * range_check_eval(w_evals[i], b)) + .fold(F::zero(), |a, v| a + v); + + let mut prover = NormSumcheckProver::new(&tau, w_evals.clone(), b); + let mut pt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let (proof_sc, prover_challenges, final_claim) = + prove_sumcheck::(&mut prover, &mut pt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + let oracle = eq_eval(&tau, &prover_challenges) + * range_check_eval(multilinear_eval(&w_evals, &prover_challenges), b); + assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); + + let verifier = NormSumcheckVerifier::new(tau, w_evals, b); + let mut vt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let verifier_challenges = + verify_sumcheck::(&proof_sc, &verifier, &mut vt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + assert_eq!(prover_challenges, verifier_challenges); + } +} diff --git a/src/protocol/sumcheck/relation_sumcheck.rs b/src/protocol/sumcheck/relation_sumcheck.rs new file mode 100644 index 00000000..12de5a7f --- /dev/null +++ b/src/protocol/sumcheck/relation_sumcheck.rs @@ -0,0 +1,345 @@ +//! Evaluation-relation sumcheck instance (F_α). +//! +//! **F_{α,τ₁}(x, y)** = w̃(x,y) · α̃(y) · m(x) +//! where m(x) = Σ_i ẽq(τ₁,i) · M̃_α(i,x). +//! +//! Proves the evaluation relation; sum equals `a = Σ_i ẽq(τ₁,i) · y_i(α)`. + +use super::{eq_evals, fold_evals, multilinear_eval}; +use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, UniPoly}; +use crate::algebra::ring::CyclotomicRing; +use crate::protocol::ring_switch::eval_ring_at; +use crate::{CanonicalField, FieldCore}; + +/// Prover for `F_{α,τ₁}(x,y) = w̃(x,y) · α̃(y) · m(x)`. +/// +/// All three constituent evaluation tables are stored at full domain size +/// (`2^{num_u + num_l}`). `α̃` is replicated along x dimensions and `m` along +/// y dimensions so that a uniform fold-by-pairs works in every round. +/// +/// Round polynomial degree is 2 (product of at most two multilinear factors +/// depending on any single variable). +pub struct RelationSumcheckProver { + w_table: Vec, + alpha_table: Vec, + m_table: Vec, + num_vars: usize, +} + +impl RelationSumcheckProver { + /// Construct from the three constituent evaluation tables. + /// + /// - `w_evals`: evaluations of `w̃` over `{0,1}^{num_u + num_l}` (full domain). + /// - `alpha_evals_y`: evaluations of `α̃` over `{0,1}^{num_l}` (compact). + /// - `m_evals_x`: evaluations of `m` over `{0,1}^{num_u}` (compact). + /// + /// The constructor extends the compact tables to the full domain by replication. + /// + /// # Panics + /// + /// Panics if table sizes don't match `2^num_u`, `2^num_l`, or `2^(num_u+num_l)`. + pub fn new( + w_evals: Vec, + alpha_evals_y: &[E], + m_evals_x: &[E], + num_u: usize, + num_l: usize, + ) -> Self { + let num_vars = num_u + num_l; + let n = 1usize << num_vars; + assert_eq!(w_evals.len(), n); + assert_eq!(alpha_evals_y.len(), 1 << num_l); + assert_eq!(m_evals_x.len(), 1 << num_u); + + let x_mask = (1usize << num_u) - 1; + let alpha_table: Vec = (0..n).map(|idx| alpha_evals_y[idx >> num_u]).collect(); + let m_table: Vec = (0..n).map(|idx| m_evals_x[idx & x_mask]).collect(); + + Self { + w_table: w_evals, + alpha_table, + m_table, + num_vars, + } + } +} + +impl SumcheckInstanceProver for RelationSumcheckProver { + fn num_rounds(&self) -> usize { + self.num_vars + } + + fn degree_bound(&self) -> usize { + 2 + } + + fn input_claim(&self) -> E { + self.w_table + .iter() + .zip(self.alpha_table.iter()) + .zip(self.m_table.iter()) + .fold(E::zero(), |acc, ((&w, &a), &m)| acc + w * a * m) + } + + fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { + let half = self.w_table.len() / 2; + let num_points = 3; // degree 2 → 3 evaluation points + let mut round_evals = vec![E::zero(); num_points]; + + for j in 0..half { + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + let a_0 = self.alpha_table[2 * j]; + let a_1 = self.alpha_table[2 * j + 1]; + let m_0 = self.m_table[2 * j]; + let m_1 = self.m_table[2 * j + 1]; + + for (t, eval) in round_evals.iter_mut().enumerate() { + let t_e = E::from_u64(t as u64); + let w_t = w_0 + t_e * (w_1 - w_0); + let a_t = a_0 + t_e * (a_1 - a_0); + let m_t = m_0 + t_e * (m_1 - m_0); + *eval = *eval + w_t * a_t * m_t; + } + } + + UniPoly::from_evals(&round_evals) + } + + fn ingest_challenge(&mut self, _round: usize, r: E) { + self.w_table = fold_evals(&self.w_table, r); + self.alpha_table = fold_evals(&self.alpha_table, r); + self.m_table = fold_evals(&self.m_table, r); + } +} + +/// Verifier for the evaluation-relation sumcheck `F_{α,τ₁}`. +pub struct RelationSumcheckVerifier { + w_evals: Vec, + alpha_evals_y: Vec, + m_evals_x: Vec, + tau: Vec, + v: Vec>, + u: Vec>, + y_ring: CyclotomicRing, + alpha: F, + num_u: usize, + num_l: usize, +} + +impl RelationSumcheckVerifier { + /// Create a new evaluation-relation sumcheck verifier. + /// + /// # Panics + /// + /// Panics if table sizes don't match `2^num_u`, `2^num_l`, or `2^(num_u+num_l)`. + #[allow(clippy::too_many_arguments)] + pub fn new( + w_evals: Vec, + alpha_evals_y: Vec, + m_evals_x: Vec, + tau: Vec, + v: Vec>, + u: Vec>, + y_ring: CyclotomicRing, + alpha: F, + num_u: usize, + num_l: usize, + ) -> Self { + assert_eq!(w_evals.len(), 1 << (num_u + num_l)); + assert_eq!(alpha_evals_y.len(), 1 << num_l); + assert_eq!(m_evals_x.len(), 1 << num_u); + Self { + w_evals, + alpha_evals_y, + m_evals_x, + tau, + v, + u, + y_ring, + alpha, + num_u, + num_l, + } + } +} + +impl SumcheckInstanceVerifier + for RelationSumcheckVerifier +{ + fn num_rounds(&self) -> usize { + self.num_u + self.num_l + } + + fn degree_bound(&self) -> usize { + 2 + } + + fn input_claim(&self) -> F { + let y_a: Vec = self + .v + .iter() + .chain(self.u.iter()) + .chain(std::iter::once(&self.y_ring)) + .map(|r| eval_ring_at(r, &self.alpha)) + .collect(); + + let eq_tau = eq_evals(&self.tau); + let mut acc = F::zero(); + for (i, eq_i) in eq_tau.iter().enumerate() { + let y_i = if i < y_a.len() { y_a[i] } else { F::zero() }; + acc = acc + *eq_i * y_i; + } + acc + } + + fn expected_output_claim(&self, challenges: &[F]) -> F { + let (x_challenges, y_challenges) = challenges.split_at(self.num_u); + let w_val = multilinear_eval(&self.w_evals, challenges); + let alpha_val = multilinear_eval(&self.alpha_evals_y, y_challenges); + let m_val = multilinear_eval(&self.m_evals_x, x_challenges); + w_val * alpha_val * m_val + } +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::algebra::Fp64; + use crate::primitives::multilinear_evals::DenseMultilinearEvals; + use crate::protocol::commitment_scheme::rederive_alpha_and_m_a; + use crate::protocol::sumcheck::eq_evals; + use crate::protocol::transcript::labels; + use crate::protocol::{ + prove_sumcheck, verify_sumcheck, Blake2bTranscript, CommitmentConfig, CommitmentScheme, + DefaultCommitmentConfig, HachiCommitmentScheme, Transcript, + }; + use crate::{CanonicalField, FieldCore}; + + type F = Fp64<4294967197>; + + #[test] + fn relation_sumcheck_uses_prove_w_evals() { + let alpha_bits = DefaultCommitmentConfig::D.trailing_zeros() as usize; + let num_vars = DefaultCommitmentConfig::R + DefaultCommitmentConfig::M + alpha_bits; + let len = 1usize << num_vars; + let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); + let poly = DenseMultilinearEvals::new_padded(evals); + + let setup = HachiCommitmentScheme::setup_prover(num_vars); + let (commitment, hint) = HachiCommitmentScheme::commit(&poly, &setup).unwrap(); + + let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); + let mut prover_transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let proof = HachiCommitmentScheme::prove( + &setup, + &poly, + &opening_point, + Some(hint), + &mut prover_transcript, + &commitment, + ) + .unwrap(); + + let (alpha, m_a_vec) = + rederive_alpha_and_m_a(&proof, &setup, &opening_point, &commitment).unwrap(); + + let d = DefaultCommitmentConfig::D; + assert_eq!(proof.sumcheck_aux.w.len() % d, 0); + let w_u = proof.sumcheck_aux.w.len() / d; + let rows = DefaultCommitmentConfig::N_D + + DefaultCommitmentConfig::N_B + + 1 + + 1 + + DefaultCommitmentConfig::N_A; + assert!(rows > 0); + assert_eq!(m_a_vec.len() % rows, 0); + let cols = m_a_vec.len() / rows; + assert_eq!(w_u, cols); + + let num_u = cols.next_power_of_two().trailing_zeros() as usize; + let num_l = alpha_bits; + let n = 1usize << (num_u + num_l); + + let mut w_evals = vec![F::zero(); n]; + let y_len = 1usize << num_l; + let x_len = 1usize << num_u; + for x in 0..x_len { + for y in 0..y_len { + let src = y + (x << num_l); + if src < proof.sumcheck_aux.w.len() { + let dst = x + (y << num_u); + w_evals[dst] = proof.sumcheck_aux.w[src]; + } + } + } + + let num_i = rows.next_power_of_two().trailing_zeros() as usize; + let tau1: Vec = (0..num_i).map(|i| F::from_u64((i + 5) as u64)).collect(); + let eq_tau1 = eq_evals(&tau1); + + let mut m_evals_x = vec![F::zero(); x_len]; + for x in 0..x_len { + let mut acc = F::zero(); + for i in 0..(1usize << num_i) { + let row_val = if i < rows && x < cols { + m_a_vec[i * cols + x] + } else { + F::zero() + }; + acc = acc + eq_tau1[i] * row_val; + } + m_evals_x[x] = acc; + } + + let mut alpha_evals_y = vec![F::zero(); y_len]; + let mut power = F::one(); + for val in alpha_evals_y.iter_mut() { + *val = power; + power = power * alpha; + } + + let x_mask = x_len - 1; + let alpha_full: Vec = (0..n).map(|idx| alpha_evals_y[idx >> num_u]).collect(); + let m_full: Vec = (0..n).map(|idx| m_evals_x[idx & x_mask]).collect(); + let _claim: F = (0..n) + .map(|i| w_evals[i] * alpha_full[i] * m_full[i]) + .fold(F::zero(), |a, v| a + v); + + let mut prover = + RelationSumcheckProver::new(w_evals.clone(), &alpha_evals_y, &m_evals_x, num_u, num_l); + let mut pt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let (proof_sc, prover_challenges, final_claim) = + prove_sumcheck::(&mut prover, &mut pt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + let (x_ch, y_ch) = prover_challenges.split_at(num_u); + let oracle = multilinear_eval(&w_evals, &prover_challenges) + * multilinear_eval(&alpha_evals_y, y_ch) + * multilinear_eval(&m_evals_x, x_ch); + assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); + + let verifier = RelationSumcheckVerifier::new( + w_evals, + alpha_evals_y, + m_evals_x, + tau1, + proof.v.clone(), + commitment.u.clone(), + proof.y_ring, + alpha, + num_u, + num_l, + ); + let mut vt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let verifier_challenges = + verify_sumcheck::(&proof_sc, &verifier, &mut vt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + assert_eq!(prover_challenges, verifier_challenges); + } +} diff --git a/src/protocol/transcript/blake2b.rs b/src/protocol/transcript/blake2b.rs new file mode 100644 index 00000000..c72fba39 --- /dev/null +++ b/src/protocol/transcript/blake2b.rs @@ -0,0 +1,82 @@ +//! Blake2b transcript implementation for protocol-layer Fiat-Shamir. + +use super::Transcript; +use crate::primitives::serialization::HachiSerialize; +use crate::{CanonicalField, FieldCore}; +use blake2::{Blake2b512, Digest}; +use std::marker::PhantomData; + +/// Blake2b512 transcript with labeled framing. +#[derive(Clone)] +pub struct Blake2bTranscript +where + F: FieldCore + CanonicalField + 'static, +{ + hasher: Blake2b512, + _field: PhantomData, +} + +impl Blake2bTranscript +where + F: FieldCore + CanonicalField + 'static, +{ + #[inline] + fn append_bytes_impl(&mut self, label: &[u8], bytes: &[u8]) { + self.hasher.update(label); + self.hasher.update((bytes.len() as u64).to_le_bytes()); + self.hasher.update(bytes); + } + + #[inline] + fn challenge_bytes(&mut self, label: &[u8]) -> [u8; 64] { + self.hasher.update(label); + let digest = self.hasher.clone().finalize(); + let mut out = [0u8; 64]; + out.copy_from_slice(digest.as_slice()); + self.hasher.update(out); + out + } +} + +impl Transcript for Blake2bTranscript +where + F: FieldCore + CanonicalField + 'static, +{ + fn new(domain_label: &[u8]) -> Self { + let mut hasher = Blake2b512::new(); + hasher.update(domain_label); + Self { + hasher, + _field: PhantomData, + } + } + + fn append_bytes(&mut self, label: &[u8], bytes: &[u8]) { + self.append_bytes_impl(label, bytes); + } + + fn append_field(&mut self, label: &[u8], x: &F) { + self.append_bytes_impl(label, &x.to_canonical_u128().to_le_bytes()); + } + + fn append_serde(&mut self, label: &[u8], s: &S) { + let mut bytes = Vec::new(); + s.serialize_compressed(&mut bytes) + .expect("HachiSerialize should not fail"); + self.append_bytes_impl(label, &bytes); + } + + fn challenge_scalar(&mut self, label: &[u8]) -> F { + let bytes = self.challenge_bytes(label); + let mut lo = [0u8; 16]; + lo.copy_from_slice(&bytes[..16]); + let sampled = u128::from_le_bytes(lo); + F::from_canonical_u128_reduced(sampled) + } + + fn reset(&mut self, domain_label: &[u8]) { + let mut hasher = Blake2b512::new(); + hasher.update(domain_label); + self.hasher = hasher; + } +} diff --git a/src/protocol/transcript/keccak.rs b/src/protocol/transcript/keccak.rs new file mode 100644 index 00000000..8fa3855c --- /dev/null +++ b/src/protocol/transcript/keccak.rs @@ -0,0 +1,82 @@ +//! Keccak transcript implementation for protocol-layer Fiat-Shamir. + +use super::Transcript; +use crate::primitives::serialization::HachiSerialize; +use crate::{CanonicalField, FieldCore}; +use sha3::{Digest, Keccak256}; +use std::marker::PhantomData; + +/// Keccak256 transcript with labeled framing. +#[derive(Clone)] +pub struct KeccakTranscript +where + F: FieldCore + CanonicalField + 'static, +{ + hasher: Keccak256, + _field: PhantomData, +} + +impl KeccakTranscript +where + F: FieldCore + CanonicalField + 'static, +{ + #[inline] + fn append_bytes_impl(&mut self, label: &[u8], bytes: &[u8]) { + self.hasher.update(label); + self.hasher.update((bytes.len() as u64).to_le_bytes()); + self.hasher.update(bytes); + } + + #[inline] + fn challenge_bytes(&mut self, label: &[u8]) -> [u8; 32] { + self.hasher.update(label); + let digest = self.hasher.clone().finalize(); + let mut out = [0u8; 32]; + out.copy_from_slice(digest.as_slice()); + self.hasher.update(out); + out + } +} + +impl Transcript for KeccakTranscript +where + F: FieldCore + CanonicalField + 'static, +{ + fn new(domain_label: &[u8]) -> Self { + let mut hasher = Keccak256::new(); + hasher.update(domain_label); + Self { + hasher, + _field: PhantomData, + } + } + + fn append_bytes(&mut self, label: &[u8], bytes: &[u8]) { + self.append_bytes_impl(label, bytes); + } + + fn append_field(&mut self, label: &[u8], x: &F) { + self.append_bytes_impl(label, &x.to_canonical_u128().to_le_bytes()); + } + + fn append_serde(&mut self, label: &[u8], s: &S) { + let mut bytes = Vec::new(); + s.serialize_compressed(&mut bytes) + .expect("HachiSerialize should not fail"); + self.append_bytes_impl(label, &bytes); + } + + fn challenge_scalar(&mut self, label: &[u8]) -> F { + let bytes = self.challenge_bytes(label); + let mut lo = [0u8; 16]; + lo.copy_from_slice(&bytes[..16]); + let sampled = u128::from_le_bytes(lo); + F::from_canonical_u128_reduced(sampled) + } + + fn reset(&mut self, domain_label: &[u8]) { + let mut hasher = Keccak256::new(); + hasher.update(domain_label); + self.hasher = hasher; + } +} diff --git a/src/protocol/transcript/labels.rs b/src/protocol/transcript/labels.rs new file mode 100644 index 00000000..f5d93952 --- /dev/null +++ b/src/protocol/transcript/labels.rs @@ -0,0 +1,69 @@ +//! Hachi-native transcript labels. +//! +//! These constants are the single source of truth for protocol transcript +//! labels in Hachi core. External integrations should translate at adapter +//! boundaries instead of introducing foreign label names here. + +/// Top-level protocol domain label. +pub const DOMAIN_HACHI_PROTOCOL: &[u8] = b"hachi/protocol"; + +/// Absorb commitment object(s) (paper §4.1). +pub const ABSORB_COMMITMENT: &[u8] = b"hachi/absorb/commitment"; +/// Absorb claimed openings/evaluations before relation reduction (paper §4.2). +pub const ABSORB_EVALUATION_CLAIMS: &[u8] = b"hachi/absorb/evaluation-claims"; +/// Challenge for the evaluation-to-linear-relation reduction (paper §4.2). +pub const CHALLENGE_LINEAR_RELATION: &[u8] = b"hachi/challenge/linear-relation"; +/// Absorb ring-switch relation messages (paper §4.3). +pub const ABSORB_RING_SWITCH_MESSAGE: &[u8] = b"hachi/absorb/ring-switch-message"; +/// Challenge used by ring-switching relation checks (paper §4.3). +pub const CHALLENGE_RING_SWITCH: &[u8] = b"hachi/challenge/ring-switch"; +/// Absorb sparse-challenge sampling context (e.g. for short/sparse ring `c`). +pub const ABSORB_SPARSE_CHALLENGE: &[u8] = b"hachi/absorb/sparse-challenge"; +/// Challenge bytes used to sample sparse challenges (e.g. ring `c` with weight ω). +pub const CHALLENGE_SPARSE_CHALLENGE: &[u8] = b"hachi/challenge/sparse-challenge"; +/// Absorb the initial sumcheck claim before round messages begin. +pub const ABSORB_SUMCHECK_CLAIM: &[u8] = b"hachi/absorb/sumcheck-claim"; +/// Absorb per-round sumcheck messages (paper §4.3). +pub const ABSORB_SUMCHECK_ROUND: &[u8] = b"hachi/absorb/sumcheck-round"; +/// Challenge sampled per sumcheck round (paper §4.3). +pub const CHALLENGE_SUMCHECK_ROUND: &[u8] = b"hachi/challenge/sumcheck-round"; +/// Absorb recursion/stop-condition message payloads (paper §4.5). +pub const ABSORB_STOP_CONDITION: &[u8] = b"hachi/absorb/stop-condition"; +/// Challenge sampled for recursion stop-condition checks (paper §4.5). +pub const CHALLENGE_STOP_CONDITION: &[u8] = b"hachi/challenge/stop-condition"; + +/// Absorb the prover's stage-1 message `v = D · ŵ` (paper §4.2, Figure 3). +pub const ABSORB_PROVER_V: &[u8] = b"hachi/absorb/prover-stage1-v"; +/// Challenge label for stage-1 fold (sampling sparse `c_i`). +pub const CHALLENGE_STAGE1_FOLD: &[u8] = b"hachi/challenge/stage1-fold"; + +/// Absorb the `w` coefficient vector before sumcheck (paper §4.3). +pub const ABSORB_SUMCHECK_W: &[u8] = b"hachi/absorb/sumcheck-w"; +/// Challenge for sampling `τ₀` (F_0 range-check batching point, paper §4.3). +pub const CHALLENGE_TAU0: &[u8] = b"hachi/challenge/tau0"; +/// Challenge for sampling `τ₁` (F_α evaluation-relation batching point, paper §4.3). +pub const CHALLENGE_TAU1: &[u8] = b"hachi/challenge/tau1"; + +/// Return all Hachi-core transcript labels. +pub fn all_labels() -> &'static [&'static [u8]] { + &[ + DOMAIN_HACHI_PROTOCOL, + ABSORB_COMMITMENT, + ABSORB_EVALUATION_CLAIMS, + CHALLENGE_LINEAR_RELATION, + ABSORB_RING_SWITCH_MESSAGE, + CHALLENGE_RING_SWITCH, + ABSORB_SPARSE_CHALLENGE, + CHALLENGE_SPARSE_CHALLENGE, + ABSORB_SUMCHECK_CLAIM, + ABSORB_SUMCHECK_ROUND, + CHALLENGE_SUMCHECK_ROUND, + ABSORB_STOP_CONDITION, + CHALLENGE_STOP_CONDITION, + ABSORB_PROVER_V, + CHALLENGE_STAGE1_FOLD, + ABSORB_SUMCHECK_W, + CHALLENGE_TAU0, + CHALLENGE_TAU1, + ] +} diff --git a/src/protocol/transcript/mod.rs b/src/protocol/transcript/mod.rs new file mode 100644 index 00000000..7ccd5be9 --- /dev/null +++ b/src/protocol/transcript/mod.rs @@ -0,0 +1,37 @@ +//! Protocol transcript contracts and implementations. + +mod blake2b; +mod keccak; +pub mod labels; + +use crate::{CanonicalField, FieldCore, HachiSerialize}; + +pub use blake2b::Blake2bTranscript; +pub use keccak::KeccakTranscript; + +/// Transcript interface for protocol Fiat-Shamir transforms. +/// +/// The protocol layer is label-aware and uses deterministic byte encoding for +/// all absorbed values. +pub trait Transcript: Clone + Send + Sync + 'static +where + F: FieldCore + CanonicalField, +{ + /// Construct a new transcript under a domain label. + fn new(domain_label: &[u8]) -> Self; + + /// Append labeled raw bytes. + fn append_bytes(&mut self, label: &[u8], bytes: &[u8]); + + /// Append a field element with deterministic encoding. + fn append_field(&mut self, label: &[u8], x: &F); + + /// Append a serializable protocol value. + fn append_serde(&mut self, label: &[u8], s: &S); + + /// Derive a challenge scalar under the provided label. + fn challenge_scalar(&mut self, label: &[u8]) -> F; + + /// Reset transcript state under a new domain label. + fn reset(&mut self, domain_label: &[u8]); +} diff --git a/src/test_utils.rs b/src/test_utils.rs new file mode 100644 index 00000000..2bf775f0 --- /dev/null +++ b/src/test_utils.rs @@ -0,0 +1,123 @@ +//! Shared test configuration and helpers. +//! +//! This module is only compiled under `#[cfg(test)]` and provides common +//! building blocks for both unit tests (inside `src/`) and integration +//! tests (inside `tests/`). + +use crate::algebra::{CyclotomicRing, Fp64}; +use crate::protocol::commitment::CommitmentConfig; +use crate::{CanonicalField, FieldCore}; + +pub type F = Fp64<4294967197>; +pub const D: usize = 64; + +#[derive(Clone)] +pub struct TinyConfig; + +impl CommitmentConfig for TinyConfig { + const D: usize = 64; + const M: usize = 1; + const R: usize = 1; + const N_A: usize = 2; + const N_B: usize = 2; + const N_D: usize = 2; + const LOG_BASIS: u32 = 4; + const DELTA: usize = 9; + const TAU: usize = 4; + const BETA: u128 = 1_000_000; + const CHALLENGE_WEIGHT: usize = 3; +} + +pub const BLOCK_LEN: usize = 1 << TinyConfig::M; +pub const NUM_BLOCKS: usize = 1 << TinyConfig::R; +pub const DELTA: usize = TinyConfig::DELTA; +pub const LOG_BASIS: u32 = TinyConfig::LOG_BASIS; +pub const N_A: usize = TinyConfig::N_A; +pub const TAU: usize = TinyConfig::TAU; + +pub fn mat_vec_mul( + mat: &[Vec>], + vec: &[CyclotomicRing], +) -> Vec> { + mat.iter() + .map(|row| { + assert_eq!(row.len(), vec.len()); + row.iter() + .zip(vec.iter()) + .fold(CyclotomicRing::::zero(), |acc, (a, x)| { + acc + (*a * *x) + }) + }) + .collect() +} + +pub fn sample_blocks() -> Vec>> { + (0..NUM_BLOCKS) + .map(|bi| { + (0..BLOCK_LEN) + .map(|bj| { + let coeffs = + std::array::from_fn(|k| F::from_u64((bi * 1_000 + bj * 100 + k) as u64)); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect() + }) + .collect() +} + +pub fn sample_a() -> Vec { + (0..BLOCK_LEN) + .map(|j| F::from_u64((j * 10 + 1) as u64)) + .collect() +} + +pub fn sample_b() -> Vec { + (0..NUM_BLOCKS) + .map(|i| F::from_u64((i * 7 + 3) as u64)) + .collect() +} + +pub fn field_gadget_recompose( + parts: &[CyclotomicRing], + log_basis: u32, +) -> CyclotomicRing { + let b = F::from_u64(1u64 << log_basis); + let mut result = CyclotomicRing::::zero(); + let mut b_power = F::one(); + for part in parts { + result += part.scale(&b_power); + b_power = b_power * b; + } + result +} + +pub fn recompose_z_hat(z_hat: &[CyclotomicRing]) -> Vec> { + z_hat + .chunks(TAU) + .map(|chunk| field_gadget_recompose(chunk, LOG_BASIS)) + .collect() +} + +pub fn gadget_recompose_vec(x_hat: &[CyclotomicRing]) -> Vec> { + x_hat + .chunks(DELTA) + .map(|chunk| field_gadget_recompose(chunk, LOG_BASIS)) + .collect() +} + +pub fn field_gadget_recompose_vec(v: &[CyclotomicRing]) -> Vec> { + v.chunks(DELTA) + .map(|chunk| field_gadget_recompose(chunk, LOG_BASIS)) + .collect() +} + +pub fn a_transpose_gadget_times_vec(a: &[F], z: &[CyclotomicRing]) -> CyclotomicRing { + let recomposed = field_gadget_recompose_vec(z); + assert_eq!(recomposed.len(), a.len()); + recomposed + .iter() + .zip(a.iter()) + .fold(CyclotomicRing::::zero(), |acc, (z_j, a_j)| { + acc + z_j.scale(a_j) + }) +} diff --git a/tests/algebra.rs b/tests/algebra.rs new file mode 100644 index 00000000..cbb51aeb --- /dev/null +++ b/tests/algebra.rs @@ -0,0 +1,1058 @@ +#![allow(missing_docs)] + +#[cfg(test)] +mod tests { + use num_bigint::BigUint; + use rand::{rngs::StdRng, SeedableRng}; + + use hachi_pcs::algebra::ntt::butterfly::{forward_ntt, inverse_ntt, NttTwiddles}; + use hachi_pcs::algebra::poly::Poly; + use hachi_pcs::algebra::tables::{Q32_DATA, Q32_MODULUS, Q32_NUM_PRIMES, Q32_PRIMES}; + use hachi_pcs::algebra::{ + pseudo_mersenne_modulus, Pow2Offset128Field, Pow2OffsetPrimeSpec, POW2_OFFSET_MAX, + POW2_OFFSET_PRIMES, POW2_OFFSET_TABLE, + }; + use hachi_pcs::algebra::{ + CyclotomicCrtNtt, CyclotomicRing, Fp128, Fp2, Fp2Config, Fp32, Fp4, Fp4Config, Fp64, LimbQ, + MontCoeff, Prime128M13M4P0, Prime128M37P3P0, Prime128M52M3P0, Prime128M54P4P0, + Prime128M8M4M1M0, ScalarBackend, VectorModule, + }; + use hachi_pcs::primitives::serialization::SerializationError; + use hachi_pcs::{ + CanonicalField, FieldCore, FieldSampling, HachiDeserialize, HachiSerialize, Invertible, + Module, PseudoMersenneField, + }; + + const P_159: u128 = 340282366920938463463374607431768211297u128; + + #[test] + fn fp32_basic_arith() { + type F = Fp32<251>; + let a = F::from_u64(17); + let b = F::from_u64(99); + assert_eq!((a + b).to_canonical_u32(), 116); + assert_eq!((a * b).to_canonical_u32(), (17u32 * 99) % 251); + + let inv = a.inv().unwrap(); + assert_eq!(a * inv, F::one()); + } + + #[test] + fn fp64_hachi_q_inv() { + type F = Fp64<4294967197>; + let two = F::from_u64(2); + let inv2 = two.inv().unwrap(); + assert_eq!(two * inv2, F::one()); + } + + #[test] + fn fp128_basic_arith() { + type F = Fp128; + + let a = F::from_u64(123); + let b = F::from_u64(456); + let c = a * b + a - b; + let inv = c.inv().unwrap(); + assert_eq!(c * inv, F::one()); + } + + fn rand_u128(rng: &mut R) -> u128 { + let lo = rng.next_u64() as u128; + let hi = rng.next_u64() as u128; + lo | (hi << 64) + } + + fn biguint_to_u128(x: &num_bigint::BigUint) -> u128 { + let mut bytes = x.to_bytes_le(); + bytes.resize(16, 0); + let mut arr = [0u8; 16]; + arr.copy_from_slice(&bytes[..16]); + u128::from_le_bytes(arr) + } + + fn big_mul_mod_u128(a: u128, b: u128, p: u128) -> u128 { + let n = BigUint::from(a) * BigUint::from(b); + let r = n % BigUint::from(p); + biguint_to_u128(&r) + } + + fn check_solinas_prime< + S: CanonicalField + FieldCore + Invertible + PseudoMersenneField + std::fmt::Debug, + >( + p: u128, + iters: usize, + seed: u64, + ) { + assert_eq!(::MODULUS_BITS, 128); + assert_eq!( + ::MODULUS_OFFSET, + 0u128.wrapping_sub(p) + ); + assert_eq!(std::mem::size_of::(), 16); + + let mut rng = StdRng::seed_from_u64(seed); + + for _ in 0..iters { + let a_raw = rand_u128(&mut rng); + let b_raw = rand_u128(&mut rng); + + let a = S::from_canonical_u128_reduced(a_raw); + let b = S::from_canonical_u128_reduced(b_raw); + + // Canonical range invariant. + assert!(a.to_canonical_u128() < p); + assert!(b.to_canonical_u128() < p); + + // Add/sub/neg identities. + assert_eq!(a + S::zero(), a); + assert_eq!(a - S::zero(), a); + assert_eq!(a + (-a), S::zero()); + + // Multiplicative identity. + assert_eq!(a * S::one(), a); + + // BigUint oracle for mul and sqr (exercises reduction). + let aa = a.to_canonical_u128(); + let bb = b.to_canonical_u128(); + let got_mul = (a * b).to_canonical_u128(); + let exp_mul = big_mul_mod_u128(aa, bb, p); + assert_eq!(got_mul, exp_mul); + + let got_sqr = (a * a).to_canonical_u128(); + let exp_sqr = big_mul_mod_u128(aa, aa, p); + assert_eq!(got_sqr, exp_sqr); + + // Inversion checks (skip explicit inv on zero). + let inv = a.inv_or_zero(); + if a.is_zero() { + assert_eq!(inv, S::zero()); + } else { + assert_eq!(a * inv, S::one()); + assert_eq!(a.inv().unwrap(), inv); + } + } + } + + #[test] + fn fp128_sparse_primes_match_biguint_oracle() { + // These are the five sparse `2^128 - c` primes we care about. + const P13: u128 = 0xffffffffffffffffffffffffffffdff1u128; + const P37: u128 = 0xffffffffffffffffffffffe000000009u128; + const P52: u128 = 0xffffffffffffffffffeffffffffffff9u128; + const P54: u128 = 0xffffffffffffffffffc0000000000011u128; + const P275: u128 = 0xfffffffffffffffffffffffffffffeedu128; + + check_solinas_prime::(P13, 2_000, 13); + check_solinas_prime::(P37, 2_000, 37); + check_solinas_prime::(P52, 2_000, 52); + check_solinas_prime::(P54, 2_000, 54); + check_solinas_prime::(P275, 2_000, 275); + } + + struct NR; + impl Fp2Config> for NR { + fn non_residue() -> Fp32<251> { + -Fp32::<251>::one() + } + } + + struct NR4; + impl Fp4Config, NR> for NR4 { + fn non_residue() -> Fp2, NR> { + Fp2::new(Fp32::<251>::zero(), Fp32::<251>::one()) + } + } + + #[test] + fn fp2_fp4_inversion_smoke() { + type F = Fp32<251>; + type F2 = Fp2; + type F4 = Fp4; + + let x = F2::new(F::from_u64(3), F::from_u64(7)); + let inv = x.inv().unwrap(); + assert!((x * inv) == F2::one()); + + let y = F4::new( + F2::new(F::from_u64(5), F::from_u64(1)), + F2::new(F::from_u64(2), F::from_u64(9)), + ); + let invy = y.inv().unwrap(); + assert!((y * invy) == F4::one()); + } + + #[test] + fn vector_module_ops() { + type F = Fp32<251>; + + let a = VectorModule::([F::from_u64(1), F::from_u64(2), F::from_u64(3)]); + let b = VectorModule::([F::from_u64(3), F::from_u64(4), F::from_u64(5)]); + + let c = a + b; + assert_eq!(c.0[0], F::from_u64(4)); + + let d = a.scale(&F::from_u64(7)); + assert_eq!(d.0[1], F::from_u64(14)); + } + + #[test] + fn inv_zero_returns_none() { + assert!(Fp32::<251>::zero().inv().is_none()); + assert!(Fp64::<4294967197>::zero().inv().is_none()); + assert!(Fp128::::zero().inv().is_none()); + } + + #[test] + fn inv_or_zero_behavior_for_prime_fields() { + type F32 = Fp32<251>; + assert_eq!(F32::zero().inv_or_zero(), F32::zero()); + let x32 = F32::from_u64(17); + let inv32 = x32.inv_or_zero(); + assert_eq!(x32 * inv32, F32::one()); + + type F64 = Fp64<4294967197>; + assert_eq!(F64::zero().inv_or_zero(), F64::zero()); + let x64 = F64::from_u64(2); + let inv64 = x64.inv_or_zero(); + assert_eq!(x64 * inv64, F64::one()); + + type F128 = Fp128; + assert_eq!(F128::zero().inv_or_zero(), F128::zero()); + let x128 = F128::from_u64(12345); + let inv128 = x128.inv_or_zero(); + assert_eq!(x128 * inv128, F128::one()); + } + + #[test] + fn field_identities_fp32() { + type F = Fp32<251>; + let a = F::from_u64(42); + let b = F::from_u64(73); + let c = F::from_u64(11); + + // Additive identity + assert_eq!(a + F::zero(), a); + // Multiplicative identity + assert_eq!(a * F::one(), a); + // Additive inverse + assert_eq!(a + (-a), F::zero()); + // Distributivity + assert_eq!(a * (b + c), a * b + a * c); + // Commutativity + assert_eq!(a * b, b * a); + assert_eq!(a + b, b + a); + } + + #[test] + fn field_identities_fp64() { + type F = Fp64<4294967197>; + let a = F::from_u64(123456); + let b = F::from_u64(789012); + let c = F::from_u64(345678); + + assert_eq!(a + F::zero(), a); + assert_eq!(a * F::one(), a); + assert_eq!(a + (-a), F::zero()); + assert_eq!(a * (b + c), a * b + a * c); + } + + #[test] + fn field_identities_fp128() { + type F = Fp128; + let a = F::from_u64(999999); + let b = F::from_u64(888888); + let c = F::from_u64(777777); + + assert_eq!(a + F::zero(), a); + assert_eq!(a * F::one(), a); + assert_eq!(a + (-a), F::zero()); + assert_eq!(a * (b + c), a * b + a * c); + } + + #[test] + fn serialization_round_trip_fp32() { + type F = Fp32<251>; + let val = F::from_u64(42); + let mut buf = Vec::new(); + val.serialize_compressed(&mut buf).unwrap(); + let restored = F::deserialize_compressed(&buf[..]).unwrap(); + assert_eq!(val, restored); + } + + #[test] + fn serialization_round_trip_fp64() { + type F = Fp64<4294967197>; + let val = F::from_u64(123456789); + let mut buf = Vec::new(); + val.serialize_compressed(&mut buf).unwrap(); + let restored = F::deserialize_compressed(&buf[..]).unwrap(); + assert_eq!(val, restored); + } + + #[test] + fn serialization_round_trip_fp128() { + type F = Fp128; + let val = F::from_u64(999999999); + let mut buf = Vec::new(); + val.serialize_compressed(&mut buf).unwrap(); + let restored = F::deserialize_compressed(&buf[..]).unwrap(); + assert_eq!(val, restored); + } + + #[test] + fn serialization_round_trip_ext() { + type F = Fp32<251>; + type F2 = Fp2; + let val = F2::new(F::from_u64(3), F::from_u64(7)); + let mut buf = Vec::new(); + val.serialize_compressed(&mut buf).unwrap(); + let restored = F2::deserialize_compressed(&buf[..]).unwrap(); + assert!(val == restored); + } + + #[test] + fn serialization_round_trip_fp4() { + type F = Fp32<251>; + type F2 = Fp2; + type F4 = Fp4; + + let val = F4::new( + F2::new(F::from_u64(5), F::from_u64(1)), + F2::new(F::from_u64(2), F::from_u64(9)), + ); + let mut buf = Vec::new(); + val.serialize_compressed(&mut buf).unwrap(); + let restored = F4::deserialize_compressed(&buf[..]).unwrap(); + assert!(val == restored); + } + + #[test] + fn serialization_round_trip_vector_module() { + type F = Fp32<251>; + let val = VectorModule::([F::from_u64(1), F::from_u64(2), F::from_u64(3)]); + let mut buf = Vec::new(); + val.serialize_compressed(&mut buf).unwrap(); + let restored = VectorModule::::deserialize_compressed(&buf[..]).unwrap(); + assert_eq!(val, restored); + } + + #[test] + fn serialization_round_trip_poly() { + type F = Fp32<251>; + + let val = Poly::([ + F::from_u64(7), + F::from_u64(11), + F::from_u64(13), + F::from_u64(29), + ]); + let mut buf = Vec::new(); + val.serialize_compressed(&mut buf).unwrap(); + let restored = Poly::::deserialize_compressed(&buf[..]).unwrap(); + assert_eq!(val, restored); + } + + #[test] + fn deserialize_checked_rejects_non_canonical_field_elements() { + type F32 = Fp32<251>; + let bad32 = 251u32.to_le_bytes(); + let err32 = F32::deserialize_compressed(&bad32[..]).unwrap_err(); + assert!(matches!(err32, SerializationError::InvalidData(_))); + let unchecked32 = F32::deserialize_compressed_unchecked(&bad32[..]).unwrap(); + assert_eq!(unchecked32, F32::zero()); + + type F64 = Fp64<4294967197>; + let bad64 = 4294967197u64.to_le_bytes(); + let err64 = F64::deserialize_compressed(&bad64[..]).unwrap_err(); + assert!(matches!(err64, SerializationError::InvalidData(_))); + let unchecked64 = F64::deserialize_compressed_unchecked(&bad64[..]).unwrap(); + assert_eq!(unchecked64, F64::zero()); + + type F128 = Fp128; + let bad128 = P_159.to_le_bytes(); + let err128 = F128::deserialize_compressed(&bad128[..]).unwrap_err(); + assert!(matches!(err128, SerializationError::InvalidData(_))); + let unchecked128 = F128::deserialize_compressed_unchecked(&bad128[..]).unwrap(); + assert_eq!(unchecked128, F128::zero()); + + // Sparse 128-bit prime: same checked/unchecked behavior. + type S13 = Prime128M13M4P0; + const P13: u128 = 0xffffffffffffffffffffffffffffdff1u128; + let bad13 = P13.to_le_bytes(); + let err13 = S13::deserialize_compressed(&bad13[..]).unwrap_err(); + assert!(matches!(err13, SerializationError::InvalidData(_))); + let unchecked13 = S13::deserialize_compressed_unchecked(&bad13[..]).unwrap(); + assert_eq!(unchecked13, S13::zero()); + } + + #[test] + fn fp2_conjugate_and_norm() { + type F = Fp32<251>; + type F2 = Fp2; + let x = F2::new(F::from_u64(3), F::from_u64(7)); + let conj = x.conjugate(); + assert!(conj == F2::new(F::from_u64(3), -F::from_u64(7))); + // For Fp2 with u^2 = -1: norm = c0^2 + c1^2 = 9 + 49 = 58 + assert_eq!(x.norm(), F::from_u64(58)); + // x * conjugate(x) should embed the norm into Fp2 + let prod = x * conj; + assert!(prod == F2::new(F::from_u64(58), F::zero())); + } + + #[test] + fn fp2_distributivity() { + type F = Fp32<251>; + type F2 = Fp2; + let a = F2::new(F::from_u64(3), F::from_u64(7)); + let b = F2::new(F::from_u64(11), F::from_u64(5)); + let c = F2::new(F::from_u64(2), F::from_u64(9)); + assert!(a * (b + c) == a * b + a * c); + } + + #[test] + fn limbq_from_to_u128_round_trip() { + for &val in &[0u128, 1, 12345, 123456789, (1u128 << 28) - 1] { + let limb: LimbQ<3> = LimbQ::from(val); + assert_eq!( + u128::try_from(limb).unwrap(), + val, + "round-trip failed for {val}" + ); + } + } + + #[test] + fn limbq_add_sub_inverse() { + let a: LimbQ<3> = LimbQ::from(12345u128); + let b: LimbQ<3> = LimbQ::from(6789u128); + let sum = a + b; + let diff = sum - b; + assert_eq!(diff, a); + } + + #[test] + fn limbq_ordering() { + let a: LimbQ<3> = LimbQ::from(100u128); + let b: LimbQ<3> = LimbQ::from(200u128); + assert!(a < b); + assert!(b > a); + assert_eq!(a, a); + } + + #[test] + fn qdata_q_matches_const() { + let q_from_data = Q32_DATA.q_u128().unwrap(); + assert_eq!(q_from_data, Q32_MODULUS as u128); + } + + #[test] + fn ntt_normalize_in_range() { + for prime in &Q32_PRIMES { + for &a in &[0i16, 1, -1, 100, -100, prime.p - 1, -(prime.p - 1)] { + let n = prime.normalize(MontCoeff::from_raw(a)); + assert!( + n.raw() >= 0 && n.raw() < prime.p, + "normalize({a}) = {} for p={}", + n.raw(), + prime.p + ); + } + } + } + + #[test] + fn ntt_mul_commutative() { + let prime = Q32_PRIMES[0]; + let a = MontCoeff::from_raw(1234); + let b = MontCoeff::from_raw(5678); + assert_eq!(prime.mul(a, b), prime.mul(b, a)); + } + + #[test] + fn mont_coeff_round_trip() { + for prime in &Q32_PRIMES { + for &val in &[0i16, 1, 2, 100, prime.p - 1] { + let mont = prime.from_canonical(val); + let back = prime.to_canonical(mont); + assert_eq!(back, val, "round-trip failed for val={val}, p={}", prime.p); + } + } + } + + #[test] + fn poly_add_sub_neg() { + type F = Fp32<251>; + let a = Poly::([F::from_u64(1), F::from_u64(2), F::from_u64(3)]); + let b = Poly::([F::from_u64(10), F::from_u64(20), F::from_u64(30)]); + + let sum = a + b; + assert_eq!(sum.0[0], F::from_u64(11)); + assert_eq!(sum.0[1], F::from_u64(22)); + assert_eq!(sum.0[2], F::from_u64(33)); + + let diff = b - a; + assert_eq!(diff.0[0], F::from_u64(9)); + + let neg_a = -a; + assert_eq!(a + neg_a, Poly::zero()); + } + + #[test] + fn cyclotomic_ring_negacyclic_property() { + type F = Fp32<251>; + type R = CyclotomicRing; + + // X in the ring: [0, 1, 0, 0] + let x = R::x(); + + // X^2 + let x2 = x * x; + let expected_x2 = R::from_coefficients([F::zero(), F::zero(), F::one(), F::zero()]); + assert_eq!(x2, expected_x2); + + // X^4 should equal -1 (because X^4 + 1 = 0 in the ring) + let x4 = x2 * x2; + assert_eq!(x4, -R::one(), "X^D should equal -1 in Z_q[X]/(X^D + 1)"); + } + + #[test] + fn cyclotomic_ring_mul_identity() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients([ + F::from_u64(3), + F::from_u64(7), + F::from_u64(11), + F::from_u64(42), + ]); + assert_eq!(a * R::one(), a); + assert_eq!(R::one() * a, a); + } + + #[test] + fn cyclotomic_ring_mul_zero() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients([ + F::from_u64(3), + F::from_u64(7), + F::from_u64(11), + F::from_u64(42), + ]); + assert_eq!(a * R::zero(), R::zero()); + } + + #[test] + fn cyclotomic_ring_commutativity() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients([ + F::from_u64(3), + F::from_u64(7), + F::from_u64(11), + F::from_u64(42), + ]); + let b = R::from_coefficients([ + F::from_u64(5), + F::from_u64(13), + F::from_u64(99), + F::from_u64(1), + ]); + assert_eq!(a * b, b * a); + } + + #[test] + fn cyclotomic_ring_distributivity() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients([ + F::from_u64(3), + F::from_u64(7), + F::from_u64(11), + F::from_u64(42), + ]); + let b = R::from_coefficients([ + F::from_u64(5), + F::from_u64(13), + F::from_u64(99), + F::from_u64(1), + ]); + let c = R::from_coefficients([ + F::from_u64(2), + F::from_u64(9), + F::from_u64(50), + F::from_u64(77), + ]); + assert_eq!(a * (b + c), a * b + a * c); + } + + #[test] + fn cyclotomic_ring_associativity() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients([ + F::from_u64(3), + F::from_u64(7), + F::from_u64(11), + F::from_u64(42), + ]); + let b = R::from_coefficients([ + F::from_u64(5), + F::from_u64(13), + F::from_u64(99), + F::from_u64(1), + ]); + let c = R::from_coefficients([ + F::from_u64(2), + F::from_u64(9), + F::from_u64(50), + F::from_u64(77), + ]); + assert_eq!((a * b) * c, a * (b * c)); + } + + #[test] + fn cyclotomic_ring_additive_inverse() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients([ + F::from_u64(3), + F::from_u64(7), + F::from_u64(11), + F::from_u64(42), + ]); + assert_eq!(a + (-a), R::zero()); + } + + #[test] + fn cyclotomic_ring_serialization_round_trip() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients([ + F::from_u64(3), + F::from_u64(7), + F::from_u64(11), + F::from_u64(42), + ]); + let mut buf = Vec::new(); + a.serialize_compressed(&mut buf).unwrap(); + let restored = R::deserialize_compressed(&buf[..]).unwrap(); + assert_eq!(a, restored); + } + + #[test] + fn cyclotomic_ring_degree_64() { + type F = Fp64<4294967197>; + type R = CyclotomicRing; + + // X^64 = -1 in Z_q[X]/(X^64 + 1) + let x = R::x(); + let mut power = R::one(); + for _ in 0..64 { + power *= x; + } + assert_eq!(power, -R::one(), "X^64 should equal -1"); + } + + #[test] + fn ntt_forward_inverse_round_trip() { + let prime = Q32_PRIMES[0]; + let tw = NttTwiddles::<64>::compute(prime); + + // Create a test polynomial in Montgomery form. + let original: [MontCoeff; 64] = + std::array::from_fn(|i| prime.from_canonical((i as i16) % prime.p)); + + // Forward then inverse should give back the original. + let mut a = original; + forward_ntt(&mut a, prime, &tw); + inverse_ntt(&mut a, prime, &tw); + + // Normalize and compare. + for (i, (got, expected)) in a.iter().zip(original.iter()).enumerate() { + let got_canon = prime.to_canonical(prime.normalize(*got)); + let exp_canon = prime.to_canonical(prime.normalize(*expected)); + assert_eq!( + got_canon, exp_canon, + "NTT round-trip mismatch at index {i}: got {got_canon}, expected {exp_canon}" + ); + } + } + + #[test] + fn ntt_forward_inverse_all_primes() { + for (pi, prime) in Q32_PRIMES.iter().enumerate() { + let tw = NttTwiddles::<64>::compute(*prime); + + let original: [_; 64] = + std::array::from_fn(|i| prime.from_canonical(((i * (pi + 1)) as i16) % prime.p)); + + let mut a = original; + forward_ntt(&mut a, *prime, &tw); + inverse_ntt(&mut a, *prime, &tw); + + for (i, (got, expected)) in a.iter().zip(original.iter()).enumerate() { + let g = prime.to_canonical(prime.normalize(*got)); + let e = prime.to_canonical(prime.normalize(*expected)); + assert_eq!( + g, e, + "prime[{pi}] p={}: round-trip mismatch at index {i}", + prime.p + ); + } + } + } + + #[test] + fn cyclotomic_ntt_crt_round_trip_q32() { + type F = Fp64<{ Q32_MODULUS }>; + type R = CyclotomicRing; + type N = CyclotomicCrtNtt; + + let twiddles: [NttTwiddles<64>; Q32_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::<64>::compute(Q32_PRIMES[k])); + + let coeffs: [F; 64] = + std::array::from_fn(|i| F::from_u64(((i as u64 * 17) + 5) % Q32_MODULUS)); + let ring = R::from_coefficients(coeffs); + let ntt = N::from_ring(&ring, &Q32_PRIMES, &twiddles); + let round_trip = ntt.to_ring(&Q32_PRIMES, &twiddles, &Q32_DATA); + + assert_eq!(ring, round_trip); + } + + #[test] + fn cyclotomic_ntt_reduced_ops_are_stable() { + type F = Fp64<{ Q32_MODULUS }>; + type R = CyclotomicRing; + type N = CyclotomicCrtNtt; + + let twiddles: [NttTwiddles<64>; Q32_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::<64>::compute(Q32_PRIMES[k])); + + let a = R::from_coefficients(std::array::from_fn(|i| { + F::from_u64(((i as u64 * 3) + 1) % Q32_MODULUS) + })); + let b = R::from_coefficients(std::array::from_fn(|i| { + F::from_u64(((i as u64 * 11) + 7) % Q32_MODULUS) + })); + + let ntt_a = N::from_ring(&a, &Q32_PRIMES, &twiddles); + let ntt_b = N::from_ring(&b, &Q32_PRIMES, &twiddles); + + let sum = ntt_a.add_reduced(&ntt_b, &Q32_PRIMES); + let back = sum.sub_reduced(&ntt_b, &Q32_PRIMES); + assert_eq!(back, ntt_a); + + let zero_ntt = ntt_a.add_reduced(&ntt_a.neg_reduced(&Q32_PRIMES), &Q32_PRIMES); + let zero_ring = zero_ntt.to_ring(&Q32_PRIMES, &twiddles, &Q32_DATA); + assert_eq!(zero_ring, R::zero()); + } + + #[test] + fn backend_path_matches_default_scalar_path() { + type F = Fp64<{ Q32_MODULUS }>; + type R = CyclotomicRing; + type N = CyclotomicCrtNtt; + + let twiddles: [NttTwiddles<64>; Q32_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::<64>::compute(Q32_PRIMES[k])); + let ring = R::from_coefficients(std::array::from_fn(|i| { + F::from_u64(((i as u64 * 13) + 9) % Q32_MODULUS) + })); + + let default_ntt = N::from_ring(&ring, &Q32_PRIMES, &twiddles); + let backend_ntt = + N::from_ring_with_backend::(&ring, &Q32_PRIMES, &twiddles); + assert_eq!(default_ntt, backend_ntt); + + let default_back = default_ntt.to_ring(&Q32_PRIMES, &twiddles, &Q32_DATA); + let backend_back = backend_ntt.to_ring_with_backend::( + &Q32_PRIMES, + &twiddles, + &Q32_DATA, + ); + assert_eq!(default_back, backend_back); + } + + #[test] + fn field_sampling_respects_modulus() { + type F = Fp32<251>; + let mut rng = StdRng::seed_from_u64(42); + for _ in 0..1024 { + let x = F::sample(&mut rng); + assert!(x.to_canonical_u32() < 251); + } + } + + #[test] + fn pow2_offset_registry_is_consistent() { + fn assert_is_pseudo_mersenne() {} + assert_is_pseudo_mersenne::(); + + for Pow2OffsetPrimeSpec { + bits, + offset, + modulus, + .. + } in POW2_OFFSET_PRIMES + { + assert!((offset as u128) <= POW2_OFFSET_MAX); + assert_eq!(POW2_OFFSET_TABLE[bits as usize], offset as i16); + assert_eq!( + Some(modulus), + pseudo_mersenne_modulus(bits, offset as u128), + "2^k-offset modulus mismatch for k={bits}, offset={offset}" + ); + assert_eq!(modulus % 8, 5); + } + + let x = Pow2Offset128Field::from_u64(1234567); + let inv = x.inv().unwrap(); + assert_eq!(x * inv, Pow2Offset128Field::one()); + } + + #[test] + fn cyclotomic_sigma_is_ring_automorphism() { + type F = Fp32<251>; + type R = CyclotomicRing; + let a = R::from_coefficients(std::array::from_fn(|i| F::from_u64((3 * i + 1) as u64))); + let b = R::from_coefficients(std::array::from_fn(|i| F::from_u64((5 * i + 2) as u64))); + + let k1 = 3usize; + let k2 = 5usize; + let two_d = 16usize; + + assert_eq!(a.sigma(1), a); + assert_eq!(a.sigma_m1().sigma_m1(), a); + assert_eq!(a.sigma(k1).sigma(k2), a.sigma((k1 * k2) % two_d)); + assert_eq!((a * b).sigma(k1), a.sigma(k1) * b.sigma(k1)); + } + + #[test] + fn cyclotomic_balanced_pow2_decompose_recompose_round_trip() { + type F = Fp64<{ Q32_MODULUS }>; + type R = CyclotomicRing; + + let ring = R::from_coefficients(std::array::from_fn(|i| { + F::from_u64(((i as u64 * 73) + 17) % Q32_MODULUS) + })); + + // Q32 balanced base-16: 9 levels absorb the carry-out near q/2. + let digits = ring.balanced_decompose_pow2(9, 4); + let round_trip = R::gadget_recompose_pow2(&digits, 4); + assert_eq!(round_trip, ring); + } + + #[test] + fn sparse_pm1_challenge_has_expected_weight() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let mut rng = StdRng::seed_from_u64(123); + let challenge = R::sample_sparse_pm1(&mut rng, 11); + assert_eq!(challenge.hamming_weight(), 11); + + for c in challenge.coefficients() { + let x = c.to_canonical_u32(); + if x != 0 { + assert!(x == 1 || x == 250, "nonzero coefficient must be +/-1"); + } + } + } + + #[test] + fn negacyclic_shift_equals_mul_by_monomial() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients(std::array::from_fn(|i| F::from_u64((3 * i + 1) as u64))); + + for k in 0..8 { + let mut monomial_coeffs = [F::zero(); 8]; + monomial_coeffs[k] = F::one(); + let monomial = R::from_coefficients(monomial_coeffs); + assert_eq!( + a.negacyclic_shift(k), + a * monomial, + "negacyclic_shift({k}) != mul by X^{k}" + ); + } + + assert_eq!(a.negacyclic_shift(0), a); + assert_eq!( + a.negacyclic_shift(8), + a, + "shift by D should be identity mod D" + ); + } + + #[test] + fn negacyclic_shift_degree_64() { + type F = Fp64<4294967197>; + type R = CyclotomicRing; + + let a = R::from_coefficients(std::array::from_fn(|i| F::from_u64((7 * i + 3) as u64))); + let x = R::x(); + let mut x_pow = R::one(); + for k in 0..64 { + assert_eq!( + a.negacyclic_shift(k), + a * x_pow, + "negacyclic_shift({k}) mismatch at D=64" + ); + x_pow *= x; + } + } + + #[test] + fn mul_by_monomial_sum_matches_ring_mul() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients(std::array::from_fn(|i| F::from_u64((5 * i + 2) as u64))); + + // Sum of X^1 + X^3 + X^5 + let positions = [1, 3, 5]; + let mut sparse = [F::zero(); 8]; + for &p in &positions { + sparse[p] = F::one(); + } + let sparse_ring = R::from_coefficients(sparse); + + assert_eq!( + a.mul_by_monomial_sum(&positions), + a * sparse_ring, + "mul_by_monomial_sum should equal ring mul by sparse element" + ); + } + + #[test] + fn mul_by_monomial_sum_single_position_equals_shift() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 1) as u64))); + for k in 0..8 { + assert_eq!( + a.mul_by_monomial_sum(&[k]), + a.negacyclic_shift(k), + "single-position monomial_sum should equal negacyclic_shift" + ); + } + } + + #[test] + fn mul_by_monomial_sum_empty_is_zero() { + type F = Fp32<251>; + type R = CyclotomicRing; + + let a = R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 1) as u64))); + assert_eq!(a.mul_by_monomial_sum(&[]), R::zero()); + } + + #[test] + fn mul_by_sparse_matches_schoolbook() { + use hachi_pcs::algebra::SparseChallenge; + + type F = Fp64<4294967197>; + type R = CyclotomicRing; + + let a = R::from_coefficients(std::array::from_fn(|i| F::from_u64((3 * i + 7) as u64))); + + let challenge = SparseChallenge { + positions: vec![2, 17, 41], + coeffs: vec![1, -1, 1], + }; + let dense: R = challenge.to_dense().unwrap(); + + let via_sparse = a.mul_by_sparse(&challenge); + let via_schoolbook = a * dense; + + assert_eq!( + via_sparse, via_schoolbook, + "mul_by_sparse must equal schoolbook multiplication" + ); + } + + #[test] + fn mul_by_sparse_with_all_negative_coeffs() { + use hachi_pcs::algebra::SparseChallenge; + + type F = Fp64<4294967197>; + type R = CyclotomicRing; + + let a = R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 1) as u64))); + + let challenge = SparseChallenge { + positions: vec![0, 5, 63], + coeffs: vec![-1, -1, -1], + }; + let dense: R = challenge.to_dense().unwrap(); + + assert_eq!(a.mul_by_sparse(&challenge), a * dense); + } + + #[test] + fn is_zero_detects_zero_and_nonzero() { + type F = Fp32<251>; + type R = CyclotomicRing; + + assert!(R::zero().is_zero()); + assert!(!R::one().is_zero()); + + let a = R::from_coefficients(std::array::from_fn(|i| F::from_u64(i as u64))); + assert!(!a.is_zero()); + } + + #[test] + fn kron_scalars_matches_kron_row_constant_rings() { + type F = Fp64<4294967197>; + type R = CyclotomicRing; + + let scalars_a: Vec = (0..4).map(|i| F::from_u64(i * 3 + 1)).collect(); + let scalars_b: Vec = (0..3).map(|i| F::from_u64(i * 7 + 2)).collect(); + + let rings_a: Vec = scalars_a + .iter() + .map(|&s| { + let mut c = [F::zero(); 16]; + c[0] = s; + R::from_coefficients(c) + }) + .collect(); + let rings_b: Vec = scalars_b + .iter() + .map(|&s| { + let mut c = [F::zero(); 16]; + c[0] = s; + R::from_coefficients(c) + }) + .collect(); + + let via_ring: Vec = rings_a + .iter() + .flat_map(|l| rings_b.iter().map(move |r| *l * *r)) + .collect(); + + let via_scalar: Vec = scalars_a + .iter() + .flat_map(|&l| { + scalars_b.iter().map(move |&r| { + let mut c = [F::zero(); 16]; + c[0] = l * r; + R::from_coefficients(c) + }) + }) + .collect(); + + assert_eq!(via_ring, via_scalar); + } +} diff --git a/tests/commitment_contract.rs b/tests/commitment_contract.rs new file mode 100644 index 00000000..dc300613 --- /dev/null +++ b/tests/commitment_contract.rs @@ -0,0 +1,236 @@ +#![allow(missing_docs)] + +use hachi_pcs::algebra::Fp64; +use hachi_pcs::protocol::commitment::{DummyProof, HachiCommitment}; +use hachi_pcs::protocol::transcript::labels; +use hachi_pcs::protocol::{ + AppendToTranscript, Blake2bTranscript, CommitmentScheme, StreamingCommitmentScheme, Transcript, +}; +use hachi_pcs::{CanonicalField, FieldCore, HachiError, Polynomial}; + +type F = Fp64<4294967197>; + +#[derive(Clone)] +struct SimplePoly { + coeffs: Vec, +} + +impl Polynomial for SimplePoly { + fn num_vars(&self) -> usize { + self.coeffs.len().saturating_sub(1) + } + + fn evaluate(&self, point: &[F]) -> F { + assert_eq!(point.len(), self.num_vars()); + let mut acc = self.coeffs[0]; + for (i, r_i) in point.iter().enumerate() { + acc = acc + self.coeffs[i + 1] * *r_i; + } + acc + } + + fn coeffs(&self) -> Vec { + self.coeffs.clone() + } +} + +#[derive(Clone)] +struct DummySetup { + _max_num_vars: usize, +} + +#[derive(Clone)] +struct DummyScheme; + +impl CommitmentScheme for DummyScheme { + type ProverSetup = DummySetup; + type VerifierSetup = DummySetup; + type Commitment = HachiCommitment; + type Proof = DummyProof; + type OpeningProofHint = HachiCommitment; + + fn setup_prover(max_num_vars: usize) -> Self::ProverSetup { + DummySetup { + _max_num_vars: max_num_vars, + } + } + + fn setup_verifier(setup: &Self::ProverSetup) -> Self::VerifierSetup { + setup.clone() + } + + fn commit>( + poly: &P, + _setup: &Self::ProverSetup, + ) -> Result<(Self::Commitment, Self::OpeningProofHint), HachiError> { + let zero = vec![F::zero(); poly.num_vars()]; + let c = HachiCommitment(poly.evaluate(&zero).to_canonical_u128()); + Ok((c, c)) + } + + fn prove, P: Polynomial>( + setup: &Self::ProverSetup, + poly: &P, + opening_point: &[F], + hint: Option, + transcript: &mut T, + _commitment: &Self::Commitment, + ) -> Result { + if opening_point.len() != poly.num_vars() { + return Err(HachiError::InvalidPointDimension { + expected: poly.num_vars(), + actual: opening_point.len(), + }); + } + + let absorb_commitment = if let Some(h) = hint { + h + } else { + Self::commit(poly, setup)?.0 + }; + absorb_commitment.append_to_transcript(labels::ABSORB_COMMITMENT, transcript); + + let q = transcript.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); + let opening = poly.evaluate(opening_point); + Ok(DummyProof( + opening.to_canonical_u128() ^ q.to_canonical_u128(), + )) + } + + fn verify>( + proof: &Self::Proof, + _setup: &Self::VerifierSetup, + transcript: &mut T, + _opening_point: &[F], + opening: &F, + commitment: &Self::Commitment, + ) -> Result<(), HachiError> { + commitment.append_to_transcript(labels::ABSORB_COMMITMENT, transcript); + let q = transcript.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); + let expected = opening.to_canonical_u128() ^ q.to_canonical_u128(); + if proof.0 == expected { + Ok(()) + } else { + Err(HachiError::InvalidProof) + } + } + + fn combine_commitments(commitments: &[Self::Commitment], coeffs: &[F]) -> Self::Commitment { + let acc = commitments + .iter() + .zip(coeffs.iter()) + .fold(0u128, |sum, (c, coeff)| { + sum.wrapping_add(c.0.wrapping_mul(coeff.to_canonical_u128())) + }); + HachiCommitment(acc) + } + + fn combine_hints(hints: Vec, coeffs: &[F]) -> Self::OpeningProofHint { + let acc = hints + .iter() + .zip(coeffs.iter()) + .fold(0u128, |sum, (h, coeff)| { + sum.wrapping_add(h.0.wrapping_mul(coeff.to_canonical_u128())) + }); + HachiCommitment(acc) + } + + fn protocol_name() -> &'static [u8] { + b"HachiDummy" + } +} + +impl StreamingCommitmentScheme for DummyScheme { + type ChunkState = HachiCommitment; + + fn process_chunk(_setup: &Self::ProverSetup, chunk: &[F]) -> Self::ChunkState { + let sum = chunk + .iter() + .fold(0u128, |acc, x| acc.wrapping_add(x.to_canonical_u128())); + HachiCommitment(sum) + } + + fn process_chunk_onehot( + _setup: &Self::ProverSetup, + onehot_k: usize, + chunk: &[Option], + ) -> Self::ChunkState { + let sum = chunk.iter().fold(0u128, |acc, x| { + let v = x.unwrap_or(0) as u128; + acc.wrapping_add(v) + }); + HachiCommitment(sum.wrapping_add(onehot_k as u128)) + } + + fn aggregate_chunks( + _setup: &Self::ProverSetup, + _onehot_k: Option, + chunks: &[Self::ChunkState], + ) -> (Self::Commitment, Self::OpeningProofHint) { + let sum = chunks.iter().fold(0u128, |acc, c| acc.wrapping_add(c.0)); + let c = HachiCommitment(sum); + (c, c) + } +} + +#[test] +fn commitment_scheme_round_trip() { + let poly = SimplePoly { + coeffs: vec![F::from_u64(3), F::from_u64(5), F::from_u64(7)], + }; + let opening_point = [F::from_u64(11), F::from_u64(13)]; + let opening = poly.evaluate(&opening_point); + + let psetup = DummyScheme::setup_prover(poly.num_vars()); + let vsetup = DummyScheme::setup_verifier(&psetup); + + let (commitment, hint) = DummyScheme::commit(&poly, &psetup).unwrap(); + + let mut prover_t = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let proof = DummyScheme::prove( + &psetup, + &poly, + &opening_point, + Some(hint), + &mut prover_t, + &commitment, + ) + .unwrap(); + + let mut verifier_t = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + DummyScheme::verify( + &proof, + &vsetup, + &mut verifier_t, + &opening_point, + &opening, + &commitment, + ) + .unwrap(); +} + +#[test] +fn combine_commitments_and_hints_are_consistent() { + let c1 = HachiCommitment(10); + let c2 = HachiCommitment(20); + let coeffs = [F::from_u64(3), F::from_u64(7)]; + + let combined_c = DummyScheme::combine_commitments(&[c1, c2], &coeffs); + let combined_h = DummyScheme::combine_hints(vec![c1, c2], &coeffs); + + let expected = 10u128 + .wrapping_mul(coeffs[0].to_canonical_u128()) + .wrapping_add(20u128.wrapping_mul(coeffs[1].to_canonical_u128())); + assert_eq!(combined_c.0, expected); + assert_eq!(combined_h.0, expected); +} + +#[test] +fn streaming_chunk_path_aggregates() { + let setup = DummyScheme::setup_prover(4); + let c1 = DummyScheme::process_chunk(&setup, &[F::from_u64(1), F::from_u64(2)]); + let c2 = DummyScheme::process_chunk_onehot(&setup, 8, &[Some(3), None, Some(5)]); + + let (commitment, hint) = DummyScheme::aggregate_chunks(&setup, Some(8), &[c1, c2]); + assert_eq!(commitment, hint); +} diff --git a/tests/hachi_sumcheck.rs b/tests/hachi_sumcheck.rs new file mode 100644 index 00000000..69f16bf4 --- /dev/null +++ b/tests/hachi_sumcheck.rs @@ -0,0 +1,225 @@ +#![allow(missing_docs)] + +use hachi_pcs::algebra::ring::CyclotomicRing; +use hachi_pcs::algebra::Fp64; +use hachi_pcs::protocol::sumcheck::norm_sumcheck::{NormSumcheckProver, NormSumcheckVerifier}; +use hachi_pcs::protocol::sumcheck::relation_sumcheck::{ + RelationSumcheckProver, RelationSumcheckVerifier, +}; +use hachi_pcs::protocol::sumcheck::{eq_eval, eq_evals, multilinear_eval, range_check_eval}; +use hachi_pcs::protocol::transcript::labels; +use hachi_pcs::protocol::{prove_sumcheck, verify_sumcheck, Blake2bTranscript, Transcript}; +use hachi_pcs::{CanonicalField, FieldCore, FieldSampling}; +use rand::rngs::StdRng; +use rand::SeedableRng; +use std::time::Instant; + +type F = Fp64<4294967197>; + +fn run_f0_e2e(num_u: usize, num_l: usize, b: usize) { + let num_vars = num_u + num_l; + let n = 1usize << num_vars; + let mut rng = StdRng::seed_from_u64(0xF0); + + let w_evals: Vec = (0..n).map(|i| F::from_u64((i % b) as u64)).collect(); + let tau0: Vec = (0..num_vars).map(|_| F::sample(&mut rng)).collect(); + + let t0 = Instant::now(); + let mut prover = NormSumcheckProver::new(&tau0, w_evals.clone(), b); + let mut pt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let (proof, prover_challenges, final_claim) = + prove_sumcheck::(&mut prover, &mut pt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + let prove_time = t0.elapsed(); + + // Sanity: prover's final claim matches oracle evaluation. + let oracle = eq_eval(&tau0, &prover_challenges) + * range_check_eval(multilinear_eval(&w_evals, &prover_challenges), b); + assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); + + // ---- Verifier ---- + let t1 = Instant::now(); + let verifier = NormSumcheckVerifier::new(tau0, w_evals, b); + let mut vt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let verifier_challenges = verify_sumcheck::(&proof, &verifier, &mut vt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + let verify_time = t1.elapsed(); + + assert_eq!(prover_challenges, verifier_challenges); + + eprintln!( + "[F0 e2e] num_u={num_u} num_l={num_l} b={b} n=2^{num_vars}={n} \ + prove={prove_time:.2?} verify={verify_time:.2?} \ + rounds={} degree={}", + proof.round_polys.len(), + 2 * b, + ); +} + +#[test] +fn f0_sumcheck_e2e_small() { + run_f0_e2e(3, 2, 2); +} + +#[test] +fn f0_sumcheck_e2e() { + run_f0_e2e(4, 3, 2); +} + +#[test] +fn f0_sumcheck_e2e_larger_b() { + run_f0_e2e(3, 3, 3); +} + +fn run_f_alpha_e2e(num_u: usize, num_i: usize) { + let num_l = D.trailing_zeros() as usize; + let num_vars = num_u + num_l; + let n = 1usize << num_vars; + let mut rng = StdRng::seed_from_u64(0xFA); + + let w_evals: Vec = (0..n).map(|_| F::sample(&mut rng)).collect(); + let alpha_evals_y: Vec = (0..D).map(|_| F::sample(&mut rng)).collect(); + let m_alpha_evals: Vec = (0..(1usize << (num_i + num_u))) + .map(|_| F::sample(&mut rng)) + .collect(); + let tau1: Vec = (0..num_i).map(|_| F::sample(&mut rng)).collect(); + + // Compute m(x) = Σ_i ẽq(τ₁, i) · M̃_α(i, x) + let eq_tau1 = eq_evals(&tau1); + let num_x = 1usize << num_u; + let m_evals_x: Vec = (0..num_x) + .map(|x_idx| { + (0..(1usize << num_i)) + .map(|i_idx| eq_tau1[i_idx] * m_alpha_evals[i_idx * num_x + x_idx]) + .fold(F::zero(), |a, v| a + v) + }) + .collect(); + + // Compute y_a[i] = Σ_x M̃_α(i,x) · w_α(x), where w_α(x) = Σ_y w(x,y) · α̃(y) + let num_y = D; + let num_rows = 1usize << num_i; + let w_alpha: Vec = (0..num_x) + .map(|x| { + (0..num_y) + .map(|y| w_evals[x + y * num_x] * alpha_evals_y[y]) + .fold(F::zero(), |a, v| a + v) + }) + .collect(); + let y_a: Vec = (0..num_rows) + .map(|i| { + (0..num_x) + .map(|x| m_alpha_evals[i * num_x + x] * w_alpha[x]) + .fold(F::zero(), |a, v| a + v) + }) + .collect(); + + // Embed y_a values as constant ring elements for the verifier. + let v_rings: Vec> = y_a + .iter() + .map(|&val| { + let mut coeffs = [F::zero(); D]; + coeffs[0] = val; + CyclotomicRing::from_coefficients(coeffs) + }) + .collect(); + let u_rings: Vec> = vec![]; + let u_eval_ring = CyclotomicRing::::zero(); + let ring_alpha = F::one(); + + let t0 = Instant::now(); + let mut prover = + RelationSumcheckProver::new(w_evals.clone(), &alpha_evals_y, &m_evals_x, num_u, num_l); + let mut pt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let (proof, prover_challenges, final_claim) = + prove_sumcheck::(&mut prover, &mut pt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + let prove_time = t0.elapsed(); + + // Sanity: prover's final claim matches oracle evaluation. + let (x_ch, y_ch) = prover_challenges.split_at(num_u); + let oracle = multilinear_eval(&w_evals, &prover_challenges) + * multilinear_eval(&alpha_evals_y, y_ch) + * multilinear_eval(&m_evals_x, x_ch); + assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); + + let t1 = Instant::now(); + let verifier = RelationSumcheckVerifier::::new( + w_evals, + alpha_evals_y, + m_evals_x, + tau1, + v_rings, + u_rings, + u_eval_ring, + ring_alpha, + num_u, + num_l, + ); + let mut vt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let verifier_challenges = verify_sumcheck::(&proof, &verifier, &mut vt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + let verify_time = t1.elapsed(); + + assert_eq!(prover_challenges, verifier_challenges); + + eprintln!( + "[Fα e2e] num_u={num_u} num_l={num_l} num_i={num_i} n=2^{num_vars}={n} \ + prove={prove_time:.2?} verify={verify_time:.2?} \ + rounds={} degree=2", + proof.round_polys.len(), + ); +} + +#[test] +fn f_alpha_sumcheck_e2e_small() { + run_f_alpha_e2e::<4>(3, 2); +} + +#[test] +fn f_alpha_sumcheck_e2e() { + run_f_alpha_e2e::<8>(4, 3); +} + +#[test] +fn f_alpha_sumcheck_e2e_asymmetric() { + run_f_alpha_e2e::<4>(5, 4); +} + +#[test] +fn from_evals_matches_direct_polynomial() { + use hachi_pcs::protocol::UniPoly; + + // Verify that interpolation at integer points reproduces the polynomial. + let mut rng = StdRng::seed_from_u64(0xEE); + + for degree in 0..6usize { + let coeffs: Vec = (0..=degree).map(|_| F::sample(&mut rng)).collect(); + let poly = UniPoly::from_coeffs(coeffs); + + let evals: Vec = (0..=degree) + .map(|t| poly.evaluate(&F::from_u64(t as u64))) + .collect(); + let reconstructed = UniPoly::from_evals(&evals); + + for x_u64 in [0u64, 1, 2, 3, 7, 13] { + let x = F::from_u64(x_u64); + assert_eq!( + poly.evaluate(&x), + reconstructed.evaluate(&x), + "degree {degree}, x={x_u64}" + ); + } + } +} diff --git a/tests/label_schedule.rs b/tests/label_schedule.rs new file mode 100644 index 00000000..c943b83b --- /dev/null +++ b/tests/label_schedule.rs @@ -0,0 +1,63 @@ +#![allow(missing_docs)] + +use hachi_pcs::algebra::Fp64; +use hachi_pcs::protocol::transcript::labels; +use hachi_pcs::protocol::{Blake2bTranscript, Transcript}; + +type F = Fp64<4294967197>; + +#[test] +fn label_namespace_does_not_include_dory_literals() { + let banned = ["vmv_", "beta", "alpha", "gamma", "final_e", "dory"]; + for label in labels::all_labels() { + let text = std::str::from_utf8(label).expect("labels must be valid utf8 literals"); + for needle in &banned { + assert!( + !text.contains(needle), + "label `{text}` must not contain banned token `{needle}`" + ); + } + } +} + +fn run_hachi_schedule>(transcript: &mut T) -> (F, F, F) { + transcript.append_bytes(labels::ABSORB_COMMITMENT, b"C"); + transcript.append_bytes(labels::ABSORB_EVALUATION_CLAIMS, b"O"); + let c_linear_relation = transcript.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); + + transcript.append_bytes(labels::ABSORB_RING_SWITCH_MESSAGE, b"RS"); + let c_ring_switch = transcript.challenge_scalar(labels::CHALLENGE_RING_SWITCH); + + transcript.append_bytes(labels::ABSORB_SUMCHECK_ROUND, b"SC1"); + let c_sumcheck = transcript.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND); + transcript.append_bytes(labels::ABSORB_STOP_CONDITION, b"STOP"); + let _ = transcript.challenge_scalar(labels::CHALLENGE_STOP_CONDITION); + + (c_linear_relation, c_ring_switch, c_sumcheck) +} + +#[test] +fn schedule_is_replayable_with_hachi_labels() { + let mut prover = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let mut verifier = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + assert_eq!( + run_hachi_schedule(&mut prover), + run_hachi_schedule(&mut verifier) + ); +} + +#[test] +fn schedule_detects_reordered_round_messages() { + let mut t1 = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let mut t2 = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + t1.append_bytes(labels::ABSORB_COMMITMENT, b"C"); + t1.append_bytes(labels::ABSORB_EVALUATION_CLAIMS, b"O"); + let a = t1.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); + + t2.append_bytes(labels::ABSORB_EVALUATION_CLAIMS, b"O"); + t2.append_bytes(labels::ABSORB_COMMITMENT, b"C"); + let b = t2.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); + + assert_ne!(a, b); +} diff --git a/tests/onehot_commitment.rs b/tests/onehot_commitment.rs new file mode 100644 index 00000000..f338f266 --- /dev/null +++ b/tests/onehot_commitment.rs @@ -0,0 +1,145 @@ +#![allow(missing_docs)] + +use hachi_pcs::protocol::commitment::{HachiCommitmentCore, RingCommitmentScheme}; +use hachi_pcs::test_utils::*; +use hachi_pcs::{CanonicalField, FieldCore}; + +type Core = HachiCommitmentCore; + +fn psetup() -> >::ProverSetup { + >::setup(16) + .unwrap() + .0 +} + +/// Compare the optimized one-hot path against the default dense path. +/// +/// The default implementation materializes the full vector and calls +/// `commit_coeffs`. The optimized impl uses sparse inner Ajtai. +/// Both must produce identical (commitment, s_all, t_hat_all). +fn assert_onehot_matches_dense(onehot_k: usize, indices: &[usize]) { + let setup = psetup(); + + // Optimized sparse path. + let (c_sparse, s_sparse, t_sparse) = + >::commit_onehot(onehot_k, indices, &setup) + .unwrap(); + + // Reference: materialize the full one-hot vector, pack into ring elements, + // and commit via the dense path. + let total_field = indices.len() * onehot_k; + let total_ring = total_field / D; + let mut field_elems = vec![F::zero(); total_field]; + for (c, &idx) in indices.iter().enumerate() { + field_elems[c * onehot_k + idx] = F::from_u64(1); + } + let ring_coeffs: Vec> = (0..total_ring) + .map(|r| { + let coeffs: [F; D] = std::array::from_fn(|i| field_elems[r * D + i]); + hachi_pcs::algebra::CyclotomicRing::from_coefficients(coeffs) + }) + .collect(); + let (c_dense, s_dense, t_dense) = + >::commit_coeffs(&ring_coeffs, &setup) + .unwrap(); + + assert_eq!(c_sparse, c_dense, "commitments must match"); + assert_eq!(s_sparse, s_dense, "s_all (decomposed witness) must match"); + assert_eq!( + t_sparse, t_dense, + "t_hat_all (decomposed inner output) must match" + ); +} + +#[test] +fn onehot_k_gt_d_basic() { + // K=128, D=64 => K/D=2, T=2 => T*K=256 => 4 ring elements + assert_onehot_matches_dense(128, &[0, 64]); +} + +#[test] +fn onehot_k_gt_d_various_positions() { + assert_onehot_matches_dense(128, &[127, 0]); + assert_onehot_matches_dense(128, &[63, 65]); + assert_onehot_matches_dense(128, &[32, 96]); +} + +#[test] +fn onehot_k_much_gt_d() { + // K=256, D=64 => K/D=4, T=1 => T*K=256 => 4 ring elements + assert_onehot_matches_dense(256, &[0]); + assert_onehot_matches_dense(256, &[63]); + assert_onehot_matches_dense(256, &[64]); + assert_onehot_matches_dense(256, &[255]); + assert_onehot_matches_dense(256, &[100]); +} + +#[test] +fn onehot_k_eq_d_basic() { + // K=64=D, T=4 => 4 ring elements, each is a monomial X^{idx}. + assert_onehot_matches_dense(64, &[0, 0, 0, 0]); +} + +#[test] +fn onehot_k_eq_d_varied() { + assert_onehot_matches_dense(64, &[0, 31, 32, 63]); + assert_onehot_matches_dense(64, &[1, 2, 3, 4]); + assert_onehot_matches_dense(64, &[63, 63, 63, 63]); +} + +#[test] +fn onehot_k_lt_d_basic() { + // K=16, D=64 => D/K=4, T=16 => T*K=256 => 4 ring elements. + // Each ring element spans 4 chunks, so has 4 nonzero coefficients. + let indices: Vec = (0..16).map(|i| i % 16).collect(); + assert_onehot_matches_dense(16, &indices); +} + +#[test] +fn onehot_k_lt_d_all_zeros() { + let indices = vec![0; 16]; + assert_onehot_matches_dense(16, &indices); +} + +#[test] +fn onehot_k_lt_d_all_max() { + let indices = vec![15; 16]; + assert_onehot_matches_dense(16, &indices); +} + +#[test] +fn onehot_k_lt_d_mixed() { + let indices = vec![0, 15, 7, 3, 12, 1, 8, 14, 5, 10, 2, 9, 6, 11, 4, 13]; + assert_onehot_matches_dense(16, &indices); +} + +#[test] +fn onehot_k_lt_d_ratio_2() { + // K=32, D=64 => D/K=2, T=8 => T*K=256 => 4 ring elements. + let indices = vec![0, 31, 16, 8, 24, 4, 12, 20]; + assert_onehot_matches_dense(32, &indices); +} + +#[test] +fn onehot_rejects_non_divisible_k_and_d() { + let setup = psetup(); + let result = + >::commit_onehot(17, &[0; 4], &setup); + assert!(result.is_err()); +} + +#[test] +fn onehot_rejects_out_of_range_index() { + let setup = psetup(); + let result = + >::commit_onehot(64, &[0, 64, 0, 0], &setup); + assert!(result.is_err()); +} + +#[test] +fn onehot_rejects_wrong_total_size() { + let setup = psetup(); + let result = + >::commit_onehot(64, &[0, 0, 0], &setup); + assert!(result.is_err()); +} diff --git a/tests/primality.rs b/tests/primality.rs new file mode 100644 index 00000000..0d7a3a8f --- /dev/null +++ b/tests/primality.rs @@ -0,0 +1,124 @@ +#![allow(missing_docs)] + +use hachi_pcs::algebra::{pseudo_mersenne_modulus, Pow2OffsetPrimeSpec, POW2_OFFSET_PRIMES}; + +// Strong probable-prime test using multiple fixed bases. +// This is not a formal primality certificate, but is sufficient as a +// practical regression guard for the current Pow2Offset profiles. +fn is_probable_prime_miller_rabin(n: u128) -> bool { + if n < 2 { + return false; + } + if n % 2 == 0 { + return n == 2; + } + + const SMALL_PRIMES: [u128; 11] = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]; + for p in SMALL_PRIMES { + if n == p { + return true; + } + if n % p == 0 { + return false; + } + } + + let (d, s) = decompose_pow2(n - 1); + const BASES: [u128; 24] = [ + 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, + ]; + + 'outer: for a in BASES { + if a >= n { + continue; + } + let mut x = pow_mod(a, d, n); + if x == 1 || x == n - 1 { + continue; + } + for _ in 1..s { + x = mul_mod(x, x, n); + if x == n - 1 { + continue 'outer; + } + } + return false; + } + + true +} + +fn decompose_pow2(mut d: u128) -> (u128, u32) { + let mut s = 0u32; + while d % 2 == 0 { + d >>= 1; + s += 1; + } + (d, s) +} + +fn pow_mod(mut base: u128, mut exp: u128, modulus: u128) -> u128 { + let mut result = 1u128; + base %= modulus; + while exp > 0 { + if (exp & 1) == 1 { + result = mul_mod(result, base, modulus); + } + base = mul_mod(base, base, modulus); + exp >>= 1; + } + result +} + +fn mul_mod(mut a: u128, mut b: u128, modulus: u128) -> u128 { + let mut result = 0u128; + a %= modulus; + b %= modulus; + while b > 0 { + if (b & 1) == 1 { + result = add_mod(result, a, modulus); + } + a = add_mod(a, a, modulus); + b >>= 1; + } + result +} + +fn add_mod(a: u128, b: u128, modulus: u128) -> u128 { + if a >= modulus - b { + a - (modulus - b) + } else { + a + b + } +} + +#[test] +fn pow2_offset_profiles_are_probable_primes() { + for Pow2OffsetPrimeSpec { + bits, + offset, + modulus, + } in POW2_OFFSET_PRIMES + { + assert_eq!( + Some(modulus), + pseudo_mersenne_modulus(bits, offset as u128), + "profile formula mismatch for bits={bits}, offset={offset}" + ); + assert!( + is_probable_prime_miller_rabin(modulus), + "Miller-Rabin rejected bits={bits}, offset={offset}, q={modulus}" + ); + } +} + +#[test] +fn miller_rabin_rejects_known_composites() { + let composites: [u128; 9] = [4, 9, 15, 21, 341, 561, 645, 1105, 1729]; + for n in composites { + assert!( + !is_probable_prime_miller_rabin(n), + "composite unexpectedly accepted: {n}" + ); + } +} diff --git a/tests/ring_commitment_core.rs b/tests/ring_commitment_core.rs new file mode 100644 index 00000000..2fa20bee --- /dev/null +++ b/tests/ring_commitment_core.rs @@ -0,0 +1,184 @@ +#![allow(missing_docs)] + +use hachi_pcs::algebra::CyclotomicRing; +use hachi_pcs::error::HachiError; +use hachi_pcs::protocol::commitment::{ + CommitmentConfig, DefaultCommitmentConfig, HachiCommitmentCore, RingCommitmentScheme, +}; +use hachi_pcs::test_utils::*; + +#[derive(Clone)] +struct BadDegreeConfig; + +impl CommitmentConfig for BadDegreeConfig { + const D: usize = 32; + const M: usize = 4; + const R: usize = 2; + const N_A: usize = 8; + const N_B: usize = 4; + const N_D: usize = 4; + const LOG_BASIS: u32 = 4; + const DELTA: usize = 8; + const TAU: usize = 4; + const BETA: u128 = 1_000_000; + const CHALLENGE_WEIGHT: usize = 3; +} + +#[derive(Clone)] +struct BadDigitBudgetConfig; + +impl CommitmentConfig for BadDigitBudgetConfig { + const D: usize = 64; + const M: usize = 4; + const R: usize = 2; + const N_A: usize = 8; + const N_B: usize = 4; + const N_D: usize = 4; + const LOG_BASIS: u32 = 32; + const DELTA: usize = 5; // 160 > 128 + const TAU: usize = 4; + const BETA: u128 = 1_000_000; + const CHALLENGE_WEIGHT: usize = 3; +} + +#[test] +fn setup_shape_is_consistent() { + let (p1, v1) = + >::setup(16).unwrap(); + let (p2, v2) = + >::setup(16).unwrap(); + + assert_eq!(p1.max_num_vars, 16); + assert_eq!(v1.max_num_vars, 16); + assert_eq!(p2.max_num_vars, 16); + assert_eq!(v2.max_num_vars, 16); + assert_eq!(p1.A.len(), TinyConfig::N_A); + assert_eq!(p1.A[0].len(), (1usize << TinyConfig::M) * TinyConfig::DELTA); + assert_eq!(p1.B.len(), TinyConfig::N_B); + assert_eq!( + p1.B[0].len(), + TinyConfig::N_A * TinyConfig::DELTA * (1usize << TinyConfig::R) + ); +} + +#[test] +fn commit_is_deterministic_and_shape_consistent() { + let (psetup, _) = + >::setup(16).unwrap(); + let blocks = sample_blocks(); + + let (c1, s1, t1) = + >::commit_ring_blocks( + &blocks, &psetup, + ) + .unwrap(); + let (c2, s2, t2) = + >::commit_ring_blocks( + &blocks, &psetup, + ) + .unwrap(); + + assert_eq!(c1, c2); + assert_eq!(s1, s2); + assert_eq!(t1, t2); + + let num_blocks = 1usize << TinyConfig::R; + let block_len = 1usize << TinyConfig::M; + assert_eq!(c1.u.len(), TinyConfig::N_B); + assert_eq!(s1.len(), num_blocks); + assert_eq!(t1.len(), num_blocks); + assert!(s1.iter().all(|s| s.len() == block_len * TinyConfig::DELTA)); + assert!(t1 + .iter() + .all(|t| t.len() == TinyConfig::N_A * TinyConfig::DELTA)); +} + +#[test] +fn commit_ring_coeffs_matches_block_commitment() { + let (psetup, _) = + >::setup(16).unwrap(); + let blocks = sample_blocks(); + + let (c_blocks, s_blocks, t_blocks) = + >::commit_ring_blocks( + &blocks, &psetup, + ) + .unwrap(); + + let num_blocks = 1usize << TinyConfig::R; + let block_len = 1usize << TinyConfig::M; + let mut f_coeffs = Vec::with_capacity(num_blocks * block_len); + for j in 0..block_len { + for block in blocks.iter().take(num_blocks) { + f_coeffs.push(block[j]); + } + } + + let (c_coeffs, s_coeffs, t_coeffs) = + >::commit_coeffs( + &f_coeffs, &psetup, + ) + .unwrap(); + + assert_eq!(c_blocks, c_coeffs); + assert_eq!(s_blocks, s_coeffs); + assert_eq!(t_blocks, t_coeffs); +} + +#[test] +fn opening_satisfies_inner_and_outer_equations() { + let (psetup, _) = + >::setup(16).unwrap(); + let blocks = sample_blocks(); + let (commitment, s, t_hat) = + >::commit_ring_blocks( + &blocks, &psetup, + ) + .unwrap(); + + for i in 0..s.len() { + let lhs = mat_vec_mul(&psetup.A, &s[i]); + let rhs: Vec> = (0..TinyConfig::N_A) + .map(|j| { + let start = j * TinyConfig::DELTA; + let end = start + TinyConfig::DELTA; + CyclotomicRing::gadget_recompose_pow2(&t_hat[i][start..end], TinyConfig::LOG_BASIS) + }) + .collect(); + assert_eq!(lhs, rhs); + } + + let t_hat_flat: Vec> = + t_hat.iter().flat_map(|x| x.iter().copied()).collect(); + let outer = mat_vec_mul(&psetup.B, &t_hat_flat); + assert_eq!(outer, commitment.u); +} + +#[test] +fn default_config_has_expected_shape() { + assert_eq!(DefaultCommitmentConfig::D, 16); + assert_eq!(1usize << DefaultCommitmentConfig::M, 16); + assert_eq!(1usize << DefaultCommitmentConfig::R, 4); + let delta = DefaultCommitmentConfig::DELTA; + assert!(delta > 0); +} + +#[test] +fn setup_rejects_mismatched_degree() { + let err = >::setup(16) + .unwrap_err(); + match err { + HachiError::InvalidSetup(msg) => assert!(msg.contains("mismatches")), + other => panic!("unexpected error: {other:?}"), + } +} + +#[test] +fn setup_rejects_invalid_digit_budget() { + let err = >::setup(16) + .unwrap_err(); + match err { + HachiError::InvalidSetup(msg) => assert!(msg.contains("DELTA * LOG_BASIS")), + other => panic!("unexpected error: {other:?}"), + } +} diff --git a/tests/sparse_challenge.rs b/tests/sparse_challenge.rs new file mode 100644 index 00000000..16eb8ee4 --- /dev/null +++ b/tests/sparse_challenge.rs @@ -0,0 +1,98 @@ +#![allow(missing_docs)] + +use hachi_pcs::algebra::fields::LiftBase; +use hachi_pcs::algebra::ring::{CyclotomicRing, SparseChallenge, SparseChallengeConfig}; +use hachi_pcs::algebra::Fp64; +use hachi_pcs::protocol::challenges::sparse::sparse_challenge_from_transcript; +use hachi_pcs::protocol::transcript::labels::DOMAIN_HACHI_PROTOCOL; +use hachi_pcs::protocol::transcript::{Blake2bTranscript, Transcript}; +use hachi_pcs::{CanonicalField, FieldCore}; + +type F = Fp64<4294967197>; + +const D: usize = 16; + +fn dense_eval>(alpha: E, x: &CyclotomicRing) -> E { + let mut acc = E::zero(); + let mut pow = E::one(); + for c in x.coefficients().iter().copied() { + acc = acc + E::lift_base(c) * pow; + pow = pow * alpha; + } + acc +} + +#[test] +fn sparse_challenge_validate_and_to_dense() { + let cfg = SparseChallengeConfig { + weight: 3, + nonzero_coeffs: vec![-1, 1], + }; + cfg.validate::().unwrap(); + + let s = SparseChallenge { + positions: vec![0, 7, 12], + coeffs: vec![1, -1, 1], + }; + s.validate::().unwrap(); + assert_eq!(s.hamming_weight(), 3); + assert_eq!(s.l1_norm(), 3); + + let dense = s.to_dense::().unwrap(); + assert_eq!(dense.hamming_weight(), 3); + assert_eq!(dense.coefficients()[0], F::one()); + assert_eq!(dense.coefficients()[7], -F::one()); + assert_eq!(dense.coefficients()[12], F::one()); +} + +#[test] +fn sparse_eval_at_alpha_matches_dense_eval() { + let alpha = F::from_u64(5); + let alpha_pows = { + let mut out = Vec::with_capacity(D); + let mut acc = F::one(); + for _ in 0..D { + out.push(acc); + acc = acc * alpha; + } + out + }; + + let s = SparseChallenge { + positions: vec![1, 3, 9], + coeffs: vec![2, -1, 1], + }; + let dense = s.to_dense::().unwrap(); + + let sparse_eval = s.eval_at_alpha::(&alpha_pows).unwrap(); + let dense_eval = dense_eval::(alpha, &dense); + assert_eq!(sparse_eval, dense_eval); +} + +#[test] +fn sparse_challenge_sampling_is_deterministic_and_exact_weight() { + let cfg = SparseChallengeConfig { + weight: 8, + nonzero_coeffs: vec![-1, 1], + }; + + let mut t1 = Blake2bTranscript::::new(DOMAIN_HACHI_PROTOCOL); + let mut t2 = Blake2bTranscript::::new(DOMAIN_HACHI_PROTOCOL); + + // Make transcript state non-empty to avoid degenerate behavior. + t1.append_field(b"seed", &F::from_u64(123)); + t2.append_field(b"seed", &F::from_u64(123)); + + let c1 = sparse_challenge_from_transcript::(&mut t1, b"c", 0, &cfg).unwrap(); + let c2 = sparse_challenge_from_transcript::(&mut t2, b"c", 0, &cfg).unwrap(); + assert_eq!(c1, c2); + c1.validate::().unwrap(); + assert_eq!(c1.hamming_weight(), cfg.weight); + assert_eq!(c1.l1_norm(), cfg.weight as u64); + + // Different instance_idx should change the sample. + let mut t3 = Blake2bTranscript::::new(DOMAIN_HACHI_PROTOCOL); + t3.append_field(b"seed", &F::from_u64(123)); + let c3 = sparse_challenge_from_transcript::(&mut t3, b"c", 1, &cfg).unwrap(); + assert_ne!(c1, c3); +} diff --git a/tests/sumcheck_core.rs b/tests/sumcheck_core.rs new file mode 100644 index 00000000..a9c58f28 --- /dev/null +++ b/tests/sumcheck_core.rs @@ -0,0 +1,304 @@ +#![allow(missing_docs)] + +use std::time::Instant; + +use hachi_pcs::algebra::Fp64; +use hachi_pcs::protocol::transcript::labels; +use hachi_pcs::protocol::{ + prove_sumcheck, verify_sumcheck, Blake2bTranscript, CompressedUniPoly, SumcheckInstanceProver, + SumcheckInstanceVerifier, SumcheckProof, Transcript, UniPoly, +}; +use hachi_pcs::{CanonicalField, FieldCore, FieldSampling}; +use rand::rngs::StdRng; +use rand::RngCore; +use rand::SeedableRng; + +type F = Fp64<4294967197>; + +#[test] +fn compressed_unipoly_round_trip_and_eval() { + let mut rng = StdRng::seed_from_u64(123); + + for degree in 0..8usize { + let coeffs: Vec = (0..=degree).map(|_| F::sample(&mut rng)).collect(); + let poly = UniPoly::from_coeffs(coeffs); + + // Hint is g(0) + g(1). + let hint = poly.evaluate(&F::zero()) + poly.evaluate(&F::one()); + + let compressed = poly.compress(); + let decompressed = compressed.decompress(&hint); + + // Decompression should be functionally equivalent (it may materialize + // a trailing zero linear term for constant polynomials). + for x_u64 in [0u64, 1, 2, 3, 17] { + let x = F::from_u64(x_u64); + let direct = poly.evaluate(&x); + let decompressed_direct = decompressed.evaluate(&x); + let via_hint = compressed.eval_from_hint(&hint, &x); + assert_eq!(direct, decompressed_direct); + assert_eq!(direct, via_hint); + } + } +} + +#[test] +fn sumcheck_proof_verifier_driver_is_transcript_deterministic() { + // This test checks that the verifier driver absorbs messages and samples challenges + // consistently, and that the returned (final_claim, r_vec) matches a manual replay. + let mut rng = StdRng::seed_from_u64(999); + + let num_rounds = 5usize; + let degree_bound = 7usize; + + // Build random per-round univariates (degree <= degree_bound), compress them. + let round_polys: Vec> = (0..num_rounds) + .map(|_| { + let deg = (rng.next_u32() as usize) % (degree_bound + 1); + let coeffs: Vec = (0..=deg).map(|_| F::sample(&mut rng)).collect(); + UniPoly::from_coeffs(coeffs).compress() + }) + .collect(); + + let proof = SumcheckProof { round_polys }; + let claim0 = F::sample(&mut rng); + + // Verifier run. + let mut t1 = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let (final_claim_1, r_1) = proof + .verify::(claim0, num_rounds, degree_bound, &mut t1, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + // Manual replay with a fresh transcript (must match). + let mut t2 = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let mut claim = claim0; + let mut r_manual = Vec::with_capacity(num_rounds); + for poly in &proof.round_polys { + t2.append_serde(labels::ABSORB_SUMCHECK_ROUND, poly); + let r_i = t2.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND); + r_manual.push(r_i); + claim = poly.eval_from_hint(&claim, &r_i); + } + + assert_eq!(r_1, r_manual); + assert_eq!(final_claim_1, claim); +} + +/// Evaluate a multilinear polynomial (given by its boolean-hypercube evaluations +/// in little-endian bit order) at an arbitrary point via iterated folding. +fn multilinear_eval(evals: &[E], point: &[E]) -> E { + let mut current = evals.to_vec(); + for r in point { + let half = current.len() / 2; + let mut next = Vec::with_capacity(half); + for i in 0..half { + next.push(current[2 * i] + *r * (current[2 * i + 1] - current[2 * i])); + } + current = next; + } + current[0] +} + +struct DenseSumcheckProver { + evals: Vec, + num_vars: usize, +} + +impl SumcheckInstanceProver for DenseSumcheckProver { + fn num_rounds(&self) -> usize { + self.num_vars + } + + fn degree_bound(&self) -> usize { + 1 + } + + fn input_claim(&self) -> E { + self.evals.iter().copied().fold(E::zero(), |a, b| a + b) + } + + fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { + let half = self.evals.len() / 2; + let mut eval_0 = E::zero(); + let mut eval_1 = E::zero(); + for i in 0..half { + eval_0 = eval_0 + self.evals[2 * i]; + eval_1 = eval_1 + self.evals[2 * i + 1]; + } + // g(X) = eval_0 + (eval_1 - eval_0) * X (degree 1) + UniPoly::from_coeffs(vec![eval_0, eval_1 - eval_0]) + } + + fn ingest_challenge(&mut self, _round: usize, r: E) { + let half = self.evals.len() / 2; + let mut new_evals = Vec::with_capacity(half); + for i in 0..half { + new_evals.push(self.evals[2 * i] + r * (self.evals[2 * i + 1] - self.evals[2 * i])); + } + self.evals = new_evals; + } +} + +struct DenseSumcheckVerifier { + evals: Vec, + num_vars: usize, + claim: E, +} + +impl SumcheckInstanceVerifier for DenseSumcheckVerifier { + fn num_rounds(&self) -> usize { + self.num_vars + } + + fn degree_bound(&self) -> usize { + 1 + } + + fn input_claim(&self) -> E { + self.claim + } + + fn expected_output_claim(&self, challenges: &[E]) -> E { + multilinear_eval(&self.evals, challenges) + } +} + +#[test] +fn prove_and_verify_single_sumcheck() { + let num_vars = 4; + let n = 1 << num_vars; + + let evals: Vec = (1..=n).map(|i| F::from_u64(i as u64)).collect(); + let claim: F = evals.iter().copied().fold(F::zero(), |a, b| a + b); + + let mut prover = DenseSumcheckProver { + evals: evals.clone(), + num_vars, + }; + + let mut prover_transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let (proof, prover_challenges, _final_claim) = + prove_sumcheck::(&mut prover, &mut prover_transcript, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + let verifier = DenseSumcheckVerifier { + evals, + num_vars, + claim, + }; + + let mut verifier_transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let verifier_challenges = + verify_sumcheck::(&proof, &verifier, &mut verifier_transcript, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + assert_eq!(prover_challenges, verifier_challenges); +} + +#[test] +fn verify_rejects_wrong_claim() { + let num_vars = 3; + let n = 1 << num_vars; + + let evals: Vec = (1..=n).map(|i| F::from_u64(i as u64)).collect(); + let correct_claim: F = evals.iter().copied().fold(F::zero(), |a, b| a + b); + let wrong_claim = correct_claim + F::one(); + + // Prove with correct claim. + let mut prover = DenseSumcheckProver { + evals: evals.clone(), + num_vars, + }; + let mut pt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let (proof, _, _) = prove_sumcheck::(&mut prover, &mut pt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + // Verify with *wrong* claim — should fail. + let verifier = DenseSumcheckVerifier { + evals, + num_vars, + claim: wrong_claim, + }; + let mut vt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let result = verify_sumcheck::(&proof, &verifier, &mut vt, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }); + + assert!(result.is_err()); +} + +/// End-to-end sumcheck over 2^20 random field elements. +/// +/// The prover holds a multilinear polynomial f with 2^20 evaluations and +/// proves that Σ_{b ∈ {0,1}^20} f(b) = claimed_sum. The verifier checks the +/// proof using only the proof transcript and the oracle evaluation f(r). +#[test] +fn e2e_sumcheck_2_pow_20() { + let num_vars = 20; + let n: usize = 1 << num_vars; // 1,048,576 + + let mut rng = StdRng::seed_from_u64(42); + let evals: Vec = (0..n).map(|_| F::sample(&mut rng)).collect(); + let claim: F = evals.iter().copied().fold(F::zero(), |a, b| a + b); + + let t0 = Instant::now(); + + let mut prover = DenseSumcheckProver { + evals: evals.clone(), + num_vars, + }; + let mut prover_transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let (proof, prover_challenges, final_claim) = + prove_sumcheck::(&mut prover, &mut prover_transcript, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + let prove_time = t0.elapsed(); + + // Proof is just 20 compressed univariate polynomials (degree 1 each). + assert_eq!(proof.round_polys.len(), num_vars); + + // Sanity: final claim must equal f evaluated at the challenge point. + let oracle_eval = multilinear_eval(&evals, &prover_challenges); + assert_eq!(final_claim, oracle_eval); + + let t1 = Instant::now(); + + let verifier = DenseSumcheckVerifier { + evals, + num_vars, + claim, + }; + let mut verifier_transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let verifier_challenges = + verify_sumcheck::(&proof, &verifier, &mut verifier_transcript, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + let verify_time = t1.elapsed(); + + assert_eq!(prover_challenges, verifier_challenges); + + eprintln!( + "[e2e_sumcheck_2_pow_20] n=2^{num_vars}={n} \ + prove={prove_time:.2?} verify={verify_time:.2?} \ + rounds={} degree=1", + proof.round_polys.len() + ); +} diff --git a/tests/sumcheck_prover_driver.rs b/tests/sumcheck_prover_driver.rs new file mode 100644 index 00000000..d309a36d --- /dev/null +++ b/tests/sumcheck_prover_driver.rs @@ -0,0 +1,98 @@ +#![allow(missing_docs)] + +use hachi_pcs::algebra::Fp64; +use hachi_pcs::protocol::transcript::labels; +use hachi_pcs::protocol::{ + prove_sumcheck, Blake2bTranscript, SumcheckInstanceProver, Transcript, UniPoly, +}; +use hachi_pcs::{FieldCore, FieldSampling}; +use rand::rngs::StdRng; +use rand::SeedableRng; + +type F = Fp64<4294967197>; + +/// A tiny prover-side sumcheck instance for a multilinear function in evaluation-table form. +/// +/// Variable order convention: the current round binds the least-significant index bit first, +/// i.e. pairs are `(i<<1)|0` and `(i<<1)|1` (matches the common LSB-first sumcheck table fold). +struct DenseTableSumcheck { + table: Vec, +} + +impl DenseTableSumcheck { + fn new(table: Vec) -> Self { + assert!(table.len().is_power_of_two()); + Self { table } + } +} + +impl SumcheckInstanceProver for DenseTableSumcheck { + fn num_rounds(&self) -> usize { + self.table.len().trailing_zeros() as usize + } + + fn degree_bound(&self) -> usize { + 1 + } + + fn input_claim(&self) -> F { + self.table.iter().copied().fold(F::zero(), |a, b| a + b) + } + + fn compute_round_univariate(&mut self, _round: usize, _previous_claim: F) -> UniPoly { + let half = self.table.len() / 2; + let mut s0 = F::zero(); + let mut s1 = F::zero(); + for i in 0..half { + s0 = s0 + self.table[i << 1]; + s1 = s1 + self.table[(i << 1) | 1]; + } + // g(X) = s0 + (s1 - s0) X + UniPoly::from_coeffs(vec![s0, s1 - s0]) + } + + fn ingest_challenge(&mut self, _round: usize, r_round: F) { + let half = self.table.len() / 2; + let mut next = Vec::with_capacity(half); + let one_minus = F::one() - r_round; + for i in 0..half { + let v0 = self.table[i << 1]; + let v1 = self.table[(i << 1) | 1]; + next.push(one_minus * v0 + r_round * v1); + } + self.table = next; + } +} + +#[test] +fn prover_driver_produces_proof_that_verifier_replays() { + let mut rng = StdRng::seed_from_u64(2026); + let num_rounds = 8usize; + let n = 1usize << num_rounds; + + let table: Vec = (0..n).map(|_| F::sample(&mut rng)).collect(); + let mut prover_inst = DenseTableSumcheck::new(table.clone()); + let mut prover_t = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let (proof, r_vec, final_claim) = + prove_sumcheck::(&mut prover_inst, &mut prover_t, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + // After folding all variables, the table should be a single value equal to f(r*). + assert_eq!(prover_inst.table.len(), 1); + assert_eq!(final_claim, prover_inst.table[0]); + + // Verifier replay must derive the same (final_claim, r_vec). + let initial_claim = table.iter().copied().fold(F::zero(), |acc, x| acc + x); + let mut verifier_t = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + verifier_t.append_serde(labels::ABSORB_SUMCHECK_CLAIM, &initial_claim); + let (final_claim_v, r_vec_v) = proof + .verify::(initial_claim, num_rounds, 1, &mut verifier_t, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(); + + assert_eq!(r_vec_v, r_vec); + assert_eq!(final_claim_v, final_claim); +} diff --git a/tests/transcript.rs b/tests/transcript.rs new file mode 100644 index 00000000..50335bec --- /dev/null +++ b/tests/transcript.rs @@ -0,0 +1,136 @@ +#![allow(missing_docs)] + +use hachi_pcs::algebra::Fp64; +use hachi_pcs::protocol::transcript::labels; +use hachi_pcs::protocol::{Blake2bTranscript, KeccakTranscript, Transcript}; + +type F = Fp64<4294967197>; + +fn sample_schedule>(transcript: &mut T) -> F { + transcript.append_bytes(labels::ABSORB_COMMITMENT, b"commitment-a"); + transcript.append_bytes(labels::ABSORB_COMMITMENT, b"commitment-b"); + transcript.append_serde(labels::ABSORB_EVALUATION_CLAIMS, &42u64); + let rho = transcript.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); + + transcript.append_bytes(labels::ABSORB_RING_SWITCH_MESSAGE, b"ring-switch"); + let zeta = transcript.challenge_scalar(labels::CHALLENGE_RING_SWITCH); + + transcript.append_field(labels::ABSORB_SUMCHECK_ROUND, &(rho + zeta)); + let r = transcript.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND); + + transcript.append_field(labels::ABSORB_STOP_CONDITION, &r); + transcript.challenge_scalar(labels::CHALLENGE_STOP_CONDITION) +} + +#[test] +fn transcript_is_deterministic_for_identical_schedule() { + let mut t1 = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let mut t2 = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let c1 = sample_schedule(&mut t1); + let c2 = sample_schedule(&mut t2); + assert_eq!(c1, c2); +} + +#[test] +fn transcript_differs_when_label_changes() { + let mut t1 = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let mut t2 = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + t1.append_bytes(labels::ABSORB_COMMITMENT, b"same-bytes"); + t2.append_bytes(labels::ABSORB_EVALUATION_CLAIMS, b"same-bytes"); + let c1 = t1.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND); + let c2 = t2.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND); + assert_ne!(c1, c2); +} + +#[test] +fn transcript_differs_when_absorb_order_changes() { + let mut t1 = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let mut t2 = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + t1.append_bytes(labels::ABSORB_COMMITMENT, b"A"); + t1.append_bytes(labels::ABSORB_EVALUATION_CLAIMS, b"B"); + + t2.append_bytes(labels::ABSORB_EVALUATION_CLAIMS, b"B"); + t2.append_bytes(labels::ABSORB_COMMITMENT, b"A"); + + let c1 = t1.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); + let c2 = t2.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); + assert_ne!(c1, c2); +} + +#[test] +fn transcript_reset_restores_domain_state() { + let mut t = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + t.append_bytes(labels::ABSORB_COMMITMENT, b"before-reset"); + let _ = t.challenge_scalar(labels::CHALLENGE_STOP_CONDITION); + + t.reset(labels::DOMAIN_HACHI_PROTOCOL); + let after_reset = sample_schedule(&mut t); + + let mut fresh = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let fresh_challenge = sample_schedule(&mut fresh); + assert_eq!(after_reset, fresh_challenge); +} + +#[test] +fn keccak_transcript_is_deterministic_for_identical_schedule() { + let mut t1 = KeccakTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let mut t2 = KeccakTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + let c1 = sample_schedule(&mut t1); + let c2 = sample_schedule(&mut t2); + assert_eq!(c1, c2); +} + +#[test] +fn keccak_transcript_differs_when_label_changes() { + let mut t1 = KeccakTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let mut t2 = KeccakTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + t1.append_bytes(labels::ABSORB_COMMITMENT, b"same-bytes"); + t2.append_bytes(labels::ABSORB_EVALUATION_CLAIMS, b"same-bytes"); + let c1 = t1.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND); + let c2 = t2.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND); + assert_ne!(c1, c2); +} + +#[test] +fn keccak_transcript_differs_when_absorb_order_changes() { + let mut t1 = KeccakTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let mut t2 = KeccakTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + + t1.append_bytes(labels::ABSORB_COMMITMENT, b"A"); + t1.append_bytes(labels::ABSORB_EVALUATION_CLAIMS, b"B"); + + t2.append_bytes(labels::ABSORB_EVALUATION_CLAIMS, b"B"); + t2.append_bytes(labels::ABSORB_COMMITMENT, b"A"); + + let c1 = t1.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); + let c2 = t2.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); + assert_ne!(c1, c2); +} + +#[test] +fn keccak_transcript_reset_restores_domain_state() { + let mut t = KeccakTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + t.append_bytes(labels::ABSORB_COMMITMENT, b"before-reset"); + let _ = t.challenge_scalar(labels::CHALLENGE_STOP_CONDITION); + + t.reset(labels::DOMAIN_HACHI_PROTOCOL); + let after_reset = sample_schedule(&mut t); + + let mut fresh = KeccakTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let fresh_challenge = sample_schedule(&mut fresh); + assert_eq!(after_reset, fresh_challenge); +} + +#[test] +fn blake2b_and_keccak_diverge_on_same_schedule() { + let mut blake = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let mut keccak = KeccakTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let b = sample_schedule(&mut blake); + let k = sample_schedule(&mut keccak); + assert_ne!(b, k); +} From 4980e1ab92686bb7e89fe223ea5e4c4cf8e7a4ab Mon Sep 17 00:00:00 2001 From: Omid Bodaghi <42227752+omibo@users.noreply.github.com> Date: Fri, 27 Feb 2026 21:39:13 -0800 Subject: [PATCH 2/5] Implement Batched Sumcheck and Gruen EQ (#2) --- src/protocol/commitment_scheme.rs | 39 ++-- src/protocol/mod.rs | 1 + src/protocol/proof.rs | 9 +- src/protocol/ring_switch.rs | 4 +- src/protocol/sumcheck/batched_sumcheck.rs | 258 +++++++++++++++++++++ src/protocol/sumcheck/eq_poly.rs | 229 ++++++++++++++++++ src/protocol/sumcheck/mod.rs | 32 +-- src/protocol/sumcheck/norm_sumcheck.rs | 57 +++-- src/protocol/sumcheck/relation_sumcheck.rs | 9 +- src/protocol/sumcheck/split_eq.rs | 213 +++++++++++++++++ src/protocol/transcript/labels.rs | 3 + tests/hachi_sumcheck.rs | 7 +- 12 files changed, 773 insertions(+), 88 deletions(-) create mode 100644 src/protocol/sumcheck/batched_sumcheck.rs create mode 100644 src/protocol/sumcheck/eq_poly.rs create mode 100644 src/protocol/sumcheck/split_eq.rs diff --git a/src/protocol/commitment_scheme.rs b/src/protocol/commitment_scheme.rs index 6da64c79..23ecc795 100644 --- a/src/protocol/commitment_scheme.rs +++ b/src/protocol/commitment_scheme.rs @@ -11,11 +11,14 @@ use crate::protocol::opening_point::RingOpeningPoint; use crate::protocol::proof::{HachiCommitmentHint, HachiProof, SumcheckAux}; use crate::protocol::quadratic_equation::QuadraticEquation; use crate::protocol::ring_switch::{ring_switch_prover, ring_switch_verifier}; +use crate::protocol::sumcheck::batched_sumcheck::{ + prove_batched_sumcheck, verify_batched_sumcheck, +}; use crate::protocol::sumcheck::norm_sumcheck::{NormSumcheckProver, NormSumcheckVerifier}; use crate::protocol::sumcheck::relation_sumcheck::{ RelationSumcheckProver, RelationSumcheckVerifier, }; -use crate::protocol::sumcheck::{prove_sumcheck, verify_sumcheck}; +use crate::protocol::sumcheck::SumcheckInstanceProver; use crate::protocol::transcript::labels::CHALLENGE_SUMCHECK_ROUND; use crate::protocol::transcript::Transcript; use crate::{CanonicalField, FieldCore, FieldSampling, Polynomial}; @@ -118,14 +121,8 @@ where // §4.3 Ring switch let rs = ring_switch_prover::(&quad_eq, transcript)?; - // Norm sumcheck (range check on w) + // Batched sumcheck: norm + relation let mut norm_prover = NormSumcheckProver::new(&rs.tau0, rs.w_evals.clone(), rs.b); - let (norm_proof, ..) = - prove_sumcheck::(&mut norm_prover, transcript, |tr| { - tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND) - })?; - - // Relation sumcheck (evaluation relation) let mut relation_prover = RelationSumcheckProver::new( rs.w_evals, &rs.alpha_evals_y, @@ -133,16 +130,18 @@ where rs.num_u, rs.num_l, ); - let (relation_proof, ..) = - prove_sumcheck::(&mut relation_prover, transcript, |tr| { + + let instances: Vec<&mut dyn SumcheckInstanceProver> = + vec![&mut norm_prover, &mut relation_prover]; + let (sumcheck_proof, ..) = + prove_batched_sumcheck::(instances, transcript, |tr| { tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND) })?; Ok(HachiProof { v: quad_eq.v, y_ring, - norm_proof, - relation_proof, + sumcheck_proof, sumcheck_aux: SumcheckAux { w: rs.w }, w_commitment: rs.w_commitment, }) @@ -192,13 +191,8 @@ where transcript, )?; - // Norm sumcheck verification (range check) + // Batched sumcheck verification: norm (F_0) + relation (F_α) let norm_verifier = NormSumcheckVerifier::new(rs.tau0, rs.w_evals.clone(), rs.b); - verify_sumcheck::(&proof.norm_proof, &norm_verifier, transcript, |tr| { - tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND) - })?; - - // Relation sumcheck verification (evaluation relation) let relation_verifier = RelationSumcheckVerifier::new( rs.w_evals, rs.alpha_evals_y, @@ -211,9 +205,12 @@ where rs.num_u, rs.num_l, ); - verify_sumcheck::( - &proof.relation_proof, - &relation_verifier, + + let verifiers: Vec<&dyn crate::protocol::sumcheck::SumcheckInstanceVerifier> = + vec![&norm_verifier, &relation_verifier]; + verify_batched_sumcheck::( + &proof.sumcheck_proof, + verifiers, transcript, |tr| tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND), )?; diff --git a/src/protocol/mod.rs b/src/protocol/mod.rs index 49997845..6f4d5581 100644 --- a/src/protocol/mod.rs +++ b/src/protocol/mod.rs @@ -23,6 +23,7 @@ pub use commitment_scheme::HachiCommitmentScheme; pub use opening_point::RingOpeningPoint; pub use proof::{HachiProof, SumcheckAux}; pub use quadratic_equation::QuadraticEquation; +pub use sumcheck::batched_sumcheck::{prove_batched_sumcheck, verify_batched_sumcheck}; pub use sumcheck::{ prove_sumcheck, verify_sumcheck, CompressedUniPoly, SumcheckInstanceProver, SumcheckInstanceVerifier, SumcheckProof, UniPoly, diff --git a/src/protocol/proof.rs b/src/protocol/proof.rs index 9a8c07e3..4a119329 100644 --- a/src/protocol/proof.rs +++ b/src/protocol/proof.rs @@ -36,10 +36,8 @@ pub struct HachiProof { pub y_ring: CyclotomicRing, /// `v = D · ŵ`. pub v: Vec>, - /// Range-check (norm) sumcheck proof (§4.3, F_0). - pub norm_proof: SumcheckProof, - /// Evaluation-relation sumcheck proof (§4.3, F_α). - pub relation_proof: SumcheckProof, + /// Batched sumcheck proof (F_0 norm + F_α relation, §4.3). + pub sumcheck_proof: SumcheckProof, /// Temporary verifier auxiliary (will be removed with recursive PCS). pub sumcheck_aux: SumcheckAux, /// Commitment to the sumcheck witness `w`. @@ -52,8 +50,7 @@ impl HachiProof { self.v.serialized_size(Compress::No) + self.y_ring.serialized_size(Compress::No) + self.sumcheck_aux.w.serialized_size(Compress::No) - + self.norm_proof.serialized_size(Compress::No) - + self.relation_proof.serialized_size(Compress::No) + + self.sumcheck_proof.serialized_size(Compress::No) + self.w_commitment.serialized_size(Compress::No) } } diff --git a/src/protocol/ring_switch.rs b/src/protocol/ring_switch.rs index 9a9d19a7..cb4bc0f9 100644 --- a/src/protocol/ring_switch.rs +++ b/src/protocol/ring_switch.rs @@ -12,7 +12,7 @@ use crate::protocol::commitment::{ RingCommitmentScheme, }; use crate::protocol::quadratic_equation::QuadraticEquation; -use crate::protocol::sumcheck::eq_evals; +use crate::protocol::sumcheck::eq_poly::EqPolynomial; use crate::protocol::transcript::labels::{ ABSORB_SUMCHECK_W, CHALLENGE_RING_SWITCH, CHALLENGE_TAU0, CHALLENGE_TAU1, }; @@ -399,7 +399,7 @@ pub(crate) fn build_m_evals_x( cols: usize, tau1: &[F], ) -> Vec { - let eq_tau1 = eq_evals(tau1); + let eq_tau1 = EqPolynomial::evals(tau1); let x_len = cols.next_power_of_two(); let mut m_evals = vec![F::zero(); x_len]; for x in 0..x_len { diff --git a/src/protocol/sumcheck/batched_sumcheck.rs b/src/protocol/sumcheck/batched_sumcheck.rs new file mode 100644 index 00000000..15673987 --- /dev/null +++ b/src/protocol/sumcheck/batched_sumcheck.rs @@ -0,0 +1,258 @@ +//! Batched sumcheck protocol. +//! +//! Implements the standard technique for batching parallel sumchecks to reduce +//! verifier cost and proof size. +//! +//! For details, refer to Jim Posen's ["Perspectives on Sumcheck Batching"](https://hackmd.io/s/HyxaupAAA). +//! We do what they describe as "front-loaded" batch sumcheck. +//! +//! Adapted from Jolt's `BatchedSumcheck` implementation. + +use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, SumcheckProof, UniPoly}; +use crate::error::HachiError; +use crate::protocol::transcript::labels; +use crate::protocol::transcript::Transcript; +use crate::{CanonicalField, FieldCore}; + +fn mul_pow_2(x: E, k: usize) -> E { + let mut result = x; + for _ in 0..k { + result = result + result; + } + result +} + +fn linear_combination(polys: &[UniPoly], coeffs: &[E]) -> UniPoly { + let max_len = polys.iter().map(|p| p.coeffs.len()).max().unwrap_or(0); + let mut result = vec![E::zero(); max_len]; + for (poly, coeff) in polys.iter().zip(coeffs.iter()) { + for (i, c) in poly.coeffs.iter().enumerate() { + result[i] = result[i] + *c * *coeff; + } + } + UniPoly::from_coeffs(result) +} + +/// Produce a batched sumcheck proof for multiple instances sharing the same +/// variable space, driving the Fiat–Shamir transcript. +/// +/// This function: +/// - absorbs each instance's initial claim, +/// - samples batching coefficients (one per instance), +/// - computes a single batched round polynomial per round as a linear +/// combination of the individual round polynomials, +/// - returns a single [`SumcheckProof`] and the derived challenge vector. +/// +/// Instances with fewer rounds than the maximum are padded with constant +/// "dummy" round polynomials (the Jolt "front-loaded" approach). +/// +/// # Panics +/// +/// Panics if `instances` is empty or if 2 is not invertible in the field. +/// +/// # Errors +/// +/// Returns an error if the field inverse of 2 does not exist. +pub fn prove_batched_sumcheck( + mut instances: Vec<&mut dyn SumcheckInstanceProver>, + transcript: &mut T, + mut sample_challenge: S, +) -> Result<(SumcheckProof, Vec), HachiError> +where + F: FieldCore + CanonicalField, + T: Transcript, + E: FieldCore + CanonicalField, + S: FnMut(&mut T) -> E, +{ + assert!(!instances.is_empty()); + + let max_num_rounds = instances + .iter() + .map(|inst| inst.num_rounds()) + .max() + .unwrap(); + + // Absorb individual input claims. + for inst in instances.iter() { + let claim = inst.input_claim(); + transcript.append_serde(labels::ABSORB_SUMCHECK_CLAIM, &claim); + } + + // Sample one batching coefficient per instance. + let batching_coeffs: Vec = (0..instances.len()) + .map(|_| sample_challenge(transcript)) + .collect(); + + // To see why we may need to scale by a power of two, consider a batch of + // two sumchecks: + // claim_a = \sum_x P(x) where x \in {0, 1}^M + // claim_b = \sum_{x, y} Q(x, y) where x \in {0, 1}^M, y \in {0, 1}^N + // Then the batched sumcheck is: + // \sum_{x, y} A * P(x) + B * Q(x, y) where A and B are batching coefficients + // = A * \sum_y \sum_x P(x) + B * \sum_{x, y} Q(x, y) + // = A * \sum_y claim_a + B * claim_b + // = A * 2^N * claim_a + B * claim_b + let mut individual_claims: Vec = instances + .iter() + .map(|inst| { + let n = inst.num_rounds(); + let claim = inst.input_claim(); + mul_pow_2(claim, max_num_rounds - n) + }) + .collect(); + + let two_inv = E::from_u64(2) + .inv() + .expect("2 must be invertible in the field"); + + let mut round_polys = Vec::with_capacity(max_num_rounds); + let mut challenges = Vec::with_capacity(max_num_rounds); + + for round in 0..max_num_rounds { + let univariate_polys: Vec> = instances + .iter_mut() + .zip(individual_claims.iter()) + .map(|(inst, previous_claim)| { + let n = inst.num_rounds(); + let offset = max_num_rounds - n; + let active = round >= offset && round < offset + n; + if active { + inst.compute_round_univariate(round - offset, *previous_claim) + } else { + // Variable is "dummy" for this instance: polynomial is independent of it, + // so the round univariate is constant with H(0)=H(1)=previous_claim/2. + UniPoly::from_coeffs(vec![*previous_claim * two_inv]) + } + }) + .collect(); + + let batched_poly = linear_combination(&univariate_polys, &batching_coeffs); + + #[cfg(debug_assertions)] + { + let g0 = batched_poly.evaluate(&E::zero()); + let g1 = batched_poly.evaluate(&E::one()); + let batched_claim: E = individual_claims + .iter() + .zip(batching_coeffs.iter()) + .map(|(c, b)| *c * *b) + .fold(E::zero(), |a, v| a + v); + debug_assert!( + g0 + g1 == batched_claim, + "round {round}: H(0) + H(1) != batched claim" + ); + } + + let compressed = batched_poly.compress(); + transcript.append_serde(labels::ABSORB_SUMCHECK_ROUND, &compressed); + let r_j = sample_challenge(transcript); + challenges.push(r_j); + + // Update individual claims from each instance's own univariate. + for (claim, poly) in individual_claims.iter_mut().zip(univariate_polys.iter()) { + *claim = poly.evaluate(&r_j); + } + + // Ingest challenge into each active instance. + for inst in instances.iter_mut() { + let n = inst.num_rounds(); + let offset = max_num_rounds - n; + let active = round >= offset && round < offset + n; + if active { + inst.ingest_challenge(round - offset, r_j); + } + } + + round_polys.push(compressed); + } + + for inst in instances.iter_mut() { + inst.finalize(); + } + + Ok((SumcheckProof { round_polys }, challenges)) +} + +/// Verify a batched sumcheck proof. +/// +/// This function: +/// - absorbs each verifier instance's initial claim, +/// - re-derives the batching coefficients, +/// - computes the batched initial claim, +/// - verifies the proof against the batched claim, +/// - checks that the final output matches the batched expected output claims. +/// +/// Returns the challenge vector on success. +/// +/// # Panics +/// +/// Panics if `verifiers` is empty. +/// +/// # Errors +/// +/// Returns [`HachiError::InvalidProof`] if the batched output claim does not +/// match the expected value, or propagates per-round verification errors. +pub fn verify_batched_sumcheck( + proof: &SumcheckProof, + verifiers: Vec<&dyn SumcheckInstanceVerifier>, + transcript: &mut T, + mut sample_challenge: S, +) -> Result, HachiError> +where + F: FieldCore + CanonicalField, + T: Transcript, + E: FieldCore + CanonicalField, + S: FnMut(&mut T) -> E, +{ + assert!(!verifiers.is_empty()); + + let max_degree = verifiers.iter().map(|v| v.degree_bound()).max().unwrap(); + let max_num_rounds = verifiers.iter().map(|v| v.num_rounds()).max().unwrap(); + + // Absorb individual input claims. + for v in verifiers.iter() { + let claim = v.input_claim(); + transcript.append_serde(labels::ABSORB_SUMCHECK_CLAIM, &claim); + } + + // Re-derive batching coefficients. + let batching_coeffs: Vec = (0..verifiers.len()) + .map(|_| sample_challenge(transcript)) + .collect(); + + // Compute the combined initial claim with power-of-two scaling. + let batched_claim: E = verifiers + .iter() + .zip(batching_coeffs.iter()) + .map(|(v, coeff)| { + let n = v.num_rounds(); + let claim = v.input_claim(); + mul_pow_2(claim, max_num_rounds - n) * *coeff + }) + .fold(E::zero(), |a, v| a + v); + + let (output_claim, r_sumcheck) = proof.verify::( + batched_claim, + max_num_rounds, + max_degree, + transcript, + &mut sample_challenge, + )?; + + // Compute the expected batched output claim from each verifier instance. + let expected_output_claim: E = verifiers + .iter() + .zip(batching_coeffs.iter()) + .map(|(v, coeff)| { + let offset = max_num_rounds - v.num_rounds(); + let r_slice = &r_sumcheck[offset..offset + v.num_rounds()]; + v.expected_output_claim(r_slice) * *coeff + }) + .fold(E::zero(), |a, v| a + v); + + if output_claim != expected_output_claim { + return Err(HachiError::InvalidProof); + } + + Ok(r_sumcheck) +} diff --git a/src/protocol/sumcheck/eq_poly.rs b/src/protocol/sumcheck/eq_poly.rs new file mode 100644 index 00000000..1b562cd0 --- /dev/null +++ b/src/protocol/sumcheck/eq_poly.rs @@ -0,0 +1,229 @@ +//! Utilities for the equality polynomial `eq(x, y) = Πᵢ (xᵢ yᵢ + (1 − xᵢ)(1 − yᵢ))`. +//! +//! The equality polynomial evaluates to 1 when `x = y` (over the boolean hypercube) +//! and 0 otherwise. Its multilinear extension (MLE) is used throughout sumcheck +//! protocols. +//! +//! Adapted from Jolt's `EqPolynomial` implementation. +//! +//! ## Bit / index order: Little-endian +//! +//! The evaluation tables produced by this module use **little-endian** bit order: +//! entry `b` (as an integer index) corresponds to the boolean vector where +//! bit `k` of `b` equals `x[k]`. In other words, `r[0]` corresponds to the +//! **least-significant bit** (bit 0) and `r[n-1]` to the MSB. + +use crate::FieldCore; +use std::marker::PhantomData; + +/// Utilities for the equality polynomial `eq(x, y) = Πᵢ (xᵢ yᵢ + (1 − xᵢ)(1 − yᵢ))`. +pub struct EqPolynomial(PhantomData); + +impl EqPolynomial { + /// Compute the MLE of the equality polynomial at two points: + /// `eq(x, y) = Πᵢ (xᵢ yᵢ + (1 − xᵢ)(1 − yᵢ))`. + /// + /// # Panics + /// + /// Panics if `x.len() != y.len()`. + pub fn mle(x: &[E], y: &[E]) -> E { + assert_eq!(x.len(), y.len()); + x.iter() + .zip(y.iter()) + .map(|(&x_i, &y_i)| x_i * y_i + (E::one() - x_i) * (E::one() - y_i)) + .fold(E::one(), |acc, v| acc * v) + } + + /// Compute the zero selector: `eq(r, 0) = Πᵢ (1 − rᵢ)`. + pub fn zero_selector(r: &[E]) -> E { + r.iter().fold(E::one(), |acc, &r_i| acc * (E::one() - r_i)) + } + + /// Compute the full evaluation table `{ eq(r, x) : x ∈ {0,1}^n }`. + /// + /// Uses **little-endian** bit order: entry `b` has bit `k` of `b` + /// corresponding to `r[k]`. + /// + /// For a scaled table, use [`Self::evals_with_scaling`]. + pub fn evals(r: &[E]) -> Vec { + Self::evals_with_scaling(r, None) + } + + /// Compute the full evaluation table with optional scaling: + /// `scaling_factor · eq(r, x)` for all `x ∈ {0,1}^n`. + /// + /// Uses the same **little-endian** index order as [`Self::evals`]. + /// If `scaling_factor` is `None`, defaults to 1 (no scaling). + pub fn evals_with_scaling(r: &[E], scaling_factor: Option) -> Vec { + #[cfg(feature = "parallel")] + { + const PARALLEL_THRESHOLD: usize = 16; + if r.len() > PARALLEL_THRESHOLD { + return Self::evals_parallel(r, scaling_factor); + } + } + Self::evals_serial(r, scaling_factor) + } + + /// Serial (single-threaded) version of [`Self::evals_with_scaling`]. + /// + /// Uses **little-endian** index order. + pub fn evals_serial(r: &[E], scaling_factor: Option) -> Vec { + let size = 1usize << r.len(); + let mut evals = vec![E::zero(); size]; + evals[0] = scaling_factor.unwrap_or(E::one()); + let mut len = 1usize; + for &t in r.iter().rev() { + let one_minus_t = E::one() - t; + for j in (0..len).rev() { + evals[2 * j + 1] = evals[j] * t; + evals[2 * j] = evals[j] * one_minus_t; + } + len *= 2; + } + evals + } + + /// Compute eq evaluations and cache intermediate tables. + /// + /// Returns `result` where `result[j]` contains evaluations for the prefix + /// `r[..j]`: `result[j][x] = eq(r[..j], x)` for `x ∈ {0,1}^j`. + /// + /// So `result[0] = [1]`, `result[1]` has 2 entries, ..., and `result[n]` + /// equals [`Self::evals(r)`]. + pub fn evals_cached(r: &[E]) -> Vec> { + Self::evals_cached_with_scaling(r, None) + } + + /// Like [`Self::evals_cached`], but with optional scaling. + pub fn evals_cached_with_scaling(r: &[E], scaling_factor: Option) -> Vec> { + let mut result: Vec> = (0..r.len() + 1).map(|i| vec![E::zero(); 1 << i]).collect(); + result[0][0] = scaling_factor.unwrap_or(E::one()); + for j in 0..r.len() { + let idx = r.len() - 1 - j; + let t = r[idx]; + let one_minus_t = E::one() - t; + let prev_len = 1 << j; + for i in (0..prev_len).rev() { + result[j + 1][2 * i + 1] = result[j][i] * t; + result[j + 1][2 * i] = result[j][i] * one_minus_t; + } + } + result + } + + /// Parallel version of [`Self::evals_with_scaling`]. + /// + /// Uses rayon to compute the largest layers of the DP tree in parallel. + /// Uses the same **little-endian** index order as [`Self::evals`]. + #[cfg(feature = "parallel")] + pub fn evals_parallel(r: &[E], scaling_factor: Option) -> Vec { + use rayon::prelude::*; + + let final_size = 1usize << r.len(); + let mut evals = vec![E::zero(); final_size]; + evals[0] = scaling_factor.unwrap_or(E::one()); + let mut size = 1; + + // Forward iteration (r[0] first) produces little-endian ordering. + for &r_i in r.iter() { + let (evals_left, evals_right) = evals.split_at_mut(size); + let (evals_right, _) = evals_right.split_at_mut(size); + + evals_left + .par_iter_mut() + .zip(evals_right.par_iter_mut()) + .for_each(|(x, y)| { + *y = *x * r_i; + *x = *x - *y; + }); + + size *= 2; + } + + evals + } +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::algebra::Fp64; + use crate::{CanonicalField, FieldSampling}; + use rand::rngs::StdRng; + use rand::SeedableRng; + + type F = Fp64<4294967197>; + + #[test] + fn evals_matches_mle_pointwise() { + let mut rng = StdRng::seed_from_u64(0xEE); + for n in 1..8 { + let r: Vec = (0..n).map(|_| F::sample(&mut rng)).collect(); + let table = EqPolynomial::evals(&r); + assert_eq!(table.len(), 1 << n); + for (idx, &val) in table.iter().enumerate() { + let bits: Vec = (0..n) + .map(|k| { + if (idx >> k) & 1 == 1 { + F::one() + } else { + F::zero() + } + }) + .collect(); + let expected = EqPolynomial::mle(&r, &bits); + assert_eq!(val, expected, "n={n} idx={idx}"); + } + } + } + + #[test] + fn evals_with_scaling_scales_uniformly() { + let mut rng = StdRng::seed_from_u64(0xAB); + let r: Vec = (0..5).map(|_| F::sample(&mut rng)).collect(); + let scale = F::from_u64(7); + let unscaled = EqPolynomial::evals(&r); + let scaled = EqPolynomial::evals_with_scaling(&r, Some(scale)); + for (u, s) in unscaled.iter().zip(scaled.iter()) { + assert_eq!(*s, *u * scale); + } + } + + #[test] + fn evals_cached_last_matches_evals() { + let mut rng = StdRng::seed_from_u64(0xCD); + for n in 1..8 { + let r: Vec = (0..n).map(|_| F::sample(&mut rng)).collect(); + let table = EqPolynomial::evals(&r); + let cached = EqPolynomial::evals_cached(&r); + assert_eq!(cached.len(), n + 1); + assert_eq!(cached[0], vec![F::one()]); + assert_eq!(*cached.last().unwrap(), table); + } + } + + #[test] + fn zero_selector_matches_mle_at_origin() { + let mut rng = StdRng::seed_from_u64(0x00); + for n in 1..8 { + let r: Vec = (0..n).map(|_| F::sample(&mut rng)).collect(); + let zeros = vec![F::zero(); n]; + let expected = EqPolynomial::mle(&r, &zeros); + let actual = EqPolynomial::zero_selector(&r); + assert_eq!(actual, expected, "n={n}"); + } + } + + #[cfg(feature = "parallel")] + #[test] + fn evals_parallel_matches_serial() { + let mut rng = StdRng::seed_from_u64(0xFF); + for n in 1..20 { + let r: Vec = (0..n).map(|_| F::sample(&mut rng)).collect(); + let serial = EqPolynomial::evals_serial(&r, None); + let parallel = EqPolynomial::evals_parallel(&r, None); + assert_eq!(serial, parallel, "n={n}"); + } + } +} diff --git a/src/protocol/sumcheck/mod.rs b/src/protocol/sumcheck/mod.rs index 2bba5ca0..9788b60e 100644 --- a/src/protocol/sumcheck/mod.rs +++ b/src/protocol/sumcheck/mod.rs @@ -19,8 +19,11 @@ //! duplicates the essential sumcheck data types and transcript-driving logic as a //! pragmatic workaround. +pub mod batched_sumcheck; +pub mod eq_poly; pub mod norm_sumcheck; pub mod relation_sumcheck; +pub mod split_eq; use crate::error::HachiError; use crate::primitives::serialization::{ @@ -572,35 +575,6 @@ where Ok(challenges) } -/// Build the full eq polynomial evaluation table. -/// -/// Returns a vector of size `2^{tau.len()}` where entry `b` (interpreted as a -/// little-endian bit string, i.e. bit `k` of `b` corresponds to `τ[k]`) equals -/// `ẽq(τ, b) = Π_i (τ_i·b_i + (1−τ_i)(1−b_i))`. -pub fn eq_evals(tau: &[E]) -> Vec { - let size = 1usize << tau.len(); - let mut evals = vec![E::zero(); size]; - evals[0] = E::one(); - let mut len = 1usize; - for &t in tau.iter().rev() { - let one_minus_t = E::one() - t; - for j in (0..len).rev() { - evals[2 * j + 1] = evals[j] * t; - evals[2 * j] = evals[j] * one_minus_t; - } - len *= 2; - } - evals -} - -/// Evaluate ẽq(τ, r) at a single point. -pub fn eq_eval(tau: &[E], point: &[E]) -> E { - debug_assert_eq!(tau.len(), point.len()); - tau.iter().zip(point).fold(E::one(), |acc, (&t, &r)| { - acc * (t * r + (E::one() - t) * (E::one() - r)) - }) -} - /// Evaluate the range-check polynomial `w · Π_{k=1}^{b−1} (w − k)(w + k)`. /// /// This polynomial vanishes exactly when `w ∈ {−(b−1), …, b−1}`. diff --git a/src/protocol/sumcheck/norm_sumcheck.rs b/src/protocol/sumcheck/norm_sumcheck.rs index e1b72490..3fd5aa83 100644 --- a/src/protocol/sumcheck/norm_sumcheck.rs +++ b/src/protocol/sumcheck/norm_sumcheck.rs @@ -5,16 +5,21 @@ //! Proves that all entries of w̃ lie in {−(b−1), …, b−1}; the sum over the //! boolean hypercube should equal zero when the range constraint holds. -use super::{eq_eval, eq_evals, fold_evals, multilinear_eval, range_check_eval}; +use super::eq_poly::EqPolynomial; +use super::split_eq::GruenSplitEq; +use super::{fold_evals, multilinear_eval, range_check_eval}; use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, UniPoly}; use crate::{CanonicalField, FieldCore}; /// Prover for `F_{0,τ₀}(x,y) = ẽq(τ₀,(x,y)) · w̃(x,y) · range_check(w̃(x,y), b)`. /// -/// Stores `eq` and `w` evaluation tables separately so the composite can be -/// evaluated at the `2b + 1` points needed per round (degree `2b`). -pub struct NormSumcheckProver { - eq_table: Vec, +/// Uses the Gruen/Dao-Thaler optimization: the eq polynomial is factored into +/// a running scalar and split tables instead of being stored as a full table +/// and folded each round. The round polynomial is computed as `l(X) · q(X)` +/// where `l(X)` is the linear eq factor and `q(X)` is the inner sum without +/// the current-variable eq contribution. +pub struct NormSumcheckProver { + split_eq: GruenSplitEq, w_table: Vec, num_vars: usize, b: usize, @@ -30,7 +35,7 @@ impl NormSumcheckProver { let num_vars = tau.len(); assert_eq!(w_evals.len(), 1 << num_vars); Self { - eq_table: eq_evals(tau), + split_eq: GruenSplitEq::new(tau), w_table: w_evals, num_vars, b, @@ -52,30 +57,36 @@ impl SumcheckInstanceProver for NormSumcheckPr } fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { - let half = self.eq_table.len() / 2; - let degree = 2 * self.b; - let num_points = degree + 1; - let mut round_evals = vec![E::zero(); num_points]; + let half = self.w_table.len() / 2; + let degree_q = 2 * self.b - 1; + let num_points_q = degree_q + 1; + let mut q_evals = vec![E::zero(); num_points_q]; + + let (e_first, e_second) = self.split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + let first_bits = num_first.trailing_zeros(); for j in 0..half { - let eq_0 = self.eq_table[2 * j]; - let eq_1 = self.eq_table[2 * j + 1]; + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = self.w_table[2 * j]; let w_1 = self.w_table[2 * j + 1]; - for (t, eval) in round_evals.iter_mut().enumerate() { + for (t, eval) in q_evals.iter_mut().enumerate() { let t_e = E::from_u64(t as u64); - let eq_t = eq_0 + t_e * (eq_1 - eq_0); let w_t = w_0 + t_e * (w_1 - w_0); - *eval = *eval + eq_t * range_check_eval(w_t, self.b); + *eval = *eval + eq_rem * range_check_eval(w_t, self.b); } } - UniPoly::from_evals(&round_evals) + let q_poly = UniPoly::from_evals(&q_evals); + self.split_eq.gruen_mul(&q_poly) } fn ingest_challenge(&mut self, _round: usize, r: E) { - self.eq_table = fold_evals(&self.eq_table, r); + self.split_eq.bind(r); self.w_table = fold_evals(&self.w_table, r); } } @@ -120,7 +131,7 @@ impl SumcheckInstanceVerifier for NormSumcheck } fn expected_output_claim(&self, challenges: &[E]) -> E { - let eq_val = eq_eval(&self.tau, challenges); + let eq_val = EqPolynomial::mle(&self.tau, challenges); let w_val = multilinear_eval(&self.w_evals, challenges); eq_val * range_check_eval(w_val, self.b) } @@ -133,7 +144,7 @@ mod tests { use crate::algebra::Fp64; use crate::primitives::multilinear_evals::DenseMultilinearEvals; use crate::protocol::ring_switch::build_w_coeffs; - use crate::protocol::sumcheck::eq_evals; + use crate::protocol::sumcheck::eq_poly::EqPolynomial; use crate::protocol::transcript::labels; use crate::protocol::{ prove_sumcheck, verify_sumcheck, Blake2bTranscript, CommitmentConfig, CommitmentScheme, @@ -165,7 +176,7 @@ mod tests { let tau: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); let b = 1usize << DefaultCommitmentConfig::LOG_BASIS; - let eq_table = eq_evals(&tau); + let eq_table = EqPolynomial::evals(&tau); let _claim: F = (0..w_evals.len()) .map(|i| eq_table[i] * range_check_eval(w_evals[i], b)) .fold(F::zero(), |a, v| a + v); @@ -178,7 +189,7 @@ mod tests { }) .unwrap(); - let oracle = eq_eval(&tau, &prover_challenges) + let oracle = EqPolynomial::mle(&tau, &prover_challenges) * range_check_eval(multilinear_eval(&w_evals, &prover_challenges), b); assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); @@ -225,7 +236,7 @@ mod tests { .collect(); let b = 1usize << DefaultCommitmentConfig::LOG_BASIS; - let eq_table = eq_evals(&tau); + let eq_table = EqPolynomial::evals(&tau); let _claim: F = (0..w_evals.len()) .map(|i| eq_table[i] * range_check_eval(w_evals[i], b)) .fold(F::zero(), |a, v| a + v); @@ -238,7 +249,7 @@ mod tests { }) .unwrap(); - let oracle = eq_eval(&tau, &prover_challenges) + let oracle = EqPolynomial::mle(&tau, &prover_challenges) * range_check_eval(multilinear_eval(&w_evals, &prover_challenges), b); assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); diff --git a/src/protocol/sumcheck/relation_sumcheck.rs b/src/protocol/sumcheck/relation_sumcheck.rs index 12de5a7f..44e3c3c2 100644 --- a/src/protocol/sumcheck/relation_sumcheck.rs +++ b/src/protocol/sumcheck/relation_sumcheck.rs @@ -5,7 +5,8 @@ //! //! Proves the evaluation relation; sum equals `a = Σ_i ẽq(τ₁,i) · y_i(α)`. -use super::{eq_evals, fold_evals, multilinear_eval}; +use super::eq_poly::EqPolynomial; +use super::{fold_evals, multilinear_eval}; use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, UniPoly}; use crate::algebra::ring::CyclotomicRing; use crate::protocol::ring_switch::eval_ring_at; @@ -184,7 +185,7 @@ impl SumcheckInstanceVerifier .map(|r| eval_ring_at(r, &self.alpha)) .collect(); - let eq_tau = eq_evals(&self.tau); + let eq_tau = EqPolynomial::evals(&self.tau); let mut acc = F::zero(); for (i, eq_i) in eq_tau.iter().enumerate() { let y_i = if i < y_a.len() { y_a[i] } else { F::zero() }; @@ -208,7 +209,7 @@ mod tests { use crate::algebra::Fp64; use crate::primitives::multilinear_evals::DenseMultilinearEvals; use crate::protocol::commitment_scheme::rederive_alpha_and_m_a; - use crate::protocol::sumcheck::eq_evals; + use crate::protocol::sumcheck::eq_poly::EqPolynomial; use crate::protocol::transcript::labels; use crate::protocol::{ prove_sumcheck, verify_sumcheck, Blake2bTranscript, CommitmentConfig, CommitmentScheme, @@ -276,7 +277,7 @@ mod tests { let num_i = rows.next_power_of_two().trailing_zeros() as usize; let tau1: Vec = (0..num_i).map(|i| F::from_u64((i + 5) as u64)).collect(); - let eq_tau1 = eq_evals(&tau1); + let eq_tau1 = EqPolynomial::evals(&tau1); let mut m_evals_x = vec![F::zero(); x_len]; for x in 0..x_len { diff --git a/src/protocol/sumcheck/split_eq.rs b/src/protocol/sumcheck/split_eq.rs new file mode 100644 index 00000000..1f10dbfe --- /dev/null +++ b/src/protocol/sumcheck/split_eq.rs @@ -0,0 +1,213 @@ +//! Gruen/Dao-Thaler split equality polynomial for efficient sumcheck. +//! +//! Factors `eq(τ, x)` into a running scalar, a linear factor for the current +//! variable, and precomputed split tables for the remaining variables. This +//! avoids maintaining and folding a full-size eq table during sumcheck. +//! +//! For details, see . +//! +//! Adapted from Jolt's `GruenSplitEqPolynomial`. +//! +//! ## Variable Layout (forward binding, little-endian) +//! +//! ```text +//! τ = [τ_current, τ_first_half, τ_second_half] +//! 1 var m vars (n-1-m) vars +//! ``` +//! +//! where `m = (n-1) / 2` and `n = τ.len()`. +//! +//! After binding `τ_current`, the next variable comes from `τ_first_half`, +//! then from `τ_second_half`. Suffix-cached eq tables for each half enable +//! O(1) pops per round instead of an O(2^n) fold. + +use super::eq_poly::EqPolynomial; +use super::UniPoly; +use crate::{CanonicalField, FieldCore}; + +/// Split equality polynomial with Gruen scalar accumulation. +/// +/// Instead of storing and folding a full eq table each round, this struct +/// maintains: +/// - `current_scalar`: accumulated `eq(τ_bound, r_bound)` from already-bound +/// variables +/// - `E_first` / `E_second`: suffix-cached eq tables for two halves of the +/// remaining (unbound, non-current) variables +/// +/// The eq contribution for a pair index `j` in the inner sum is: +/// ```text +/// eq_remaining(j) = E_first[j_low] · E_second[j_high] +/// ``` +/// and the full round polynomial is `l(X) · q(X)` where `l(X)` is the linear +/// eq factor for the current variable. +#[allow(non_snake_case)] +pub struct GruenSplitEq { + tau: Vec, + current_round: usize, + current_scalar: E, + /// Suffix-cached eq tables for the first half of remaining variables. + /// `E_first[k]` = `eq(τ[split-k..split], ·)` with `2^k` entries. + /// Invariant: never empty; `E_first[0] = [1]`. + E_first: Vec>, + /// Suffix-cached eq tables for the second half of remaining variables. + /// `E_second[k]` = `eq(τ[n-k..n], ·)` with `2^k` entries. + /// Invariant: never empty; `E_second[0] = [1]`. + E_second: Vec>, +} + +#[allow(non_snake_case)] +impl GruenSplitEq { + /// Create a new split-eq from the full challenge vector `τ`. + /// + /// Precomputes suffix-cached eq tables for two halves of `τ[1..n]`. + /// + /// # Panics + /// + /// Panics if `tau` is empty. + pub fn new(tau: &[E]) -> Self { + let n = tau.len(); + assert!(n >= 1); + let m = (n - 1) / 2; + let split = 1 + m; + let first_half = &tau[1..split]; + let second_half = &tau[split..n]; + let E_first = EqPolynomial::evals_cached(first_half); + let E_second = EqPolynomial::evals_cached(second_half); + Self { + tau: tau.to_vec(), + current_round: 0, + current_scalar: E::one(), + E_first, + E_second, + } + } + + /// The accumulated scalar `Π_{k < current_round} eq(τ[k], r[k])`. + pub fn current_scalar(&self) -> E { + self.current_scalar + } + + /// The τ value for the variable about to be bound. + pub fn current_tau(&self) -> E { + self.tau[self.current_round] + } + + /// Return the current top-level split-eq tables `(E_first, E_second)`. + /// + /// For a pair index `j` in the inner sum, the eq factor for the + /// remaining (non-current) variables is: + /// ```text + /// eq_remaining(j) = E_first[j & (E_first.len()-1)] + /// · E_second[j >> E_first.len().trailing_zeros()] + /// ``` + /// + /// # Panics + /// + /// Panics if either `E_first` or `E_second` is empty (invariant violation). + pub fn remaining_eq_tables(&self) -> (&[E], &[E]) { + ( + self.E_first.last().expect("E_first is never empty"), + self.E_second.last().expect("E_second is never empty"), + ) + } + + /// Bind the current variable to challenge `r`, advancing to the next round. + /// + /// Updates `current_scalar` with `eq(τ[current_round], r)` and pops the + /// appropriate split table level. + pub fn bind(&mut self, r: E) { + let tau_k = self.tau[self.current_round]; + self.current_scalar = + self.current_scalar * (tau_k * r + (E::one() - tau_k) * (E::one() - r)); + self.current_round += 1; + if self.E_first.len() > 1 { + self.E_first.pop(); + } else if self.E_second.len() > 1 { + self.E_second.pop(); + } + } + + /// Compute the round polynomial `s(X) = l(X) · q(X)` from the inner + /// polynomial `q` (given as evaluations at integer points `0, 1, ..., d`). + /// + /// `l(X) = current_scalar · eq(τ_current, X)` is the linear eq factor + /// for the current variable. The result has degree `d + 1`. + pub fn gruen_mul(&self, q_poly: &UniPoly) -> UniPoly { + let tau_k = self.current_tau(); + let scalar = self.current_scalar(); + let l_0 = scalar * (E::one() - tau_k); + let l_1 = scalar * tau_k; + let slope = l_1 - l_0; + let mut coeffs = vec![E::zero(); q_poly.coeffs.len() + 1]; + for (i, &c) in q_poly.coeffs.iter().enumerate() { + coeffs[i] = coeffs[i] + c * l_0; + coeffs[i + 1] = coeffs[i + 1] + c * slope; + } + UniPoly::from_coeffs(coeffs) + } +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::algebra::Fp64; + use crate::protocol::sumcheck::fold_evals; + use crate::FieldSampling; + use rand::rngs::StdRng; + use rand::SeedableRng; + + type F = Fp64<4294967197>; + + #[test] + fn gruen_eq_matches_full_eq_table() { + let mut rng = StdRng::seed_from_u64(0xBB); + for n in 1..10 { + let tau: Vec = (0..n).map(|_| F::sample(&mut rng)).collect(); + let mut full_eq = EqPolynomial::evals(&tau); + let mut split_eq = GruenSplitEq::new(&tau); + + for _round in 0..n { + let half = full_eq.len() / 2; + let (e_first, e_second) = split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + + for j in 0..half { + let j_low = j & (num_first - 1); + let j_high = j >> num_first.trailing_zeros(); + let eq_rem = e_first[j_low] * e_second[j_high]; + + let tau_k = split_eq.current_tau(); + let scalar = split_eq.current_scalar(); + let eq_0 = scalar * (F::one() - tau_k) * eq_rem; + let eq_1 = scalar * tau_k * eq_rem; + + assert_eq!(eq_0, full_eq[2 * j], "n={n} round={_round} j={j} eq_0"); + assert_eq!(eq_1, full_eq[2 * j + 1], "n={n} round={_round} j={j} eq_1"); + } + + let r = F::sample(&mut rng); + full_eq = fold_evals(&full_eq, r); + split_eq.bind(r); + } + } + } + + #[test] + fn gruen_mul_matches_direct_product() { + let mut rng = StdRng::seed_from_u64(0xCC); + let tau: Vec = (0..5).map(|_| F::sample(&mut rng)).collect(); + let split_eq = GruenSplitEq::new(&tau); + + let q = UniPoly::from_coeffs(vec![F::from_u64(3), F::from_u64(7), F::from_u64(2)]); + let s = split_eq.gruen_mul(&q); + + let tau_k = split_eq.current_tau(); + let scalar = split_eq.current_scalar(); + for t in 0..10u64 { + let x = F::from_u64(t); + let l_x = scalar * (tau_k * x + (F::one() - tau_k) * (F::one() - x)); + let q_x = q.evaluate(&x); + assert_eq!(s.evaluate(&x), l_x * q_x, "t={t}"); + } + } +} diff --git a/src/protocol/transcript/labels.rs b/src/protocol/transcript/labels.rs index f5d93952..0cfa6d4a 100644 --- a/src/protocol/transcript/labels.rs +++ b/src/protocol/transcript/labels.rs @@ -27,6 +27,8 @@ pub const ABSORB_SUMCHECK_CLAIM: &[u8] = b"hachi/absorb/sumcheck-claim"; pub const ABSORB_SUMCHECK_ROUND: &[u8] = b"hachi/absorb/sumcheck-round"; /// Challenge sampled per sumcheck round (paper §4.3). pub const CHALLENGE_SUMCHECK_ROUND: &[u8] = b"hachi/challenge/sumcheck-round"; +/// Challenge for batched sumcheck coefficient sampling. +pub const CHALLENGE_SUMCHECK_BATCH: &[u8] = b"hachi/challenge/sumcheck-batch"; /// Absorb recursion/stop-condition message payloads (paper §4.5). pub const ABSORB_STOP_CONDITION: &[u8] = b"hachi/absorb/stop-condition"; /// Challenge sampled for recursion stop-condition checks (paper §4.5). @@ -58,6 +60,7 @@ pub fn all_labels() -> &'static [&'static [u8]] { ABSORB_SUMCHECK_CLAIM, ABSORB_SUMCHECK_ROUND, CHALLENGE_SUMCHECK_ROUND, + CHALLENGE_SUMCHECK_BATCH, ABSORB_STOP_CONDITION, CHALLENGE_STOP_CONDITION, ABSORB_PROVER_V, diff --git a/tests/hachi_sumcheck.rs b/tests/hachi_sumcheck.rs index 69f16bf4..86b843f0 100644 --- a/tests/hachi_sumcheck.rs +++ b/tests/hachi_sumcheck.rs @@ -2,11 +2,12 @@ use hachi_pcs::algebra::ring::CyclotomicRing; use hachi_pcs::algebra::Fp64; +use hachi_pcs::protocol::sumcheck::eq_poly::EqPolynomial; use hachi_pcs::protocol::sumcheck::norm_sumcheck::{NormSumcheckProver, NormSumcheckVerifier}; use hachi_pcs::protocol::sumcheck::relation_sumcheck::{ RelationSumcheckProver, RelationSumcheckVerifier, }; -use hachi_pcs::protocol::sumcheck::{eq_eval, eq_evals, multilinear_eval, range_check_eval}; +use hachi_pcs::protocol::sumcheck::{multilinear_eval, range_check_eval}; use hachi_pcs::protocol::transcript::labels; use hachi_pcs::protocol::{prove_sumcheck, verify_sumcheck, Blake2bTranscript, Transcript}; use hachi_pcs::{CanonicalField, FieldCore, FieldSampling}; @@ -36,7 +37,7 @@ fn run_f0_e2e(num_u: usize, num_l: usize, b: usize) { let prove_time = t0.elapsed(); // Sanity: prover's final claim matches oracle evaluation. - let oracle = eq_eval(&tau0, &prover_challenges) + let oracle = EqPolynomial::mle(&tau0, &prover_challenges) * range_check_eval(multilinear_eval(&w_evals, &prover_challenges), b); assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); @@ -91,7 +92,7 @@ fn run_f_alpha_e2e(num_u: usize, num_i: usize) { let tau1: Vec = (0..num_i).map(|_| F::sample(&mut rng)).collect(); // Compute m(x) = Σ_i ẽq(τ₁, i) · M̃_α(i, x) - let eq_tau1 = eq_evals(&tau1); + let eq_tau1 = EqPolynomial::evals(&tau1); let num_x = 1usize << num_u; let m_evals_x: Vec = (0..num_x) .map(|x_idx| { From 36455aba7c1025f3588afa468bf72acbcfb4124a Mon Sep 17 00:00:00 2001 From: Quang Dao Date: Mon, 2 Mar 2026 10:11:55 -0800 Subject: [PATCH 3/5] Parallelism, CRT-NTT, extension fields, streaming commitment, fused sumcheck (#3) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * Add rayon parallelism behind `parallel` feature flag (enabled by default) - New src/parallel.rs with cfg_iter!/cfg_into_iter!/cfg_chunks! macros that dispatch to rayon parallel iterators when `parallel` is enabled - Parallelize protocol hot paths: ring polynomial division, w_evals construction, M_alpha evaluation, ring vector evaluation, packed ring poly evaluation, coefficients-to-ring reduction, quadratic equation folding, and sumcheck round polynomial computation - All 174 tests pass with and without the parallel feature Made-with: Cursor * Add e2e benchmark and make HachiCommitmentScheme generic over config - Make HachiCommitmentScheme generic over so different configs (and thus num_vars) can be used without code duplication. - Remove hardcoded DefaultCommitmentConfig::D from ring_switch.rs; WCommitmentConfig and commit_w now flow D generically. - Add benches/hachi_e2e.rs with configs sweeping nv=10,14,18,20. Made-with: Cursor * Refactor CRT-NTT backend: generalize over PrimeWidth, add Q128 support Make NTT primitives (NttPrime, NttTwiddles, MontCoeff, CyclotomicCrtNtt) generic over PrimeWidth (i16/i32) instead of hardcoding i16. Replace the monolithic QData struct with separate GarnerData and per-prime NttPrime arrays. Add Q128 parameter set (5 × i32 primes, D ≤ 1024) alongside the existing Q32 set. Simplify ScalarBackend by removing the const-generic limb count from to_ring_with_backend. Made-with: Cursor * Add extension field arithmetic and refactor sumcheck trait bounds Split CanonicalField into FromSmallInt (from_{u,i}{8,16,32,64} for all fields) and CanonicalField (u128 repr, base fields only). Implement FromSmallInt, Eq, Debug for Fp2/Fp4. Add ExtField trait with EXT_DEGREE and from_base_slice. Optimize extension field arithmetic: Karatsuba multiplication for Fp2 and Fp4 (3 base muls instead of 4), specialized squaring (2 base muls for Fp2), non-residue IS_NEG_ONE specialization. Add concrete configs (TwoNr, NegOneNr, UnitNr) and type aliases Ext2, Ext4. Add transpose-based packed extension fields (PackedFp2, PackedFp4) for SIMD acceleration, following Plonky3's approach. Relax sumcheck bounds from E: CanonicalField to E: FromSmallInt (or E: FieldCore where spurious). Add sample_ext_challenge transcript helper. Includes tests for extension field sumcheck execution. Made-with: Cursor * Fix CRT+NTT correctness and optimize negacyclic NTT pipeline Correctness fixes: - Rewrite negacyclic NTT as twist + cyclic DIF/DIT pair (no bit-reversal permutation), correctly diagonalizing X^D+1. - Center coefficient→CRT mapping and Garner reconstruction to handle negacyclic sign wrapping consistently. - Fix i32 Montgomery csubp/caddp overflow via branchless i64 widening. - Fix q128 centering overflow in balanced_decompose_pow2 (avoid casting q≈2^128 into i128). - Remove dense-protocol schoolbook fallback; all mat-vec now routes through CRT+NTT. Performance optimizations: - Precompute per-stage twiddle roots in NttTwiddles (eliminate runtime pow_mod per butterfly stage). - Forward DIF butterfly skips reduce_range before Montgomery mul (safe because mul absorbs unreduced input). - Hoist centered-coefficient computation out of per-prime loop in from_ring. - Add fused pointwise multiply-accumulate for mat-vec inner loop. - Add batched mat_vec_mul_crt_ntt_many that precomputes matrix NTT once and reuses across many input vectors. - Wire commit_ring_blocks to batched A*s path. Benchmarks (D=64, Q32/K=6): - Single-prime forward+inverse NTT: 1.14µs → 0.43µs (2.7x) - CRT round-trip: 10.7µs → 6.3µs (1.7x) - Commit nv10: ~70% faster, nv20: ~47% faster Made-with: Cursor * Cache CRT+NTT matrix representations in setup to avoid repeated conversion The dense mat-vec paths (commit_ring_blocks, commit_onehot B-mul, compute_v) previously converted coefficient-form matrices to CRT+NTT on every call. Now the setup eagerly converts A, B, D into an NttMatrixCache and all dense operations use the pre-converted form. Coefficient-form matrices are retained for the onehot inner-product path and ring-switch/generate_m. Made-with: Cursor * Remove dead code (HachiRoutines, domains/, redundant trait methods) and extract shared field utilities - Delete unused HachiRoutines trait and dead algebra/domains/ module - Remove redundant FieldCore::add/sub/mul and Module::add/neg (covered by ops traits) - Extract is_pow2_u64, log2_pow2_u64, mul64_wide into fields/util.rs to deduplicate Made-with: Cursor * Unify Blake2b and Keccak transcript backends into generic HashTranscript Replace separate blake2b.rs and keccak.rs with a single generic HashTranscript parameterized by hash function. Blake2bTranscript and KeccakTranscript are now type aliases. Made-with: Cursor * Fix sumcheck degree bug, split types, in-place fold, CommitWitness, rename configs, add soundness test - Fix CompressedUniPoly::degree() off-by-one that could let malformed proofs pass - Split sumcheck/mod.rs: extract types into types.rs, relocate multilinear_eval and fold_evals to algebra/poly.rs - Replace allocating fold_evals with in-place fold_evals_in_place - Add debug_assert guards to multilinear_eval and fold_evals_in_place - Introduce CommitWitness struct to replace error-prone 3-tuple returns - Rename DefaultCommitmentConfig to SmallTestCommitmentConfig, add ProductionFp128CommitmentConfig - Add verify_rejects_wrong_opening negative test for verifier soundness Made-with: Cursor * fix(test): resolve clippy needless_range_loop in algebra tests Use iter().enumerate() for schoolbook convolution loops and array::from_fn for pointwise NTT operations. Made-with: Cursor * Refactor commitment setup to runtime layout and staged artifacts. This removes compile-time commitment shape locks, derives beta from runtime layout, and threads layout-aware setup through commit/prove/verify with setup serialization roundtrip coverage. Made-with: Cursor * Soundness hardening: panic-free verifier, Fiat-Shamir binding, NTT overflow fix - Verifier path never panics; all errors return HachiError - Bind commitment, opening point, and y_ring in Fiat-Shamir transcript - Fix i16 csubp/caddp overflow by widening to i32 - multilinear_eval returns Result with dimension checks - build_w_evals validates w.len() is a multiple of d - UniPoly::degree uses saturating_sub instead of expect - Serialize usize as u64 for 32/64-bit portability - Fix from_i64(i64::MIN) via unsigned_abs - Remove Transcript::reset from public trait (move to inherent) - Add batched_sumcheck verifier empty-input guard Made-with: Cursor * Hoist fully qualified paths to use statements in touched files Replace inline crate::protocol::commitment::HachiCommitmentLayout, hachi_pcs::algebra::backend::{CrtReconstruct, NttPrimeOps}, and hachi_pcs::algebra::CyclotomicRing with top-level use imports. Made-with: Cursor * Dispatch norm sumcheck kernels by range size. Route small-b rounds through the point-eval interpolation kernel and keep the affine-coefficient kernel for larger b, while adding deterministic baseline-vs-dispatched benchmarks and parity tests to validate correctness across both strategies. Made-with: Cursor * Format commitment-related files for readability. Apply non-functional formatting and import ordering cleanups across commitment, ring-switch, and benchmark/test files to keep the codebase style consistent. Made-with: Cursor * Format: cargo fmt pass on commitment-related files Made-with: Cursor * feat: sequential coefficient ordering + streaming commitment Change coefficient-to-ring packing from strided to sequential, enabling true streaming where each trace chunk maps to exactly one inner Ajtai block. Implement StreamingCommitmentScheme for HachiCommitmentScheme. - reduce_coeffs_to_ring_elements: sequential packing (chunks_exact(D)) - prove/verify: opening point split flipped to (inner, outer) - ring_opening_point_from_field: outer split flipped to (M first, R second) - commit_coeffs: sequential block distribution - map_onehot_to_sparse_blocks: sequential block distribution - HachiChunkState + process_chunk / process_chunk_onehot / aggregate_chunks - Streaming commit tests (matches non-streaming, prove/verify roundtrip) Made-with: Cursor * refactor: decompose verify_batched_sumcheck into composable steps Split the monolithic verify_batched_sumcheck into three pieces: - verify_batched_sumcheck_rounds: replay rounds, return intermediate state - compute_batched_expected_output_claim: query verifier instances - check_batched_output_claim: enforce equality This enables callers (e.g. Greyhound) to intercept the intermediate sumcheck state before the final oracle check. The original function is preserved as a convenience wrapper. Made-with: Cursor * feat: accept Option in commit_onehot for sparse one-hot support Allows None entries in one-hot index arrays to represent inactive cycles. Adds public commit_onehot free function returning both commitment and hint. Made-with: Cursor * feat: submatrix commit for polynomials smaller than setup max commit_coeffs now accepts ring coefficient vectors shorter than the layout's full size, padding each block internally. prove/verify pad the opening point with zeros so the transcript stays consistent. This avoids materializing huge zero-padded field-element arrays. Made-with: Cursor * feat: add HachiSerialize impls for proof types Implement HachiSerialize/HachiDeserialize for HachiProof, HachiCommitmentHint, and SumcheckAux so they can be serialized through the ArkBridge adapter in Jolt. Made-with: Cursor * fix: relax balanced_decompose_pow2 assertion for 128-bit fields Allow levels * log_basis up to 128 + log_basis. For Fp128 with LOG_BASIS=4, the decomposition needs 33 levels (132 bits total) because 32 levels can't represent the full signed range [-q/2, q/2). The extra level's digit is at most ±1 and the i128 arithmetic remains safe since the quotient shrinks monotonically. Made-with: Cursor * feat: add DynamicSmallTestCommitmentConfig Same D=16 security parameters as SmallTestCommitmentConfig but derives layout from max_num_vars instead of using a fixed (4,2) shape. Made-with: Cursor * perf: true submatrix in commit_coeffs — skip zero blocks Short polynomials no longer pad to block_len. commit_coeffs accepts fewer ring elements than num_blocks * block_len, decomposes only the non-zero blocks, and fills remaining entries with zero s/t_hat without allocation or mat-vec multiplication. Also relax debug_assert in mat_vec_mul_precomputed to >= (zip handles the shorter vector correctly). Made-with: Cursor * fix: use inner_width for zero_s in commit_coeffs/commit_onehot prove expects s[i] to have inner_width entries. Use the correct length for zero blocks to match the dense path's decompose_block output size. Made-with: Cursor * fix: configure rayon with 64MB stack for D>=512 ring elements CRT-NTT conversion puts ~28KB on the stack per ring element ([[MontCoeff; D]; K] + [i128; D]). With D=512 and the commit call chain depth, rayon's default thread stack overflows. ensure_large_thread_stack() is called from setup() and is safe to call multiple times (only the first configures the pool). Made-with: Cursor * feat: add commit_mixed for mega-polynomial commitment Exposes MegaPolyBlock enum (Dense/OneHot/Zero) and commit_mixed() which processes heterogeneous blocks in a single commitment. This lets Jolt pack all witness polynomials into one Hachi commitment (one block per polynomial) instead of N independent commitments. Also makes SparseBlockEntry and map_onehot_to_sparse_blocks public so callers can construct one-hot block descriptors. Made-with: Cursor * perf: drop s vectors from CommitWitness and HachiCommitmentHint The basis-decomposed s_i vectors (one per block, each block_len*delta ring elements) were stored in both CommitWitness and HachiCommitmentHint. At production parameters (D=512, block_len=2048, delta=32), each s_i is 512 MB — storing all 64 of them consumed ~32 GB. Instead, recompute s_i on the fly in compute_w_hat and compute_z_hat from ring_coeffs using decompose_block. Peak memory drops from O(blocks * block_len * delta) to O(block_len * delta) per thread. Also adds setup_with_layout for caller-specified HachiCommitmentLayout, and makes decompose_block, SparseBlockEntry, map_onehot_to_sparse_blocks public for downstream (Jolt) mega-polynomial integration. Made-with: Cursor * chore: untrack docs/ and paper/ from version control Keep these files locally for reference but remove from the committed tree. They can be selectively re-added later. Made-with: Cursor * perf: fused sumcheck, split-eq streaming, compact w_evals — 8x memory reduction Refactor the Hachi proving pipeline to eliminate the 13 GB matrix M and 2.6 GB vector z from memory, reducing peak prover allocation from ~30 GB to ~3.7 GB. Key changes: - QuadraticEquation: remove m/z fields; add compute_r_split_eq (split-eq factoring replaces full Kronecker materialization) and compute_m_a_streaming (row-at-a-time M·α evaluation). - ring_switch: decompose z_pre on the fly in build_w_coeffs; add build_w_evals_compact returning Vec for round-0 storage (all entries fit in [-8, 7] from balanced_decompose_pow2 with LOG_BASIS=4). - HachiSumcheckProver: fused norm+relation prover sharing a single w_table. Round 0 uses WTable::Compact(Vec), folding to WTable::Full(Vec) at half size after the first challenge. - HachiSumcheckVerifier: fused verifier combining both oracle checks with a batching_coeff sampled from the transcript. - Remove dead batched mat-vec functions from linear.rs. - Import hygiene: shorten crate::algebra::ring::X to crate::algebra::X; hoist mid-function use statements to top-level. Made-with: Cursor * revert: remove ensure_large_thread_stack rayon config Stack sizing for D>=512 ring elements should be handled by the caller, not baked into the library's setup path. Made-with: Cursor --- Cargo.toml | 10 +- benches/field_arith.rs | 2 +- benches/hachi_e2e.rs | 189 +++++ benches/norm_sumcheck.rs | 203 ++++++ benches/ring_ntt.rs | 17 +- src/algebra/backend/scalar.rs | 193 ++--- src/algebra/backend/traits.rs | 49 +- src/algebra/domains/coeff.rs | 6 - src/algebra/domains/crt_ntt.rs | 6 - src/algebra/domains/mod.rs | 7 - src/algebra/fields/ext.rs | 326 ++++++++- src/algebra/fields/fp128.rs | 59 +- src/algebra/fields/fp32.rs | 22 +- src/algebra/fields/fp64.rs | 59 +- src/algebra/fields/lift.rs | 59 +- src/algebra/fields/mod.rs | 7 +- src/algebra/fields/packed.rs | 2 +- src/algebra/fields/packed_ext.rs | 415 +++++++++++ src/algebra/fields/packed_neon.rs | 15 +- src/algebra/fields/util.rs | 38 + src/algebra/mod.rs | 20 +- src/algebra/module.rs | 8 - src/algebra/ntt/butterfly.rs | 187 +++-- src/algebra/ntt/crt.rs | 73 +- src/algebra/ntt/mod.rs | 4 +- src/algebra/ntt/prime.rs | 362 +++++++--- src/algebra/ntt/tables.rs | 234 +++--- src/algebra/poly.rs | 70 +- src/algebra/ring/crt_ntt_repr.rs | 256 ++++--- src/algebra/ring/cyclotomic.rs | 16 +- src/algebra/ring/mod.rs | 2 +- src/lib.rs | 8 +- src/parallel.rs | 56 ++ src/primitives/arithmetic.rs | 75 +- src/primitives/serialization.rs | 32 +- src/protocol/commitment/commit.rs | 605 ++++++++++++++-- src/protocol/commitment/config.rs | 334 +++++++-- src/protocol/commitment/mod.rs | 19 +- src/protocol/commitment/onehot.rs | 37 +- src/protocol/commitment/scheme.rs | 101 ++- src/protocol/commitment/utils/crt_ntt.rs | 133 ++++ src/protocol/commitment/utils/linear.rs | 325 ++++++++- src/protocol/commitment/utils/mod.rs | 3 +- src/protocol/commitment_scheme.rs | 622 +++++++++++++--- src/protocol/mod.rs | 12 +- src/protocol/proof.rs | 124 +++- src/protocol/quadratic_equation.rs | 667 +++++++++++------- src/protocol/ring_switch.rs | 472 +++++++++---- src/protocol/sumcheck/batched_sumcheck.rs | 139 +++- src/protocol/sumcheck/eq_poly.rs | 2 +- src/protocol/sumcheck/hachi_sumcheck.rs | 548 ++++++++++++++ src/protocol/sumcheck/mod.rs | 451 +----------- src/protocol/sumcheck/norm_sumcheck.rs | 584 +++++++++++++-- src/protocol/sumcheck/relation_sumcheck.rs | 174 +++-- src/protocol/sumcheck/split_eq.rs | 10 +- src/protocol/sumcheck/types.rs | 378 ++++++++++ .../transcript/{blake2b.rs => hash.rs} | 49 +- src/protocol/transcript/keccak.rs | 82 --- src/protocol/transcript/mod.rs | 25 +- src/test_utils.rs | 15 +- tests/algebra.rs | 475 ++++++++++++- tests/commitment_contract.rs | 2 +- tests/hachi_sumcheck.rs | 11 +- tests/onehot_commitment.rs | 43 +- tests/ring_commitment_core.rs | 157 +++-- tests/sparse_challenge.rs | 2 +- tests/sumcheck_core.rs | 24 +- tests/sumcheck_prover_driver.rs | 1 - 68 files changed, 7388 insertions(+), 2325 deletions(-) create mode 100644 benches/hachi_e2e.rs create mode 100644 benches/norm_sumcheck.rs delete mode 100644 src/algebra/domains/coeff.rs delete mode 100644 src/algebra/domains/crt_ntt.rs delete mode 100644 src/algebra/domains/mod.rs create mode 100644 src/algebra/fields/packed_ext.rs create mode 100644 src/algebra/fields/util.rs create mode 100644 src/parallel.rs create mode 100644 src/protocol/commitment/utils/crt_ntt.rs create mode 100644 src/protocol/sumcheck/hachi_sumcheck.rs create mode 100644 src/protocol/sumcheck/types.rs rename src/protocol/transcript/{blake2b.rs => hash.rs} (56%) delete mode 100644 src/protocol/transcript/keccak.rs diff --git a/Cargo.toml b/Cargo.toml index d6e45663..ab91eead 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -32,7 +32,7 @@ include = [ all-features = true [features] -default = [] +default = ["parallel"] parallel = ["dep:rayon"] [dependencies] @@ -63,6 +63,14 @@ harness = false name = "fp64_reduce_probe" harness = false +[[bench]] +name = "hachi_e2e" +harness = false + +[[bench]] +name = "norm_sumcheck" +harness = false + [lints.rust] missing_docs = "warn" unreachable_pub = "warn" diff --git a/benches/field_arith.rs b/benches/field_arith.rs index 9caf70d8..c3b04578 100644 --- a/benches/field_arith.rs +++ b/benches/field_arith.rs @@ -10,7 +10,7 @@ use hachi_pcs::algebra::{ Pow2Offset24Field, Pow2Offset30Field, Pow2Offset31Field, Pow2Offset32Field, Pow2Offset40Field, Pow2Offset48Field, Pow2Offset56Field, Pow2Offset64Field, }; -use hachi_pcs::{CanonicalField, FieldCore, FieldSampling, Invertible}; +use hachi_pcs::{CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible}; use rand::{rngs::StdRng, RngCore, SeedableRng}; use std::env; #[cfg(feature = "parallel")] diff --git a/benches/hachi_e2e.rs b/benches/hachi_e2e.rs new file mode 100644 index 00000000..d21b2f3f --- /dev/null +++ b/benches/hachi_e2e.rs @@ -0,0 +1,189 @@ +#![allow(missing_docs)] + +use criterion::{black_box, criterion_group, criterion_main, BenchmarkId, Criterion}; +use hachi_pcs::algebra::Fp128; +use hachi_pcs::error::HachiError; +use hachi_pcs::primitives::multilinear_evals::DenseMultilinearEvals; +use hachi_pcs::protocol::commitment::{HachiCommitmentLayout, ProductionFp128CommitmentConfig}; +use hachi_pcs::protocol::commitment_scheme::HachiCommitmentScheme; +use hachi_pcs::protocol::transcript::Blake2bTranscript; +use hachi_pcs::protocol::CommitmentConfig; +use hachi_pcs::{CommitmentScheme, FromSmallInt, Polynomial, Transcript}; +use std::time::Duration; + +type F = Fp128<0xfffffffffffffffffffffffffffffeed>; + +const D: usize = ProductionFp128CommitmentConfig::D; + +macro_rules! bench_config { + ($name:ident, M = $m:expr, R = $r:expr) => { + #[derive(Clone, Copy, Debug)] + struct $name; + impl CommitmentConfig for $name { + const D: usize = D; + const N_A: usize = ProductionFp128CommitmentConfig::N_A; + const N_B: usize = ProductionFp128CommitmentConfig::N_B; + const N_D: usize = ProductionFp128CommitmentConfig::N_D; + const LOG_BASIS: u32 = ProductionFp128CommitmentConfig::LOG_BASIS; + const DELTA: usize = ProductionFp128CommitmentConfig::DELTA; + const TAU: usize = ProductionFp128CommitmentConfig::TAU; + const CHALLENGE_WEIGHT: usize = ProductionFp128CommitmentConfig::CHALLENGE_WEIGHT; + + fn commitment_layout( + _max_num_vars: usize, + ) -> Result { + HachiCommitmentLayout::new::($m, $r) + } + } + }; +} + +bench_config!(CfgNv10, M = 4, R = 2); +bench_config!(CfgNv14, M = 6, R = 4); +bench_config!(CfgNv18, M = 8, R = 6); +bench_config!(CfgNv20, M = 8, R = 8); + +fn num_vars() -> usize { + let alpha = Cfg::D.trailing_zeros() as usize; + let layout = Cfg::commitment_layout(0).expect("benchmark layout"); + layout.m_vars + layout.r_vars + alpha +} + +fn make_poly(nv: usize) -> DenseMultilinearEvals { + let len = 1usize << nv; + let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); + DenseMultilinearEvals::new_padded(evals) +} + +fn opening_point(nv: usize) -> Vec { + (0..nv).map(|i| F::from_u64((i + 2) as u64)).collect() +} + +fn bench_phases(c: &mut Criterion, label: &str) +where + HachiCommitmentScheme: CommitmentScheme, +{ + type S = HachiCommitmentScheme; + let nv = num_vars::(); + let poly = make_poly(nv); + let pt = opening_point(nv); + + let mut group = c.benchmark_group(format!("hachi/{label}/nv{nv}")); + if nv >= 18 { + group.sample_size(10); + group.measurement_time(Duration::from_secs(30)); + } + + group.bench_function("setup", |b| { + b.iter(|| black_box( as CommitmentScheme>::setup_prover(black_box(nv)))) + }); + + let setup = as CommitmentScheme>::setup_prover(nv); + + group.bench_function("commit", |b| { + b.iter(|| { + black_box( + as CommitmentScheme>::commit(black_box(&poly), black_box(&setup)) + .unwrap(), + ) + }) + }); + + let (commitment, hint) = as CommitmentScheme>::commit(&poly, &setup).unwrap(); + + group.bench_function("prove", |b| { + b.iter(|| { + let mut transcript = Blake2bTranscript::::new(b"bench"); + black_box( + as CommitmentScheme>::prove( + black_box(&setup), + black_box(&poly), + black_box(&pt), + Some(hint.clone()), + &mut transcript, + black_box(&commitment), + ) + .unwrap(), + ) + }) + }); + + let verifier_setup = as CommitmentScheme>::setup_verifier(&setup); + let opening = poly.evaluate(&pt); + let mut prover_transcript = Blake2bTranscript::::new(b"bench"); + let proof = as CommitmentScheme>::prove( + &setup, + &poly, + &pt, + Some(hint), + &mut prover_transcript, + &commitment, + ) + .unwrap(); + + group.bench_function("verify", |b| { + b.iter(|| { + let mut transcript = Blake2bTranscript::::new(b"bench"); + as CommitmentScheme>::verify( + black_box(&proof), + black_box(&verifier_setup), + &mut transcript, + black_box(&pt), + black_box(&opening), + black_box(&commitment), + ) + .unwrap(); + }) + }); + + group.bench_function(BenchmarkId::new("e2e", nv), |b| { + b.iter(|| { + let (cm, h) = as CommitmentScheme>::commit(&poly, &setup).unwrap(); + let mut pt_tr = Blake2bTranscript::::new(b"bench"); + let pf = as CommitmentScheme>::prove( + &setup, + &poly, + &pt, + Some(h), + &mut pt_tr, + &cm, + ) + .unwrap(); + let mut vt_tr = Blake2bTranscript::::new(b"bench"); + as CommitmentScheme>::verify( + &pf, + &verifier_setup, + &mut vt_tr, + &pt, + &opening, + &cm, + ) + .unwrap(); + black_box(()) + }) + }); + + group.finish(); +} + +fn bench_nv10(c: &mut Criterion) { + bench_phases::(c, "fp128_p275"); +} +fn bench_nv14(c: &mut Criterion) { + bench_phases::(c, "fp128_p275"); +} +fn bench_nv18(c: &mut Criterion) { + bench_phases::(c, "fp128_p275"); +} +fn bench_nv20(c: &mut Criterion) { + bench_phases::(c, "fp128_p275"); +} + +criterion_group!( + hachi_benches, + bench_nv10, + bench_nv14, + bench_nv18, + bench_nv20 +); +criterion_main!(hachi_benches); diff --git a/benches/norm_sumcheck.rs b/benches/norm_sumcheck.rs new file mode 100644 index 00000000..655d6cab --- /dev/null +++ b/benches/norm_sumcheck.rs @@ -0,0 +1,203 @@ +#![allow(missing_docs)] + +use criterion::{black_box, criterion_group, criterion_main, BatchSize, BenchmarkId, Criterion}; +use hachi_pcs::algebra::Fp128; +use hachi_pcs::protocol::sumcheck::norm_sumcheck::NormSumcheckProver; +use hachi_pcs::protocol::sumcheck::split_eq::GruenSplitEq; +use hachi_pcs::protocol::sumcheck::{ + fold_evals_in_place, prove_sumcheck, range_check_eval, SumcheckInstanceProver, UniPoly, +}; +use hachi_pcs::protocol::transcript::labels; +use hachi_pcs::protocol::Blake2bTranscript; +use hachi_pcs::{FieldCore, FromSmallInt, Transcript}; +use rand::rngs::StdRng; +use rand::{Rng, SeedableRng}; +#[cfg(feature = "parallel")] +use rayon::prelude::*; +use std::time::Duration; + +type F = Fp128<0xfffffffffffffffffffffffffffffeed>; + +/// Baseline prover keeps the pre-dispatch point-eval kernel for apples-to-apples benchmarks. +/// It is intentionally local to this bench and should not be used in production code. +struct BaselineNormSumcheckProver { + split_eq: GruenSplitEq, + w_table: Vec, + num_vars: usize, + b: usize, +} + +impl BaselineNormSumcheckProver { + fn new(tau: &[E], w_evals: Vec, b: usize) -> Self { + let num_vars = tau.len(); + assert_eq!(w_evals.len(), 1 << num_vars); + Self { + split_eq: GruenSplitEq::new(tau), + w_table: w_evals, + num_vars, + b, + } + } +} + +impl SumcheckInstanceProver for BaselineNormSumcheckProver { + fn num_rounds(&self) -> usize { + self.num_vars + } + + fn degree_bound(&self) -> usize { + 2 * self.b + } + + fn input_claim(&self) -> E { + E::zero() + } + + fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { + let half = self.w_table.len() / 2; + let degree_q = 2 * self.b - 1; + let num_points_q = degree_q + 1; + + let (e_first, e_second) = self.split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + let first_bits = num_first.trailing_zeros(); + let b = self.b; + + #[cfg(feature = "parallel")] + let q_evals = { + (0..half) + .into_par_iter() + .fold( + || vec![E::zero(); num_points_q], + |mut evals, j| { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + for (t, eval) in evals.iter_mut().enumerate() { + let t_e = E::from_u64(t as u64); + let w_t = w_0 + t_e * (w_1 - w_0); + *eval = *eval + eq_rem * range_check_eval(w_t, b); + } + evals + }, + ) + .reduce( + || vec![E::zero(); num_points_q], + |mut a, b_vec| { + for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { + *ai = *ai + *bi; + } + a + }, + ) + }; + #[cfg(not(feature = "parallel"))] + let q_evals = { + let mut q_evals = vec![E::zero(); num_points_q]; + for j in 0..half { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + for (t, eval) in q_evals.iter_mut().enumerate() { + let t_e = E::from_u64(t as u64); + let w_t = w_0 + t_e * (w_1 - w_0); + *eval = *eval + eq_rem * range_check_eval(w_t, b); + } + } + q_evals + }; + + let q_poly = UniPoly::from_evals(&q_evals); + self.split_eq.gruen_mul(&q_poly) + } + + fn ingest_challenge(&mut self, _round: usize, r: E) { + self.split_eq.bind(r); + fold_evals_in_place(&mut self.w_table, r); + } +} + +#[derive(Clone)] +struct NormCase { + num_vars: usize, + b: usize, + tau: Vec, + w_evals: Vec, +} + +fn build_case(num_vars: usize, b: usize, seed: u64) -> NormCase { + let mut rng = StdRng::seed_from_u64(seed); + let n = 1usize << num_vars; + let tau: Vec = (0..num_vars) + .map(|_| F::from_u64(rng.gen_range(0u64..(1u64 << 24)))) + .collect(); + let w_evals: Vec = (0..n) + .map(|_| F::from_u64(rng.gen_range(0u64..(1u64 << 24)))) + .collect(); + NormCase { + num_vars, + b, + tau, + w_evals, + } +} + +fn bench_norm_sumcheck(c: &mut Criterion) { + let cases = [ + build_case(10, 4, 0xA11CE001), + build_case(10, 8, 0xA11CE002), + build_case(14, 4, 0xA11CE003), + build_case(14, 8, 0xA11CE004), + build_case(14, 16, 0xA11CE005), + build_case(18, 8, 0xA11CE006), + ]; + + let mut group = c.benchmark_group("norm_sumcheck"); + group.warm_up_time(Duration::from_secs(8)); + group.measurement_time(Duration::from_secs(24)); + group.sample_size(35); + + for case in &cases { + let case_tag = format!("nv{}_b{}", case.num_vars, case.b); + group.bench_function(BenchmarkId::new("baseline", &case_tag), |bencher| { + bencher.iter_batched( + || BaselineNormSumcheckProver::new(&case.tau, case.w_evals.clone(), case.b), + |mut prover| { + let mut transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + black_box( + prove_sumcheck::(&mut prover, &mut transcript, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(), + ) + }, + BatchSize::SmallInput, + ); + }); + + group.bench_function(BenchmarkId::new("dispatched", &case_tag), |bencher| { + bencher.iter_batched( + || NormSumcheckProver::new(&case.tau, case.w_evals.clone(), case.b), + |mut prover| { + let mut transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + black_box( + prove_sumcheck::(&mut prover, &mut transcript, |tr| { + tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND) + }) + .unwrap(), + ) + }, + BatchSize::SmallInput, + ); + }); + } + + group.finish(); +} + +criterion_group!(benches, bench_norm_sumcheck); +criterion_main!(benches); diff --git a/benches/ring_ntt.rs b/benches/ring_ntt.rs index 546f9b9d..aa2ac9ff 100644 --- a/benches/ring_ntt.rs +++ b/benches/ring_ntt.rs @@ -2,13 +2,13 @@ use criterion::{black_box, criterion_group, criterion_main, Criterion}; use hachi_pcs::algebra::ntt::butterfly::{forward_ntt, inverse_ntt, NttTwiddles}; -use hachi_pcs::algebra::tables::{Q32_DATA, Q32_MODULUS, Q32_NUM_PRIMES, Q32_PRIMES}; +use hachi_pcs::algebra::tables::{q32_garner, Q32_MODULUS, Q32_NUM_PRIMES, Q32_PRIMES}; use hachi_pcs::algebra::{CyclotomicCrtNtt, CyclotomicRing, Fp64, MontCoeff}; -use hachi_pcs::CanonicalField; +use hachi_pcs::FromSmallInt; type F = Fp64<{ Q32_MODULUS }>; type R = CyclotomicRing; -type N = CyclotomicCrtNtt; +type N = CyclotomicCrtNtt; fn sample_ring(seed: u64) -> R { let coeffs = std::array::from_fn(|i| { @@ -30,8 +30,8 @@ fn bench_ring_schoolbook_mul(c: &mut Criterion) { fn bench_ntt_single_prime_round_trip(c: &mut Criterion) { let prime = Q32_PRIMES[0]; - let tw = NttTwiddles::<64>::compute(prime); - let base: [MontCoeff; 64] = + let tw = NttTwiddles::::compute(prime); + let base: [MontCoeff; 64] = std::array::from_fn(|i| prime.from_canonical(((i * 5 + 7) as i16) % prime.p)); c.bench_function("ntt_single_prime_forward_inverse_d64", |b| { @@ -46,13 +46,14 @@ fn bench_ntt_single_prime_round_trip(c: &mut Criterion) { fn bench_crt_round_trip(c: &mut Criterion) { let ring = sample_ring(19); - let twiddles: [NttTwiddles<64>; Q32_NUM_PRIMES] = - std::array::from_fn(|k| NttTwiddles::<64>::compute(Q32_PRIMES[k])); + let twiddles: [NttTwiddles; Q32_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::compute(Q32_PRIMES[k])); + let garner = q32_garner(); c.bench_function("ring_ntt_crt_round_trip_d64_k6", |b| { b.iter(|| { let ntt = N::from_ring(black_box(&ring), &Q32_PRIMES, &twiddles); - let back: R = ntt.to_ring(&Q32_PRIMES, &twiddles, &Q32_DATA); + let back: R = ntt.to_ring(&Q32_PRIMES, &twiddles, &garner); black_box(back) }) }); diff --git a/src/algebra/backend/scalar.rs b/src/algebra/backend/scalar.rs index ce0f0dc7..1ef4c7da 100644 --- a/src/algebra/backend/scalar.rs +++ b/src/algebra/backend/scalar.rs @@ -1,191 +1,94 @@ -//! Default scalar backend wiring existing CRT+NTT kernels. +//! Default scalar backend: delegates to NTT kernels and uses Garner's +//! algorithm for CRT reconstruction. use super::traits::{CrtReconstruct, NttPrimeOps, NttTransform}; use crate::algebra::ntt::butterfly::{forward_ntt, inverse_ntt, NttTwiddles}; -use crate::algebra::ntt::crt::QData; -use crate::algebra::ntt::prime::{MontCoeff, NttPrime}; +use crate::algebra::ntt::crt::GarnerData; +use crate::algebra::ntt::prime::{MontCoeff, NttPrime, PrimeWidth}; use crate::algebra::ring::CrtNttConvertibleField; /// Default scalar backend implementation. #[derive(Debug, Clone, Copy, Default)] pub struct ScalarBackend; -impl NttPrimeOps for ScalarBackend { +impl NttPrimeOps for ScalarBackend { #[inline] - fn from_canonical(prime: NttPrime, value: i16) -> MontCoeff { + fn from_canonical(prime: NttPrime, value: W) -> MontCoeff { prime.from_canonical(value) } #[inline] - fn to_canonical(prime: NttPrime, value: MontCoeff) -> i16 { + fn to_canonical(prime: NttPrime, value: MontCoeff) -> W { prime.to_canonical(value) } #[inline] - fn reduce(prime: NttPrime, value: MontCoeff) -> MontCoeff { - prime.reduce(value) + fn reduce_range(prime: NttPrime, value: MontCoeff) -> MontCoeff { + prime.reduce_range(value) } #[inline] fn pointwise_mul( - prime: NttPrime, - out: &mut [MontCoeff; D], - lhs: &[MontCoeff; D], - rhs: &[MontCoeff; D], + prime: NttPrime, + out: &mut [MontCoeff; D], + lhs: &[MontCoeff; D], + rhs: &[MontCoeff; D], ) { prime.pointwise_mul(out, lhs, rhs); } } -impl NttTransform for ScalarBackend { +impl NttTransform for ScalarBackend { #[inline] - fn forward_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles) { + fn forward_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles) { forward_ntt(limb, prime, twiddles); } #[inline] - fn inverse_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles) { + fn inverse_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles) { inverse_ntt(limb, prime, twiddles); } } -impl CrtReconstruct for ScalarBackend { +impl CrtReconstruct for ScalarBackend { fn reconstruct( - primes: &[NttPrime; K], - canonical_limbs: &[[i16; D]; K], - qdata: &QData, + primes: &[NttPrime; K], + canonical: &[[W; D]; K], + garner: &GarnerData, ) -> [F; D] { - let q = qdata.q_u128().expect("q must fit in u128"); - let prime_moduli: [u128; K] = std::array::from_fn(|k| { - u128::try_from(primes[k].p).expect("CRT prime modulus must be positive") - }); - let big_p = prime_moduli.iter().fold(1u128, |acc, p| { - acc.checked_mul(*p) - .expect("product of CRT primes must fit u128") - }); - let crt_m: [u128; K] = std::array::from_fn(|k| big_p / prime_moduli[k]); - let crt_inv: [u16; K] = std::array::from_fn(|k| { - let inv = mod_inverse( - (crt_m[k] % prime_moduli[k]) as i128, - prime_moduli[k] as i128, - ); - u16::try_from(inv).expect("CRT inverse must fit u16 for small-prime backend") - }); - let mut coeffs = [F::zero(); D]; for (d, coeff) in coeffs.iter_mut().enumerate() { - let mut acc: u128 = 0; - for k in 0..K { - let ck_i16 = canonical_limbs[k][d]; - debug_assert!(ck_i16 >= 0 && ck_i16 < primes[k].p); - let ck = u16::try_from(ck_i16).expect("canonical residue must fit u16"); - - // Multiply by tiny residues/inverses (<= 15 bits) in fixed-time - // loops, then accumulate modulo P. - let term = mul_mod_by_small_u16(crt_m[k], ck, big_p); - let term = mul_mod_by_small_u16(term, crt_inv[k], big_p); - acc = add_mod_u128(acc, term, big_p); + // Garner mixed-radix decomposition (all arithmetic in i64, mod p_i). + let mut v = [0i64; K]; + v[0] = canonical[0][d].to_i64(); + for i in 1..K { + let pi = primes[i].p.to_i64(); + let mut temp = canonical[i][d].to_i64(); + #[allow(clippy::needless_range_loop)] + for j in 0..i { + temp -= v[j]; + temp = ((temp % pi) + pi) % pi; + temp = (temp * garner.gamma[i][j].to_i64()) % pi; + } + // Center the mixed-radix digit to keep the final reconstruction + // in a small signed range when inputs are centered. + if temp > pi / 2 { + temp -= pi; + } + v[i] = temp; } - // Final projection into [0, q) without variable-latency division. - let reduced = reduce_u128_divfree(acc, q); - *coeff = F::from_q_residue_u128(reduced); + // Horner accumulation in the target field F. + let mut result = F::from_i64(v[0]); + let mut partial_prod = F::from_i64(primes[0].p.to_i64()); + for i in 1..K { + result = result + F::from_i64(v[i]) * partial_prod; + if i + 1 < K { + partial_prod = partial_prod * F::from_i64(primes[i].p.to_i64()); + } + } + *coeff = result; } - coeffs } } - -fn mod_inverse(a: i128, modulus: i128) -> i128 { - let (mut t, mut new_t) = (0i128, 1i128); - let (mut r, mut new_r) = (modulus, ((a % modulus) + modulus) % modulus); - - while new_r != 0 { - let q = r / new_r; - (t, new_t) = (new_t, t - q * new_t); - (r, new_r) = (new_r, r - q * new_r); - } - - assert_eq!(r, 1, "CRT inverse does not exist"); - (t % modulus + modulus) % modulus -} - -#[inline] -fn add_mod_u128(a: u128, b: u128, modulus: u128) -> u128 { - debug_assert!(a < modulus); - debug_assert!(b < modulus); - - let (sum_lo, carry) = a.overflowing_add(b); - let hi = carry as u128; - let (sub_lo, borrow) = sum_lo.overflowing_sub(modulus); - let sum_ge_modulus = (!borrow) as u128; - let should_sub = hi | sum_ge_modulus; - let mask = should_sub.wrapping_neg(); - (sum_lo & !mask) | (sub_lo & mask) -} - -#[inline] -fn mul_mod_by_small_u16(a: u128, b: u16, modulus: u128) -> u128 { - debug_assert!(a < modulus); - let mut acc = 0u128; - let mut cur = a; - for i in 0..16 { - let candidate = add_mod_u128(acc, cur, modulus); - let bit = ((b >> i) & 1) as u128; - let mask = bit.wrapping_neg(); - acc = (acc & !mask) | (candidate & mask); - cur = add_mod_u128(cur, cur, modulus); - } - acc -} - -#[inline] -fn reduce_u128_divfree(x: u128, modulus: u128) -> u128 { - debug_assert!(modulus > 0); - let mut rem = 0u128; - for i in (0..128).rev() { - rem = (rem << 1) | ((x >> i) & 1); - let (candidate, borrow) = rem.overflowing_sub(modulus); - let mask = 0u128.wrapping_sub((!borrow) as u128); - rem = (candidate & mask) | (rem & !mask); - } - rem -} - -#[cfg(test)] -mod tests { - use super::{add_mod_u128, mul_mod_by_small_u16, reduce_u128_divfree}; - - #[test] - fn add_mod_matches_native_when_sum_fits_u128() { - let modulus = (1u128 << 100) - 159; - for i in 0..4096u128 { - let a = (i * 104_729 + 17) % modulus; - let b = (i * 130_363 + 31) % modulus; - let expected = (a + b) % modulus; - assert_eq!(add_mod_u128(a, b, modulus), expected); - } - } - - #[test] - fn mul_mod_small_matches_native_when_product_fits_u128() { - let modulus = (1u128 << 100) - 159; - for i in 0..4096u128 { - let a = (i * 786_433 + 19) % modulus; - let b = ((i * 97 + 7) & 0xFFFF) as u16; - let expected = (a * (b as u128)) % modulus; - assert_eq!(mul_mod_by_small_u16(a, b, modulus), expected); - } - } - - #[test] - fn reduce_u128_divfree_matches_native_mod() { - let modulus = (1u128 << 100) - 159; - for i in 0..4096u128 { - let x = (i.wrapping_mul(1_146_989_321_207u128)) - ^ (i.rotate_left(37)) - ^ 0xA5A5_A5A5_A5A5_A5A5_A5A5_A5A5_A5A5_A5A5u128; - assert_eq!(reduce_u128_divfree(x, modulus), x % modulus); - } - } -} diff --git a/src/algebra/backend/traits.rs b/src/algebra/backend/traits.rs index d6c8a5a0..118a5f1f 100644 --- a/src/algebra/backend/traits.rs +++ b/src/algebra/backend/traits.rs @@ -1,56 +1,59 @@ //! Backend traits for CRT+NTT execution semantics. +//! +//! All traits are generic over `W: PrimeWidth` to support both +//! `i16` (primes < 2^14) and `i32` (primes < 2^30) NTT backends. use crate::algebra::ntt::butterfly::NttTwiddles; -use crate::algebra::ntt::crt::QData; -use crate::algebra::ntt::prime::{MontCoeff, NttPrime}; +use crate::algebra::ntt::crt::GarnerData; +use crate::algebra::ntt::prime::{MontCoeff, NttPrime, PrimeWidth}; use crate::algebra::ring::CrtNttConvertibleField; /// Per-prime arithmetic primitives used by CRT+NTT domains. -pub trait NttPrimeOps { +pub trait NttPrimeOps { /// Convert canonical coefficient to backend prime representation. - fn from_canonical(prime: NttPrime, value: i16) -> MontCoeff; + fn from_canonical(prime: NttPrime, value: W) -> MontCoeff; /// Convert backend prime representation back to canonical coefficient. - fn to_canonical(prime: NttPrime, value: MontCoeff) -> i16; + fn to_canonical(prime: NttPrime, value: MontCoeff) -> W; - /// Range-reduce one backend prime coefficient. - fn reduce(prime: NttPrime, value: MontCoeff) -> MontCoeff; + /// Range-reduce one coefficient from `(-2p, 2p)` to `(-p, p)`. + fn reduce_range(prime: NttPrime, value: MontCoeff) -> MontCoeff; /// Pointwise multiplication in backend prime representation. fn pointwise_mul( - prime: NttPrime, - out: &mut [MontCoeff; D], - lhs: &[MontCoeff; D], - rhs: &[MontCoeff; D], + prime: NttPrime, + out: &mut [MontCoeff; D], + lhs: &[MontCoeff; D], + rhs: &[MontCoeff; D], ); } /// Forward/inverse transform kernels for one NTT limb. -pub trait NttTransform { +pub trait NttTransform { /// Forward transform from coefficient limb to NTT limb. - fn forward_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles); + fn forward_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles); /// Inverse transform from NTT limb to coefficient limb. - fn inverse_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles); + fn inverse_ntt(limb: &mut [MontCoeff; D], prime: NttPrime, twiddles: &NttTwiddles); } -/// CRT reconstruction contract from per-prime canonical coefficients. -pub trait CrtReconstruct { +/// CRT reconstruction from per-prime canonical coefficients via Garner's algorithm. +pub trait CrtReconstruct { /// Reconstruct coefficient-domain values from canonical CRT residues. fn reconstruct( - primes: &[NttPrime; K], - canonical_limbs: &[[i16; D]; K], - qdata: &QData, + primes: &[NttPrime; K], + canonical_limbs: &[[W; D]; K], + garner: &GarnerData, ) -> [F; D]; } /// Convenience composition trait for full ring backend capability. -pub trait RingBackend: - NttPrimeOps + NttTransform + CrtReconstruct +pub trait RingBackend: + NttPrimeOps + NttTransform + CrtReconstruct { } -impl RingBackend for T where - T: NttPrimeOps + NttTransform + CrtReconstruct +impl RingBackend for T where + T: NttPrimeOps + NttTransform + CrtReconstruct { } diff --git a/src/algebra/domains/coeff.rs b/src/algebra/domains/coeff.rs deleted file mode 100644 index 461a2fd4..00000000 --- a/src/algebra/domains/coeff.rs +++ /dev/null @@ -1,6 +0,0 @@ -//! Coefficient-domain representation boundary. - -use crate::algebra::ring::CyclotomicRing; - -/// Coefficient-domain ring representation. -pub type CoeffDomain = CyclotomicRing; diff --git a/src/algebra/domains/crt_ntt.rs b/src/algebra/domains/crt_ntt.rs deleted file mode 100644 index 48fe2263..00000000 --- a/src/algebra/domains/crt_ntt.rs +++ /dev/null @@ -1,6 +0,0 @@ -//! CRT+NTT-domain representation boundary. - -use crate::algebra::ring::CyclotomicCrtNtt; - -/// CRT+NTT-domain ring representation. -pub type CrtNttDomain = CyclotomicCrtNtt; diff --git a/src/algebra/domains/mod.rs b/src/algebra/domains/mod.rs deleted file mode 100644 index fa140308..00000000 --- a/src/algebra/domains/mod.rs +++ /dev/null @@ -1,7 +0,0 @@ -//! Explicit domain-layer aliases for ring representations. - -pub mod coeff; -pub mod crt_ntt; - -pub use coeff::CoeffDomain; -pub use crt_ntt::CrtNttDomain; diff --git a/src/algebra/fields/ext.rs b/src/algebra/fields/ext.rs index 29061e9b..c341b6fa 100644 --- a/src/algebra/fields/ext.rs +++ b/src/algebra/fields/ext.rs @@ -4,7 +4,33 @@ use crate::algebra::module::VectorModule; use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; -use crate::{FieldCore, FieldSampling}; +use crate::{FieldCore, FieldSampling, FromSmallInt}; + +/// `Fp2Config` with non-residue = -1. +/// +/// Valid when `p ≡ 3 (mod 4)`, i.e. -1 is a quadratic non-residue. +pub struct NegOneNr; + +impl Fp2Config for NegOneNr { + const IS_NEG_ONE: bool = true; + + fn non_residue() -> F { + -F::one() + } +} + +/// `Fp2Config` with non-residue = 2. +/// +/// Valid when `p ≡ 5 (mod 8)`, i.e. 2 is a quadratic non-residue. +/// All Hachi pseudo-Mersenne primes (`2^k - c` with `c ≡ 3 mod 8`) +/// satisfy this. +pub struct TwoNr; + +impl Fp2Config for TwoNr { + fn non_residue() -> F { + F::from_u64(2) + } +} use rand_core::RngCore; use std::io::{Read, Write}; use std::marker::PhantomData; @@ -12,6 +38,12 @@ use std::ops::{Add, Mul, Neg, Sub}; /// Parameters for an `Fp2` quadratic extension over base field `F`. pub trait Fp2Config { + /// Whether the non-residue is -1. + /// + /// When `true`, multiplication by the non-residue is a free negation and + /// the Karatsuba/squaring routines can avoid a base-field multiply. + const IS_NEG_ONE: bool = false; + /// Non-residue `NR` such that `u^2 = NR`. fn non_residue() -> F; } @@ -36,6 +68,18 @@ impl> Fp2 { } } + /// Multiply a base-field element by the non-residue. + /// + /// When `IS_NEG_ONE` is true this is just a negation (no multiply). + #[inline(always)] + fn mul_nr(x: F) -> F { + if C::IS_NEG_ONE { + -x + } else { + C::non_residue() * x + } + } + /// Return the conjugate `c0 - c1 * u`. #[inline] pub fn conjugate(self) -> Self { @@ -45,8 +89,16 @@ impl> Fp2 { /// Return the norm in the base field: `c0^2 - NR * c1^2`. #[inline] pub fn norm(self) -> F { - let nr = C::non_residue(); - (self.c0 * self.c0) - (nr * (self.c1 * self.c1)) + (self.c0 * self.c0) - Self::mul_nr(self.c1 * self.c1) + } +} + +impl> std::fmt::Debug for Fp2 { + fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { + f.debug_struct("Fp2") + .field("c0", &self.c0) + .field("c1", &self.c1) + .finish() } } @@ -70,6 +122,8 @@ impl> PartialEq for Fp2 { } } +impl> Eq for Fp2 {} + impl> Add for Fp2 { type Output = Self; fn add(self, rhs: Self) -> Self::Output { @@ -91,12 +145,12 @@ impl> Neg for Fp2 { impl> Mul for Fp2 { type Output = Self; fn mul(self, rhs: Self) -> Self::Output { - let nr = C::non_residue(); - let a0 = self.c0; - let a1 = self.c1; - let b0 = rhs.c0; - let b1 = rhs.c1; - Self::new((a0 * b0) + (nr * (a1 * b1)), (a0 * b1) + (a1 * b0)) + let v0 = self.c0 * rhs.c0; + let v1 = self.c1 * rhs.c1; + Self::new( + v0 + Self::mul_nr(v1), + (self.c0 + self.c1) * (rhs.c0 + rhs.c1) - v0 - v1, + ) } } @@ -172,16 +226,13 @@ impl> FieldCore for Fp2 { self.c0.is_zero() && self.c1.is_zero() } - fn add(&self, rhs: &Self) -> Self { - *self + *rhs - } - - fn sub(&self, rhs: &Self) -> Self { - *self - *rhs - } - - fn mul(&self, rhs: &Self) -> Self { - *self * *rhs + /// Specialized squaring: 2 base-field multiplications instead of 3. + /// + /// `(c0 + c1·u)^2 = (c0^2 + NR·c1^2) + (2·c0·c1)·u` + fn square(&self) -> Self { + let v0 = self.c0 * self.c0; + let v1 = self.c1 * self.c1; + Self::new(v0 + Self::mul_nr(v1), (self.c0 + self.c0) * self.c1) } fn inv(self) -> Option { @@ -199,12 +250,33 @@ impl> FieldSampling for Fp } } +impl> FromSmallInt for Fp2 { + fn from_u64(val: u64) -> Self { + Self::new(F::from_u64(val), F::zero()) + } + + fn from_i64(val: i64) -> Self { + Self::new(F::from_i64(val), F::zero()) + } +} + /// Parameters for an `Fp4` quadratic extension over `Fp2`. pub trait Fp4Config> { /// Non-residue `NR2` in `Fp2` such that `v^2 = NR2`. fn non_residue() -> Fp2; } +/// `Fp4Config` with non-residue `u ∈ Fp2` (the element `(0, 1)`). +/// +/// This is the standard tower choice: `Fp4 = Fp2[v] / (v^2 - u)`. +pub struct UnitNr; + +impl> Fp4Config for UnitNr { + fn non_residue() -> Fp2 { + Fp2::new(F::zero(), F::one()) + } +} + /// Quartic extension element `c0 + c1 * v` over `Fp2`, where `v^2 = NR2`. pub struct Fp4, C4: Fp4Config> { /// Constant term. @@ -233,6 +305,17 @@ impl, C4: Fp4Config> Fp4 { } } +impl, C4: Fp4Config> std::fmt::Debug + for Fp4 +{ + fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { + f.debug_struct("Fp4") + .field("c0", &self.c0) + .field("c1", &self.c1) + .finish() + } +} + impl, C4: Fp4Config> Clone for Fp4 { fn clone(&self) -> Self { *self @@ -256,6 +339,8 @@ impl, C4: Fp4Config> PartialEq for Fp4, C4: Fp4Config> Eq for Fp4 {} + impl, C4: Fp4Config> Add for Fp4 { type Output = Self; fn add(self, rhs: Self) -> Self::Output { @@ -278,11 +363,12 @@ impl, C4: Fp4Config> Mul for Fp4 Self::Output { let nr2 = C4::non_residue(); - let a0 = self.c0; - let a1 = self.c1; - let b0 = rhs.c0; - let b1 = rhs.c1; - Self::new((a0 * b0) + (nr2 * (a1 * b1)), (a0 * b1) + (a1 * b0)) + let v0 = self.c0 * rhs.c0; + let v1 = self.c1 * rhs.c1; + Self::new( + v0 + (nr2 * v1), + (self.c0 + self.c1) * (rhs.c0 + rhs.c1) - v0 - v1, + ) } } @@ -360,16 +446,11 @@ impl, C4: Fp4Config> FieldCore for self.c0.is_zero() && self.c1.is_zero() } - fn add(&self, rhs: &Self) -> Self { - *self + *rhs - } - - fn sub(&self, rhs: &Self) -> Self { - *self - *rhs - } - - fn mul(&self, rhs: &Self) -> Self { - *self * *rhs + fn square(&self) -> Self { + let nr2 = C4::non_residue(); + let v0 = self.c0.square(); + let v1 = self.c1.square(); + Self::new(v0 + nr2 * v1, (self.c0 + self.c0) * self.c1) } fn inv(self) -> Option { @@ -389,6 +470,18 @@ impl, C4: Fp4Config, C4: Fp4Config> FromSmallInt + for Fp4 +{ + fn from_u64(val: u64) -> Self { + Self::new(Fp2::from_u64(val), Fp2::zero()) + } + + fn from_i64(val: i64) -> Self { + Self::new(Fp2::from_i64(val), Fp2::zero()) + } +} + // Scalar * VectorModule impls for extension scalars. impl Mul, N>> for Fp2 @@ -444,3 +537,168 @@ where self * *rhs } } + +// Convenience aliases for extension fields with NR = 2 (valid for all Hachi +// pseudo-Mersenne primes where p ≡ 5 mod 8). + +/// Quadratic extension over any `F` with non-residue 2. +pub type Ext2 = Fp2; + +/// Quartic extension as tower `Ext2[v]/(v^2 - u)`. +pub type Ext4 = Fp4; + +#[cfg(test)] +mod tests { + use super::*; + use crate::algebra::fields::lift::ExtField; + use crate::algebra::Fp64; + use crate::{FieldCore, FieldSampling, FromSmallInt}; + use rand::rngs::StdRng; + use rand::SeedableRng; + + type F = Fp64<4294967197>; + type E2 = Ext2; + type E4 = Ext4; + + #[test] + fn fp2_add_sub_identity() { + let a = E2::new(F::from_u64(3), F::from_u64(5)); + let b = E2::new(F::from_u64(7), F::from_u64(11)); + let c = a + b; + assert_eq!(c - b, a); + assert_eq!(c - a, b); + } + + #[test] + fn fp2_mul_one() { + let a = E2::new(F::from_u64(42), F::from_u64(13)); + assert_eq!(a * E2::one(), a); + assert_eq!(E2::one() * a, a); + } + + #[test] + fn fp2_mul_commutativity() { + let mut rng = StdRng::seed_from_u64(1234); + let a = E2::sample(&mut rng); + let b = E2::sample(&mut rng); + assert_eq!(a * b, b * a); + } + + #[test] + fn fp2_karatsuba_matches_schoolbook() { + let mut rng = StdRng::seed_from_u64(5678); + for _ in 0..100 { + let a = E2::sample(&mut rng); + let b = E2::sample(&mut rng); + let nr = >::non_residue(); + let expected = E2::new( + (a.c0 * b.c0) + (nr * (a.c1 * b.c1)), + (a.c0 * b.c1) + (a.c1 * b.c0), + ); + assert_eq!(a * b, expected); + } + } + + #[test] + fn fp2_square_matches_mul() { + let mut rng = StdRng::seed_from_u64(9012); + for _ in 0..100 { + let a = E2::sample(&mut rng); + assert_eq!(a.square(), a * a, "square mismatch for {a:?}"); + } + } + + #[test] + fn fp2_inv() { + let mut rng = StdRng::seed_from_u64(3456); + for _ in 0..50 { + let a = E2::sample(&mut rng); + if !a.is_zero() { + let inv = a.inv().unwrap(); + assert_eq!(a * inv, E2::one()); + } + } + } + + #[test] + fn fp4_mul_commutativity() { + let mut rng = StdRng::seed_from_u64(7890); + let a = E4::sample(&mut rng); + let b = E4::sample(&mut rng); + assert_eq!(a * b, b * a); + } + + #[test] + fn fp4_square_matches_mul() { + let mut rng = StdRng::seed_from_u64(1111); + for _ in 0..50 { + let a = E4::sample(&mut rng); + assert_eq!(a.square(), a * a); + } + } + + #[test] + fn fp4_inv() { + let mut rng = StdRng::seed_from_u64(2222); + for _ in 0..50 { + let a = E4::sample(&mut rng); + if !a.is_zero() { + let inv = a.inv().unwrap(); + assert_eq!(a * inv, E4::one()); + } + } + } + + #[test] + fn from_small_int_fp2() { + let a = E2::from_u64(42); + assert_eq!(a, E2::new(F::from_u64(42), F::zero())); + + let b = E2::from_i64(-3); + assert_eq!(b, E2::new(F::from_i64(-3), F::zero())); + + let c = E2::from_u8(7); + assert_eq!(c, E2::from_u64(7)); + + let d = E2::from_u32(100_000); + assert_eq!(d, E2::from_u64(100_000)); + } + + #[test] + fn from_small_int_fp4() { + let a = E4::from_u64(42); + assert_eq!(a, E4::new(E2::from_u64(42), E2::zero())); + + let b = E4::from_i64(-7); + assert_eq!(b, E4::new(E2::from_i64(-7), E2::zero())); + } + + #[test] + fn ext_field_degree() { + assert_eq!(>::EXT_DEGREE, 1); + assert_eq!(>::EXT_DEGREE, 2); + assert_eq!(>::EXT_DEGREE, 4); + } + + #[test] + fn ext_field_from_base_slice() { + let c0 = F::from_u64(3); + let c1 = F::from_u64(5); + let e2 = E2::from_base_slice(&[c0, c1]); + assert_eq!(e2, E2::new(c0, c1)); + + let c2 = F::from_u64(7); + let c3 = F::from_u64(11); + let e4 = E4::from_base_slice(&[c0, c1, c2, c3]); + assert_eq!(e4, E4::new(E2::new(c0, c1), E2::new(c2, c3))); + } + + #[test] + fn eq_impl() { + let a = E2::new(F::from_u64(1), F::from_u64(2)); + let b = E2::new(F::from_u64(1), F::from_u64(2)); + let c = E2::new(F::from_u64(1), F::from_u64(3)); + assert_eq!(a, b); + assert_ne!(a, c); + } +} diff --git a/src/algebra/fields/fp128.rs b/src/algebra/fields/fp128.rs index 09248062..99f3fc5b 100644 --- a/src/algebra/fields/fp128.rs +++ b/src/algebra/fields/fp128.rs @@ -18,7 +18,9 @@ use rand_core::RngCore; use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; -use crate::{CanonicalField, FieldCore, FieldSampling, Invertible, PseudoMersenneField}; +use crate::{ + CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, PseudoMersenneField, +}; /// Pack two u64 limbs into `[lo, hi]`. #[inline(always)] @@ -38,44 +40,7 @@ const fn to_u128(x: [u64; 2]) -> u128 { x[0] as u128 | (x[1] as u128) << 64 } -/// `a * b` widening to 128 bits; returns `(lo64, hi64)`. -#[inline(always)] -fn mul64_wide(a: u64, b: u64) -> (u64, u64) { - #[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] - { - // Safety: this block is compiled only when `bmi2` is enabled. - unsafe { mul64_wide_bmi2(a, b) } - } - #[cfg(not(all(target_arch = "x86_64", target_feature = "bmi2")))] - { - let prod = (a as u128) * (b as u128); - (prod as u64, (prod >> 64) as u64) - } -} - -#[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] -#[inline(always)] -unsafe fn mul64_wide_bmi2(a: u64, b: u64) -> (u64, u64) { - let mut hi = 0; - // Safety: caller guarantees CPU support via cfg-gated compilation. - let lo = unsafe { std::arch::x86_64::_mulx_u64(a, b, &mut hi) }; - (lo, hi) -} - -#[inline(always)] -const fn is_pow2_u64(x: u64) -> bool { - x != 0 && (x & (x - 1)) == 0 -} - -#[inline(always)] -const fn log2_pow2_u64(mut x: u64) -> u32 { - let mut k = 0u32; - while x > 1 { - x >>= 1; - k += 1; - } - k -} +use super::util::{is_pow2_u64, log2_pow2_u64, mul64_wide}; /// 128-bit prime field element for primes `p = 2^128 − c` with `c < 2^64`. /// @@ -770,18 +735,6 @@ impl FieldCore for Fp128

{ self.0 == [0, 0] } - fn add(&self, rhs: &Self) -> Self { - *self + *rhs - } - - fn sub(&self, rhs: &Self) -> Self { - *self - *rhs - } - - fn mul(&self, rhs: &Self) -> Self { - *self * *rhs - } - fn inv(self) -> Option { let inv = self.inv_or_zero(); if self.is_zero() { @@ -816,7 +769,7 @@ impl FieldSampling for Fp128

{ } } -impl CanonicalField for Fp128

{ +impl FromSmallInt for Fp128

{ fn from_u64(val: u64) -> Self { // For Fp128 pseudo-Mersenne primes, p = 2^128 - c with c < 2^64. // Therefore any u64 is always canonical (< p), so this can be a @@ -832,7 +785,9 @@ impl CanonicalField for Fp128

{ -Self::from_u64(val.unsigned_abs()) } } +} +impl CanonicalField for Fp128

{ fn to_canonical_u128(self) -> u128 { to_u128(self.0) } diff --git a/src/algebra/fields/fp32.rs b/src/algebra/fields/fp32.rs index 0a834698..9be1b7b3 100644 --- a/src/algebra/fields/fp32.rs +++ b/src/algebra/fields/fp32.rs @@ -11,7 +11,9 @@ use rand_core::RngCore; use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; -use crate::{CanonicalField, FieldCore, FieldSampling, Invertible, PseudoMersenneField}; +use crate::{ + CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, PseudoMersenneField, +}; use std::io::{Read, Write}; /// Prime field element for primes `p = 2^k − c` stored as `u32`. @@ -299,18 +301,6 @@ impl FieldCore for Fp32

{ self.0 == 0 } - fn add(&self, rhs: &Self) -> Self { - *self + *rhs - } - - fn sub(&self, rhs: &Self) -> Self { - *self - *rhs - } - - fn mul(&self, rhs: &Self) -> Self { - *self * *rhs - } - fn inv(self) -> Option { let inv = self.inv_or_zero(); if self.is_zero() { @@ -336,7 +326,7 @@ impl FieldSampling for Fp32

{ } } -impl CanonicalField for Fp32

{ +impl FromSmallInt for Fp32

{ fn from_u64(val: u64) -> Self { Self(Self::reduce_u64(val)) } @@ -345,10 +335,12 @@ impl CanonicalField for Fp32

{ if val >= 0 { Self::from_u64(val as u64) } else { - -Self::from_u64((-val) as u64) + -Self::from_u64(val.unsigned_abs()) } } +} +impl CanonicalField for Fp32

{ fn to_canonical_u128(self) -> u128 { self.0 as u128 } diff --git a/src/algebra/fields/fp64.rs b/src/algebra/fields/fp64.rs index a56e3c1c..8b81218e 100644 --- a/src/algebra/fields/fp64.rs +++ b/src/algebra/fields/fp64.rs @@ -11,45 +11,12 @@ use rand_core::RngCore; use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; -use crate::{CanonicalField, FieldCore, FieldSampling, Invertible, PseudoMersenneField}; +use crate::{ + CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, PseudoMersenneField, +}; use std::io::{Read, Write}; -#[inline(always)] -const fn is_pow2_u64(x: u64) -> bool { - x != 0 && (x & (x - 1)) == 0 -} - -#[inline(always)] -const fn log2_pow2_u64(mut x: u64) -> u32 { - let mut k = 0u32; - while x > 1 { - x >>= 1; - k += 1; - } - k -} - -#[inline(always)] -fn mul64_wide(a: u64, b: u64) -> (u64, u64) { - #[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] - { - unsafe { mul64_wide_bmi2(a, b) } - } - #[cfg(not(all(target_arch = "x86_64", target_feature = "bmi2")))] - { - let prod = (a as u128) * (b as u128); - (prod as u64, (prod >> 64) as u64) - } -} - -#[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] -#[inline(always)] -unsafe fn mul64_wide_bmi2(a: u64, b: u64) -> (u64, u64) { - let mut hi = 0; - // Safety: caller guarantees CPU support via cfg-gated compilation. - let lo = unsafe { std::arch::x86_64::_mulx_u64(a, b, &mut hi) }; - (lo, hi) -} +use super::util::{is_pow2_u64, log2_pow2_u64, mul64_wide}; /// Prime field element for primes `p = 2^k − c` stored as `u64`. /// @@ -438,18 +405,6 @@ impl FieldCore for Fp64

{ self.0 == 0 } - fn add(&self, rhs: &Self) -> Self { - *self + *rhs - } - - fn sub(&self, rhs: &Self) -> Self { - *self - *rhs - } - - fn mul(&self, rhs: &Self) -> Self { - *self * *rhs - } - fn inv(self) -> Option { let inv = self.inv_or_zero(); if self.is_zero() { @@ -477,7 +432,7 @@ impl FieldSampling for Fp64

{ } } -impl CanonicalField for Fp64

{ +impl FromSmallInt for Fp64

{ fn from_u64(val: u64) -> Self { Self(Self::reduce_u128(val as u128)) } @@ -486,10 +441,12 @@ impl CanonicalField for Fp64

{ if val >= 0 { Self::from_u64(val as u64) } else { - -Self::from_u64((-val) as u64) + -Self::from_u64(val.unsigned_abs()) } } +} +impl CanonicalField for Fp64

{ fn to_canonical_u128(self) -> u128 { self.0 as u128 } diff --git a/src/algebra/fields/lift.rs b/src/algebra/fields/lift.rs index 5e243c9c..e05a8aa7 100644 --- a/src/algebra/fields/lift.rs +++ b/src/algebra/fields/lift.rs @@ -2,7 +2,7 @@ use crate::algebra::fields::ext::{Fp2, Fp2Config, Fp4, Fp4Config}; use crate::primitives::serialization::Valid; -use crate::FieldCore; +use crate::{FieldCore, FromSmallInt}; /// Lift a base-field element into an extension field. /// @@ -12,6 +12,63 @@ pub trait LiftBase: FieldCore { fn lift_base(x: F) -> Self; } +/// An algebraic extension of base field `F`. +/// +/// Provides the extension degree and a constructor from a slice of base-field +/// coefficients (in the canonical basis `{1, u, u^2, ...}`). +pub trait ExtField: FieldCore + LiftBase + FromSmallInt { + /// Extension degree: `[Self : F]`. + const EXT_DEGREE: usize; + + /// Construct from a coefficient slice `[c0, c1, ..., c_{d-1}]`. + /// + /// # Panics + /// Panics if `coeffs.len() != Self::EXT_DEGREE`. + fn from_base_slice(coeffs: &[F]) -> Self; +} + +impl ExtField for F { + const EXT_DEGREE: usize = 1; + + #[inline] + fn from_base_slice(coeffs: &[F]) -> Self { + assert_eq!(coeffs.len(), 1); + coeffs[0] + } +} + +impl ExtField for Fp2 +where + F: FieldCore + FromSmallInt + Valid, + C: Fp2Config, +{ + const EXT_DEGREE: usize = 2; + + #[inline] + fn from_base_slice(coeffs: &[F]) -> Self { + assert_eq!(coeffs.len(), 2); + Self::new(coeffs[0], coeffs[1]) + } +} + +impl ExtField for Fp4 +where + F: FieldCore + FromSmallInt + Valid, + C2: Fp2Config, + C4: Fp4Config, +{ + const EXT_DEGREE: usize = 4; + + #[inline] + fn from_base_slice(coeffs: &[F]) -> Self { + assert_eq!(coeffs.len(), 4); + Self::new( + Fp2::new(coeffs[0], coeffs[1]), + Fp2::new(coeffs[2], coeffs[3]), + ) + } +} + impl LiftBase for F { #[inline] fn lift_base(x: F) -> Self { diff --git a/src/algebra/fields/mod.rs b/src/algebra/fields/mod.rs index d255852a..85cf56d0 100644 --- a/src/algebra/fields/mod.rs +++ b/src/algebra/fields/mod.rs @@ -18,17 +18,20 @@ pub mod packed_avx2; target_feature = "avx512dq" ))] pub mod packed_avx512; +#[allow(missing_docs)] +pub mod packed_ext; #[cfg(all(target_arch = "aarch64", target_feature = "neon"))] pub mod packed_neon; pub mod pseudo_mersenne; +pub(crate) mod util; -pub use ext::{Fp2, Fp2Config, Fp4, Fp4Config}; +pub use ext::{Ext2, Ext4, Fp2, Fp2Config, Fp4, Fp4Config, NegOneNr, TwoNr, UnitNr}; pub use fp128::{ Fp128, Prime128M13M4P0, Prime128M37P3P0, Prime128M52M3P0, Prime128M54P4P0, Prime128M8M4M1M0, }; pub use fp32::Fp32; pub use fp64::Fp64; -pub use lift::LiftBase; +pub use lift::{ExtField, LiftBase}; pub use packed::{ Fp128Packing, Fp32Packing, Fp64Packing, HasPacking, NoPacking, PackedField, PackedValue, }; diff --git a/src/algebra/fields/packed.rs b/src/algebra/fields/packed.rs index e66063a9..eaf15ab2 100644 --- a/src/algebra/fields/packed.rs +++ b/src/algebra/fields/packed.rs @@ -236,7 +236,7 @@ mod tests { Pow2Offset24Field, Pow2Offset31Field, Pow2Offset32Field, Pow2Offset40Field, Pow2Offset64Field, Prime128M13M4P0, }; - use crate::{CanonicalField, FieldCore, FieldSampling}; + use crate::{CanonicalField, FieldCore, FieldSampling, FromSmallInt}; use rand::{rngs::StdRng, RngCore, SeedableRng}; fn rand_u128(rng: &mut R) -> u128 { diff --git a/src/algebra/fields/packed_ext.rs b/src/algebra/fields/packed_ext.rs new file mode 100644 index 00000000..5bf061d9 --- /dev/null +++ b/src/algebra/fields/packed_ext.rs @@ -0,0 +1,415 @@ +//! Packed extension field types using transpose-based packing. +//! +//! A `PackedFp2` stores `[PF; 2]` where `PF` is the packed base field. +//! Each `PF` lane contains the corresponding coefficient of an `Fp2` element. +//! This enables WIDTH-fold parallel arithmetic over `Fp2` using existing SIMD +//! base-field operations. + +use crate::algebra::fields::ext::{Fp2, Fp2Config, Fp4, Fp4Config}; +use crate::algebra::fields::packed::{HasPacking, PackedField, PackedValue}; +use crate::primitives::serialization::Valid; +use crate::FieldCore; +use core::ops::{Add, Mul, Sub}; + +/// Packed `Fp2` elements stored in transpose layout: `[PF; 2]`. +/// +/// If `PF` has width `W`, this represents `W` parallel `Fp2` values. +pub struct PackedFp2, PF: PackedField> { + pub c0: PF, + pub c1: PF, + _marker: std::marker::PhantomData (F, C)>, +} + +impl, PF: PackedField> Clone for PackedFp2 { + fn clone(&self) -> Self { + *self + } +} + +impl, PF: PackedField> Copy for PackedFp2 {} + +impl, PF: PackedField> std::fmt::Debug + for PackedFp2 +{ + fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { + f.debug_struct("PackedFp2").finish_non_exhaustive() + } +} + +impl, PF: PackedField> PackedFp2 { + #[inline] + pub fn new(c0: PF, c1: PF) -> Self { + Self { + c0, + c1, + _marker: std::marker::PhantomData, + } + } + + #[inline] + fn mul_nr(x: PF) -> PF { + if C::IS_NEG_ONE { + let zero = PF::broadcast(F::zero()); + zero - x + } else { + PF::broadcast(C::non_residue()) * x + } + } +} + +impl PackedValue for PackedFp2 +where + F: FieldCore + Valid + 'static, + C: Fp2Config + 'static, + PF: PackedField, +{ + type Value = Fp2; + const WIDTH: usize = PF::WIDTH; + + fn from_fn(mut f: G) -> Self + where + G: FnMut(usize) -> Self::Value, + { + let mut c0s = Vec::with_capacity(PF::WIDTH); + let mut c1s = Vec::with_capacity(PF::WIDTH); + for i in 0..PF::WIDTH { + let val = f(i); + c0s.push(val.c0); + c1s.push(val.c1); + } + Self::new(PF::from_fn(|i| c0s[i]), PF::from_fn(|i| c1s[i])) + } + + fn extract(&self, lane: usize) -> Self::Value { + Fp2::new(self.c0.extract(lane), self.c1.extract(lane)) + } +} + +impl Add for PackedFp2 +where + F: FieldCore, + C: Fp2Config, + PF: PackedField, +{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + Self::new(self.c0 + rhs.c0, self.c1 + rhs.c1) + } +} + +impl Sub for PackedFp2 +where + F: FieldCore, + C: Fp2Config, + PF: PackedField, +{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + Self::new(self.c0 - rhs.c0, self.c1 - rhs.c1) + } +} + +impl Mul for PackedFp2 +where + F: FieldCore, + C: Fp2Config, + PF: PackedField, +{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + let v0 = self.c0 * rhs.c0; + let v1 = self.c1 * rhs.c1; + Self::new( + v0 + Self::mul_nr(v1), + (self.c0 + self.c1) * (rhs.c0 + rhs.c1) - v0 - v1, + ) + } +} + +impl PackedField for PackedFp2 +where + F: FieldCore + Valid + 'static, + C: Fp2Config + 'static, + PF: PackedField, +{ + type Scalar = Fp2; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self::new(PF::broadcast(value.c0), PF::broadcast(value.c1)) + } +} + +impl HasPacking for Fp2 +where + F: FieldCore + Valid + HasPacking + 'static, + C: Fp2Config + 'static, +{ + type Packing = PackedFp2; +} + +/// Packed `Fp4` elements stored in transpose layout: `[PackedFp2; 2]`. +pub struct PackedFp4< + F: FieldCore, + C2: Fp2Config, + C4: Fp4Config, + PF: PackedField, +> { + pub c0: PackedFp2, + pub c1: PackedFp2, + _marker: std::marker::PhantomData C4>, +} + +impl Clone for PackedFp4 +where + F: FieldCore, + C2: Fp2Config, + C4: Fp4Config, + PF: PackedField, +{ + fn clone(&self) -> Self { + *self + } +} + +impl Copy for PackedFp4 +where + F: FieldCore, + C2: Fp2Config, + C4: Fp4Config, + PF: PackedField, +{ +} + +impl std::fmt::Debug for PackedFp4 +where + F: FieldCore, + C2: Fp2Config, + C4: Fp4Config, + PF: PackedField, +{ + fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { + f.debug_struct("PackedFp4").finish_non_exhaustive() + } +} + +impl PackedFp4 +where + F: FieldCore, + C2: Fp2Config, + C4: Fp4Config, + PF: PackedField, +{ + #[inline] + pub fn new(c0: PackedFp2, c1: PackedFp2) -> Self { + Self { + c0, + c1, + _marker: std::marker::PhantomData, + } + } +} + +impl PackedValue for PackedFp4 +where + F: FieldCore + Valid + 'static, + C2: Fp2Config + 'static, + C4: Fp4Config + 'static, + PF: PackedField, +{ + type Value = Fp4; + const WIDTH: usize = PF::WIDTH; + + fn from_fn(mut f: G) -> Self + where + G: FnMut(usize) -> Self::Value, + { + let mut c0s: Vec> = Vec::with_capacity(PF::WIDTH); + let mut c1s: Vec> = Vec::with_capacity(PF::WIDTH); + for i in 0..PF::WIDTH { + let val = f(i); + c0s.push(val.c0); + c1s.push(val.c1); + } + Self::new( + PackedFp2::from_fn(|i| c0s[i]), + PackedFp2::from_fn(|i| c1s[i]), + ) + } + + fn extract(&self, lane: usize) -> Self::Value { + Fp4::new(self.c0.extract(lane), self.c1.extract(lane)) + } +} + +impl Add for PackedFp4 +where + F: FieldCore, + C2: Fp2Config, + C4: Fp4Config, + PF: PackedField, +{ + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + Self::new(self.c0 + rhs.c0, self.c1 + rhs.c1) + } +} + +impl Sub for PackedFp4 +where + F: FieldCore, + C2: Fp2Config, + C4: Fp4Config, + PF: PackedField, +{ + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + Self::new(self.c0 - rhs.c0, self.c1 - rhs.c1) + } +} + +impl Mul for PackedFp4 +where + F: FieldCore + Valid + 'static, + C2: Fp2Config + 'static, + C4: Fp4Config, + PF: PackedField, +{ + type Output = Self; + #[inline] + fn mul(self, rhs: Self) -> Self { + let nr2 = PackedFp2::broadcast(C4::non_residue()); + let v0 = self.c0 * rhs.c0; + let v1 = self.c1 * rhs.c1; + Self::new( + v0 + nr2 * v1, + (self.c0 + self.c1) * (rhs.c0 + rhs.c1) - v0 - v1, + ) + } +} + +impl PackedField for PackedFp4 +where + F: FieldCore + Valid + 'static, + C2: Fp2Config + 'static, + C4: Fp4Config + 'static, + PF: PackedField, +{ + type Scalar = Fp4; + + #[inline] + fn broadcast(value: Self::Scalar) -> Self { + Self::new( + PackedFp2::broadcast(value.c0), + PackedFp2::broadcast(value.c1), + ) + } +} + +impl HasPacking for Fp4 +where + F: FieldCore + Valid + HasPacking + 'static, + C2: Fp2Config + 'static, + C4: Fp4Config + 'static, +{ + type Packing = PackedFp4; +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::algebra::fields::ext::{Ext2, Ext4, TwoNr, UnitNr}; + use crate::algebra::Fp64; + use crate::{FieldSampling, FromSmallInt}; + use rand::rngs::StdRng; + use rand::SeedableRng; + + type F = Fp64<4294967197>; + type E2 = Ext2; + type E4 = Ext4; + type PE2 = PackedFp2::Packing>; + type PE4 = PackedFp4::Packing>; + + #[test] + fn packed_fp2_add() { + let mut rng = StdRng::seed_from_u64(100); + let width = ::WIDTH; + let a_elems: Vec = (0..width).map(|_| E2::sample(&mut rng)).collect(); + let b_elems: Vec = (0..width).map(|_| E2::sample(&mut rng)).collect(); + + let pa = PE2::from_fn(|i| a_elems[i]); + let pb = PE2::from_fn(|i| b_elems[i]); + let pc = pa + pb; + + for i in 0..width { + assert_eq!(pc.extract(i), a_elems[i] + b_elems[i]); + } + } + + #[test] + fn packed_fp2_mul() { + let mut rng = StdRng::seed_from_u64(200); + let width = ::WIDTH; + let a_elems: Vec = (0..width).map(|_| E2::sample(&mut rng)).collect(); + let b_elems: Vec = (0..width).map(|_| E2::sample(&mut rng)).collect(); + + let pa = PE2::from_fn(|i| a_elems[i]); + let pb = PE2::from_fn(|i| b_elems[i]); + let pc = pa * pb; + + for i in 0..width { + assert_eq!( + pc.extract(i), + a_elems[i] * b_elems[i], + "packed Fp2 mul mismatch at lane {i}" + ); + } + } + + #[test] + fn packed_fp2_broadcast() { + let val = E2::new(F::from_u64(7), F::from_u64(11)); + let packed = PE2::broadcast(val); + let width = ::WIDTH; + for i in 0..width { + assert_eq!(packed.extract(i), val); + } + } + + #[test] + fn packed_fp4_mul() { + let mut rng = StdRng::seed_from_u64(300); + let width = ::WIDTH; + let a_elems: Vec = (0..width).map(|_| E4::sample(&mut rng)).collect(); + let b_elems: Vec = (0..width).map(|_| E4::sample(&mut rng)).collect(); + + let pa = PE4::from_fn(|i| a_elems[i]); + let pb = PE4::from_fn(|i| b_elems[i]); + let pc = pa * pb; + + for i in 0..width { + assert_eq!( + pc.extract(i), + a_elems[i] * b_elems[i], + "packed Fp4 mul mismatch at lane {i}" + ); + } + } + + #[test] + fn pack_unpack_roundtrip_fp2() { + let mut rng = StdRng::seed_from_u64(400); + let width = ::WIDTH; + let elems: Vec = (0..width * 3).map(|_| E2::sample(&mut rng)).collect(); + + let packed = PE2::pack_slice(&elems); + let unpacked = PE2::unpack_slice(&packed); + + assert_eq!(elems, unpacked); + } +} diff --git a/src/algebra/fields/packed_neon.rs b/src/algebra/fields/packed_neon.rs index aeeea0ef..a50f73a0 100644 --- a/src/algebra/fields/packed_neon.rs +++ b/src/algebra/fields/packed_neon.rs @@ -52,20 +52,7 @@ const fn modulus_hi() -> u64 { (P >> 64) as u64 } -#[inline(always)] -const fn is_pow2_u64(x: u64) -> bool { - x != 0 && (x & (x - 1)) == 0 -} - -#[inline(always)] -const fn log2_pow2_u64(mut x: u64) -> u32 { - let mut k = 0u32; - while x > 1 { - x >>= 1; - k += 1; - } - k -} +use super::util::{is_pow2_u64, log2_pow2_u64}; impl PackedFp128Neon

{ const C: u128 = { diff --git a/src/algebra/fields/util.rs b/src/algebra/fields/util.rs new file mode 100644 index 00000000..9496f1ce --- /dev/null +++ b/src/algebra/fields/util.rs @@ -0,0 +1,38 @@ +//! Shared helpers for field arithmetic backends. + +#[inline(always)] +pub(crate) const fn is_pow2_u64(x: u64) -> bool { + x != 0 && (x & (x - 1)) == 0 +} + +#[inline(always)] +pub(crate) const fn log2_pow2_u64(mut x: u64) -> u32 { + let mut k = 0u32; + while x > 1 { + x >>= 1; + k += 1; + } + k +} + +/// `a * b` widening to 128 bits; returns `(lo64, hi64)`. +#[inline(always)] +pub(crate) fn mul64_wide(a: u64, b: u64) -> (u64, u64) { + #[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] + { + unsafe { mul64_wide_bmi2(a, b) } + } + #[cfg(not(all(target_arch = "x86_64", target_feature = "bmi2")))] + { + let prod = (a as u128) * (b as u128); + (prod as u64, (prod >> 64) as u64) + } +} + +#[cfg(all(target_arch = "x86_64", target_feature = "bmi2"))] +#[inline(always)] +unsafe fn mul64_wide_bmi2(a: u64, b: u64) -> (u64, u64) { + let mut hi = 0; + let lo = unsafe { std::arch::x86_64::_mulx_u64(a, b, &mut hi) }; + (lo, hi) +} diff --git a/src/algebra/mod.rs b/src/algebra/mod.rs index 8a5cc194..21aea776 100644 --- a/src/algebra/mod.rs +++ b/src/algebra/mod.rs @@ -6,7 +6,6 @@ //! - Low-level NTT and CRT+NTT arithmetic scaffolding (`ntt`) pub mod backend; -pub mod domains; pub mod fields; pub mod module; pub mod ntt; @@ -15,20 +14,19 @@ pub mod ring; // Flat re-exports for convenience. pub use backend::{CrtReconstruct, NttPrimeOps, NttTransform, RingBackend, ScalarBackend}; -pub use domains::{CoeffDomain, CrtNttDomain}; pub use fields::{ - is_pow2_offset, pow2_offset, pseudo_mersenne_modulus, Fp128, Fp128Packing, Fp2, Fp2Config, - Fp32, Fp32Packing, Fp4, Fp4Config, Fp64, Fp64Packing, HasPacking, NoPacking, PackedField, - PackedValue, Pow2Offset128Field, Pow2Offset24Field, Pow2Offset30Field, Pow2Offset31Field, - Pow2Offset32Field, Pow2Offset40Field, Pow2Offset48Field, Pow2Offset56Field, Pow2Offset64Field, - Pow2OffsetPrimeSpec, Prime128M13M4P0, Prime128M37P3P0, Prime128M52M3P0, Prime128M54P4P0, - Prime128M8M4M1M0, POW2_OFFSET_IMPLEMENTED_MAX_BITS, POW2_OFFSET_MAX, POW2_OFFSET_PRIMES, - POW2_OFFSET_TABLE, + is_pow2_offset, pow2_offset, pseudo_mersenne_modulus, ExtField, Fp128, Fp128Packing, Fp2, + Fp2Config, Fp32, Fp32Packing, Fp4, Fp4Config, Fp64, Fp64Packing, HasPacking, LiftBase, + NoPacking, PackedField, PackedValue, Pow2Offset128Field, Pow2Offset24Field, Pow2Offset30Field, + Pow2Offset31Field, Pow2Offset32Field, Pow2Offset40Field, Pow2Offset48Field, Pow2Offset56Field, + Pow2Offset64Field, Pow2OffsetPrimeSpec, Prime128M13M4P0, Prime128M37P3P0, Prime128M52M3P0, + Prime128M54P4P0, Prime128M8M4M1M0, POW2_OFFSET_IMPLEMENTED_MAX_BITS, POW2_OFFSET_MAX, + POW2_OFFSET_PRIMES, POW2_OFFSET_TABLE, }; pub use module::VectorModule; pub use ntt::tables; -pub use ntt::{LimbQ, MontCoeff, NttPrime, QData, RADIX_BITS}; +pub use ntt::{GarnerData, LimbQ, MontCoeff, NttPrime, PrimeWidth, RADIX_BITS}; pub use ring::{ - CrtNttConvertibleField, CyclotomicCrtNtt, CyclotomicRing, SparseChallenge, + CrtNttConvertibleField, CrtNttParamSet, CyclotomicCrtNtt, CyclotomicRing, SparseChallenge, SparseChallengeConfig, }; diff --git a/src/algebra/module.rs b/src/algebra/module.rs index 6cfdb554..b924a0ae 100644 --- a/src/algebra/module.rs +++ b/src/algebra/module.rs @@ -127,14 +127,6 @@ where Self::zero_vec() } - fn add(&self, rhs: &Self) -> Self { - *self + *rhs - } - - fn neg(&self) -> Self { - -*self - } - fn scale(&self, k: &Self::Scalar) -> Self { // Delegate to Scalar * VectorModule to satisfy the Module trait’s scalar bounds. *k * *self diff --git a/src/algebra/ntt/butterfly.rs b/src/algebra/ntt/butterfly.rs index 9f58da94..fd0f6e53 100644 --- a/src/algebra/ntt/butterfly.rs +++ b/src/algebra/ntt/butterfly.rs @@ -1,133 +1,182 @@ //! NTT butterfly transforms for negacyclic rings `Z_p[X]/(X^D + 1)`. //! -//! Uses a merged negacyclic Cooley-Tukey / Gentleman-Sande butterfly where -//! the twist factors for `X^D + 1` are folded directly into the twiddles. -//! Twiddle factors are powers of `psi`, a primitive `2D`-th root of unity -//! (`psi^D = -1 mod p`), rather than a `D`-th root. +//! Implements a negacyclic NTT via the standard **twist + cyclic NTT** method. //! -//! TODO(perf): migrate twiddle tables to compile-time `const` arrays once -//! parameter sets are finalized. +//! Let `psi` be a primitive `2D`-th root of unity (`psi^D = -1 mod p`) and +//! `omega = psi^2`, a primitive `D`-th root of unity. For polynomials modulo +//! `X^D + 1`, we: +//! - pre-twist coefficients by `psi^i` +//! - run a cyclic size-`D` NTT using `omega` +//! - inverse-cyclic NTT using `omega^{-1}` +//! - post-untwist by `psi^{-i}` -use super::prime::{MontCoeff, NttPrime}; +use super::prime::{MontCoeff, NttPrime, PrimeWidth}; /// Precomputed twiddle factors for a specific prime and degree `D`. /// /// `D` must be a power of two. -pub struct NttTwiddles { - /// Twiddle factors in Montgomery form, indexed by bit-reversed position. - /// `zetas[i] = from_canonical(psi^{brv(i)})` for `i = 0..D`. - /// Index 0 is unused by the forward NTT but set to the Montgomery form of 1. - pub(crate) zetas: [MontCoeff; D], +pub struct NttTwiddles { + /// Stage roots for iterative forward cyclic NTT in Montgomery form. + pub(crate) fwd_wlen: [MontCoeff; D], + /// Stage roots for iterative inverse cyclic NTT in Montgomery form. + pub(crate) inv_wlen: [MontCoeff; D], + /// Number of active stages in the twiddle arrays (`log2(D)`). + pub(crate) num_stages: usize, + /// Twist factors `psi^i` for negacyclic embedding, in Montgomery form. + pub(crate) psi_pows: [MontCoeff; D], + /// Untwist factors `psi^{-i}`, in Montgomery form. + pub(crate) psi_inv_pows: [MontCoeff; D], /// `D^{-1} mod p` in Montgomery form, used for inverse NTT final scaling. - pub(crate) d_inv: MontCoeff, + pub(crate) d_inv: MontCoeff, } -impl NttTwiddles { +impl NttTwiddles { /// Compute twiddle factors for the given prime. /// - /// Finds a primitive `2D`-th root of unity mod `p`, then fills the - /// twiddle table in bit-reversed order. All values are stored in - /// Montgomery form. + /// Finds a primitive `2D`-th root `psi` and derives `omega = psi^2`. + /// Fills cyclic forward/inverse twiddles for `omega` and twist/untwist + /// tables for `psi`. All values are stored in Montgomery form. /// /// # Panics /// /// Panics if `D` is not a power of two, or if `2D` does not divide `p - 1`. - pub fn compute(prime: NttPrime) -> Self { + pub fn compute(prime: NttPrime) -> Self { assert!(D.is_power_of_two(), "D must be a power of two"); - let p = prime.p as i64; + let p = prime.p.to_i64(); assert!( (p - 1) % (2 * D as i64) == 0, "2D must divide p - 1 for NTT roots to exist" ); - let n = D.trailing_zeros(); let psi = find_primitive_root_2d(p, D); + let omega = (psi * psi) % p; + let omega_inv = pow_mod(omega, p - 2, p); - let mut zetas = [MontCoeff::from_raw(0); D]; - for (i, z) in zetas.iter_mut().enumerate() { - let brv_i = bit_reverse(i, n); - let power = pow_mod(psi, brv_i as i64, p) as i16; - *z = prime.from_canonical(power); + let psi_inv = pow_mod(psi, p - 2, p); + let mut psi_pows = [MontCoeff::from_raw(W::default()); D]; + let mut psi_inv_pows = [MontCoeff::from_raw(W::default()); D]; + let mut cur = 1i64; + let mut cur_inv = 1i64; + for i in 0..D { + psi_pows[i] = prime.from_canonical(W::from_i64(cur)); + psi_inv_pows[i] = prime.from_canonical(W::from_i64(cur_inv)); + cur = (cur * psi) % p; + cur_inv = (cur_inv * psi_inv) % p; } - let d_inv_canonical = pow_mod(D as i64, p - 2, p) as i16; - let d_inv = prime.from_canonical(d_inv_canonical); + let mut fwd_wlen = [MontCoeff::from_raw(W::default()); D]; + let mut inv_wlen = [MontCoeff::from_raw(W::default()); D]; + let mut len = 1usize; + let mut stage = 0usize; + while len < D { + let exp = (D / (2 * len)) as i64; + fwd_wlen[stage] = prime.from_canonical(W::from_i64(pow_mod(omega, exp, p))); + inv_wlen[stage] = prime.from_canonical(W::from_i64(pow_mod(omega_inv, exp, p))); + len *= 2; + stage += 1; + } + + let d_inv_canonical = pow_mod(D as i64, p - 2, p); + let d_inv = prime.from_canonical(W::from_i64(d_inv_canonical)); - Self { zetas, d_inv } + Self { + fwd_wlen, + inv_wlen, + num_stages: stage, + psi_pows, + psi_inv_pows, + d_inv, + } } } -/// Forward negacyclic NTT (Cooley-Tukey, decimation-in-time). +/// Forward negacyclic NTT (twist + cyclic Gentleman-Sande DIF). /// /// Transforms `D` coefficients in-place from coefficient form to NTT -/// evaluation form. Both outputs of each butterfly are Barrett-reduced +/// evaluation form. Both outputs of each butterfly are range-reduced /// to prevent overflow. -/// -/// After this call, the coefficients represent evaluations at -/// `psi^{2*brv(i)+1}` for `i = 0..D-1`. -pub fn forward_ntt(a: &mut [MontCoeff; D], prime: NttPrime, tw: &NttTwiddles) { - let mut k = 1usize; +pub fn forward_ntt( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + for (ai, psi) in a.iter_mut().zip(tw.psi_pows.iter()) { + *ai = prime.mul(*ai, *psi); + } + + let one = prime.from_canonical(W::from_i64(1)); + let mut len = D / 2; - while len >= 1 { - let mut start = 0; + let mut stage = tw.num_stages; + while len > 0 { + stage -= 1; + let wlen = tw.fwd_wlen[stage]; + let mut start = 0usize; while start < D { - let zeta = tw.zetas[k]; - k += 1; - for j in start..(start + len) { - let t = prime.mul(a[j + len], zeta); - let diff = a[j].raw().wrapping_sub(t.raw()); - let sum = a[j].raw().wrapping_add(t.raw()); - a[j + len] = prime.reduce(MontCoeff::from_raw(diff)); - a[j] = prime.reduce(MontCoeff::from_raw(sum)); + let mut w = one; + for j in 0..len { + let u = a[start + j]; + let v = a[start + j + len]; + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.mul(MontCoeff::from_raw(diff), w); + w = prime.mul(w, wlen); } start += 2 * len; } len /= 2; } + + // Keep exported NTT-domain coefficients in the same reduced range expected + // by add/sub reduced operations and equality checks. + prime.reduce_range_in_place(a); } -/// Inverse negacyclic NTT (Gentleman-Sande, decimation-in-frequency). +/// Inverse negacyclic NTT (cyclic Cooley-Tukey DIT + untwist). /// /// Transforms `D` evaluations in-place back to coefficient form. /// Includes the final `D^{-1}` scaling. -pub fn inverse_ntt(a: &mut [MontCoeff; D], prime: NttPrime, tw: &NttTwiddles) { - let mut k = D - 1; - let mut len = 1; - while len <= D / 2 { - let mut start = 0; +pub fn inverse_ntt( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + let one = prime.from_canonical(W::from_i64(1)); + + let mut len = 1usize; + let mut stage = 0usize; + while len < D { + let wlen = tw.inv_wlen[stage]; + let mut start = 0usize; while start < D { - let zeta = tw.zetas[k]; - k = k.wrapping_sub(1); - for j in start..(start + len) { - let t = a[j]; - let sum = t.raw().wrapping_add(a[j + len].raw()); - let diff = t.raw().wrapping_sub(a[j + len].raw()); - a[j] = prime.reduce(MontCoeff::from_raw(sum)); - // Multiply difference by negative twiddle: negate zeta. - let neg_zeta = MontCoeff::from_raw(zeta.raw().wrapping_neg()); - a[j + len] = prime.mul(MontCoeff::from_raw(diff), neg_zeta); + let mut w = one; + for j in 0..len { + let u = a[start + j]; + let v = prime.mul(a[start + j + len], w); + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.reduce_range(MontCoeff::from_raw(diff)); + w = prime.mul(w, wlen); } start += 2 * len; } len *= 2; + stage += 1; } - // Scale by D^{-1}. for c in a.iter_mut() { *c = prime.mul(*c, tw.d_inv); } -} -/// Bit-reverse an `n`-bit integer. -fn bit_reverse(x: usize, n: u32) -> usize { - x.reverse_bits() >> (usize::BITS - n) + for (ai, psi_inv) in a.iter_mut().zip(tw.psi_inv_pows.iter()) { + *ai = prime.mul(*ai, *psi_inv); + } } /// Find a primitive `2D`-th root of unity mod `p`. -/// -/// Returns `psi` in `[0, p)` such that `psi^D = -1 mod p`. fn find_primitive_root_2d(p: i64, d: usize) -> i64 { - // Find the smallest quadratic non-residue a (i.e., a^{(p-1)/2} = -1 mod p). let half = (p - 1) / 2; let exp = (p - 1) / (2 * d as i64); for a in 2..p { diff --git a/src/algebra/ntt/crt.rs b/src/algebra/ntt/crt.rs index 7df39710..e0897937 100644 --- a/src/algebra/ntt/crt.rs +++ b/src/algebra/ntt/crt.rs @@ -1,17 +1,56 @@ -//! Limb-based helpers for `q = 2^k - c` style moduli. -//! -//! Big-`q` coefficients are stored in radix `2^14` limbs. -//! This module provides a portable scalar representation with the same limb layout. +//! CRT helpers: Garner reconstruction and limb-based modular arithmetic. use std::cmp::Ordering; use std::fmt; use std::ops::{Add, Sub}; +use super::prime::{NttPrime, PrimeWidth}; + /// Limb radix bit-width (`2^14`). pub const RADIX_BITS: u32 = 14; const RADIX: i32 = 1 << RADIX_BITS; const RADIX_MASK: i32 = RADIX - 1; +/// Precomputed Garner inverse table for CRT reconstruction. +/// +/// `gamma[i][j]` = `p_j^{-1} mod p_i` for `j < i`. Upper triangle and +/// diagonal entries are zero (unused). +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct GarnerData { + /// `gamma[i][j]` = `p_j^{-1} mod p_i` for `j < i`. + pub gamma: [[W; K]; K], +} + +impl GarnerData { + /// Compute Garner constants from a set of NTT primes. + pub fn compute(primes: &[NttPrime; K]) -> Self { + let mut gamma = [[W::default(); K]; K]; + for i in 1..K { + let pi = primes[i].p.to_i64(); + #[allow(clippy::needless_range_loop)] + for j in 0..i { + let pj = primes[j].p.to_i64(); + let inv = mod_inverse_i64(pj, pi); + gamma[i][j] = W::from_i64(inv); + } + } + Self { gamma } + } +} + +/// Modular inverse via extended GCD, operating in `i64`. +fn mod_inverse_i64(a: i64, modulus: i64) -> i64 { + let (mut t, mut new_t) = (0i64, 1i64); + let (mut r, mut new_r) = (modulus, ((a % modulus) + modulus) % modulus); + while new_r != 0 { + let q = r / new_r; + (t, new_t) = (new_t, t - q * new_t); + (r, new_r) = (new_r, r - q * new_r); + } + assert_eq!(r, 1, "modular inverse does not exist"); + ((t % modulus) + modulus) % modulus +} + /// Fixed-width radix-`2^14` integer. /// /// Limbs are little-endian: `limbs[0]` is least significant. @@ -44,7 +83,6 @@ impl LimbQ { /// Conditional subtraction: if `self >= modulus`, return `self - modulus` (branchless). #[inline] pub fn csub_mod(self, modulus: Self) -> Self { - // Compute self - modulus, tracking the final borrow. let mut diff = [0u16; L]; let mut borrow = 0i32; for (i, df) in diff.iter_mut().enumerate() { @@ -56,8 +94,6 @@ impl LimbQ { *df = d as u16; } } - // borrow = -1 if self < modulus (underflowed), 0 otherwise. - // Branchless select: mask = 0xFFFF if underflow (keep self), 0 if not (keep diff). let mask = borrow as u16; let mut result = [0u16; L]; for (i, r) in result.iter_mut().enumerate() { @@ -164,26 +200,3 @@ impl fmt::Display for LimbQ { } } } - -/// CRT/q constants for a given parameter set. -#[derive(Debug, Clone, Copy, PartialEq, Eq)] -pub struct QData { - /// The modulus `q` in radix-`2^14` limbs. - pub q: LimbQ, - /// `-P mod q` in limbs (where `P = prod p_i`). - pub pmq: LimbQ, - /// `P/p_i mod q` in limbs. - pub xvec: [LimbQ; K], - /// `k` in `q = 2^k - c`. - pub logq: u32, - /// `c` in `q = 2^k - c`. - pub qoff: u16, -} - -impl QData { - /// `q` as `u128` when representable. - #[inline] - pub fn q_u128(self) -> Option { - u128::try_from(self.q).ok() - } -} diff --git a/src/algebra/ntt/mod.rs b/src/algebra/ntt/mod.rs index fffbf284..f2536363 100644 --- a/src/algebra/ntt/mod.rs +++ b/src/algebra/ntt/mod.rs @@ -6,5 +6,5 @@ pub mod prime; pub mod tables; pub use butterfly::NttTwiddles; -pub use crt::{LimbQ, QData, RADIX_BITS}; -pub use prime::{MontCoeff, NttPrime}; +pub use crt::{GarnerData, LimbQ, RADIX_BITS}; +pub use prime::{MontCoeff, NttPrime, PrimeWidth}; diff --git a/src/algebra/ntt/prime.rs b/src/algebra/ntt/prime.rs index 9b19cf22..a5646234 100644 --- a/src/algebra/ntt/prime.rs +++ b/src/algebra/ntt/prime.rs @@ -1,143 +1,340 @@ -//! Small-prime arithmetic kernels for NTT-friendly parameter sets. +//! NTT prime arithmetic kernels generic over coefficient width. //! //! Per-prime scalar operations: //! - Montgomery multiplication ([`NttPrime::mul`]) -//! - Barrett-style reduction ([`NttPrime::reduce`]) -//! - Branchless conditional add/sub +//! - Branchless conditional add/sub and range reduction //! //! Coefficients in Montgomery domain are wrapped in [`MontCoeff`] to prevent -//! accidental mixing with canonical `i16` values. +//! accidental mixing with canonical values. +//! +//! The [`PrimeWidth`] trait abstracts over `i16` (R = 2^16, for primes < 2^14) +//! and `i32` (R = 2^32, for primes < 2^30). All NTT types are generic over +//! `W: PrimeWidth`; monomorphization produces optimal code for each width. use std::fmt; +mod sealed { + pub trait Sealed {} + impl Sealed for i16 {} + impl Sealed for i32 {} +} + +/// Integer width abstraction for NTT prime arithmetic. +/// +/// Sealed with exactly two implementations: `i16` and `i32`. +pub trait PrimeWidth: + sealed::Sealed + Copy + Clone + Eq + Default + fmt::Debug + Send + Sync + 'static +{ + /// Double-width type for intermediate Montgomery products. + type Wide: Copy + Clone; + + /// log2(R) for Montgomery reduction: 16 for `i16`, 32 for `i32`. + const R_LOG: u32; + + /// Widening multiply: `a * b` as `Wide`. + fn wide_mul(a: Self, b: Self) -> Self::Wide; + + /// Truncate wide value to narrow (low half, i.e. mod R). + fn truncate(w: Self::Wide) -> Self; + + /// Arithmetic right shift of wide value by `R_LOG` bits. + fn wide_shift(w: Self::Wide) -> Self; + + /// Wide subtraction (wrapping). + fn wide_sub(a: Self::Wide, b: Self::Wide) -> Self::Wide; + + /// Wrapping addition. + fn wrapping_add(self, rhs: Self) -> Self; + /// Wrapping subtraction. + fn wrapping_sub(self, rhs: Self) -> Self; + /// Wrapping multiplication. + fn wrapping_mul(self, rhs: Self) -> Self; + /// Wrapping negation. + fn wrapping_neg(self) -> Self; + + /// Arithmetic right shift by `BITS - 1`: all-1s if negative, all-0s otherwise. + fn sign_mask(self) -> Self; + + /// Bitwise AND. + fn bitand(self, rhs: Self) -> Self; + + /// Convert from `i64` (truncating). + fn from_i64(v: i64) -> Self; + /// Convert to `i64` (sign-extending). + fn to_i64(self) -> i64; +} + +impl PrimeWidth for i16 { + type Wide = i32; + const R_LOG: u32 = 16; + + #[inline] + fn wide_mul(a: Self, b: Self) -> i32 { + (a as i32) * (b as i32) + } + #[inline] + fn truncate(w: i32) -> Self { + w as i16 + } + #[inline] + fn wide_shift(w: i32) -> Self { + (w >> 16) as i16 + } + #[inline] + fn wide_sub(a: i32, b: i32) -> i32 { + a.wrapping_sub(b) + } + #[inline] + fn wrapping_add(self, rhs: Self) -> Self { + i16::wrapping_add(self, rhs) + } + #[inline] + fn wrapping_sub(self, rhs: Self) -> Self { + i16::wrapping_sub(self, rhs) + } + #[inline] + fn wrapping_mul(self, rhs: Self) -> Self { + i16::wrapping_mul(self, rhs) + } + #[inline] + fn wrapping_neg(self) -> Self { + i16::wrapping_neg(self) + } + #[inline] + fn sign_mask(self) -> Self { + self >> 15 + } + #[inline] + fn bitand(self, rhs: Self) -> Self { + self & rhs + } + #[inline] + fn from_i64(v: i64) -> Self { + v as i16 + } + #[inline] + fn to_i64(self) -> i64 { + self as i64 + } +} + +impl PrimeWidth for i32 { + type Wide = i64; + const R_LOG: u32 = 32; + + #[inline] + fn wide_mul(a: Self, b: Self) -> i64 { + (a as i64) * (b as i64) + } + #[inline] + fn truncate(w: i64) -> Self { + w as i32 + } + #[inline] + fn wide_shift(w: i64) -> Self { + (w >> 32) as i32 + } + #[inline] + fn wide_sub(a: i64, b: i64) -> i64 { + a.wrapping_sub(b) + } + #[inline] + fn wrapping_add(self, rhs: Self) -> Self { + i32::wrapping_add(self, rhs) + } + #[inline] + fn wrapping_sub(self, rhs: Self) -> Self { + i32::wrapping_sub(self, rhs) + } + #[inline] + fn wrapping_mul(self, rhs: Self) -> Self { + i32::wrapping_mul(self, rhs) + } + #[inline] + fn wrapping_neg(self) -> Self { + i32::wrapping_neg(self) + } + #[inline] + fn sign_mask(self) -> Self { + self >> 31 + } + #[inline] + fn bitand(self, rhs: Self) -> Self { + self & rhs + } + #[inline] + fn from_i64(v: i64) -> Self { + v as i32 + } + #[inline] + fn to_i64(self) -> i64 { + self as i64 + } +} + /// A coefficient in Montgomery domain for an NTT prime. /// -/// Wraps an `i16` representing `a * R mod p` (where `R = 2^16`). +/// Wraps a `W` representing `a * R mod p` (where `R = 2^{W::R_LOG}`). /// Use [`NttPrime::from_canonical`] to enter and [`NttPrime::to_canonical`] /// to leave Montgomery domain. #[derive(Clone, Copy, PartialEq, Eq, Default)] #[repr(transparent)] -pub struct MontCoeff(i16); +pub struct MontCoeff(W); -impl MontCoeff { +impl MontCoeff { /// Wrap a raw Montgomery-domain value. - /// - /// The caller must ensure `val` is a valid Montgomery-domain representative - /// for the intended prime. #[inline] - pub const fn from_raw(val: i16) -> Self { + pub fn from_raw(val: W) -> Self { Self(val) } - /// Extract the raw `i16` (still in Montgomery domain). + /// Extract the raw value (still in Montgomery domain). #[inline] - pub const fn raw(self) -> i16 { + pub fn raw(self) -> W { self.0 } } -impl fmt::Debug for MontCoeff { +impl fmt::Debug for MontCoeff { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { - write!(f, "Mont({})", self.0) + write!(f, "Mont({:?})", self.0) } } -/// Per-prime constants for NTT arithmetic over a small prime `p < 2^14`. +/// Per-prime constants for NTT arithmetic. /// -/// All scalar operations use Montgomery representation internally. Constants -/// are stored as raw `i16` in centered signed form. +/// Generic over `W: PrimeWidth` — use `i16` for primes below 2^14 (R = 2^16), +/// or `i32` for primes below 2^30 (R = 2^32). #[derive(Debug, Clone, Copy, PartialEq, Eq)] -pub struct NttPrime { +pub struct NttPrime { /// Prime modulus. - pub p: i16, - /// `p^{-1} mod 2^{16}` (centered signed). Used in Montgomery reduction. - pub pinv: i16, - /// `round(2^{27} / p)` for Barrett-style range reduction. - pub v: i16, - /// `R mod p` where `R = 2^{16}` (centered signed). Montgomery form of 1. - pub mont: i16, + pub p: W, + /// `p^{-1} mod R` (centered signed). Used in Montgomery reduction. + pub pinv: W, + /// `R mod p` (centered signed). Montgomery form of 1. + pub mont: W, /// `R^2 mod p` (centered signed). Used for canonical → Montgomery conversion. - pub montsq: i16, - /// NTT injection scale factor (centered signed). - pub s: i16, - /// Inverse-NTT post-scale factor (centered signed). - pub f: i16, - /// CRT reconstruction factor (centered signed). - pub t: i16, + pub montsq: W, } -impl NttPrime { - /// Montgomery product: `a * b * R^{-1} mod p` where `R = 2^{16}`. - #[inline] - pub fn mul(self, a: MontCoeff, b: MontCoeff) -> MontCoeff { - MontCoeff(self.mont_mul_raw(a.0, b.0)) +impl NttPrime { + /// Derive all Montgomery constants from a raw prime value. + pub fn compute(p: W) -> Self { + let p_i64 = p.to_i64(); + debug_assert!(p_i64 > 1 && p_i64 % 2 == 1, "NTT prime must be odd and > 1"); + + // pinv via Newton's method: x_{n+1} = x_n * (2 - p * x_n). + // 5 iterations gives correctness mod 2^32 (sufficient for both i16 and i32). + let mut pinv: i64 = 1; + for _ in 0..5 { + pinv = pinv.wrapping_mul(2i64.wrapping_sub(p_i64.wrapping_mul(pinv))); + } + let pinv = W::from_i64(pinv); + + let half = p_i64 / 2; + let center = |x: i64| -> W { W::from_i64(if x > half { x - p_i64 } else { x }) }; + + let r_mod_p = ((1i128 << W::R_LOG) % (p_i64 as i128)) as i64; + let mont = center(r_mod_p); + + let rsq_mod_p = ((1i128 << (2 * W::R_LOG)) % (p_i64 as i128)) as i64; + let montsq = center(rsq_mod_p); + + Self { + p, + pinv, + mont, + montsq, + } } - /// Raw Montgomery multiply on bare `i16` values. - /// - /// Computes `(a*b - ((a*b mod R) * p_inv mod R) * p) / R`. + /// Montgomery product: `a * b * R^{-1} mod p`. #[inline] - pub(crate) fn mont_mul_raw(self, a: i16, b: i16) -> i16 { - let c = (a as i32) * (b as i32); - let t = (c as i16).wrapping_mul(self.pinv) as i32; - ((c - t * (self.p as i32)) >> 16) as i16 + pub fn mul(self, a: MontCoeff, b: MontCoeff) -> MontCoeff { + MontCoeff(self.mont_mul_raw(a.0, b.0)) } - /// Barrett-style reduction: tighten a Montgomery coefficient's range - /// toward `[0, p)` without full normalization. + /// Raw Montgomery multiply on bare `W` values. #[inline] - pub fn reduce(self, a: MontCoeff) -> MontCoeff { - let val = a.0; - let mut t = (((self.v as i32) * (val as i32) + (1 << 26)) >> 27) as i16; - t = t.wrapping_mul(self.p); - MontCoeff(val.wrapping_sub(t)) + pub(crate) fn mont_mul_raw(self, a: W, b: W) -> W { + let c = W::wide_mul(a, b); + let t = W::truncate(c).wrapping_mul(self.pinv); + let tp = W::wide_mul(t, self.p); + W::wide_shift(W::wide_sub(c, tp)) } /// Conditionally subtract `p` if `a >= p` (branchless). + /// + /// Input may be in `(-2p, 2p)` during butterflies. Both i16 and i32 paths + /// widen to avoid signed overflow: i16→i32, i32→i64. #[inline] - pub fn csubp(self, a: MontCoeff) -> MontCoeff { - let diff = a.0.wrapping_sub(self.p); - let mask = diff >> 15; - MontCoeff(diff.wrapping_add(mask & self.p)) + pub fn csubp(self, a: MontCoeff) -> MontCoeff { + if W::R_LOG == 16 { + let ai = a.0.to_i64() as i32; + let pi = self.p.to_i64() as i32; + let diff = ai - pi; + let mask = diff >> 31; + MontCoeff(W::from_i64((diff + (mask & pi)) as i64)) + } else { + let ai = a.0.to_i64(); + let pi = self.p.to_i64(); + let diff = ai - pi; + let mask = diff >> 63; + MontCoeff(W::from_i64(diff + (mask & pi))) + } } /// Conditionally add `p` if `a < 0` (branchless). + /// + /// Widened arithmetic mirrors `csubp` to avoid i16 overflow edge cases. #[inline] - pub fn caddp(self, a: MontCoeff) -> MontCoeff { - let mask = a.0 >> 15; - MontCoeff(a.0.wrapping_add(mask & self.p)) + pub fn caddp(self, a: MontCoeff) -> MontCoeff { + if W::R_LOG == 16 { + let ai = a.0.to_i64() as i32; + let pi = self.p.to_i64() as i32; + let mask = ai >> 31; + MontCoeff(W::from_i64((ai + (mask & pi)) as i64)) + } else { + let ai = a.0.to_i64(); + let pi = self.p.to_i64(); + let mask = ai >> 63; + MontCoeff(W::from_i64(ai + (mask & pi))) + } + } + + /// Range-reduce from `(-2p, 2p)` to `(-p, p)`. + #[inline] + pub fn reduce_range(self, a: MontCoeff) -> MontCoeff { + self.caddp(self.csubp(a)) } /// Fully normalize a Montgomery coefficient to `[0, p)`. #[inline] - pub fn normalize(self, a: MontCoeff) -> MontCoeff { - self.csubp(self.caddp(self.reduce(a))) + pub fn normalize(self, a: MontCoeff) -> MontCoeff { + self.csubp(self.caddp(a)) } - /// Convert a canonical `i16` into Montgomery domain: `a ↦ a * R mod p`. + /// Convert a canonical value into Montgomery domain: `a ↦ a * R mod p`. #[inline] - pub fn from_canonical(self, a: i16) -> MontCoeff { + pub fn from_canonical(self, a: W) -> MontCoeff { MontCoeff(self.mont_mul_raw(a, self.montsq)) } /// Convert from Montgomery domain to canonical `[0, p)`. #[inline] - pub fn to_canonical(self, a: MontCoeff) -> i16 { - let raw = MontCoeff(self.mont_mul_raw(a.0, 1)); + pub fn to_canonical(self, a: MontCoeff) -> W { + let raw = MontCoeff(self.mont_mul_raw(a.0, W::from_i64(1))); self.normalize(raw).0 } /// Center a canonical value from approximately `(-p, p)` into `[-p/2, p/2)`. - /// - /// First conditionally adds `p` (if negative), then subtracts `p` (if > p/2). - /// Both steps are branchless. #[inline] - pub fn center(self, a: i16) -> i16 { - let mask_neg = a >> 15; - let canonical = a.wrapping_add(mask_neg & self.p); - let half = self.p / 2; - let needs_sub = half.wrapping_sub(canonical) >> 15; - canonical.wrapping_add(needs_sub & self.p.wrapping_neg()) + pub fn center(self, a: W) -> W { + let mask_neg = a.sign_mask(); + let canonical = a.wrapping_add(mask_neg.bitand(self.p)); + let half = W::from_i64(self.p.to_i64() / 2); + let needs_sub = half.wrapping_sub(canonical).sign_mask(); + canonical.wrapping_add(needs_sub.bitand(self.p.wrapping_neg())) } /// Pointwise Montgomery multiplication of two coefficient slices. @@ -146,7 +343,12 @@ impl NttPrime { /// /// Panics if slices have different lengths. #[inline] - pub fn pointwise_mul(self, out: &mut [MontCoeff], lhs: &[MontCoeff], rhs: &[MontCoeff]) { + pub fn pointwise_mul( + self, + out: &mut [MontCoeff], + lhs: &[MontCoeff], + rhs: &[MontCoeff], + ) { assert_eq!(out.len(), lhs.len()); assert_eq!(lhs.len(), rhs.len()); for ((o, a), b) in out.iter_mut().zip(lhs.iter()).zip(rhs.iter()) { @@ -156,23 +358,23 @@ impl NttPrime { /// In-place Montgomery scaling by a constant. #[inline] - pub fn scale_in_place(self, coeffs: &mut [MontCoeff], scalar: MontCoeff) { + pub fn scale_in_place(self, coeffs: &mut [MontCoeff], scalar: MontCoeff) { for c in coeffs { *c = self.mul(*c, scalar); } } - /// In-place Barrett reduction on a coefficient slice. + /// In-place range reduction on a coefficient slice. #[inline] - pub fn reduce_in_place(self, coeffs: &mut [MontCoeff]) { + pub fn reduce_range_in_place(self, coeffs: &mut [MontCoeff]) { for c in coeffs { - *c = self.reduce(*c); + *c = self.reduce_range(*c); } } /// In-place centering of canonical values to `[-p/2, p/2)`. #[inline] - pub fn center_slice(self, coeffs: &mut [i16]) { + pub fn center_slice(self, coeffs: &mut [W]) { for c in coeffs { *c = self.center(*c); } diff --git a/src/algebra/ntt/tables.rs b/src/algebra/ntt/tables.rs index 613ccc95..70e35bd1 100644 --- a/src/algebra/ntt/tables.rs +++ b/src/algebra/ntt/tables.rs @@ -1,149 +1,215 @@ //! Deterministic parameter presets for small-prime CRT arithmetic. //! -//! Initial scope: `logq = 32` preset with six NTT-friendly primes. +//! Q32: `logq = 32` with six `i16` NTT-friendly primes (D ≤ 64). +//! Q64: `logq = 64` with `i32` NTT-friendly primes (D ≤ 1024). +//! Q128: `logq = 128` with five `i32` NTT-friendly primes (D ≤ 1024). -use super::crt::{LimbQ, QData}; +use super::crt::GarnerData; use super::prime::NttPrime; /// Polynomial degree for the base ring `Z_q[X]/(X^d + 1)`. pub const RING_DEGREE: usize = 64; +/// Maximum ring degree covered by the i32 CRT parameter sets. +pub const MAX_CRT_RING_DEGREE: usize = 1024; /// Number of CRT primes for the `logq = 32` parameter set. pub const Q32_NUM_PRIMES: usize = 6; -/// Number of radix-`2^14` limbs for `logq = 32`. -pub const Q32_NUM_LIMBS: usize = 3; - -/// Offset `c` in `q = 2^32 - c`. -pub const Q32_OFFSET: u16 = 99; - -/// `log2(q)` for the `logq = 32` parameter set. -pub const Q32_LOG_MODULUS: u32 = 32; - /// The modulus `q = 2^32 - 99`. -pub const Q32_MODULUS: u64 = (1u64 << 32) - (Q32_OFFSET as u64); +pub const Q32_MODULUS: u64 = (1u64 << 32) - 99; /// CRT primes and per-prime Montgomery constants for `logq = 32`. -pub const Q32_PRIMES: [NttPrime; Q32_NUM_PRIMES] = [ +/// +/// All constants are for `R = 2^16` (i16 width). +pub const Q32_PRIMES: [NttPrime; Q32_NUM_PRIMES] = [ NttPrime { p: 13697, pinv: 2689, - v: 9799, mont: -2949, montsq: -994, - s: 4705, - f: 3540, - t: -5758, }, NttPrime { p: 13441, pinv: 2945, - v: 9986, mont: -1669, montsq: 3274, - s: 3777, - f: -5468, - t: -1680, }, NttPrime { p: 13313, pinv: -13311, - v: 10082, mont: -1029, montsq: -6199, - s: 3325, - f: 4553, - t: -948, }, NttPrime { p: 12289, pinv: -12287, - v: 10922, mont: 4091, montsq: -1337, - s: -3, - f: 354, - t: 4472, }, NttPrime { p: 12161, pinv: 4225, - v: 11037, mont: 4731, montsq: -6040, - s: -383, - f: 5993, - t: 1653, }, NttPrime { p: 11777, pinv: -11775, - v: 11397, mont: -5126, montsq: 1389, - s: -1475, - f: -3812, - t: 1191, }, ]; -/// CRT limb constants for the `logq = 32` parameter set. -pub const Q32_DATA: QData = QData { - q: LimbQ::from_limbs([16285, 16383, 15]), - pmq: LimbQ::from_limbs([8747, 999, 12]), - xvec: [ - LimbQ::from_limbs([9406, 14930, 2]), - LimbQ::from_limbs([9295, 15936, 2]), - LimbQ::from_limbs([16336, 1061, 5]), - LimbQ::from_limbs([1006, 14584, 9]), - LimbQ::from_limbs([1315, 5273, 10]), - LimbQ::from_limbs([7927, 10169, 6]), - ], - logq: Q32_LOG_MODULUS, - qoff: Q32_OFFSET, -}; +/// Garner CRT reconstruction constants for Q32. +pub fn q32_garner() -> GarnerData { + GarnerData::compute(&Q32_PRIMES) +} + +/// Number of CRT primes for the `logq = 64` fast profile (`P > q`). +pub const Q64_NUM_PRIMES_FAST: usize = 3; +/// Number of CRT primes for the `logq = 64` conservative profile (`P > 128*q^2`). +pub const Q64_NUM_PRIMES: usize = 5; + +/// The modulus `q = 2^64 - 59`. +pub const Q64_MODULUS: u64 = u64::MAX - 58; + +/// Number of CRT primes for the `logq = 128` parameter set. +pub const Q128_NUM_PRIMES: usize = 5; + +/// The modulus `q = 2^128 - 275`. +pub const Q128_MODULUS: u128 = u128::MAX - 274; + +/// Raw 30-bit primes for D≤1024, each satisfying `2048 | (p - 1)`. +/// +/// They are ordered descending by value. +pub const D1024_RAW_PRIMES: [i32; Q128_NUM_PRIMES] = + [1073707009, 1073698817, 1073692673, 1073682433, 1073668097]; + +/// Raw 30-bit primes for Q64 fast profile (`K=3`, `P > q`). +pub const Q64_RAW_PRIMES_FAST: [i32; Q64_NUM_PRIMES_FAST] = [ + D1024_RAW_PRIMES[0], + D1024_RAW_PRIMES[1], + D1024_RAW_PRIMES[2], +]; + +/// Raw 30-bit primes for Q64 conservative profile (`K=5`, `P > 128*q^2`). +pub const Q64_RAW_PRIMES: [i32; Q64_NUM_PRIMES] = D1024_RAW_PRIMES; + +/// Raw 30-bit primes for Q128, each satisfying `2048 | (p - 1)`. +pub const Q128_RAW_PRIMES: [i32; Q128_NUM_PRIMES] = D1024_RAW_PRIMES; + +/// CRT primes and per-prime Montgomery constants for `logq = 64` fast profile. +pub fn q64_primes_fast() -> [NttPrime; Q64_NUM_PRIMES_FAST] { + std::array::from_fn(|k| NttPrime::compute(Q64_RAW_PRIMES_FAST[k])) +} + +/// Garner CRT reconstruction constants for Q64 fast profile. +pub fn q64_garner_fast() -> GarnerData { + let primes = q64_primes_fast(); + GarnerData::compute(&primes) +} + +/// CRT primes and per-prime Montgomery constants for `logq = 64` conservative profile. +pub fn q64_primes() -> [NttPrime; Q64_NUM_PRIMES] { + std::array::from_fn(|k| NttPrime::compute(Q64_RAW_PRIMES[k])) +} + +/// Garner CRT reconstruction constants for Q64 conservative profile. +pub fn q64_garner() -> GarnerData { + let primes = q64_primes(); + GarnerData::compute(&primes) +} + +/// CRT primes and per-prime Montgomery constants for `logq = 128`. +pub fn q128_primes() -> [NttPrime; Q128_NUM_PRIMES] { + std::array::from_fn(|k| NttPrime::compute(Q128_RAW_PRIMES[k])) +} + +/// Garner CRT reconstruction constants for Q128. +pub fn q128_garner() -> GarnerData { + let primes = q128_primes(); + GarnerData::compute(&primes) +} #[cfg(test)] mod tests { use super::*; - /// Verify that derived constants (`pinv`, `v`, `mont`, `montsq`) are - /// consistent with the prime `p`. Turns the magic numbers into auditable - /// values. #[test] - fn verify_prime_derived_constants() { + fn verify_q32_prime_derived_constants() { for prime in &Q32_PRIMES { - let p = prime.p; - - // pinv: p * pinv ≡ 1 (mod 2^16) - assert_eq!(p.wrapping_mul(prime.pinv), 1, "pinv failed for p={p}"); - - // v: round(2^27 / p) - let expected_v = ((1i64 << 27) + (p as i64 / 2)) / (p as i64); - assert_eq!(prime.v as i64, expected_v, "v failed for p={p}"); - - // mont: 2^16 mod p, centered to [-p/2, p/2) - let raw_mont = ((1i32 << 16) % (p as i32)) as i16; - let centered_mont = if raw_mont > p / 2 { - raw_mont - p - } else { - raw_mont - }; - assert_eq!(prime.mont, centered_mont, "mont failed for p={p}"); - - // montsq: 2^32 mod p, centered to [-p/2, p/2) - let raw_montsq = ((1i64 << 32) % (p as i64)) as i16; - let centered_montsq = if raw_montsq > p / 2 { - raw_montsq - p - } else { - raw_montsq - }; - assert_eq!(prime.montsq, centered_montsq, "montsq failed for p={p}"); + let recomputed = NttPrime::compute(prime.p); + assert_eq!( + prime.pinv, recomputed.pinv, + "pinv mismatch for p={}", + prime.p + ); + assert_eq!( + prime.mont, recomputed.mont, + "mont mismatch for p={}", + prime.p + ); + assert_eq!( + prime.montsq, recomputed.montsq, + "montsq mismatch for p={}", + prime.p + ); } } #[test] - fn verify_q_value() { - assert_eq!(Q32_DATA.q_u128().unwrap(), Q32_MODULUS as u128); + fn verify_q128_primes_are_valid() { + let primes = q128_primes(); + for np in &primes { + let p = np.p as i64; + assert!(p > 1 && p % 2 == 1, "prime must be odd and > 1"); + assert_eq!( + (p - 1) % 2048, + 0, + "2048 must divide p-1 for D=1024 NTT (p={p})" + ); + // Verify pinv: p * pinv ≡ 1 (mod 2^32) + assert_eq!( + np.p.wrapping_mul(np.pinv), + 1, + "pinv verification failed for p={p}" + ); + } + } + + #[test] + fn verify_q64_primes_are_valid() { + let primes = q64_primes(); + for np in &primes { + let p = np.p as i64; + assert!(p > 1 && p % 2 == 1, "prime must be odd and > 1"); + assert_eq!( + (p - 1) % 2048, + 0, + "2048 must divide p-1 for D=1024 NTT (p={p})" + ); + assert_eq!( + np.p.wrapping_mul(np.pinv), + 1, + "pinv verification failed for p={p}" + ); + } + } + + #[test] + fn garner_data_is_consistent() { + let garner = q32_garner(); + for (i, &prime_i) in Q32_PRIMES.iter().enumerate().skip(1) { + let pi = prime_i.p as i64; + for (j, &prime_j) in Q32_PRIMES[..i].iter().enumerate() { + let pj = prime_j.p as i64; + let g = garner.gamma[i][j] as i64; + assert_eq!( + (pj * g) % pi, + 1, + "garner gamma[{i}][{j}] not inverse of p_{j} mod p_{i}" + ); + } + } } } diff --git a/src/algebra/poly.rs b/src/algebra/poly.rs index 684aa7d8..cc69e42e 100644 --- a/src/algebra/poly.rs +++ b/src/algebra/poly.rs @@ -1,9 +1,11 @@ -//! Fixed-size polynomial container. +//! Polynomial containers and evaluation utilities. +use crate::error::HachiError; use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; use crate::FieldCore; +use crate::FromSmallInt; use std::io::{Read, Write}; /// A degree- HachiDeserialize for Poly { Ok(out) } } + +/// Evaluate the range-check polynomial `w · Π_{k=1}^{b−1} (w − k)(w + k)`. +/// +/// This polynomial vanishes exactly when `w ∈ {−(b−1), …, b−1}`. +/// Total degree in `w` is `2b − 1`. +pub fn range_check_eval(w: E, b: usize) -> E { + let mut acc = w; + for k in 1..b { + let k_e = E::from_u64(k as u64); + acc = acc * (w - k_e) * (w + k_e); + } + acc +} + +/// Evaluate a multilinear polynomial (given by boolean-hypercube evaluations in +/// little-endian bit order) at an arbitrary point via iterated folding. +/// +/// # Errors +/// +/// Returns an error if the evaluation table length is not a power of two or +/// does not match `2^point.len()`. +pub fn multilinear_eval(evals: &[E], point: &[E]) -> Result { + if !evals.len().is_power_of_two() { + return Err(HachiError::InvalidSize { + expected: 1 << point.len(), + actual: evals.len(), + }); + } + if evals.len() != 1 << point.len() { + return Err(HachiError::InvalidSize { + expected: 1 << point.len(), + actual: evals.len(), + }); + } + let mut current = evals.to_vec(); + for &r in point { + let half = current.len() / 2; + let mut next = Vec::with_capacity(half); + for i in 0..half { + next.push(current[2 * i] + r * (current[2 * i + 1] - current[2 * i])); + } + current = next; + } + Ok(current[0]) +} + +/// Fold an evaluation table in place by binding its first variable to `r`, +/// halving the table size. +/// +/// # Panics +/// +/// Panics if the evaluation table length is not a power of two or has fewer +/// than 2 elements. This is a prover-only helper where the caller guarantees +/// well-formed input. +pub fn fold_evals_in_place(evals: &mut Vec, r: E) { + assert!( + evals.len().is_power_of_two(), + "evals length must be a power of two" + ); + assert!(evals.len() >= 2, "evals must have at least 2 elements"); + let half = evals.len() / 2; + for i in 0..half { + evals[i] = evals[2 * i] + r * (evals[2 * i + 1] - evals[2 * i]); + } + evals.truncate(half); +} diff --git a/src/algebra/ring/crt_ntt_repr.rs b/src/algebra/ring/crt_ntt_repr.rs index 18e4772a..0d5d5bb1 100644 --- a/src/algebra/ring/crt_ntt_repr.rs +++ b/src/algebra/ring/crt_ntt_repr.rs @@ -1,78 +1,67 @@ //! CRT+NTT-domain representation of cyclotomic ring elements. use crate::algebra::backend::{CrtReconstruct, NttPrimeOps, NttTransform, ScalarBackend}; -use crate::algebra::fields::{Fp128, Fp32, Fp64}; use crate::algebra::ntt::butterfly::NttTwiddles; -use crate::algebra::ntt::crt::QData; -use crate::algebra::ntt::prime::{MontCoeff, NttPrime}; +use crate::algebra::ntt::crt::GarnerData; +use crate::algebra::ntt::prime::{MontCoeff, NttPrime, PrimeWidth}; use crate::{CanonicalField, FieldCore}; use super::cyclotomic::CyclotomicRing; /// CRT+NTT-domain representation of a cyclotomic ring element. /// -/// Stores `K` arrays of `D` [`MontCoeff`] values, one per CRT prime. -/// Multiplication is pointwise per prime - O(K*D) vs O(D^2) for coefficient form. +/// Stores `K` arrays of `D` [`MontCoeff`] values, one per CRT prime. +/// Multiplication is pointwise per prime — O(K*D) vs O(D^2) for coefficient form. /// -/// Use [`CyclotomicCrtNtt::from_ring`] and [`CyclotomicCrtNtt::to_ring`] to convert -/// between coefficient and CRT+NTT domains. +/// Generic over: +/// - `W: PrimeWidth` — integer width (`i16` or `i32`) +/// - `K` — number of CRT primes +/// - `D` — polynomial degree #[derive(Debug, Clone, PartialEq, Eq)] -pub struct CyclotomicCrtNtt { - pub(crate) limbs: [[MontCoeff; D]; K], +pub struct CyclotomicCrtNtt { + pub(crate) limbs: [[MontCoeff; D]; K], } -/// Field types that can safely convert to and from the CRT+NTT representation. -pub trait CrtNttConvertibleField: FieldCore + CanonicalField { - /// Reduce this field element modulo a small prime `p`. - fn mod_small_prime(self, p: i16) -> i16; - - /// Reconstruct from a residue in `[0, q)` after CRT combination. - fn from_q_residue_u128(x: u128) -> Self; -} - -impl CrtNttConvertibleField for Fp32

{ - #[inline] - fn mod_small_prime(self, p: i16) -> i16 { - (self.to_canonical_u32() % (p as u32)) as i16 - } - - #[inline] - fn from_q_residue_u128(x: u128) -> Self { - let narrowed = u32::try_from(x).expect("CRT residue does not fit in u32"); - Self::from_u64(narrowed as u64) - } -} +/// Field types that can convert to/from the CRT+NTT representation. +/// +/// Blanket-implemented for all `FieldCore + CanonicalField` types. +pub trait CrtNttConvertibleField: FieldCore + CanonicalField {} -impl CrtNttConvertibleField for Fp64

{ - #[inline] - fn mod_small_prime(self, p: i16) -> i16 { - (self.to_canonical_u64() % (p as u64)) as i16 - } +impl CrtNttConvertibleField for F {} - #[inline] - fn from_q_residue_u128(x: u128) -> Self { - let narrowed = u64::try_from(x).expect("CRT residue does not fit in u64"); - Self::from_u64(narrowed) - } +/// Bundled CRT+NTT parameters for a fixed width/prime-count/degree tuple. +/// +/// Keeps primes/twiddles/Garner constants consistent and avoids passing them +/// independently at every call site. +pub struct CrtNttParamSet { + /// CRT primes with Montgomery constants. + pub primes: [NttPrime; K], + /// Per-prime twiddle tables for forward/inverse NTT. + pub twiddles: [NttTwiddles; K], + /// Garner reconstruction constants for CRT lift-back. + pub garner: GarnerData, } -impl CrtNttConvertibleField for Fp128

{ - #[inline] - fn mod_small_prime(self, p: i16) -> i16 { - (self.to_canonical_u128() % (p as u128)) as i16 - } - - #[inline] - fn from_q_residue_u128(x: u128) -> Self { - Self::from_canonical_u128_reduced(x) +impl CrtNttParamSet { + /// Build a full parameter set from CRT primes. + /// + /// Computes per-prime twiddles and Garner reconstruction constants. + pub fn new(primes: [NttPrime; K]) -> Self { + let twiddles = std::array::from_fn(|k| NttTwiddles::compute(primes[k])); + let garner = GarnerData::compute(&primes); + Self { + primes, + twiddles, + garner, + } } } -impl CyclotomicCrtNtt { +impl CyclotomicCrtNtt { /// The additive identity (all zeros in every CRT limb). pub fn zero() -> Self { Self { - limbs: [[MontCoeff::from_raw(0); D]; K], + limbs: [[MontCoeff::from_raw(W::default()); D]; K], } } @@ -80,28 +69,59 @@ impl CyclotomicCrtNtt { /// using the default scalar backend. pub fn from_ring( ring: &CyclotomicRing, - primes: &[NttPrime; K], - twiddles: &[NttTwiddles; K], + primes: &[NttPrime; K], + twiddles: &[NttTwiddles; K], ) -> Self { Self::from_ring_with_backend::(ring, primes, twiddles) } + /// Convert a coefficient-form ring element into CRT+NTT domain + /// using a bundled parameter set and the scalar backend. + pub fn from_ring_with_params( + ring: &CyclotomicRing, + params: &CrtNttParamSet, + ) -> Self { + Self::from_ring(ring, ¶ms.primes, ¶ms.twiddles) + } + /// Convert a coefficient-form ring element into CRT+NTT domain /// through an explicit backend implementation. pub fn from_ring_with_backend< F: CrtNttConvertibleField, - B: NttPrimeOps + NttTransform, + B: NttPrimeOps + NttTransform, >( ring: &CyclotomicRing, - primes: &[NttPrime; K], - twiddles: &[NttTwiddles; K], + primes: &[NttPrime; K], + twiddles: &[NttTwiddles; K], ) -> Self { - let mut limbs = [[MontCoeff::from_raw(0); D]; K]; + let q = (-F::one()).to_canonical_u128() + 1; + let half_q = q / 2; + let centered_coeffs: [i128; D] = std::array::from_fn(|i| { + let canonical = ring.coeffs[i].to_canonical_u128(); + if canonical > half_q { + -((q - canonical) as i128) + } else { + canonical as i128 + } + }); + + let mut limbs = [[MontCoeff::from_raw(W::default()); D]; K]; for ((limb, prime), tw) in limbs.iter_mut().zip(primes.iter()).zip(twiddles.iter()) { - // Reduce each coefficient mod p and convert to Montgomery form. - for (dst, src) in limb.iter_mut().zip(ring.coeffs.iter()) { - let val = src.mod_small_prime(prime.p); - *dst = B::from_canonical(*prime, val); + // Interpret coefficients in centered form (-q/2, q/2] before reducing + // into the CRT primes. This makes the reduction map consistent with + // negacyclic subtraction (which naturally produces negative values). + let p = prime.p.to_i64() as i128; + let half_p = p / 2; + for (dst, centered) in limb.iter_mut().zip(centered_coeffs.iter()) { + let mut r = *centered % p; + if r < 0 { + r += p; + } + // Center residues into [-p/2, p/2) for stable signed arithmetic. + if r >= half_p { + r -= p; + } + *dst = B::from_canonical(*prime, W::from_i64(r as i64)); } B::forward_ntt(limb, *prime, tw); } @@ -110,28 +130,36 @@ impl CyclotomicCrtNtt { /// Convert from CRT+NTT domain back to coefficient form /// using the default scalar backend. - pub fn to_ring( + pub fn to_ring( &self, - primes: &[NttPrime; K], - twiddles: &[NttTwiddles; K], - qdata: &QData, + primes: &[NttPrime; K], + twiddles: &[NttTwiddles; K], + garner: &GarnerData, ) -> CyclotomicRing { - self.to_ring_with_backend::(primes, twiddles, qdata) + self.to_ring_with_backend::(primes, twiddles, garner) + } + + /// Convert from CRT+NTT domain back to coefficient form + /// using a bundled parameter set and the scalar backend. + pub fn to_ring_with_params( + &self, + params: &CrtNttParamSet, + ) -> CyclotomicRing { + self.to_ring(¶ms.primes, ¶ms.twiddles, ¶ms.garner) } /// Convert from CRT+NTT domain back to coefficient form /// through an explicit backend implementation. pub fn to_ring_with_backend< F: CrtNttConvertibleField, - B: NttPrimeOps + NttTransform + CrtReconstruct, - const L: usize, + B: NttPrimeOps + NttTransform + CrtReconstruct, >( &self, - primes: &[NttPrime; K], - twiddles: &[NttTwiddles; K], - qdata: &QData, + primes: &[NttPrime; K], + twiddles: &[NttTwiddles; K], + garner: &GarnerData, ) -> CyclotomicRing { - let mut canonical = [[0i16; D]; K]; + let mut canonical = [[W::default(); D]; K]; for (k, ((can, prime), tw)) in canonical .iter_mut() .zip(primes.iter()) @@ -141,105 +169,127 @@ impl CyclotomicCrtNtt { let mut limb = self.limbs[k]; B::inverse_ntt(&mut limb, *prime, tw); for (dst, src) in can.iter_mut().zip(limb.iter()) { - *dst = B::to_canonical(*prime, *src); + let canon = B::to_canonical(*prime, *src); + *dst = prime.center(canon); } } - let coeffs = B::reconstruct::(primes, &canonical, qdata); + let coeffs = B::reconstruct::(primes, &canonical, garner); CyclotomicRing::from_coefficients(coeffs) } /// Add another CRT+NTT element and reduce each coefficient with the matching /// prime to maintain valid Montgomery ranges using the scalar backend. - pub fn add_reduced(&self, rhs: &Self, primes: &[NttPrime; K]) -> Self { + pub fn add_reduced(&self, rhs: &Self, primes: &[NttPrime; K]) -> Self { self.add_reduced_with_backend::(rhs, primes) } + /// Add another CRT+NTT element and reduce using a bundled parameter set. + pub fn add_reduced_with_params(&self, rhs: &Self, params: &CrtNttParamSet) -> Self { + self.add_reduced(rhs, ¶ms.primes) + } + /// Add another CRT+NTT element and reduce each coefficient with the matching /// prime through an explicit backend implementation. - pub fn add_reduced_with_backend>( + pub fn add_reduced_with_backend>( &self, rhs: &Self, - primes: &[NttPrime; K], + primes: &[NttPrime; K], ) -> Self { let mut out = self.clone(); for (k, (limb, rhs_limb)) in out.limbs.iter_mut().zip(rhs.limbs.iter()).enumerate() { let prime = primes[k]; for (a, b) in limb.iter_mut().zip(rhs_limb.iter()) { let sum = MontCoeff::from_raw(a.raw().wrapping_add(b.raw())); - *a = B::reduce(prime, sum); + *a = B::reduce_range(prime, sum); } } out } - /// Subtract another CRT+NTT element and reduce each coefficient with the - /// matching prime to maintain valid Montgomery ranges using the scalar backend. - pub fn sub_reduced(&self, rhs: &Self, primes: &[NttPrime; K]) -> Self { + /// Subtract another CRT+NTT element and reduce using the scalar backend. + pub fn sub_reduced(&self, rhs: &Self, primes: &[NttPrime; K]) -> Self { self.sub_reduced_with_backend::(rhs, primes) } - /// Subtract another CRT+NTT element and reduce each coefficient with the - /// matching prime through an explicit backend implementation. - pub fn sub_reduced_with_backend>( + /// Subtract another CRT+NTT element and reduce using a bundled parameter set. + pub fn sub_reduced_with_params(&self, rhs: &Self, params: &CrtNttParamSet) -> Self { + self.sub_reduced(rhs, ¶ms.primes) + } + + /// Subtract another CRT+NTT element and reduce through an explicit backend. + pub fn sub_reduced_with_backend>( &self, rhs: &Self, - primes: &[NttPrime; K], + primes: &[NttPrime; K], ) -> Self { let mut out = self.clone(); for (k, (limb, rhs_limb)) in out.limbs.iter_mut().zip(rhs.limbs.iter()).enumerate() { let prime = primes[k]; for (a, b) in limb.iter_mut().zip(rhs_limb.iter()) { let diff = MontCoeff::from_raw(a.raw().wrapping_sub(b.raw())); - *a = B::reduce(prime, diff); + *a = B::reduce_range(prime, diff); } } out } - /// Negate each CRT+NTT coefficient and reduce with the matching prime - /// using the scalar backend. - pub fn neg_reduced(&self, primes: &[NttPrime; K]) -> Self { + /// Negate each CRT+NTT coefficient and reduce using the scalar backend. + pub fn neg_reduced(&self, primes: &[NttPrime; K]) -> Self { self.neg_reduced_with_backend::(primes) } - /// Negate each CRT+NTT coefficient and reduce with the matching prime - /// through an explicit backend implementation. - pub fn neg_reduced_with_backend>(&self, primes: &[NttPrime; K]) -> Self { + /// Negate each CRT+NTT coefficient and reduce using a bundled parameter set. + pub fn neg_reduced_with_params(&self, params: &CrtNttParamSet) -> Self { + self.neg_reduced(¶ms.primes) + } + + /// Negate each CRT+NTT coefficient and reduce through an explicit backend. + pub fn neg_reduced_with_backend>( + &self, + primes: &[NttPrime; K], + ) -> Self { let mut out = self.clone(); for (k, limb) in out.limbs.iter_mut().enumerate() { let prime = primes[k]; for a in limb.iter_mut() { let neg = MontCoeff::from_raw(a.raw().wrapping_neg()); - *a = B::reduce(prime, neg); + *a = B::reduce_range(prime, neg); } } out } - /// Pointwise multiplication in CRT+NTT domain. - /// - /// Each limb is multiplied pointwise using the corresponding prime's - /// Montgomery multiplication. - pub fn pointwise_mul(&self, rhs: &Self, primes: &[NttPrime; K]) -> Self { + /// Pointwise multiplication in CRT+NTT domain using the scalar backend. + pub fn pointwise_mul(&self, rhs: &Self, primes: &[NttPrime; K]) -> Self { self.pointwise_mul_with_backend::(rhs, primes) } - /// Pointwise multiplication in CRT+NTT domain through an explicit backend implementation. - pub fn pointwise_mul_with_backend>( + /// Pointwise multiplication in CRT+NTT domain using a bundled parameter set. + pub fn pointwise_mul_with_params(&self, rhs: &Self, params: &CrtNttParamSet) -> Self { + self.pointwise_mul(rhs, ¶ms.primes) + } + + /// Pointwise multiplication in CRT+NTT domain through an explicit backend. + pub fn pointwise_mul_with_backend>( &self, rhs: &Self, - primes: &[NttPrime; K], + primes: &[NttPrime; K], ) -> Self { - let mut out = [[MontCoeff::from_raw(0); D]; K]; + let mut out = [[MontCoeff::from_raw(W::default()); D]; K]; for (k, ((o, a), b)) in out .iter_mut() .zip(self.limbs.iter()) .zip(rhs.limbs.iter()) .enumerate() { - B::pointwise_mul(primes[k], o, a, b); + let prime = primes[k]; + B::pointwise_mul(prime, o, a, b); + // Keep coefficients in a bounded range for subsequent inverse NTT. + for c in o.iter_mut() { + *c = B::reduce_range(prime, *c); + } } Self { limbs: out } } diff --git a/src/algebra/ring/cyclotomic.rs b/src/algebra/ring/cyclotomic.rs index 5dd2f0fc..7ee92aa2 100644 --- a/src/algebra/ring/cyclotomic.rs +++ b/src/algebra/ring/cyclotomic.rs @@ -243,23 +243,23 @@ impl CyclotomicRing { pub fn balanced_decompose_pow2(&self, levels: usize, log_basis: u32) -> Vec { assert!(log_basis > 0 && log_basis < 128, "invalid log_basis"); assert!( - (levels as u32).saturating_mul(log_basis) <= 128, - "levels * log_basis must be <= 128" + (levels as u32).saturating_mul(log_basis) <= 128 + log_basis, + "levels * log_basis must be <= 128 + log_basis" ); let b = 1i128 << log_basis; let half_b = b / 2; - let q = (-F::one()).to_canonical_u128() as i128 + 1; + let q = (-F::one()).to_canonical_u128() + 1; let half_q = q / 2; let mut digit_planes: Vec<[F; D]> = (0..levels).map(|_| [F::zero(); D]).collect(); for i in 0..D { - let canonical = self.coeffs[i].to_canonical_u128() as i128; - let mut c = if canonical > half_q { - canonical - q + let canonical = self.coeffs[i].to_canonical_u128(); + let mut c: i128 = if canonical > half_q { + -((q - canonical) as i128) } else { - canonical + canonical as i128 }; for plane in digit_planes.iter_mut() { @@ -270,7 +270,7 @@ impl CyclotomicRing { plane[i] = if balanced >= 0 { F::from_canonical_u128_reduced(balanced as u128) } else { - F::from_canonical_u128_reduced((q + balanced) as u128) + F::from_canonical_u128_reduced(q - ((-balanced) as u128)) }; } } diff --git a/src/algebra/ring/mod.rs b/src/algebra/ring/mod.rs index 1b64555e..756854b3 100644 --- a/src/algebra/ring/mod.rs +++ b/src/algebra/ring/mod.rs @@ -4,6 +4,6 @@ pub mod crt_ntt_repr; pub mod cyclotomic; pub mod sparse_challenge; -pub use crt_ntt_repr::{CrtNttConvertibleField, CyclotomicCrtNtt}; +pub use crt_ntt_repr::{CrtNttConvertibleField, CrtNttParamSet, CyclotomicCrtNtt}; pub use cyclotomic::CyclotomicRing; pub use sparse_challenge::{SparseChallenge, SparseChallengeConfig}; diff --git a/src/lib.rs b/src/lib.rs index eb5ac81c..4d6635ef 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -45,14 +45,18 @@ pub mod algebra; /// Protocol-layer transcript and commitment abstractions pub mod protocol; +/// Conditional parallelism utilities (`cfg_iter!`, `cfg_into_iter!`, etc.) +#[doc(hidden)] +#[allow(missing_docs)] +pub mod parallel; + #[doc(hidden)] #[allow(missing_docs)] pub mod test_utils; pub use error::HachiError; pub use primitives::arithmetic::{ - CanonicalField, FieldCore, FieldSampling, HachiRoutines, Invertible, Module, - PseudoMersenneField, + CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, Module, PseudoMersenneField, }; pub use primitives::poly::{MultilinearLagrange, Polynomial}; pub use primitives::serialization::{HachiDeserialize, HachiSerialize}; diff --git a/src/parallel.rs b/src/parallel.rs new file mode 100644 index 00000000..d73c9381 --- /dev/null +++ b/src/parallel.rs @@ -0,0 +1,56 @@ +//! Conditional parallelism utilities. +//! +//! When the `parallel` feature is enabled, the `cfg_iter!` family of macros +//! expand to rayon's parallel iterators. Otherwise they fall back to standard +//! sequential iterators. + +#[cfg(feature = "parallel")] +pub use rayon::prelude::*; + +/// Returns `.par_iter()` when `parallel` is enabled, `.iter()` otherwise. +#[macro_export] +macro_rules! cfg_iter { + ($e:expr) => {{ + #[cfg(feature = "parallel")] + let it = $e.par_iter(); + #[cfg(not(feature = "parallel"))] + let it = $e.iter(); + it + }}; +} + +/// Returns `.par_iter_mut()` when `parallel` is enabled, `.iter_mut()` otherwise. +#[macro_export] +macro_rules! cfg_iter_mut { + ($e:expr) => {{ + #[cfg(feature = "parallel")] + let it = $e.par_iter_mut(); + #[cfg(not(feature = "parallel"))] + let it = $e.iter_mut(); + it + }}; +} + +/// Returns `.into_par_iter()` when `parallel` is enabled, `.into_iter()` otherwise. +#[macro_export] +macro_rules! cfg_into_iter { + ($e:expr) => {{ + #[cfg(feature = "parallel")] + let it = $e.into_par_iter(); + #[cfg(not(feature = "parallel"))] + let it = $e.into_iter(); + it + }}; +} + +/// Returns `.par_chunks(n)` when `parallel` is enabled, `.chunks(n)` otherwise. +#[macro_export] +macro_rules! cfg_chunks { + ($e:expr, $n:expr) => {{ + #[cfg(feature = "parallel")] + let it = $e.par_chunks($n); + #[cfg(not(feature = "parallel"))] + let it = $e.chunks($n); + it + }}; +} diff --git a/src/primitives/arithmetic.rs b/src/primitives/arithmetic.rs index 903b3a17..f6f1d91a 100644 --- a/src/primitives/arithmetic.rs +++ b/src/primitives/arithmetic.rs @@ -30,14 +30,13 @@ pub trait FieldCore: /// Check if element is zero fn is_zero(&self) -> bool; - /// Field addition - fn add(&self, rhs: &Self) -> Self; - - /// Field subtraction - fn sub(&self, rhs: &Self) -> Self; - - /// Field multiplication - fn mul(&self, rhs: &Self) -> Self; + /// Field squaring. + /// + /// Default is `self * self`; extension fields override with specialized + /// formulas that use fewer base-field multiplications. + fn square(&self) -> Self { + *self * *self + } /// Field inversion. /// @@ -55,14 +54,58 @@ pub trait Invertible: FieldCore { fn inv_or_zero(self) -> Self; } -/// Canonical conversion operations for field elements. -pub trait CanonicalField: FieldCore { - /// Convert from `u64`. +/// Embed small integers into a field. +/// +/// Every field contains a copy of its prime subfield, and small integers embed +/// into it canonically via reduction modulo the characteristic. This trait is +/// implementable for ALL fields — base and extension alike. +/// +/// Only `from_u64` and `from_i64` need concrete implementations; the narrower +/// widths have default impls via lossless widening. +pub trait FromSmallInt: FieldCore { + /// Embed a `u8` into the field. + fn from_u8(val: u8) -> Self { + Self::from_u64(val as u64) + } + + /// Embed an `i8` into the field. + fn from_i8(val: i8) -> Self { + Self::from_i64(val as i64) + } + + /// Embed a `u16` into the field. + fn from_u16(val: u16) -> Self { + Self::from_u64(val as u64) + } + + /// Embed an `i16` into the field. + fn from_i16(val: i16) -> Self { + Self::from_i64(val as i64) + } + + /// Embed a `u32` into the field. + fn from_u32(val: u32) -> Self { + Self::from_u64(val as u64) + } + + /// Embed an `i32` into the field. + fn from_i32(val: i32) -> Self { + Self::from_i64(val as i64) + } + + /// Embed a `u64` into the field (reduce mod characteristic). fn from_u64(val: u64) -> Self; - /// Convert from `i64`. + /// Embed an `i64` into the field (reduce mod characteristic). fn from_i64(val: i64) -> Self; +} +/// Canonical integer representation for prime (base) field elements. +/// +/// Provides a bijection between field elements and integers in `[0, p)`. +/// Only meaningful for base prime fields where elements ARE residues mod p. +/// Extension fields should NOT implement this trait. +pub trait CanonicalField: FromSmallInt { /// Return canonical integer representation as `u128`. fn to_canonical_u128(self) -> u128; @@ -120,17 +163,9 @@ pub trait Module: /// Zero element fn zero() -> Self; - /// Addition - fn add(&self, rhs: &Self) -> Self; - - /// Negation - fn neg(&self) -> Self; - /// Scalar multiplication fn scale(&self, k: &Self::Scalar) -> Self; /// Generate random module element fn random(rng: &mut R) -> Self; } - -pub trait HachiRoutines {} diff --git a/src/primitives/serialization.rs b/src/primitives/serialization.rs index eaca5481..ea14bdc3 100644 --- a/src/primitives/serialization.rs +++ b/src/primitives/serialization.rs @@ -183,13 +183,43 @@ mod primitive_impls { impl_primitive_serialization!(u32, 4); impl_primitive_serialization!(u64, 8); impl_primitive_serialization!(u128, 16); - impl_primitive_serialization!(usize, std::mem::size_of::()); impl_primitive_serialization!(i8, 1); impl_primitive_serialization!(i16, 2); impl_primitive_serialization!(i32, 4); impl_primitive_serialization!(i64, 8); impl_primitive_serialization!(i128, 16); + impl Valid for usize { + fn check(&self) -> Result<(), SerializationError> { + Ok(()) + } + } + + impl HachiSerialize for usize { + fn serialize_with_mode( + &self, + writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + (*self as u64).serialize_with_mode(writer, compress) + } + + fn serialized_size(&self, _compress: Compress) -> usize { + 8 + } + } + + impl HachiDeserialize for usize { + fn deserialize_with_mode( + reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let val = u64::deserialize_with_mode(reader, compress, validate)?; + Ok(val as usize) + } + } + impl Valid for bool { fn check(&self) -> Result<(), SerializationError> { Ok(()) diff --git a/src/protocol/commitment/commit.rs b/src/protocol/commitment/commit.rs index 485a5570..97df3007 100644 --- a/src/protocol/commitment/commit.rs +++ b/src/protocol/commitment/commit.rs @@ -1,26 +1,42 @@ //! Ring-native §4.1 commitment core implementation. use super::config::{ - ensure_block_layout, ensure_matrix_shape, ensure_supported_num_vars, validate_and_derive_layout, + ensure_block_layout, ensure_matrix_shape, ensure_supported_num_vars, + validate_and_derive_layout, HachiCommitmentLayout, }; -use super::onehot::{inner_ajtai_onehot, map_onehot_to_sparse_blocks}; -use super::scheme::RingCommitmentScheme; +use super::onehot::{inner_ajtai_onehot, map_onehot_to_sparse_blocks, SparseBlockEntry}; +use super::scheme::{CommitWitness, RingCommitmentScheme}; use super::types::RingCommitment; -use super::utils::linear::{decompose_block, decompose_rows, mat_vec_mul_unchecked}; +use super::utils::crt_ntt::{build_ntt_cache, NttMatrixCache}; +use super::utils::linear::{decompose_block, decompose_rows, mat_vec_mul_ntt_cached, MatrixSlot}; use super::utils::matrix::{derive_public_matrix, sample_public_matrix_seed, PublicMatrixSeed}; use super::CommitmentConfig; -use crate::algebra::ring::CyclotomicRing; +use crate::algebra::CyclotomicRing; use crate::error::HachiError; +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; use crate::{CanonicalField, FieldCore, FieldSampling}; +use std::io::{Read, Write}; -/// Unified setup for the ring-native commitment (§4.1) and prover (§4.2). +/// Seed-only stage for deterministic setup expansion. #[allow(non_snake_case)] #[derive(Debug, Clone, PartialEq, Eq)] -pub struct RingCommitmentSetup { +pub struct HachiSetupSeed { /// Maximum supported variable count. pub max_num_vars: usize, + /// Runtime commitment layout. + pub layout: HachiCommitmentLayout, /// Public seed used to derive commitment matrices. pub public_matrix_seed: PublicMatrixSeed, +} + +/// Expanded setup stage containing coefficient-form matrices. +#[allow(non_snake_case)] +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct HachiExpandedSetup { + /// Setup seed and runtime layout metadata. + pub seed: HachiSetupSeed, /// Inner matrix `A`. pub A: Vec>>, /// Outer matrix `B`. @@ -29,6 +45,219 @@ pub struct RingCommitmentSetup { pub D: Vec>>, } +/// Optional prepared setup stage for accelerated matrix-vector products. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct HachiPreparedSetup { + /// Pre-converted CRT+NTT matrices for dense mat-vec paths. + pub(crate) ntt_cache: NttMatrixCache, +} + +/// Prover setup artifact (expanded setup + optional runtime cache). +#[allow(non_snake_case)] +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct HachiProverSetup { + /// Expanded matrix stage used by both prover and verifier. + pub expanded: HachiExpandedSetup, + /// Optional runtime-prepared acceleration cache. + pub prepared: Option>, +} + +/// Verifier setup artifact derived from prover setup. +#[allow(non_snake_case)] +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct HachiVerifierSetup { + /// Expanded matrix stage used for verification. + pub expanded: HachiExpandedSetup, +} + +impl HachiProverSetup { + /// Runtime layout carried by this setup. + pub fn layout(&self) -> HachiCommitmentLayout { + self.expanded.seed.layout + } + + pub(crate) fn ntt_cache(&self) -> Result<&NttMatrixCache, HachiError> { + self.prepared + .as_ref() + .map(|p| &p.ntt_cache) + .ok_or_else(|| HachiError::InvalidSetup("missing prepared NTT cache".to_string())) + } +} + +impl Valid for HachiSetupSeed { + fn check(&self) -> Result<(), SerializationError> { + self.layout.check() + } +} + +impl HachiSerialize for HachiSetupSeed { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.max_num_vars + .serialize_with_mode(&mut writer, compress)?; + self.layout.serialize_with_mode(&mut writer, compress)?; + writer.write_all(&self.public_matrix_seed)?; + Ok(()) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.max_num_vars.serialized_size(compress) + self.layout.serialized_size(compress) + 32 + } +} + +impl HachiDeserialize for HachiSetupSeed { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let max_num_vars = usize::deserialize_with_mode(&mut reader, compress, validate)?; + let layout = HachiCommitmentLayout::deserialize_with_mode(&mut reader, compress, validate)?; + let mut public_matrix_seed = [0u8; 32]; + reader.read_exact(&mut public_matrix_seed)?; + let out = Self { + max_num_vars, + layout, + public_matrix_seed, + }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +impl Valid for HachiExpandedSetup { + fn check(&self) -> Result<(), SerializationError> { + self.seed.check()?; + self.A.check()?; + self.B.check()?; + self.D.check()?; + Ok(()) + } +} + +impl HachiSerialize for HachiExpandedSetup { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.seed.serialize_with_mode(&mut writer, compress)?; + self.A.serialize_with_mode(&mut writer, compress)?; + self.B.serialize_with_mode(&mut writer, compress)?; + self.D.serialize_with_mode(&mut writer, compress)?; + Ok(()) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.seed.serialized_size(compress) + + self.A.serialized_size(compress) + + self.B.serialized_size(compress) + + self.D.serialized_size(compress) + } +} + +impl HachiDeserialize for HachiExpandedSetup { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let out = Self { + seed: HachiSetupSeed::deserialize_with_mode(&mut reader, compress, validate)?, + A: Vec::>>::deserialize_with_mode( + &mut reader, + compress, + validate, + )?, + B: Vec::>>::deserialize_with_mode( + &mut reader, + compress, + validate, + )?, + D: Vec::>>::deserialize_with_mode( + &mut reader, + compress, + validate, + )?, + }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +impl Valid for HachiProverSetup { + fn check(&self) -> Result<(), SerializationError> { + self.expanded.check() + } +} + +impl HachiSerialize for HachiProverSetup { + fn serialize_with_mode( + &self, + writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + // Prepared cache is runtime-only and intentionally excluded. + self.expanded.serialize_with_mode(writer, compress) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.expanded.serialized_size(compress) + } +} + +impl HachiDeserialize for HachiProverSetup { + fn deserialize_with_mode( + reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + Ok(Self { + expanded: HachiExpandedSetup::deserialize_with_mode(reader, compress, validate)?, + prepared: None, + }) + } +} + +impl Valid for HachiVerifierSetup { + fn check(&self) -> Result<(), SerializationError> { + self.expanded.check() + } +} + +impl HachiSerialize for HachiVerifierSetup { + fn serialize_with_mode( + &self, + writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.expanded.serialize_with_mode(writer, compress) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.expanded.serialized_size(compress) + } +} + +impl HachiDeserialize for HachiVerifierSetup { + fn deserialize_with_mode( + reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + Ok(Self { + expanded: HachiExpandedSetup::deserialize_with_mode(reader, compress, validate)?, + }) + } +} + /// Concrete §4.1 commitment core. #[derive(Clone, Copy, Default)] pub struct HachiCommitmentCore; @@ -38,13 +267,13 @@ where F: FieldCore + CanonicalField + FieldSampling, Cfg: CommitmentConfig, { - type ProverSetup = RingCommitmentSetup; - type VerifierSetup = RingCommitmentSetup; + type ProverSetup = HachiProverSetup; + type VerifierSetup = HachiVerifierSetup; type Commitment = RingCommitment; fn setup(max_num_vars: usize) -> Result<(Self::ProverSetup, Self::VerifierSetup), HachiError> { - let layout = validate_and_derive_layout::()?; - ensure_supported_num_vars(max_num_vars, layout.required_vars)?; + let layout = validate_and_derive_layout::(max_num_vars)?; + ensure_supported_num_vars(max_num_vars, layout.required_num_vars::()?)?; let public_matrix_seed = sample_public_matrix_seed(); let a_matrix = derive_public_matrix::(Cfg::N_A, layout.inner_width, &public_matrix_seed, b"A"); @@ -57,90 +286,338 @@ where b"D", ); - let setup = RingCommitmentSetup { - max_num_vars, - public_matrix_seed, + let ntt_cache = build_ntt_cache::(&a_matrix, &b_matrix, &d_matrix)?; + let expanded = HachiExpandedSetup { + seed: HachiSetupSeed { + max_num_vars, + layout, + public_matrix_seed, + }, A: a_matrix, B: b_matrix, D: d_matrix, }; - ensure_matrix_shape(&setup.A, Cfg::N_A, layout.inner_width, "A")?; - ensure_matrix_shape(&setup.B, Cfg::N_B, layout.outer_width, "B")?; - ensure_matrix_shape(&setup.D, Cfg::N_D, layout.d_matrix_width, "D")?; - Ok((setup.clone(), setup)) + let prover_setup = HachiProverSetup { + expanded: expanded.clone(), + prepared: Some(HachiPreparedSetup { ntt_cache }), + }; + let verifier_setup = HachiVerifierSetup { expanded }; + ensure_matrix_shape(&prover_setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape(&prover_setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; + ensure_matrix_shape( + &prover_setup.expanded.D, + Cfg::N_D, + layout.d_matrix_width, + "D", + )?; + Ok((prover_setup, verifier_setup)) + } + + fn layout(setup: &Self::ProverSetup) -> Result { + Ok(setup.layout()) } - #[allow(clippy::type_complexity)] fn commit_ring_blocks( f_blocks: &[Vec>], setup: &Self::ProverSetup, - ) -> Result< - ( - Self::Commitment, - Vec>>, - Vec>>, - ), - HachiError, - > { - let layout = validate_and_derive_layout::()?; - ensure_supported_num_vars(setup.max_num_vars, layout.required_vars)?; + ) -> Result, HachiError> { + let layout = setup.layout(); + ensure_supported_num_vars( + setup.expanded.seed.max_num_vars, + layout.required_num_vars::()?, + )?; ensure_block_layout(f_blocks, layout)?; - ensure_matrix_shape(&setup.A, Cfg::N_A, layout.inner_width, "A")?; - ensure_matrix_shape(&setup.B, Cfg::N_B, layout.outer_width, "B")?; + ensure_matrix_shape(&setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape(&setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; - let mut s_all: Vec>> = Vec::with_capacity(layout.num_blocks); let mut t_hat_all: Vec>> = Vec::with_capacity(layout.num_blocks); let mut t_hat_flat: Vec> = Vec::with_capacity(layout.outer_width); for block in f_blocks { let s_i = decompose_block(block, Cfg::DELTA, Cfg::LOG_BASIS); - - let t_i = mat_vec_mul_unchecked(&setup.A, &s_i); + let t_i = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::A, &s_i)?; let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); t_hat_flat.extend(t_hat_i.iter().copied()); - - s_all.push(s_i); t_hat_all.push(t_hat_i); } - let u = mat_vec_mul_unchecked(&setup.B, &t_hat_flat); - Ok((RingCommitment { u }, s_all, t_hat_all)) + let u = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::B, &t_hat_flat)?; + Ok(CommitWitness { + commitment: RingCommitment { u }, + t_hat: t_hat_all, + }) + } + + fn commit_coeffs( + f_coeffs: &[CyclotomicRing], + setup: &Self::ProverSetup, + ) -> Result, HachiError> { + let layout = setup.layout(); + let num_blocks = layout.num_blocks; + let block_len = layout.block_len; + let max_len = num_blocks + .checked_mul(block_len) + .ok_or_else(|| HachiError::InvalidSetup("coefficient length overflow".to_string()))?; + if f_coeffs.len() > max_len { + return Err(HachiError::InvalidSize { + expected: max_len, + actual: f_coeffs.len(), + }); + } + + let zero_t_hat = + vec![CyclotomicRing::::zero(); Cfg::N_A.checked_mul(Cfg::DELTA).unwrap()]; + + let mut t_hat_all: Vec>> = Vec::with_capacity(num_blocks); + let mut t_hat_flat: Vec> = Vec::with_capacity(layout.outer_width); + + for i in 0..num_blocks { + let start = i * block_len; + if start >= f_coeffs.len() { + t_hat_flat.extend(zero_t_hat.iter().copied()); + t_hat_all.push(zero_t_hat.clone()); + } else { + let end = (start + block_len).min(f_coeffs.len()); + let block = &f_coeffs[start..end]; + let s_i = decompose_block(block, Cfg::DELTA, Cfg::LOG_BASIS); + let t_i = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::A, &s_i)?; + let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); + t_hat_flat.extend(t_hat_i.iter().copied()); + t_hat_all.push(t_hat_i); + } + } + + let u = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::B, &t_hat_flat)?; + Ok(CommitWitness { + commitment: RingCommitment { u }, + t_hat: t_hat_all, + }) } - #[allow(clippy::type_complexity)] fn commit_onehot( onehot_k: usize, - indices: &[usize], + indices: &[Option], setup: &Self::ProverSetup, - ) -> Result< - ( - Self::Commitment, - Vec>>, - Vec>>, - ), - HachiError, - > { - let layout = validate_and_derive_layout::()?; - ensure_supported_num_vars(setup.max_num_vars, layout.required_vars)?; - ensure_matrix_shape(&setup.A, Cfg::N_A, layout.inner_width, "A")?; - ensure_matrix_shape(&setup.B, Cfg::N_B, layout.outer_width, "B")?; - - let sparse_blocks = map_onehot_to_sparse_blocks(onehot_k, indices, Cfg::R, Cfg::M, D)?; - - let mut s_all: Vec>> = Vec::with_capacity(layout.num_blocks); + ) -> Result, HachiError> { + let layout = setup.layout(); + ensure_supported_num_vars( + setup.expanded.seed.max_num_vars, + layout.required_num_vars::()?, + )?; + ensure_matrix_shape(&setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape(&setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; + + let sparse_blocks = + map_onehot_to_sparse_blocks(onehot_k, indices, layout.r_vars, layout.m_vars, D)?; + let mut t_hat_all: Vec>> = Vec::with_capacity(layout.num_blocks); let mut t_hat_flat: Vec> = Vec::with_capacity(layout.outer_width); + let zero_t_hat = + vec![CyclotomicRing::::zero(); Cfg::N_A.checked_mul(Cfg::DELTA).unwrap()]; + for block_entries in &sparse_blocks { - let (t_i, s_i) = - inner_ajtai_onehot(&setup.A, block_entries, layout.block_len, Cfg::DELTA); - let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); - t_hat_flat.extend(t_hat_i.iter().copied()); + if block_entries.is_empty() { + t_hat_flat.extend(zero_t_hat.iter().copied()); + t_hat_all.push(zero_t_hat.clone()); + } else { + let (t_i, _s_i) = inner_ajtai_onehot( + &setup.expanded.A, + block_entries, + layout.block_len, + Cfg::DELTA, + ); + let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); + t_hat_flat.extend(t_hat_i.iter().copied()); + t_hat_all.push(t_hat_i); + } + } - s_all.push(s_i); - t_hat_all.push(t_hat_i); + let u = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::B, &t_hat_flat)?; + Ok(CommitWitness { + commitment: RingCommitment { u }, + t_hat: t_hat_all, + }) + } +} + +impl HachiCommitmentCore { + /// Create a setup with a caller-specified layout, bypassing + /// `CommitmentConfig::commitment_layout`. + /// + /// Use this when the desired `(m_vars, r_vars)` split differs from what + /// the config's heuristic would choose (e.g. mega-polynomial commitments + /// where each sub-polynomial occupies one block). + /// + /// # Errors + /// + /// Returns `HachiError` on invalid layout or matrix generation failures. + #[allow(non_snake_case)] + pub fn setup_with_layout( + layout: HachiCommitmentLayout, + ) -> Result<(HachiProverSetup, HachiVerifierSetup), HachiError> + where + F: FieldCore + CanonicalField + FieldSampling, + Cfg: CommitmentConfig, + { + let max_num_vars = layout.required_num_vars::()?; + let public_matrix_seed = sample_public_matrix_seed(); + let a_matrix = + derive_public_matrix::(Cfg::N_A, layout.inner_width, &public_matrix_seed, b"A"); + let b_matrix = + derive_public_matrix::(Cfg::N_B, layout.outer_width, &public_matrix_seed, b"B"); + let d_matrix = derive_public_matrix::( + Cfg::N_D, + layout.d_matrix_width, + &public_matrix_seed, + b"D", + ); + + let ntt_cache = build_ntt_cache::(&a_matrix, &b_matrix, &d_matrix)?; + let expanded = HachiExpandedSetup { + seed: HachiSetupSeed { + max_num_vars, + layout, + public_matrix_seed, + }, + A: a_matrix, + B: b_matrix, + D: d_matrix, + }; + let prover_setup = HachiProverSetup { + expanded: expanded.clone(), + prepared: Some(HachiPreparedSetup { ntt_cache }), + }; + let verifier_setup = HachiVerifierSetup { expanded }; + ensure_matrix_shape(&prover_setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape(&prover_setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; + ensure_matrix_shape( + &prover_setup.expanded.D, + Cfg::N_D, + layout.d_matrix_width, + "D", + )?; + Ok((prover_setup, verifier_setup)) + } +} + +/// Describes one block of a mega-polynomial commitment. +/// +/// A mega-polynomial packs multiple heterogeneous polynomials into a single +/// Hachi commitment by assigning each polynomial to its own block. Blocks +/// can be dense (arbitrary ring coefficients), sparse one-hot, or zero. +pub enum MegaPolyBlock<'a, F: FieldCore, const D: usize> { + /// Dense block: full ring coefficients (length ≤ block_len). + Dense(&'a [CyclotomicRing]), + /// One-hot block: sparse entries within this block. + OneHot(&'a [SparseBlockEntry]), + /// Empty block: all coefficients are zero (no allocation or computation). + Zero, +} + +impl HachiCommitmentCore { + /// Commit a mega-polynomial composed of heterogeneous blocks. + /// + /// Each block occupies `block_len` ring elements. Dense blocks are + /// decomposed via `balanced_decompose_pow2`; one-hot blocks use sparse + /// inner Ajtai; zero blocks are free. + /// + /// The number of blocks must equal `layout.num_blocks` (power of 2). + /// + /// # Errors + /// + /// Returns `HachiError` if the number of blocks doesn't match the layout + /// or if matrix shapes are inconsistent. + /// + /// # Panics + /// + /// Panics if `Cfg::N_A * Cfg::DELTA` overflows. + #[allow(non_snake_case)] + pub fn commit_mixed( + blocks: &[MegaPolyBlock<'_, F, D>], + setup: &HachiProverSetup, + ) -> Result, F, D>, HachiError> + where + F: FieldCore + CanonicalField + FieldSampling, + Cfg: CommitmentConfig, + { + let layout = setup.layout(); + if blocks.len() != layout.num_blocks { + return Err(HachiError::InvalidSize { + expected: layout.num_blocks, + actual: blocks.len(), + }); + } + ensure_matrix_shape(&setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape(&setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; + + let zero_t_hat = + vec![CyclotomicRing::::zero(); Cfg::N_A.checked_mul(Cfg::DELTA).unwrap()]; + + let mut t_hat_all: Vec>> = Vec::with_capacity(layout.num_blocks); + let mut t_hat_flat: Vec> = Vec::with_capacity(layout.outer_width); + + for block in blocks { + match block { + MegaPolyBlock::Zero => { + t_hat_flat.extend(zero_t_hat.iter().copied()); + t_hat_all.push(zero_t_hat.clone()); + } + MegaPolyBlock::Dense(coeffs) => { + let s_i = decompose_block(coeffs, Cfg::DELTA, Cfg::LOG_BASIS); + let t_i = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::A, &s_i)?; + let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); + t_hat_flat.extend(t_hat_i.iter().copied()); + t_hat_all.push(t_hat_i); + } + MegaPolyBlock::OneHot(sparse_entries) => { + if sparse_entries.is_empty() { + t_hat_flat.extend(zero_t_hat.iter().copied()); + t_hat_all.push(zero_t_hat.clone()); + } else { + let (t_i, _s_i) = inner_ajtai_onehot( + &setup.expanded.A, + sparse_entries, + layout.block_len, + Cfg::DELTA, + ); + let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); + t_hat_flat.extend(t_hat_i.iter().copied()); + t_hat_all.push(t_hat_i); + } + } + } } - let u = mat_vec_mul_unchecked(&setup.B, &t_hat_flat); - Ok((RingCommitment { u }, s_all, t_hat_all)) + let u = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::B, &t_hat_flat)?; + Ok(CommitWitness { + commitment: RingCommitment { u }, + t_hat: t_hat_all, + }) + } +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::primitives::{HachiDeserialize, HachiSerialize}; + use crate::test_utils::{TinyConfig, D as TestD, F as TestF}; + + #[test] + fn prover_setup_roundtrips_and_derives_same_verifier() { + let (prover_setup, verifier_setup) = + >::setup(16) + .unwrap(); + + let mut bytes = Vec::new(); + prover_setup.serialize_compressed(&mut bytes).unwrap(); + let decoded = HachiProverSetup::::deserialize_compressed(&bytes[..]).unwrap(); + + assert_eq!(decoded.expanded, prover_setup.expanded); + assert_eq!(decoded.prepared, None); + + let derived_verifier = HachiVerifierSetup { + expanded: decoded.expanded.clone(), + }; + assert_eq!(derived_verifier, verifier_setup); } } diff --git a/src/protocol/commitment/config.rs b/src/protocol/commitment/config.rs index 3150554e..3eeba2eb 100644 --- a/src/protocol/commitment/config.rs +++ b/src/protocol/commitment/config.rs @@ -3,16 +3,152 @@ use super::utils::math::checked_pow2; use crate::algebra::ring::CyclotomicRing; use crate::error::HachiError; +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; use crate::FieldCore; +use std::io::{Read, Write}; + +/// Runtime commitment layout authority for ring-native commitments. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct HachiCommitmentLayout { + /// Number of variables inside each committed block (`2^m_vars` entries). + pub m_vars: usize, + /// Number of block-select variables (`2^r_vars` blocks). + pub r_vars: usize, + /// Number of committed blocks (`2^r_vars`). + pub num_blocks: usize, + /// Number of ring elements per block (`2^m_vars`). + pub block_len: usize, + /// Width of inner matrix `A`. + pub inner_width: usize, + /// Width of outer matrix `B`. + pub outer_width: usize, + /// Width of prover matrix `D` (`delta * 2^r_vars`). + pub d_matrix_width: usize, +} + +impl HachiCommitmentLayout { + /// Build a layout from `(m_vars, r_vars)` and static config constants. + /// + /// # Errors + /// + /// Returns an error when powers or derived widths overflow. + pub fn new(m_vars: usize, r_vars: usize) -> Result { + let num_blocks = checked_pow2(r_vars)?; + let block_len = checked_pow2(m_vars)?; + let inner_width = block_len + .checked_mul(Cfg::DELTA) + .ok_or_else(|| HachiError::InvalidSetup("inner width overflow".to_string()))?; + let outer_width = Cfg::N_A + .checked_mul(Cfg::DELTA) + .and_then(|x| x.checked_mul(num_blocks)) + .ok_or_else(|| HachiError::InvalidSetup("outer width overflow".to_string()))?; + let d_matrix_width = Cfg::DELTA + .checked_mul(num_blocks) + .ok_or_else(|| HachiError::InvalidSetup("D-matrix width overflow".to_string()))?; + Ok(Self { + m_vars, + r_vars, + num_blocks, + block_len, + inner_width, + outer_width, + d_matrix_width, + }) + } + + /// Total number of outer variables consumed by ring coefficients. + /// + /// # Errors + /// + /// Returns an error if the variable count overflows. + pub fn outer_vars(&self) -> Result { + self.m_vars + .checked_add(self.r_vars) + .ok_or_else(|| HachiError::InvalidSetup("variable count overflow".to_string())) + } + + /// Required polynomial variable count for this layout (`outer + alpha`). + /// + /// # Errors + /// + /// Returns an error if the variable count overflows. + pub fn required_num_vars(&self) -> Result { + let alpha = D.trailing_zeros() as usize; + self.outer_vars()? + .checked_add(alpha) + .ok_or_else(|| HachiError::InvalidSetup("variable count overflow".to_string())) + } +} + +impl Valid for HachiCommitmentLayout { + fn check(&self) -> Result<(), SerializationError> { + if self.num_blocks == 0 || self.block_len == 0 { + return Err(SerializationError::InvalidData( + "invalid zero block layout".to_string(), + )); + } + Ok(()) + } +} + +impl HachiSerialize for HachiCommitmentLayout { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.m_vars.serialize_with_mode(&mut writer, compress)?; + self.r_vars.serialize_with_mode(&mut writer, compress)?; + self.num_blocks.serialize_with_mode(&mut writer, compress)?; + self.block_len.serialize_with_mode(&mut writer, compress)?; + self.inner_width + .serialize_with_mode(&mut writer, compress)?; + self.outer_width + .serialize_with_mode(&mut writer, compress)?; + self.d_matrix_width + .serialize_with_mode(&mut writer, compress)?; + Ok(()) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.m_vars.serialized_size(compress) + + self.r_vars.serialized_size(compress) + + self.num_blocks.serialized_size(compress) + + self.block_len.serialized_size(compress) + + self.inner_width.serialized_size(compress) + + self.outer_width.serialized_size(compress) + + self.d_matrix_width.serialized_size(compress) + } +} + +impl HachiDeserialize for HachiCommitmentLayout { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let out = Self { + m_vars: usize::deserialize_with_mode(&mut reader, compress, validate)?, + r_vars: usize::deserialize_with_mode(&mut reader, compress, validate)?, + num_blocks: usize::deserialize_with_mode(&mut reader, compress, validate)?, + block_len: usize::deserialize_with_mode(&mut reader, compress, validate)?, + inner_width: usize::deserialize_with_mode(&mut reader, compress, validate)?, + outer_width: usize::deserialize_with_mode(&mut reader, compress, validate)?, + d_matrix_width: usize::deserialize_with_mode(&mut reader, compress, validate)?, + }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} /// Parameter bundle for the ring-native commitment core (§4.1–§4.2). pub trait CommitmentConfig: Clone + Send + Sync + 'static { /// Ring degree used by `CyclotomicRing`. const D: usize; - /// Number of variables inside each committed block (`2^M` entries). - const M: usize; - /// Number of block-select variables (`2^R` blocks). - const R: usize; /// Inner Ajtai matrix row count. const N_A: usize; /// Outer commitment matrix row count. @@ -25,27 +161,56 @@ pub trait CommitmentConfig: Clone + Send + Sync + 'static { const DELTA: usize; /// Decomposition levels for the folded witness `z` (`τ` in the paper). const TAU: usize; - /// L∞ norm bound for `z` (`β` in the paper). Prover aborts if exceeded. - const BETA: u128; /// Hamming weight of sparse challenges (`ω` in the paper). const CHALLENGE_WEIGHT: usize; + + /// Choose the runtime commitment layout for `max_num_vars`. + /// + /// # Errors + /// + /// Returns an error if `max_num_vars` does not admit a valid layout. + fn commitment_layout(max_num_vars: usize) -> Result; + + /// Runtime L∞ bound for `z` (`β`) used by stage-1 folding checks. + /// + /// # Errors + /// + /// Returns an error on invalid parameters or arithmetic overflow. + fn beta_bound(layout: HachiCommitmentLayout) -> Result { + beta_linf_fold_bound(layout.r_vars, Self::CHALLENGE_WEIGHT, Self::LOG_BASIS) + } } -/// Runtime-derived dimensions from a `CommitmentConfig`. -#[derive(Debug, Clone, Copy)] -pub(super) struct CommitmentLayout { - /// Number of committed blocks (`2^R`). - pub(super) num_blocks: usize, - /// Number of ring elements per block (`2^M`). - pub(super) block_len: usize, - /// Width of inner matrix `A`. - pub(super) inner_width: usize, - /// Width of outer matrix `B`. - pub(super) outer_width: usize, - /// Width of prover matrix `D` (`δ · 2^R`). - pub(super) d_matrix_width: usize, - /// Minimum variable count supported by this config. - pub(super) required_vars: usize, +/// Deterministic upper bound for the stage-1 folded-witness infinity norm. +/// +/// This encodes the bound used in `QuadraticEquation::compute_z_hat`: +/// `||z||_inf <= 2^R * ω * (b/2)` where `b = 2^LOG_BASIS`. +/// +/// # Errors +/// +/// Returns an error when parameters are out of range or intermediate products +/// overflow `u128`. +pub(crate) fn beta_linf_fold_bound( + r: usize, + challenge_weight: usize, + log_basis: u32, +) -> Result { + if !(1..128).contains(&log_basis) { + return Err(HachiError::InvalidSetup("invalid LOG_BASIS".to_string())); + } + if r >= 128 { + return Err(HachiError::InvalidSetup("r_vars must be < 128".to_string())); + } + + let blocks = 1u128 << r; + let b = 1u128 << log_basis; + let half_b = b / 2; + + let term = blocks + .checked_mul(challenge_weight as u128) + .ok_or_else(|| HachiError::InvalidSetup("beta bound overflow".to_string()))?; + term.checked_mul(half_b) + .ok_or_else(|| HachiError::InvalidSetup("beta bound overflow".to_string())) } /// Validate static config invariants and derive runtime dimensions. @@ -54,7 +219,8 @@ pub(super) struct CommitmentLayout { /// /// Returns an error when config constants are inconsistent or overflow. pub(super) fn validate_and_derive_layout( -) -> Result { + max_num_vars: usize, +) -> Result { if D != Cfg::D { return Err(HachiError::InvalidSetup(format!( "const D={D} mismatches config D={}", @@ -69,31 +235,7 @@ pub(super) fn validate_and_derive_layout( "DELTA * LOG_BASIS must be <= 128".to_string(), )); } - - let num_blocks = checked_pow2(Cfg::R)?; - let block_len = checked_pow2(Cfg::M)?; - let inner_width = block_len - .checked_mul(Cfg::DELTA) - .ok_or_else(|| HachiError::InvalidSetup("inner width overflow".to_string()))?; - let outer_width = Cfg::N_A - .checked_mul(Cfg::DELTA) - .and_then(|x| x.checked_mul(num_blocks)) - .ok_or_else(|| HachiError::InvalidSetup("outer width overflow".to_string()))?; - let d_matrix_width = Cfg::DELTA - .checked_mul(num_blocks) - .ok_or_else(|| HachiError::InvalidSetup("D-matrix width overflow".to_string()))?; - let required_vars = Cfg::M - .checked_add(Cfg::R) - .ok_or_else(|| HachiError::InvalidSetup("variable count overflow".to_string()))?; - - Ok(CommitmentLayout { - num_blocks, - block_len, - inner_width, - outer_width, - d_matrix_width, - required_vars, - }) + Cfg::commitment_layout(max_num_vars) } /// Ensure `max_num_vars` is sufficient for config dimensions. @@ -120,7 +262,7 @@ pub(super) fn ensure_supported_num_vars( /// Returns an error when block count or per-block size mismatch. pub(super) fn ensure_block_layout( f_blocks: &[Vec>], - layout: CommitmentLayout, + layout: HachiCommitmentLayout, ) -> Result<(), HachiError> { if f_blocks.len() != layout.num_blocks { return Err(HachiError::InvalidSize { @@ -167,20 +309,104 @@ pub(super) fn ensure_matrix_shape( Ok(()) } -/// Default correctness-first config for early protocol integration. +/// Small correctness-first config for tests and local benchmarks. +/// +/// Fixed layout (m_vars=4, r_vars=2) for fast test iteration. For larger +/// polynomials, use [`DynamicSmallTestCommitmentConfig`] instead. #[derive(Clone, Copy, Debug, Default)] -pub struct DefaultCommitmentConfig; +pub struct SmallTestCommitmentConfig; -impl CommitmentConfig for DefaultCommitmentConfig { +impl CommitmentConfig for SmallTestCommitmentConfig { const D: usize = 16; - const M: usize = 4; - const R: usize = 2; const N_A: usize = 8; const N_B: usize = 4; const N_D: usize = 4; const LOG_BASIS: u32 = 4; const DELTA: usize = 9; const TAU: usize = 4; - const BETA: u128 = 1_000_000; const CHALLENGE_WEIGHT: usize = 3; + + fn commitment_layout(_max_num_vars: usize) -> Result { + HachiCommitmentLayout::new::(4, 2) + } +} + +/// D=16 config with dynamic layout that adapts to polynomial size. +/// +/// Uses the same D=16 ring dimension as [`SmallTestCommitmentConfig`] but +/// derives `m_vars`/`r_vars` from `max_num_vars`, so it can commit +/// polynomials with an arbitrary number of variables. +#[derive(Clone, Copy, Debug, Default)] +pub struct DynamicSmallTestCommitmentConfig; + +impl CommitmentConfig for DynamicSmallTestCommitmentConfig { + const D: usize = 16; + const N_A: usize = 8; + const N_B: usize = 4; + const N_D: usize = 4; + const LOG_BASIS: u32 = 4; + const DELTA: usize = 9; + const TAU: usize = 4; + const CHALLENGE_WEIGHT: usize = 3; + + fn commitment_layout(max_num_vars: usize) -> Result { + let alpha = Self::D.trailing_zeros() as usize; + let reduced_vars = max_num_vars.checked_sub(alpha).ok_or_else(|| { + HachiError::InvalidSetup("max_num_vars is smaller than alpha".to_string()) + })?; + if reduced_vars == 0 { + return Err(HachiError::InvalidSetup( + "max_num_vars must leave at least one outer variable".to_string(), + )); + } + let m_vars = reduced_vars.min(11); + let r_vars = reduced_vars - m_vars; + HachiCommitmentLayout::new::(m_vars, r_vars) + } +} + +/// Production-oriented profile for 128-bit base fields (`Fp128

`). +/// +/// This profile targets the `D = 512`, `n_A = n_B = n_D = 1` regime with +/// base-16 decomposition over ~128-bit moduli. +/// +/// Rigorous β derivation for the stage-1 folded witness `z`: +/// - In `compute_z_hat`, each coordinate is `z[j] = Σ_i s_i[j].mul_by_sparse(c_i)`. +/// - `balanced_decompose_pow2` yields per-coefficient digits in `[-b/2, b/2)` where +/// `b = 2^LOG_BASIS`, so each input coefficient has `|·| <= b/2`. +/// - Challenges use exactly `ω = CHALLENGE_WEIGHT` nonzeros in `{±1}`. +/// - Therefore each `mul_by_sparse` output coefficient is a signed sum of `ω` +/// shifted digits, hence bounded by `ω * (b/2)`. +/// - Summing over `2^R` blocks gives: +/// `||z||_inf <= 2^R * ω * (b/2)`. +/// +/// For this profile: `R=11`, `ω=19`, `b=16`, so +/// `β = 2^11 * 19 * 8 = 311_296`. +#[derive(Clone, Copy, Debug, Default)] +pub struct ProductionFp128CommitmentConfig; + +impl CommitmentConfig for ProductionFp128CommitmentConfig { + const D: usize = 512; + const N_A: usize = 1; + const N_B: usize = 1; + const N_D: usize = 1; + const LOG_BASIS: u32 = 4; + const DELTA: usize = 32; + const TAU: usize = 5; + const CHALLENGE_WEIGHT: usize = 19; + + fn commitment_layout(max_num_vars: usize) -> Result { + let alpha = Self::D.trailing_zeros() as usize; + let reduced_vars = max_num_vars.checked_sub(alpha).ok_or_else(|| { + HachiError::InvalidSetup("max_num_vars is smaller than alpha".to_string()) + })?; + if reduced_vars == 0 { + return Err(HachiError::InvalidSetup( + "max_num_vars must leave at least one outer variable".to_string(), + )); + } + let m_vars = reduced_vars.min(11); + let r_vars = reduced_vars - m_vars; + HachiCommitmentLayout::new::(m_vars, r_vars) + } } diff --git a/src/protocol/commitment/mod.rs b/src/protocol/commitment/mod.rs index 3a3b7170..2801d510 100644 --- a/src/protocol/commitment/mod.rs +++ b/src/protocol/commitment/mod.rs @@ -2,15 +2,24 @@ mod commit; mod config; -pub(crate) mod onehot; +pub mod onehot; mod scheme; mod transcript_append; mod types; -pub(crate) mod utils; +pub mod utils; -pub use commit::{HachiCommitmentCore, RingCommitmentSetup}; -pub use config::{CommitmentConfig, DefaultCommitmentConfig}; -pub use scheme::{CommitmentScheme, RingCommitmentScheme, StreamingCommitmentScheme}; +pub use commit::{ + HachiCommitmentCore, HachiExpandedSetup, HachiPreparedSetup, HachiProverSetup, HachiSetupSeed, + HachiVerifierSetup, MegaPolyBlock, +}; +pub use config::{ + CommitmentConfig, DynamicSmallTestCommitmentConfig, HachiCommitmentLayout, + ProductionFp128CommitmentConfig, SmallTestCommitmentConfig, +}; +pub use onehot::{map_onehot_to_sparse_blocks, SparseBlockEntry}; +pub use scheme::{ + CommitWitness, CommitmentScheme, RingCommitmentScheme, StreamingCommitmentScheme, +}; pub use transcript_append::AppendToTranscript; pub use types::{ DummyProof, HachiCommitment, HachiOpeningClaim, HachiOpeningPoint, RingCommitment, diff --git a/src/protocol/commitment/onehot.rs b/src/protocol/commitment/onehot.rs index ccf5998d..18b8c1dc 100644 --- a/src/protocol/commitment/onehot.rs +++ b/src/protocol/commitment/onehot.rs @@ -12,7 +12,7 @@ use crate::{CanonicalField, FieldCore}; /// Describes a nonzero ring element within one block of the commitment layout. #[derive(Debug, Clone)] -pub(crate) struct SparseBlockEntry { +pub struct SparseBlockEntry { /// Position within the block (0..2^M). pub pos_in_block: usize, /// Coefficient indices that are 1 within this ring element. @@ -35,9 +35,9 @@ pub(crate) struct SparseBlockEntry { /// Returns an error if K and D are not "nicely matched" (one must divide /// the other), if any index is out of range, or if the dimensions don't /// fill the commitment layout. -pub(crate) fn map_onehot_to_sparse_blocks( +pub fn map_onehot_to_sparse_blocks( onehot_k: usize, - indices: &[usize], + indices: &[Option], r: usize, m: usize, d: usize, @@ -74,7 +74,8 @@ pub(crate) fn map_onehot_to_sparse_blocks( // Accumulate nonzero coefficients per ring element index. let mut ring_elem_map: BTreeMap> = BTreeMap::new(); - for (c, &idx) in indices.iter().enumerate() { + for (c, opt) in indices.iter().enumerate() { + let Some(&idx) = opt.as_ref() else { continue }; if idx >= onehot_k { return Err(HachiError::InvalidInput(format!( "index {idx} out of range for chunk size K={onehot_k} at position {c}" @@ -89,14 +90,12 @@ pub(crate) fn map_onehot_to_sparse_blocks( .push(coeff_idx); } - // Distribute into blocks using the same interleaved layout as commit_coeffs: - // block_idx = ring_elem_idx % num_blocks - // pos_in_block = ring_elem_idx / num_blocks - // (equivalently: flat_idx = (pos_in_block << R) + block_idx) + // Sequential block layout matching commit_coeffs: block i = ring elements + // [i*block_len, (i+1)*block_len). let mut blocks: Vec> = vec![Vec::new(); num_blocks]; for (ring_elem_idx, nonzero_coeffs) in ring_elem_map { - let block_idx = ring_elem_idx & (num_blocks - 1); - let pos_in_block = ring_elem_idx >> r; + let block_idx = ring_elem_idx / block_len; + let pos_in_block = ring_elem_idx % block_len; blocks[block_idx].push(SparseBlockEntry { pos_in_block, nonzero_coeffs, @@ -153,6 +152,7 @@ pub(crate) fn inner_ajtai_onehot( mod tests { use super::*; use crate::test_utils::F; + use crate::FromSmallInt; #[test] fn map_onehot_k_gt_d() { @@ -160,7 +160,7 @@ mod tests { // R=1 (2 blocks), M=2 (4 per block) => 8 ring elements total let k = 16; let d = 4; - let indices = vec![3, 10]; + let indices = vec![Some(3), Some(10)]; let blocks = map_onehot_to_sparse_blocks(k, &indices, 1, 2, d).unwrap(); assert_eq!(blocks.len(), 2); @@ -180,7 +180,7 @@ mod tests { // R=1 (2 blocks), M=1 (2 per block) let k = 4; let d = 4; - let indices = vec![0, 2, 3, 1]; + let indices = vec![Some(0), Some(2), Some(3), Some(1)]; let blocks = map_onehot_to_sparse_blocks(k, &indices, 1, 1, d).unwrap(); assert_eq!(blocks.len(), 2); @@ -200,7 +200,16 @@ mod tests { // R=1 (2 blocks), M=1 (2 per block) let k = 4; let d = 8; - let indices = vec![0, 2, 3, 1, 0, 0, 3, 3]; + let indices = vec![ + Some(0), + Some(2), + Some(3), + Some(1), + Some(0), + Some(0), + Some(3), + Some(3), + ]; let blocks = map_onehot_to_sparse_blocks(k, &indices, 1, 1, d).unwrap(); assert_eq!(blocks.len(), 2); @@ -220,7 +229,7 @@ mod tests { #[test] fn map_onehot_rejects_non_divisible() { - let result = map_onehot_to_sparse_blocks(3, &[0, 1], 0, 1, 4); + let result = map_onehot_to_sparse_blocks(3, &[Some(0), Some(1)], 0, 1, 4); assert!(result.is_err()); } diff --git a/src/protocol/commitment/scheme.rs b/src/protocol/commitment/scheme.rs index df0c4301..256ce197 100644 --- a/src/protocol/commitment/scheme.rs +++ b/src/protocol/commitment/scheme.rs @@ -1,9 +1,8 @@ //! Commitment-scheme trait surface for Hachi protocol code. -use super::config::CommitmentConfig; +use super::config::{CommitmentConfig, HachiCommitmentLayout}; use super::transcript_append::AppendToTranscript; -use super::utils::math::checked_pow2; -use crate::algebra::ring::CyclotomicRing; +use crate::algebra::CyclotomicRing; use crate::error::HachiError; use crate::protocol::transcript::Transcript; use crate::{CanonicalField, FieldCore, Polynomial}; @@ -11,6 +10,19 @@ use crate::{CanonicalField, FieldCore, Polynomial}; /// Output type for batched commitments. pub(crate) type BatchCommitOutput = Result, HachiError>; +/// Witness data produced alongside a ring-native commitment. +/// +/// Contains the commitment itself plus `t_hat` (basis-decomposed inner Ajtai +/// output) from the two-layer Ajtai construction (§4.1). The decomposed input +/// vectors `s` are NOT stored; they are recomputed from `ring_coeffs` during +/// proving to avoid multi-GB memory usage at production parameters. +pub struct CommitWitness { + /// The ring commitment (outer Ajtai output `u = B · t̂`). + pub commitment: C, + /// Per-block basis-decomposed inner Ajtai output vectors. + pub t_hat: Vec>>, +} + /// Generic commitment-scheme interface used by Hachi protocol code. pub trait CommitmentScheme: Clone + Send + Sync + 'static where @@ -28,6 +40,10 @@ where type OpeningProofHint: Clone + Send + Sync; /// Build prover setup for maximum polynomial dimension. + /// + /// # Panics + /// + /// Panics if internal setup fails (programming error, not adversarial input). fn setup_prover(max_num_vars: usize) -> Self::ProverSetup; /// Derive verifier setup from prover setup. @@ -139,6 +155,13 @@ where /// Returns an error if dimensions are inconsistent with `Cfg`. fn setup(max_num_vars: usize) -> Result<(Self::ProverSetup, Self::VerifierSetup), HachiError>; + /// Read the runtime layout carried by `setup`. + /// + /// # Errors + /// + /// Returns an error when setup metadata is inconsistent. + fn layout(setup: &Self::ProverSetup) -> Result; + /// Commit to ring blocks arranged as `2^R` vectors of length `2^M`. /// /// Returns `(commitment, s, t_hat)` where `s` and `t_hat` are the @@ -147,50 +170,30 @@ where /// # Errors /// /// Returns an error if block layout mismatches config or commitment fails. - #[allow(clippy::type_complexity)] fn commit_ring_blocks( f_blocks: &[Vec>], setup: &Self::ProverSetup, - ) -> Result< - ( - Self::Commitment, - Vec>>, - Vec>>, - ), - HachiError, - >; + ) -> Result, HachiError>; /// Commit to a flat coefficient table `(f_i)_{i∈{0,1}^ℓ}` in ring form. /// - /// The input is indexed in LSB-first order (same convention as - /// `DenseMultilinearEvals`). We split the variables as: - /// - /// - outer index `i` for the first `R` variables, - /// - inner index `j` for the last `M` variables, - /// - /// We then form blocks `f_i = (f_{i||j})_{j}` (Eq. (12) in the paper). - /// - /// This prepares `f_blocks` and delegates to `commit_ring_blocks`. + /// The input uses sequential block layout: ring elements + /// `[0, block_len)` form block 0, `[block_len, 2*block_len)` form + /// block 1, and so on. This matches the sequential variable ordering + /// where M variables (position in block) are lower-order and R variables + /// (block selection) are higher-order. /// /// # Errors /// /// Returns an error if `f_coeffs.len()` does not match the configured block - /// layout, if internal index computations overflow, or if the underlying - /// commitment routine fails. - #[allow(clippy::type_complexity)] + /// layout or if the underlying commitment routine fails. fn commit_coeffs( f_coeffs: &[CyclotomicRing], setup: &Self::ProverSetup, - ) -> Result< - ( - Self::Commitment, - Vec>>, - Vec>>, - ), - HachiError, - > { - let num_blocks = checked_pow2(Cfg::R)?; - let block_len = checked_pow2(Cfg::M)?; + ) -> Result, HachiError> { + let layout = Self::layout(setup)?; + let num_blocks = layout.num_blocks; + let block_len = layout.block_len; let expected_len = num_blocks .checked_mul(block_len) .ok_or_else(|| HachiError::InvalidSetup("coefficient length overflow".to_string()))?; @@ -201,17 +204,10 @@ where }); } - let mut blocks = Vec::with_capacity(num_blocks); - for i in 0..num_blocks { - let mut block = Vec::with_capacity(block_len); - for j in 0..block_len { - let idx = (j << Cfg::R) - .checked_add(i) - .ok_or_else(|| HachiError::InvalidSetup("index overflow".to_string()))?; - block.push(f_coeffs[idx]); - } - blocks.push(block); - } + let blocks: Vec>> = f_coeffs + .chunks_exact(block_len) + .map(|chunk| chunk.to_vec()) + .collect(); Self::commit_ring_blocks(&blocks, setup) } @@ -234,19 +230,11 @@ where /// /// Returns an error if dimensions are inconsistent or any index is out /// of range. - #[allow(clippy::type_complexity)] fn commit_onehot( onehot_k: usize, - indices: &[usize], + indices: &[Option], setup: &Self::ProverSetup, - ) -> Result< - ( - Self::Commitment, - Vec>>, - Vec>>, - ), - HachiError, - > { + ) -> Result, HachiError> { let num_chunks = indices.len(); let total_field_elems = num_chunks .checked_mul(onehot_k) @@ -260,7 +248,8 @@ where // Materialize the full one-hot vector as ring elements. let total_ring_elems = total_field_elems / D; let mut ring_coeffs = vec![CyclotomicRing::::zero(); total_ring_elems]; - for (c, &idx) in indices.iter().enumerate() { + for (c, opt) in indices.iter().enumerate() { + let Some(&idx) = opt.as_ref() else { continue }; if idx >= onehot_k { return Err(HachiError::InvalidInput(format!( "index {idx} out of range for chunk size K={onehot_k} at position {c}" diff --git a/src/protocol/commitment/utils/crt_ntt.rs b/src/protocol/commitment/utils/crt_ntt.rs new file mode 100644 index 00000000..6c91e254 --- /dev/null +++ b/src/protocol/commitment/utils/crt_ntt.rs @@ -0,0 +1,133 @@ +//! Protocol-facing CRT+NTT parameter dispatch and matrix caching. + +use crate::algebra::ntt::prime::PrimeWidth; +use crate::algebra::ntt::tables::{ + q128_primes, q64_primes, MAX_CRT_RING_DEGREE, Q128_MODULUS, Q128_NUM_PRIMES, Q32_MODULUS, + Q32_NUM_PRIMES, Q32_PRIMES, Q64_MODULUS, Q64_NUM_PRIMES, RING_DEGREE, +}; +use crate::algebra::ring::{CrtNttParamSet, CyclotomicCrtNtt, CyclotomicRing}; +use crate::cfg_iter; +use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; +use crate::{CanonicalField, FieldCore}; + +use super::norm::detect_field_modulus; + +/// Supported protocol CRT+NTT parameter families. +pub(crate) enum ProtocolCrtNttParams { + Q32(CrtNttParamSet), + Q64(CrtNttParamSet), + Q128(CrtNttParamSet), +} + +/// Select a CRT+NTT parameter set from field modulus and ring degree. +/// +/// Dispatch policy: +/// - `q <= 2^32-99` and `D <= 64`: Q32 (`i16`) +/// - `q <= 2^64-59` and `D <= 1024`: Q64 (`i32`, conservative K=5) +/// - `q == 2^128-275` and `D <= 1024`: Q128 (`i32`, K=5) +/// - otherwise: explicit setup error +pub(crate) fn select_crt_ntt_params( +) -> Result, HachiError> { + if !D.is_power_of_two() { + return Err(HachiError::InvalidSetup(format!( + "CRT+NTT requires power-of-two ring degree, got D={D}" + ))); + } + if D > MAX_CRT_RING_DEGREE { + return Err(HachiError::InvalidSetup(format!( + "CRT+NTT supports D <= {MAX_CRT_RING_DEGREE}, got D={D}" + ))); + } + + let modulus = detect_field_modulus::(); + + if modulus == Q128_MODULUS { + return Ok(ProtocolCrtNttParams::Q128(CrtNttParamSet::new( + q128_primes(), + ))); + } + + if modulus <= Q32_MODULUS as u128 { + if D <= RING_DEGREE { + return Ok(ProtocolCrtNttParams::Q32(CrtNttParamSet::new(Q32_PRIMES))); + } + return Ok(ProtocolCrtNttParams::Q64(CrtNttParamSet::new(q64_primes()))); + } + + if modulus <= Q64_MODULUS as u128 { + return Ok(ProtocolCrtNttParams::Q64(CrtNttParamSet::new(q64_primes()))); + } + + Err(HachiError::InvalidSetup(format!( + "no CRT+NTT parameter set for modulus {modulus} and D={D}; supported ranges: <= {Q64_MODULUS} (with Q32/Q64 dispatch) or exactly {Q128_MODULUS}" + ))) +} + +/// Pre-converted CRT+NTT matrices, keyed by parameter family. +/// +/// Avoids repeated coefficient-to-NTT conversion on every dense mat-vec. +#[derive(Debug, Clone, PartialEq, Eq)] +#[allow(non_snake_case)] +pub(crate) enum NttMatrixCache { + Q32 { + A: Vec>>, + B: Vec>>, + D: Vec>>, + }, + Q64 { + A: Vec>>, + B: Vec>>, + D: Vec>>, + }, + Q128 { + A: Vec>>, + B: Vec>>, + D: Vec>>, + }, +} + +fn convert_mat( + mat: &[Vec>], + params: &CrtNttParamSet, +) -> Vec>> +where + F: FieldCore + CanonicalField, + W: PrimeWidth, +{ + cfg_iter!(mat) + .map(|row| { + row.iter() + .map(|a| CyclotomicCrtNtt::from_ring_with_params(a, params)) + .collect() + }) + .collect() +} + +#[allow(non_snake_case)] +pub(crate) fn build_ntt_cache( + a: &[Vec>], + b: &[Vec>], + d: &[Vec>], +) -> Result, HachiError> { + let params = select_crt_ntt_params::()?; + let cache = match ¶ms { + ProtocolCrtNttParams::Q32(p) => NttMatrixCache::Q32 { + A: convert_mat(a, p), + B: convert_mat(b, p), + D: convert_mat(d, p), + }, + ProtocolCrtNttParams::Q64(p) => NttMatrixCache::Q64 { + A: convert_mat(a, p), + B: convert_mat(b, p), + D: convert_mat(d, p), + }, + ProtocolCrtNttParams::Q128(p) => NttMatrixCache::Q128 { + A: convert_mat(a, p), + B: convert_mat(b, p), + D: convert_mat(d, p), + }, + }; + Ok(cache) +} diff --git a/src/protocol/commitment/utils/linear.rs b/src/protocol/commitment/utils/linear.rs index daca6d24..4a8e007d 100644 --- a/src/protocol/commitment/utils/linear.rs +++ b/src/protocol/commitment/utils/linear.rs @@ -1,8 +1,16 @@ //! Linear algebra helpers for ring commitment. -use crate::algebra::ring::CyclotomicRing; +use crate::algebra::ntt::{MontCoeff, PrimeWidth}; +use crate::algebra::{CrtNttParamSet, CyclotomicCrtNtt, CyclotomicRing}; +use crate::cfg_iter; +use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; use crate::{CanonicalField, FieldCore}; +use super::crt_ntt::{select_crt_ntt_params, NttMatrixCache, ProtocolCrtNttParams}; + +#[cfg(test)] pub(crate) fn mat_vec_mul_unchecked( mat: &[Vec>], vec: &[CyclotomicRing], @@ -19,7 +27,215 @@ pub(crate) fn mat_vec_mul_unchecked( +#[inline] +fn accumulate_pointwise_product_into( + acc: &mut CyclotomicCrtNtt, + lhs: &CyclotomicCrtNtt, + rhs: &CyclotomicCrtNtt, + params: &CrtNttParamSet, +) { + for k in 0..K { + let prime = params.primes[k]; + let acc_limb = &mut acc.limbs[k]; + let lhs_limb = &lhs.limbs[k]; + let rhs_limb = &rhs.limbs[k]; + for ((acc_coeff, lhs_coeff), rhs_coeff) in acc_limb + .iter_mut() + .zip(lhs_limb.iter()) + .zip(rhs_limb.iter()) + { + let prod = prime.mul(*lhs_coeff, *rhs_coeff); + let sum = MontCoeff::from_raw(acc_coeff.raw().wrapping_add(prod.raw())); + *acc_coeff = prime.reduce_range(sum); + } + } +} + +#[cfg(test)] +fn precompute_dense_mat_ntt_with_params< + F: FieldCore + CanonicalField, + W: PrimeWidth, + const K: usize, + const D: usize, +>( + mat: &[Vec>], + params: &CrtNttParamSet, +) -> Vec>> { + mat.iter() + .map(|row| { + row.iter() + .map(|a| CyclotomicCrtNtt::from_ring_with_params(a, params)) + .collect() + }) + .collect() +} + +#[cfg(test)] +fn mat_vec_mul_dense_with_params< + F: FieldCore + CanonicalField, + W: PrimeWidth, + const K: usize, + const D: usize, +>( + mat: &[Vec>], + vec: &[CyclotomicRing], + params: &CrtNttParamSet, +) -> Vec> { + let ntt_vec: Vec> = vec + .iter() + .map(|v| CyclotomicCrtNtt::from_ring_with_params(v, params)) + .collect(); + + mat.iter() + .map(|row| { + debug_assert_eq!(row.len(), ntt_vec.len()); + let mut acc = CyclotomicCrtNtt::::zero(); + for (a, x_ntt) in row.iter().zip(ntt_vec.iter()) { + let a_ntt = CyclotomicCrtNtt::from_ring_with_params(a, params); + accumulate_pointwise_product_into(&mut acc, &a_ntt, x_ntt, params); + } + acc.to_ring_with_params(params) + }) + .collect() +} + +#[cfg(test)] +fn mat_vec_mul_dense_many_with_params< + F: FieldCore + CanonicalField, + W: PrimeWidth, + const K: usize, + const D: usize, +>( + mat: &[Vec>], + vecs: &[Vec>], + params: &CrtNttParamSet, +) -> Vec>> { + let ntt_mat = precompute_dense_mat_ntt_with_params(mat, params); + vecs.iter() + .map(|vec| { + let ntt_vec: Vec> = vec + .iter() + .map(|v| CyclotomicCrtNtt::from_ring_with_params(v, params)) + .collect(); + + ntt_mat + .iter() + .map(|row_ntt| { + debug_assert_eq!(row_ntt.len(), ntt_vec.len()); + let mut acc = CyclotomicCrtNtt::::zero(); + for (a_ntt, x_ntt) in row_ntt.iter().zip(ntt_vec.iter()) { + accumulate_pointwise_product_into(&mut acc, a_ntt, x_ntt, params); + } + acc.to_ring_with_params(params) + }) + .collect() + }) + .collect() +} + +#[cfg(test)] +pub(crate) fn mat_vec_mul_crt_ntt( + mat: &[Vec>], + vec: &[CyclotomicRing], +) -> Result>, HachiError> { + let params = select_crt_ntt_params::()?; + let out = match ¶ms { + ProtocolCrtNttParams::Q32(p) => mat_vec_mul_dense_with_params(mat, vec, p), + ProtocolCrtNttParams::Q64(p) => mat_vec_mul_dense_with_params(mat, vec, p), + ProtocolCrtNttParams::Q128(p) => mat_vec_mul_dense_with_params(mat, vec, p), + }; + Ok(out) +} + +#[cfg(test)] +pub(crate) fn mat_vec_mul_crt_ntt_many( + mat: &[Vec>], + vecs: &[Vec>], +) -> Result>>, HachiError> { + let params = select_crt_ntt_params::()?; + let out = match ¶ms { + ProtocolCrtNttParams::Q32(p) => mat_vec_mul_dense_many_with_params(mat, vecs, p), + ProtocolCrtNttParams::Q64(p) => mat_vec_mul_dense_many_with_params(mat, vecs, p), + ProtocolCrtNttParams::Q128(p) => mat_vec_mul_dense_many_with_params(mat, vecs, p), + }; + Ok(out) +} + +/// Selector for which cached matrix to use. +#[derive(Debug, Clone, Copy)] +pub(crate) enum MatrixSlot { + A, + B, + D, +} + +fn mat_vec_mul_precomputed_with_params< + F: FieldCore + CanonicalField, + W: PrimeWidth, + const K: usize, + const D: usize, +>( + ntt_mat: &[Vec>], + vec: &[CyclotomicRing], + params: &CrtNttParamSet, +) -> Vec> { + let ntt_vec: Vec> = vec + .iter() + .map(|v| CyclotomicCrtNtt::from_ring_with_params(v, params)) + .collect(); + + cfg_iter!(ntt_mat) + .map(|row_ntt| { + debug_assert!(row_ntt.len() >= ntt_vec.len()); + let mut acc = CyclotomicCrtNtt::::zero(); + for (a_ntt, x_ntt) in row_ntt.iter().zip(ntt_vec.iter()) { + accumulate_pointwise_product_into(&mut acc, a_ntt, x_ntt, params); + } + acc.to_ring_with_params(params) + }) + .collect() +} + +macro_rules! dispatch_cached { + ($cache:expr, $which:expr, $params:expr, $func:ident $(, $arg:expr)*) => {{ + #[allow(non_snake_case)] + match ($cache, $params) { + (NttMatrixCache::Q32 { A, B, D: Dm }, ProtocolCrtNttParams::Q32(p)) => { + let m = match $which { MatrixSlot::A => A, MatrixSlot::B => B, MatrixSlot::D => Dm }; + $func(m, $($arg,)* p) + } + (NttMatrixCache::Q64 { A, B, D: Dm }, ProtocolCrtNttParams::Q64(p)) => { + let m = match $which { MatrixSlot::A => A, MatrixSlot::B => B, MatrixSlot::D => Dm }; + $func(m, $($arg,)* p) + } + (NttMatrixCache::Q128 { A, B, D: Dm }, ProtocolCrtNttParams::Q128(p)) => { + let m = match $which { MatrixSlot::A => A, MatrixSlot::B => B, MatrixSlot::D => Dm }; + $func(m, $($arg,)* p) + } + _ => return Err(HachiError::InvalidSetup("NTT cache / param family mismatch".into())), + } + }}; +} + +/// Dense mat-vec using a pre-converted NTT matrix from the cache. +pub(crate) fn mat_vec_mul_ntt_cached( + cache: &NttMatrixCache, + which: MatrixSlot, + vec: &[CyclotomicRing], +) -> Result>, HachiError> { + let params = select_crt_ntt_params::()?; + let out = dispatch_cached!( + cache, + which, + ¶ms, + mat_vec_mul_precomputed_with_params, + vec + ); + Ok(out) +} + +/// Basis-decompose a block of ring elements into `block.len() * delta` gadget components. +pub fn decompose_block( block: &[CyclotomicRing], delta: usize, log_basis: u32, @@ -42,3 +258,108 @@ pub(crate) fn decompose_rows( } out } + +#[cfg(test)] +mod tests { + use super::{mat_vec_mul_crt_ntt, mat_vec_mul_crt_ntt_many, mat_vec_mul_unchecked}; + use crate::algebra::{CyclotomicRing, Fp64}; + use crate::FromSmallInt; + + #[test] + fn dense_mat_vec_matches_schoolbook_q32_d64() { + type F = Fp64<4294967197>; + const D: usize = 64; + let mat: Vec>> = (0..3) + .map(|i| { + (0..4) + .map(|j| { + let coeffs = std::array::from_fn(|k| { + F::from_u64((i as u64 * 10_000 + j as u64 * 100 + k as u64 + 1) % 97) + }); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect() + }) + .collect(); + let vec: Vec> = (0..4) + .map(|j| { + let coeffs = + std::array::from_fn(|k| F::from_u64((j as u64 * 50 + k as u64 + 3) % 89)); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect(); + + let schoolbook = mat_vec_mul_unchecked(&mat, &vec); + let crt_ntt = mat_vec_mul_crt_ntt(&mat, &vec).expect("Q32 dispatch should succeed"); + assert_eq!(schoolbook, crt_ntt); + } + + #[test] + fn dense_mat_vec_matches_schoolbook_q64_dispatch_for_large_d() { + type F = Fp64<4294967197>; + const D: usize = 128; + let mat: Vec>> = (0..2) + .map(|i| { + (0..2) + .map(|j| { + let coeffs = std::array::from_fn(|k| { + F::from_u64((i as u64 * 20_000 + j as u64 * 300 + k as u64 + 7) % 113) + }); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect() + }) + .collect(); + let vec: Vec> = (0..2) + .map(|j| { + let coeffs = + std::array::from_fn(|k| F::from_u64((j as u64 * 70 + k as u64 + 11) % 101)); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect(); + + let schoolbook = mat_vec_mul_unchecked(&mat, &vec); + let crt_ntt = mat_vec_mul_crt_ntt(&mat, &vec).expect("Q64 dispatch should succeed"); + assert_eq!(schoolbook, crt_ntt); + } + + #[test] + fn dense_mat_vec_many_matches_individual_crt_ntt_q32_d64() { + type F = Fp64<4294967197>; + const D: usize = 64; + let mat: Vec>> = (0..3) + .map(|i| { + (0..4) + .map(|j| { + let coeffs = std::array::from_fn(|k| { + F::from_u64((i as u64 * 10_000 + j as u64 * 100 + k as u64 + 1) % 97) + }); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect() + }) + .collect(); + + let vecs: Vec>> = (0..3) + .map(|seed| { + (0..4) + .map(|j| { + let coeffs = std::array::from_fn(|k| { + F::from_u64((seed as u64 * 700 + j as u64 * 50 + k as u64 + 3) % 89) + }); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect() + }) + .collect(); + + let expected: Vec>> = vecs + .iter() + .map(|v| mat_vec_mul_crt_ntt(&mat, v).expect("single CRT+NTT mat-vec should succeed")) + .collect(); + + let got = + mat_vec_mul_crt_ntt_many(&mat, &vecs).expect("batched CRT+NTT mat-vec should succeed"); + assert_eq!(expected, got); + } +} diff --git a/src/protocol/commitment/utils/mod.rs b/src/protocol/commitment/utils/mod.rs index 39f38327..f7035759 100644 --- a/src/protocol/commitment/utils/mod.rs +++ b/src/protocol/commitment/utils/mod.rs @@ -1,6 +1,7 @@ //! Utility helpers for commitment internals. -pub(crate) mod linear; +pub(crate) mod crt_ntt; +pub mod linear; pub(crate) mod math; pub(crate) mod matrix; pub(crate) mod norm; diff --git a/src/protocol/commitment_scheme.rs b/src/protocol/commitment_scheme.rs index 23ecc795..d332265d 100644 --- a/src/protocol/commitment_scheme.rs +++ b/src/protocol/commitment_scheme.rs @@ -1,53 +1,60 @@ //! Commitment scheme trait implementation. -use crate::algebra::ring::CyclotomicRing; +use crate::algebra::CyclotomicRing; +use crate::cfg_into_iter; use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; use crate::primitives::poly::multilinear_lagrange_basis; +use crate::protocol::commitment::onehot::{inner_ajtai_onehot, SparseBlockEntry}; +use crate::protocol::commitment::utils::linear::{ + decompose_block, decompose_rows, mat_vec_mul_ntt_cached, MatrixSlot, +}; use crate::protocol::commitment::{ - CommitmentConfig, CommitmentScheme, DefaultCommitmentConfig, HachiCommitmentCore, - RingCommitment, RingCommitmentScheme, RingCommitmentSetup, + AppendToTranscript, CommitmentConfig, CommitmentScheme, HachiCommitmentCore, HachiProverSetup, + HachiVerifierSetup, RingCommitment, RingCommitmentScheme, StreamingCommitmentScheme, }; use crate::protocol::opening_point::RingOpeningPoint; use crate::protocol::proof::{HachiCommitmentHint, HachiProof, SumcheckAux}; use crate::protocol::quadratic_equation::QuadraticEquation; -use crate::protocol::ring_switch::{ring_switch_prover, ring_switch_verifier}; -use crate::protocol::sumcheck::batched_sumcheck::{ - prove_batched_sumcheck, verify_batched_sumcheck, -}; -use crate::protocol::sumcheck::norm_sumcheck::{NormSumcheckProver, NormSumcheckVerifier}; -use crate::protocol::sumcheck::relation_sumcheck::{ - RelationSumcheckProver, RelationSumcheckVerifier, +use crate::protocol::ring_switch::{build_w_evals, ring_switch_prover, ring_switch_verifier}; +use crate::protocol::sumcheck::hachi_sumcheck::{HachiSumcheckProver, HachiSumcheckVerifier}; +use crate::protocol::sumcheck::{prove_sumcheck, verify_sumcheck}; +use crate::protocol::transcript::labels::{ + ABSORB_COMMITMENT, ABSORB_EVALUATION_CLAIMS, CHALLENGE_SUMCHECK_BATCH, CHALLENGE_SUMCHECK_ROUND, }; -use crate::protocol::sumcheck::SumcheckInstanceProver; -use crate::protocol::transcript::labels::CHALLENGE_SUMCHECK_ROUND; use crate::protocol::transcript::Transcript; -use crate::{CanonicalField, FieldCore, FieldSampling, Polynomial}; +use crate::{CanonicalField, FieldCore, FieldSampling, FromSmallInt, Polynomial}; #[cfg(test)] -use crate::protocol::ring_switch::{eval_ring_matrix_at, expand_m_a}; +use crate::protocol::quadratic_equation::compute_m_a_streaming; +#[cfg(test)] +use crate::protocol::ring_switch::expand_m_a; #[cfg(test)] use crate::protocol::transcript::labels::{ ABSORB_SUMCHECK_W, CHALLENGE_RING_SWITCH, DOMAIN_HACHI_PROTOCOL, }; #[cfg(test)] use crate::protocol::transcript::Blake2bTranscript; +#[cfg(test)] +use crate::protocol::SmallTestCommitmentConfig; -type Cfg = DefaultCommitmentConfig; -const D: usize = Cfg::D; - -/// Placeholder for the end-to-end PCS wrapper. +/// End-to-end PCS wrapper, generic over ring degree `D` and config `Cfg`. #[derive(Clone, Copy, Debug, Default)] -pub struct HachiCommitmentScheme; +pub struct HachiCommitmentScheme { + _cfg: std::marker::PhantomData, +} -impl CommitmentScheme for HachiCommitmentScheme +impl CommitmentScheme for HachiCommitmentScheme where F: FieldCore + CanonicalField + FieldSampling, + Cfg: CommitmentConfig, { - type ProverSetup = RingCommitmentSetup; - type VerifierSetup = RingCommitmentSetup; - type Commitment = RingCommitment; - type Proof = HachiProof; - type OpeningProofHint = HachiCommitmentHint; + type ProverSetup = HachiProverSetup; + type VerifierSetup = HachiVerifierSetup; + type Commitment = RingCommitment; + type Proof = HachiProof; + type OpeningProofHint = HachiCommitmentHint; fn setup_prover(max_num_vars: usize) -> Self::ProverSetup { let (setup, _) = @@ -57,7 +64,9 @@ where } fn setup_verifier(setup: &Self::ProverSetup) -> Self::VerifierSetup { - setup.clone() + HachiVerifierSetup { + expanded: setup.expanded.clone(), + } } fn commit>( @@ -66,17 +75,15 @@ where ) -> Result<(Self::Commitment, Self::OpeningProofHint), HachiError> { let ring_coeffs = reduce_coeffs_to_ring_elements::(poly.num_vars(), &poly.coeffs())?; - let (commitment, s, t_hat) = >::commit_coeffs(&ring_coeffs, setup)?; + let w = >::commit_coeffs( + &ring_coeffs, + setup, + )?; let hint = HachiCommitmentHint { - s, - t_hat, + t_hat: w.t_hat, ring_coeffs, }; - Ok((commitment, hint)) + Ok((w.commitment, hint)) } fn prove, P: Polynomial>( @@ -90,26 +97,41 @@ where let hint = hint.ok_or_else(|| { HachiError::InvalidInput("missing commitment hint for proving".to_string()) })?; - let num_vars = poly.num_vars(); + let _num_vars = poly.num_vars(); let alpha = Cfg::D.trailing_zeros() as usize; - let reduced_len = num_vars - .checked_sub(alpha) - .ok_or_else(|| HachiError::InvalidSetup("reduction length underflow".to_string()))?; - if opening_point.len() < reduced_len { + if opening_point.len() < alpha { return Err(HachiError::InvalidPointDimension { - expected: reduced_len, + expected: alpha, actual: opening_point.len(), }); } + let layout = >::layout(setup)?; + let target_num_vars = layout.m_vars + layout.r_vars + alpha; + if opening_point.len() > target_num_vars { + return Err(HachiError::InvalidPointDimension { + expected: target_num_vars, + actual: opening_point.len(), + }); + } + let mut padded_point = opening_point.to_vec(); + padded_point.resize(target_num_vars, F::zero()); + let outer_point = &padded_point[alpha..]; + let ring_opening_point = - ring_opening_point_from_field::(&opening_point[..reduced_len], Cfg::R, Cfg::M)?; + ring_opening_point_from_field::(outer_point, layout.r_vars, layout.m_vars)?; + + let y_ring = evaluate_packed_ring_poly::(&hint.ring_coeffs, outer_point); - let y_ring = - evaluate_packed_ring_poly::(&hint.ring_coeffs, &opening_point[..reduced_len]); + // Fiat-Shamir: bind commitment, opening point, and y_ring before any challenges. + commitment.append_to_transcript(ABSORB_COMMITMENT, transcript); + for pt in &padded_point { + transcript.append_field(ABSORB_EVALUATION_CLAIMS, pt); + } + transcript.append_serde(ABSORB_EVALUATION_CLAIMS, &y_ring); // §4.2 Quadratic equation - let quad_eq = QuadraticEquation::::new_prover( + let mut quad_eq = QuadraticEquation::::new_prover( setup, &ring_opening_point, &hint, @@ -119,22 +141,25 @@ where )?; // §4.3 Ring switch - let rs = ring_switch_prover::(&quad_eq, transcript)?; + let rs = ring_switch_prover::(&mut quad_eq, &setup.expanded, transcript)?; + + // Sample batching coefficient for fused sumcheck + let batching_coeff: F = transcript.challenge_scalar(CHALLENGE_SUMCHECK_BATCH); - // Batched sumcheck: norm + relation - let mut norm_prover = NormSumcheckProver::new(&rs.tau0, rs.w_evals.clone(), rs.b); - let mut relation_prover = RelationSumcheckProver::new( + // Fused sumcheck: norm + relation with shared w_table + let mut fused_prover = HachiSumcheckProver::new( + batching_coeff, rs.w_evals, + &rs.tau0, + rs.b, &rs.alpha_evals_y, &rs.m_evals_x, rs.num_u, rs.num_l, ); - let instances: Vec<&mut dyn SumcheckInstanceProver> = - vec![&mut norm_prover, &mut relation_prover]; let (sumcheck_proof, ..) = - prove_batched_sumcheck::(instances, transcript, |tr| { + prove_sumcheck::(&mut fused_prover, transcript, |tr| { tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND) })?; @@ -156,11 +181,24 @@ where commitment: &Self::Commitment, ) -> Result<(), HachiError> { let alpha_bits = Cfg::D.trailing_zeros() as usize; - let reduced_len = opening_point.len().checked_sub(alpha_bits).ok_or_else(|| { - HachiError::InvalidSetup("opening point length underflow".to_string()) - })?; - let reduced_opening_point = &opening_point[..reduced_len]; - let inner_point = &opening_point[reduced_len..]; + if opening_point.len() < alpha_bits { + return Err(HachiError::InvalidSetup( + "opening point length underflow".to_string(), + )); + } + let layout = setup.expanded.seed.layout; + let target_num_vars = layout.m_vars + layout.r_vars + alpha_bits; + let mut padded_point = opening_point.to_vec(); + padded_point.resize(target_num_vars, F::zero()); + let inner_point = &padded_point[..alpha_bits]; + let reduced_opening_point = &padded_point[alpha_bits..]; + + // Fiat-Shamir: bind commitment, opening point, and y_ring before any challenges. + commitment.append_to_transcript(ABSORB_COMMITMENT, transcript); + for pt in &padded_point { + transcript.append_field(ABSORB_EVALUATION_CLAIMS, pt); + } + transcript.append_serde(ABSORB_EVALUATION_CLAIMS, &proof.y_ring); // §3.1 trace check let v = reduce_inner_openings_to_ring_elements::(inner_point)?; @@ -172,8 +210,11 @@ where } // §4.2 Quadratic equation - let ring_opening_point = - ring_opening_point_from_field::(reduced_opening_point, Cfg::R, Cfg::M)?; + let ring_opening_point = ring_opening_point_from_field::( + reduced_opening_point, + layout.r_vars, + layout.m_vars, + )?; let quad_eq = QuadraticEquation::::new_verifier( setup, &ring_opening_point, @@ -186,15 +227,24 @@ where // §4.3 Ring switch (verifier side) let rs = ring_switch_verifier::( &quad_eq, + &setup.expanded, &proof.sumcheck_aux.w, &proof.w_commitment, transcript, )?; - // Batched sumcheck verification: norm (F_0) + relation (F_α) - let norm_verifier = NormSumcheckVerifier::new(rs.tau0, rs.w_evals.clone(), rs.b); - let relation_verifier = RelationSumcheckVerifier::new( - rs.w_evals, + // Sample batching coefficient for fused sumcheck (must match prover) + let batching_coeff: F = transcript.challenge_scalar(CHALLENGE_SUMCHECK_BATCH); + + // Build full w_evals for verifier from the witness vector w. + let (w_evals_full, _, _) = build_w_evals(&proof.sumcheck_aux.w, Cfg::D)?; + + // Fused sumcheck verification: norm (F_0) + relation (F_α) + let fused_verifier = HachiSumcheckVerifier::new( + batching_coeff, + w_evals_full, + rs.tau0, + rs.b, rs.alpha_evals_y, rs.m_evals_x, rs.tau1, @@ -206,11 +256,9 @@ where rs.num_l, ); - let verifiers: Vec<&dyn crate::protocol::sumcheck::SumcheckInstanceVerifier> = - vec![&norm_verifier, &relation_verifier]; - verify_batched_sumcheck::( + verify_sumcheck::( &proof.sumcheck_proof, - verifiers, + &fused_verifier, transcript, |tr| tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND), )?; @@ -231,28 +279,233 @@ where } } +/// Commit to a one-hot polynomial, returning both the commitment and a +/// complete `HachiCommitmentHint` (including `ring_coeffs` needed by `prove`). +/// +/// # Errors +/// +/// Returns an error if dimensions are inconsistent, any index is out of +/// range, or the underlying commitment routine fails. +pub fn commit_onehot( + onehot_k: usize, + indices: &[Option], + setup: &HachiProverSetup, +) -> Result<(RingCommitment, HachiCommitmentHint), HachiError> +where + F: FieldCore + CanonicalField + FieldSampling, + Cfg: CommitmentConfig, +{ + let num_chunks = indices.len(); + let total_field_elems = num_chunks + .checked_mul(onehot_k) + .ok_or_else(|| HachiError::InvalidInput("T*K overflow".into()))?; + if total_field_elems % D != 0 { + return Err(HachiError::InvalidInput(format!( + "T*K={total_field_elems} is not divisible by D={D}" + ))); + } + + // Build ring_coeffs (needed for prove) from the sparse one-hot indices. + let total_ring_elems = total_field_elems / D; + let mut ring_coeffs = vec![CyclotomicRing::::zero(); total_ring_elems]; + for (c, opt) in indices.iter().enumerate() { + let Some(&idx) = opt.as_ref() else { continue }; + let field_pos = c * onehot_k + idx; + let ring_idx = field_pos / D; + let coeff_idx = field_pos % D; + ring_coeffs[ring_idx].coeffs[coeff_idx] = F::one(); + } + + let w = >::commit_onehot( + onehot_k, indices, setup, + )?; + + let hint = HachiCommitmentHint { + t_hat: w.t_hat, + ring_coeffs, + }; + Ok((w.commitment, hint)) +} + +/// Per-block intermediate state for streaming Hachi commitment. +/// +/// Each chunk corresponds to one Ajtai inner block: `D * block_len` field +/// elements packed into `block_len` ring elements, decomposed, and multiplied +/// by the inner matrix A. +#[derive(Clone, PartialEq, Eq)] +pub struct HachiChunkState { + /// Original ring elements for this block (needed for `ring_coeffs` hint). + pub block: Vec>, + /// Basis-decomposed input vector `s_i = G^{-1}(block)`. + pub s_i: Vec>, + /// Basis-decomposed inner Ajtai output `t̂_i = G^{-1}(A · s_i)`. + pub t_hat_i: Vec>, +} + +impl std::fmt::Debug for HachiChunkState { + fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { + f.debug_struct("HachiChunkState") + .field("block_len", &self.block.len()) + .field("s_i_len", &self.s_i.len()) + .field("t_hat_i_len", &self.t_hat_i.len()) + .finish() + } +} + +impl StreamingCommitmentScheme for HachiCommitmentScheme +where + F: FieldCore + CanonicalField + FieldSampling, + Cfg: CommitmentConfig, +{ + type ChunkState = HachiChunkState; + + fn process_chunk(setup: &Self::ProverSetup, chunk: &[F]) -> Self::ChunkState { + assert!( + chunk.len() % D == 0, + "chunk length {} is not divisible by D={}", + chunk.len(), + D + ); + + let block: Vec> = chunk + .chunks_exact(D) + .map(|c| CyclotomicRing::from_coefficients(std::array::from_fn(|j| c[j]))) + .collect(); + + let s_i = decompose_block(&block, Cfg::DELTA, Cfg::LOG_BASIS); + let t_i = + mat_vec_mul_ntt_cached(setup.ntt_cache().expect("NTT cache"), MatrixSlot::A, &s_i) + .expect("inner Ajtai"); + let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); + + HachiChunkState { + block, + s_i, + t_hat_i, + } + } + + fn process_chunk_onehot( + setup: &Self::ProverSetup, + onehot_k: usize, + chunk: &[Option], + ) -> Self::ChunkState { + let layout = >::layout(setup) + .expect("layout"); + let block_len = layout.block_len; + + let num_field_elems = chunk.len() * onehot_k; + assert!( + num_field_elems % D == 0, + "chunk cycles * K = {num_field_elems} is not divisible by D={D}", + ); + + // Build sparse entries and original block ring elements. + let num_ring_elems = num_field_elems / D; + let mut ring_block = vec![CyclotomicRing::::zero(); num_ring_elems]; + let mut ring_elem_map: std::collections::BTreeMap> = + std::collections::BTreeMap::new(); + for (c, opt) in chunk.iter().enumerate() { + if let Some(k) = opt { + let field_pos = c * onehot_k + k; + let ring_elem_idx = field_pos / D; + let coeff_idx = field_pos % D; + ring_block[ring_elem_idx].coeffs[coeff_idx] = F::one(); + ring_elem_map + .entry(ring_elem_idx) + .or_default() + .push(coeff_idx); + } + } + + let sparse_entries: Vec = ring_elem_map + .into_iter() + .map(|(ring_elem_idx, nonzero_coeffs)| SparseBlockEntry { + pos_in_block: ring_elem_idx, + nonzero_coeffs, + }) + .collect(); + + let (t_i, s_i) = + inner_ajtai_onehot(&setup.expanded.A, &sparse_entries, block_len, Cfg::DELTA); + let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); + + HachiChunkState { + block: ring_block, + s_i, + t_hat_i, + } + } + + fn aggregate_chunks( + setup: &Self::ProverSetup, + _onehot_k: Option, + chunks: &[Self::ChunkState], + ) -> (Self::Commitment, Self::OpeningProofHint) { + let t_hat_flat: Vec> = chunks + .iter() + .flat_map(|c| c.t_hat_i.iter().copied()) + .collect(); + + let u = mat_vec_mul_ntt_cached( + setup.ntt_cache().expect("NTT cache"), + MatrixSlot::B, + &t_hat_flat, + ) + .expect("outer Ajtai"); + + let t_hat_all: Vec>> = + chunks.iter().map(|c| c.t_hat_i.clone()).collect(); + let ring_coeffs: Vec> = chunks + .iter() + .flat_map(|c| c.block.iter().copied()) + .collect(); + + let commitment = RingCommitment { u }; + let hint = HachiCommitmentHint { + t_hat: t_hat_all, + ring_coeffs, + }; + (commitment, hint) + } +} + /// Re-derive the ring-switch challenge `alpha` and the expanded `M_a` vector /// by replaying the transcript from the proof data and setup, exactly as the /// verifier does. #[cfg(test)] -pub(crate) fn rederive_alpha_and_m_a( - proof: &HachiProof, - setup: &>::ProverSetup, +pub(crate) fn rederive_alpha_and_m_a( + proof: &HachiProof, + setup: &HachiVerifierSetup, opening_point: &[F], - commitment: &>::Commitment, + commitment: &RingCommitment, ) -> Result<(F, Vec), HachiError> where F: FieldCore + CanonicalField + FieldSampling + 'static, + Cfg: CommitmentConfig, { let alpha_bits = Cfg::D.trailing_zeros() as usize; - let reduced_len = opening_point - .len() - .checked_sub(alpha_bits) - .ok_or_else(|| HachiError::InvalidSetup("opening point length underflow".to_string()))?; - let ring_opening_point = - ring_opening_point_from_field::(&opening_point[..reduced_len], Cfg::R, Cfg::M)?; + if opening_point.len() < alpha_bits { + return Err(HachiError::InvalidSetup( + "opening point length underflow".to_string(), + )); + } + let layout = setup.expanded.seed.layout; + let ring_opening_point = ring_opening_point_from_field::( + &opening_point[alpha_bits..], + layout.r_vars, + layout.m_vars, + )?; let mut transcript = Blake2bTranscript::::new(DOMAIN_HACHI_PROTOCOL); - let quad_eq = QuadraticEquation::::new_verifier( + + // Replay the same Fiat-Shamir absorptions the real verifier performs. + commitment.append_to_transcript(ABSORB_COMMITMENT, &mut transcript); + for pt in opening_point { + transcript.append_field(ABSORB_EVALUATION_CLAIMS, pt); + } + transcript.append_serde(ABSORB_EVALUATION_CLAIMS, &proof.y_ring); + + let quad_eq = QuadraticEquation::::new_verifier( setup, &ring_opening_point, &proof.v, @@ -262,8 +515,13 @@ where )?; transcript.append_serde(ABSORB_SUMCHECK_W, &proof.w_commitment); let alpha: F = transcript.challenge_scalar(CHALLENGE_RING_SWITCH); - let m_a = eval_ring_matrix_at::(quad_eq.m(), &alpha); - let m_a_vec = expand_m_a::(&m_a, alpha)?; + let m_a = compute_m_a_streaming::( + &setup.expanded, + quad_eq.opening_point(), + &quad_eq.challenges, + &alpha, + )?; + let m_a_vec = expand_m_a::(&m_a, alpha)?; Ok((alpha, m_a_vec)) } @@ -289,8 +547,10 @@ fn ring_opening_point_from_field( }); } - let b = lagrange_weights(&opening_point[..r_vars]); - let a = lagrange_weights(&opening_point[r_vars..]); + // Sequential ordering: M variables (position in block) come first, + // R variables (block selection) come second. + let a = lagrange_weights(&opening_point[..m_vars]); + let b = lagrange_weights(&opening_point[m_vars..]); Ok(RingOpeningPoint { a, b }) } @@ -320,19 +580,16 @@ fn reduce_coeffs_to_ring_elements( }); } - let outer_vars = num_vars - alpha; - let outer_len = 1usize - .checked_shl(outer_vars as u32) - .ok_or_else(|| HachiError::InvalidInput(format!("2^{outer_vars} does not fit usize")))?; - - let mut out = Vec::with_capacity(outer_len); - for i in 0..outer_len { - let coeffs = std::array::from_fn(|j| { - let idx = i + (j << outer_vars); - coeffs[idx] - }); - out.push(CyclotomicRing::from_coefficients(coeffs)); - } + // Sequential packing: ring element i = coeffs[i*D .. (i+1)*D]. + // The first alpha variables (LSBs) become coefficient slots within each + // ring element; the remaining outer_vars variables index ring elements. + let outer_len = expected_len / D; + let out: Vec> = cfg_into_iter!(0..outer_len) + .map(|i| { + let ring_coeffs = std::array::from_fn(|j| coeffs[i * D + j]); + CyclotomicRing::from_coefficients(ring_coeffs) + }) + .collect(); Ok(out) } @@ -355,16 +612,30 @@ fn evaluate_packed_ring_poly( outer_point: &[F], ) -> CyclotomicRing { let weights = lagrange_weights(outer_point); - debug_assert_eq!(weights.len(), packed_coeffs.len()); - packed_coeffs - .iter() - .zip(weights.iter()) - .fold(CyclotomicRing::::zero(), |acc, (f_i, w_i)| { - acc + f_i.scale(w_i) - }) + debug_assert!(weights.len() >= packed_coeffs.len()); + #[cfg(feature = "parallel")] + { + packed_coeffs + .par_iter() + .zip(weights.par_iter()) + .fold( + || CyclotomicRing::::zero(), + |acc, (f_i, w_i)| acc + f_i.scale(w_i), + ) + .reduce(|| CyclotomicRing::::zero(), |a, b| a + b) + } + #[cfg(not(feature = "parallel"))] + { + packed_coeffs + .iter() + .zip(weights.iter()) + .fold(CyclotomicRing::::zero(), |acc, (f_i, w_i)| { + acc + f_i.scale(w_i) + }) + } } -fn trace(u: &CyclotomicRing) -> F { +fn trace(u: &CyclotomicRing) -> F { let d = F::from_u64(D as u64); u.coefficients()[0] * d } @@ -376,28 +647,31 @@ mod tests { use crate::protocol::commitment::CommitmentConfig; use crate::protocol::transcript::Blake2bTranscript; use crate::test_utils::F; - use crate::{CommitmentScheme, Polynomial}; + use crate::{CommitmentScheme, FromSmallInt, Polynomial}; + + type Cfg = SmallTestCommitmentConfig; + type Scheme = HachiCommitmentScheme<{ Cfg::D }, Cfg>; #[test] fn verify_passes_for_consistent_opening() { let alpha = Cfg::D.trailing_zeros() as usize; - let num_vars = Cfg::R + Cfg::M + alpha; + let layout = Cfg::commitment_layout(16).unwrap(); + let num_vars = layout.m_vars + layout.r_vars + alpha; let len = 1usize << num_vars; let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); let poly = DenseMultilinearEvals::new_padded(evals); - let setup = >::setup_prover(num_vars); - let verifier_setup = >::setup_verifier(&setup); + let setup = >::setup_prover(num_vars); + let verifier_setup = >::setup_verifier(&setup); - let (commitment, hint) = - >::commit(&poly, &setup).unwrap(); + let (commitment, hint) = >::commit(&poly, &setup).unwrap(); let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); let opening = poly.evaluate(&opening_point); let mut prover_transcript = Blake2bTranscript::::new(b"test/prove"); - let proof = >::prove( + let proof = >::prove( &setup, &poly, &opening_point, @@ -408,7 +682,7 @@ mod tests { .unwrap(); let mut verifier_transcript = Blake2bTranscript::::new(b"test/prove"); - let result = >::verify( + let result = >::verify( &proof, &verifier_setup, &mut verifier_transcript, @@ -419,4 +693,132 @@ mod tests { assert!(result.is_ok()); } + + #[test] + fn verify_rejects_wrong_opening() { + let alpha = Cfg::D.trailing_zeros() as usize; + let layout = Cfg::commitment_layout(16).unwrap(); + let num_vars = layout.m_vars + layout.r_vars + alpha; + let len = 1usize << num_vars; + + let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); + let poly = DenseMultilinearEvals::new_padded(evals); + + let setup = >::setup_prover(num_vars); + let verifier_setup = >::setup_verifier(&setup); + + let (commitment, hint) = >::commit(&poly, &setup).unwrap(); + + let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); + let opening = poly.evaluate(&opening_point); + + let mut prover_transcript = Blake2bTranscript::::new(b"test/prove"); + let proof = >::prove( + &setup, + &poly, + &opening_point, + Some(hint), + &mut prover_transcript, + &commitment, + ) + .unwrap(); + + let wrong_opening = opening + F::one(); + let mut verifier_transcript = Blake2bTranscript::::new(b"test/prove"); + let result = >::verify( + &proof, + &verifier_setup, + &mut verifier_transcript, + &opening_point, + &wrong_opening, + &commitment, + ); + + assert!( + result.is_err(), + "verify must reject an incorrect opening value" + ); + } + + #[test] + fn streaming_commit_matches_non_streaming() { + let alpha = Cfg::D.trailing_zeros() as usize; + let layout = Cfg::commitment_layout(16).unwrap(); + let num_vars = layout.m_vars + layout.r_vars + alpha; + let len = 1usize << num_vars; + + let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); + let poly = DenseMultilinearEvals::new_padded(evals.clone()); + + let setup = >::setup_prover(num_vars); + + // Non-streaming commit + let (non_streaming_commitment, non_streaming_hint) = + >::commit(&poly, &setup).unwrap(); + + // Streaming commit: split field elements into chunks of D * block_len + let chunk_size = Cfg::D * layout.block_len; + let chunks: Vec> = evals + .chunks_exact(chunk_size) + .map(|chunk| >::process_chunk(&setup, chunk)) + .collect(); + + let (streaming_commitment, streaming_hint) = + >::aggregate_chunks(&setup, None, &chunks); + + assert_eq!(non_streaming_commitment, streaming_commitment); + assert_eq!(non_streaming_hint, streaming_hint); + } + + #[test] + fn streaming_commit_then_prove_verify() { + let alpha = Cfg::D.trailing_zeros() as usize; + let layout = Cfg::commitment_layout(16).unwrap(); + let num_vars = layout.m_vars + layout.r_vars + alpha; + let len = 1usize << num_vars; + + let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); + let poly = DenseMultilinearEvals::new_padded(evals.clone()); + + let setup = >::setup_prover(num_vars); + let verifier_setup = >::setup_verifier(&setup); + + // Streaming commit + let chunk_size = Cfg::D * layout.block_len; + let chunks: Vec> = evals + .chunks_exact(chunk_size) + .map(|chunk| >::process_chunk(&setup, chunk)) + .collect(); + let (commitment, hint) = + >::aggregate_chunks(&setup, None, &chunks); + + // Prove and verify with streaming-produced commitment + hint + let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); + let opening = poly.evaluate(&opening_point); + + let mut prover_transcript = Blake2bTranscript::::new(b"test/stream"); + let proof = >::prove( + &setup, + &poly, + &opening_point, + Some(hint), + &mut prover_transcript, + &commitment, + ) + .unwrap(); + + let mut verifier_transcript = Blake2bTranscript::::new(b"test/stream"); + let result = >::verify( + &proof, + &verifier_setup, + &mut verifier_transcript, + &opening_point, + &opening, + &commitment, + ); + assert!( + result.is_ok(), + "streaming commit should produce valid proofs" + ); + } } diff --git a/src/protocol/mod.rs b/src/protocol/mod.rs index 6f4d5581..27b5ac70 100644 --- a/src/protocol/mod.rs +++ b/src/protocol/mod.rs @@ -15,11 +15,13 @@ pub mod sumcheck; pub mod transcript; pub use commitment::{ - AppendToTranscript, CommitmentConfig, CommitmentScheme, DefaultCommitmentConfig, DummyProof, - HachiCommitment, HachiCommitmentCore, HachiOpeningClaim, HachiOpeningPoint, RingCommitment, - RingCommitmentScheme, RingCommitmentSetup, StreamingCommitmentScheme, + AppendToTranscript, CommitmentConfig, CommitmentScheme, DummyProof, + DynamicSmallTestCommitmentConfig, HachiCommitment, HachiCommitmentCore, HachiCommitmentLayout, + HachiExpandedSetup, HachiOpeningClaim, HachiOpeningPoint, HachiPreparedSetup, HachiProverSetup, + HachiSetupSeed, HachiVerifierSetup, ProductionFp128CommitmentConfig, RingCommitment, + RingCommitmentScheme, SmallTestCommitmentConfig, StreamingCommitmentScheme, }; -pub use commitment_scheme::HachiCommitmentScheme; +pub use commitment_scheme::{commit_onehot, HachiChunkState, HachiCommitmentScheme}; pub use opening_point::RingOpeningPoint; pub use proof::{HachiProof, SumcheckAux}; pub use quadratic_equation::QuadraticEquation; @@ -28,4 +30,4 @@ pub use sumcheck::{ prove_sumcheck, verify_sumcheck, CompressedUniPoly, SumcheckInstanceProver, SumcheckInstanceVerifier, SumcheckProof, UniPoly, }; -pub use transcript::{Blake2bTranscript, KeccakTranscript, Transcript}; +pub use transcript::{sample_ext_challenge, Blake2bTranscript, KeccakTranscript, Transcript}; diff --git a/src/protocol/proof.rs b/src/protocol/proof.rs index 4a119329..c020f7b7 100644 --- a/src/protocol/proof.rs +++ b/src/protocol/proof.rs @@ -1,16 +1,21 @@ //! Proof structures for the Hachi protocol. -use crate::algebra::ring::CyclotomicRing; -use crate::primitives::serialization::Compress; +use crate::algebra::CyclotomicRing; +use crate::primitives::serialization::{Compress, SerializationError}; +use crate::primitives::serialization::{Valid, Validate}; use crate::protocol::commitment::RingCommitment; use crate::protocol::sumcheck::SumcheckProof; -use crate::{FieldCore, HachiSerialize}; +use crate::{FieldCore, HachiDeserialize, HachiSerialize}; +use std::io::{Read, Write}; /// Prover-side hint produced at commitment time. +/// +/// Stores the ring-level coefficients and the decomposed inner-Ajtai outputs +/// `t̂_i`. The basis-decomposed inputs `s_i` are NOT stored; they are +/// recomputed from `ring_coeffs` during proving to avoid multi-GB memory +/// usage at production parameters. #[derive(Debug, Clone, PartialEq, Eq)] pub struct HachiCommitmentHint { - /// Decomposed `s_i` blocks from the commitment phase. - pub s: Vec>>, /// Decomposed `t̂_i` blocks from the commitment phase. pub t_hat: Vec>>, /// Ring coefficients from the §3.1 reduction (evaluation table). @@ -54,3 +59,112 @@ impl HachiProof { + self.w_commitment.serialized_size(Compress::No) } } + +impl HachiSerialize for SumcheckAux { + fn serialize_with_mode( + &self, + writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.w.serialize_with_mode(writer, compress) + } + fn serialized_size(&self, compress: Compress) -> usize { + self.w.serialized_size(compress) + } +} + +impl Valid for SumcheckAux { + fn check(&self) -> Result<(), SerializationError> { + Ok(()) + } +} + +impl HachiDeserialize for SumcheckAux { + fn deserialize_with_mode( + reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + Ok(Self { + w: Vec::::deserialize_with_mode(reader, compress, validate)?, + }) + } +} + +impl HachiSerialize for HachiCommitmentHint { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.t_hat.serialize_with_mode(&mut writer, compress)?; + self.ring_coeffs.serialize_with_mode(&mut writer, compress) + } + fn serialized_size(&self, compress: Compress) -> usize { + self.t_hat.serialized_size(compress) + self.ring_coeffs.serialized_size(compress) + } +} + +impl Valid for HachiCommitmentHint { + fn check(&self) -> Result<(), SerializationError> { + Ok(()) + } +} + +impl HachiDeserialize for HachiCommitmentHint { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + Ok(Self { + t_hat: Vec::deserialize_with_mode(&mut reader, compress, validate)?, + ring_coeffs: Vec::deserialize_with_mode(&mut reader, compress, validate)?, + }) + } +} + +impl HachiSerialize for HachiProof { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.y_ring.serialize_with_mode(&mut writer, compress)?; + self.v.serialize_with_mode(&mut writer, compress)?; + self.sumcheck_proof + .serialize_with_mode(&mut writer, compress)?; + self.sumcheck_aux + .serialize_with_mode(&mut writer, compress)?; + self.w_commitment.serialize_with_mode(&mut writer, compress) + } + fn serialized_size(&self, compress: Compress) -> usize { + self.y_ring.serialized_size(compress) + + self.v.serialized_size(compress) + + self.sumcheck_proof.serialized_size(compress) + + self.sumcheck_aux.serialized_size(compress) + + self.w_commitment.serialized_size(compress) + } +} + +impl Valid for HachiProof { + fn check(&self) -> Result<(), SerializationError> { + Ok(()) + } +} + +impl HachiDeserialize for HachiProof { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + Ok(Self { + y_ring: CyclotomicRing::deserialize_with_mode(&mut reader, compress, validate)?, + v: Vec::deserialize_with_mode(&mut reader, compress, validate)?, + sumcheck_proof: SumcheckProof::deserialize_with_mode(&mut reader, compress, validate)?, + sumcheck_aux: SumcheckAux::deserialize_with_mode(&mut reader, compress, validate)?, + w_commitment: RingCommitment::deserialize_with_mode(&mut reader, compress, validate)?, + }) + } +} diff --git a/src/protocol/quadratic_equation.rs b/src/protocol/quadratic_equation.rs index 16114ffa..092a017e 100644 --- a/src/protocol/quadratic_equation.rs +++ b/src/protocol/quadratic_equation.rs @@ -3,36 +3,64 @@ //! This module encapsulates the stage-1 prover logic and the generation of //! the quadratic equation components M, y, z, and v. -use crate::algebra::ring::{CyclotomicRing, SparseChallenge, SparseChallengeConfig}; +use crate::algebra::{CyclotomicRing, SparseChallenge, SparseChallengeConfig}; +use crate::cfg_iter; use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; use crate::protocol::challenges::sparse::sample_sparse_challenges; -use crate::protocol::commitment::utils::linear::mat_vec_mul_unchecked; +use crate::protocol::commitment::utils::crt_ntt::NttMatrixCache; +use crate::protocol::commitment::utils::linear::{ + decompose_block, mat_vec_mul_ntt_cached, MatrixSlot, +}; use crate::protocol::commitment::utils::norm::{detect_field_modulus, vec_inf_norm}; -use crate::protocol::commitment::{CommitmentConfig, RingCommitment, RingCommitmentSetup}; +use crate::protocol::commitment::{ + CommitmentConfig, HachiCommitmentLayout, HachiExpandedSetup, HachiProverSetup, + HachiVerifierSetup, RingCommitment, +}; use crate::protocol::opening_point::RingOpeningPoint; use crate::protocol::proof::HachiCommitmentHint; +use crate::protocol::ring_switch::eval_ring_at; use crate::protocol::transcript::labels::{ABSORB_PROVER_V, CHALLENGE_STAGE1_FOLD}; use crate::protocol::transcript::Transcript; use crate::{CanonicalField, FieldCore}; /// **Steps 1–3.** Compute `w_i = a^T G_{2^m} s_i` and decompose: `ŵ_i = G_1^{-1}(w_i)`. +/// +/// Recomputes each block's `s_i` from `ring_coeffs` on the fly to avoid +/// storing all `s_i` simultaneously (which can be tens of GB at production +/// parameters). fn compute_w_hat( opening_point: &RingOpeningPoint, - s: &[Vec>], + ring_coeffs: &[CyclotomicRing], + layout: HachiCommitmentLayout, ) -> Vec>> where F: FieldCore + CanonicalField, Cfg: CommitmentConfig, { let a = &opening_point.a; - let block_len = 1usize << Cfg::M; + let block_len = layout.block_len; let delta = Cfg::DELTA; let log_basis = Cfg::LOG_BASIS; debug_assert_eq!(a.len(), block_len); - s.iter() - .map(|s_i| { + let blocks: Vec<&[CyclotomicRing]> = (0..layout.num_blocks) + .map(|i| { + let start = i * block_len; + let end = (start + block_len).min(ring_coeffs.len()); + if start < ring_coeffs.len() { + &ring_coeffs[start..end] + } else { + &[] as &[CyclotomicRing] + } + }) + .collect(); + + cfg_iter!(blocks) + .map(|block| { + let s_i = decompose_block(block, delta, log_basis); let mut w_i = CyclotomicRing::::zero(); for (j, a_j) in a.iter().enumerate().take(block_len) { let start = j * delta; @@ -46,67 +74,85 @@ where } /// **Step 4.** Compute `v = D · ŵ` (first prover message). -#[allow(non_snake_case)] fn compute_v( - d: &[Vec>], + cache: &NttMatrixCache, w_hat: &[Vec>], -) -> Vec> { +) -> Result>, HachiError> { let w_hat_flat: Vec> = w_hat.iter().flat_map(|v| v.iter().copied()).collect(); - mat_vec_mul_unchecked(d, &w_hat_flat) + mat_vec_mul_ntt_cached(cache, MatrixSlot::D, &w_hat_flat) } -/// **Steps 7–9.** Fold `z = Σ c_i · s_i`, check `‖z‖_∞ ≤ β`, and decompose `ẑ = J^{-1}(z)`. -fn compute_z_hat( - s: &[Vec>], +/// **Steps 7–9.** Fold `z_pre = Σ c_i · s_i` and check `‖z_pre‖_∞ ≤ β`. +/// +/// Returns the pre-decomposition `z` vector (before gadget decomposition into +/// `ẑ = J^{-1}(z_pre)`). Callers that need `z_hat` can apply +/// `balanced_decompose_pow2(TAU, LOG_BASIS)` themselves. +fn compute_z_pre( + ring_coeffs: &[CyclotomicRing], challenges: &[SparseChallenge], + layout: HachiCommitmentLayout, ) -> Result>, HachiError> where F: FieldCore + CanonicalField, Cfg: CommitmentConfig, { - debug_assert_eq!(challenges.len(), s.len()); - let len = s[0].len(); - let mut z = vec![CyclotomicRing::::zero(); len]; - for (c_i, s_i) in challenges.iter().zip(s.iter()) { - for (z_j, s_ij) in z.iter_mut().zip(s_i.iter()) { - *z_j += s_ij.mul_by_sparse(c_i); + let block_len = layout.block_len; + let delta = Cfg::DELTA; + let log_basis = Cfg::LOG_BASIS; + let inner_width = block_len * delta; + + debug_assert_eq!(challenges.len(), layout.num_blocks); + + let mut z = vec![CyclotomicRing::::zero(); inner_width]; + + for (i, c_i) in challenges.iter().enumerate() { + let start = i * block_len; + let end = (start + block_len).min(ring_coeffs.len()); + let block = if start < ring_coeffs.len() { + &ring_coeffs[start..end] + } else { + &[] as &[CyclotomicRing] + }; + let s_i = decompose_block(block, delta, log_basis); + for (j, z_j) in z.iter_mut().enumerate() { + *z_j += s_i[j].mul_by_sparse(c_i); } } let modulus = detect_field_modulus::(); let norm = vec_inf_norm(&z, modulus); - if norm > Cfg::BETA { + let beta = Cfg::beta_bound(layout)?; + if norm > beta { return Err(HachiError::InvalidInput(format!( - "prover abort: ||z||_inf = {norm} > beta = {}", - Cfg::BETA + "prover abort: ||z||_inf = {norm} > beta = {beta}" ))); } - Ok(z.iter() - .flat_map(|z_j| z_j.balanced_decompose_pow2(Cfg::TAU, Cfg::LOG_BASIS)) - .collect()) + Ok(z) } /// Stage-1 quadratic equation state for the Hachi protocol. /// /// Encapsulates the relation $M(x) \cdot z = y(x) + (X^D + 1) \cdot r(x)$ -/// along with intermediate prover witness data (`w_hat`, `z_hat`, `hint`). +/// along with intermediate prover witness data (`w_hat`, `z_pre`, `hint`). +/// +/// M and z are never materialized — split-eq factoring computes their +/// products on-the-fly via `compute_r_split_eq` and `compute_m_a_streaming`. pub struct QuadraticEquation { /// Stage-1 proof vector `v = D · ŵ`. pub v: Vec>, /// Stage-1 folding challenges (sparse representation). pub challenges: Vec, - /// Matrix `M`. - m: Vec>>, /// Vector `y`. y: Vec>, - /// Vector `z` (prover only). - z: Option>>, + /// Opening point (a, b) Lagrange weights. + opening_point: RingOpeningPoint, + /// Pre-decomposition folded witness `z_pre = Σ c_i · s_i` (prover only). + /// Replaces both `z_hat` and `z`: `z_hat = J^{-1}(z_pre)`. + z_pre: Option>>, /// Decomposed `ŵ_i = G_1^{-1}(w_i)` (prover only). w_hat: Option>>>, - /// Decomposed `ẑ = J^{-1}(z)` (prover only). - z_hat: Option>>, /// Commitment hint (prover only). hint: Option>, @@ -125,18 +171,16 @@ where /// Returns an error if the norm check, challenge sampling, or matrix /// generation fails. pub fn new_prover>( - setup: &RingCommitmentSetup, + setup: &HachiProverSetup, ring_opening_point: &RingOpeningPoint, hint: &HachiCommitmentHint, transcript: &mut T, commitment: &RingCommitment, y_ring: &CyclotomicRing, ) -> Result { - // Steps 1–3: w_i = a^T G_{2^m} s_i, then ŵ_i = G_1^{-1}(w_i) - let w_hat = compute_w_hat::(ring_opening_point, &hint.s); - - // Step 4: v = D · ŵ - let v = compute_v(&setup.D, &w_hat); + let layout = setup.layout(); + let w_hat = compute_w_hat::(ring_opening_point, &hint.ring_coeffs, layout); + let v = compute_v(setup.ntt_cache()?, &w_hat)?; // Step 5: append v to transcript transcript.append_serde(ABSORB_PROVER_V, &v); @@ -149,25 +193,21 @@ where let challenges = sample_sparse_challenges::( transcript, CHALLENGE_STAGE1_FOLD, - 1usize << Cfg::R, + layout.num_blocks, &challenge_cfg, )?; - // Steps 7–9: z = Σ c_i · s_i, check ‖z‖_∞ ≤ β, then ẑ = J^{-1}(z) - let z_hat = compute_z_hat::(&hint.s, &challenges)?; + let z_pre = compute_z_pre::(&hint.ring_coeffs, &challenges, layout)?; - let m = generate_m::(setup, ring_opening_point, &challenges)?; let y = generate_y::(&v, &commitment.u, y_ring)?; - let z = generate_z(&w_hat, &hint.t_hat, &z_hat); Ok(Self { v, challenges, - m, y, - z: Some(z), + opening_point: ring_opening_point.clone(), + z_pre: Some(z_pre), w_hat: Some(w_hat), - z_hat: Some(z_hat), hint: Some(hint.clone()), _marker: std::marker::PhantomData, }) @@ -179,69 +219,80 @@ where /// /// Returns an error if challenge derivation fails. pub fn new_verifier>( - setup: &RingCommitmentSetup, + setup: &HachiVerifierSetup, ring_opening_point: &RingOpeningPoint, v: &Vec>, transcript: &mut T, commitment: &RingCommitment, y_ring: &CyclotomicRing, ) -> Result { - let challenges = derive_stage1_challenges::(transcript, v)?; - let m = generate_m::(setup, ring_opening_point, &challenges)?; + let layout = setup.expanded.seed.layout; + let challenges = + derive_stage1_challenges::(transcript, v, layout.num_blocks)?; let y = generate_y::(v, &commitment.u, y_ring)?; Ok(Self { v: v.to_vec(), challenges, - m, y, - z: None, + opening_point: ring_opening_point.clone(), + z_pre: None, w_hat: None, - z_hat: None, hint: None, _marker: std::marker::PhantomData, }) } - /// Get the matrix M. - pub fn m(&self) -> &[Vec>] { - &self.m - } - /// Get the vector y. pub fn y(&self) -> &[CyclotomicRing] { &self.y } - /// Get the vector z (returns None if constructed by verifier). - pub fn z(&self) -> Option<&[CyclotomicRing]> { - self.z.as_deref() - } - /// Get the vector v. pub fn v(&self) -> &[CyclotomicRing] { &self.v } + /// Get the opening point (a, b) Lagrange weights. + pub fn opening_point(&self) -> &RingOpeningPoint { + &self.opening_point + } + + /// Get the pre-decomposition folded witness `z_pre` (prover only). + pub fn z_pre(&self) -> Option<&[CyclotomicRing]> { + self.z_pre.as_deref() + } + + /// Take ownership of `z_pre`, leaving `None` in its place. + pub fn take_z_pre(&mut self) -> Option>> { + self.z_pre.take() + } + /// Get the decomposed witness `ŵ` (prover only). pub fn w_hat(&self) -> Option<&[Vec>]> { self.w_hat.as_deref() } - /// Get the decomposed folded witness `ẑ` (prover only). - pub fn z_hat(&self) -> Option<&[CyclotomicRing]> { - self.z_hat.as_deref() + /// Take ownership of `w_hat`, leaving `None` in its place. + pub fn take_w_hat(&mut self) -> Option>>> { + self.w_hat.take() } /// Get the commitment hint (prover only). pub fn hint(&self) -> Option<&HachiCommitmentHint> { self.hint.as_ref() } + + /// Take ownership of the hint, leaving `None` in its place. + pub fn take_hint(&mut self) -> Option> { + self.hint.take() + } } pub(crate) fn derive_stage1_challenges( transcript: &mut T, v: &Vec>, + num_blocks: usize, ) -> Result, HachiError> where F: FieldCore + CanonicalField, @@ -251,9 +302,6 @@ where weight: Cfg::CHALLENGE_WEIGHT, nonzero_coeffs: vec![-1, 1], }; - let num_blocks = 1usize - .checked_shl(Cfg::R as u32) - .ok_or_else(|| HachiError::InvalidSetup("2^R does not fit usize".to_string()))?; transcript.append_serde(ABSORB_PROVER_V, v); sample_sparse_challenges::( transcript, @@ -263,12 +311,6 @@ where ) } -fn constant_ring(value: F) -> CyclotomicRing { - let mut coeffs = [F::zero(); D]; - coeffs[0] = value; - CyclotomicRing::from_coefficients(coeffs) -} - fn gadget_row_scalars(levels: usize, log_basis: u32) -> Vec { let base = F::from_canonical_u128_reduced(1u128 << log_basis); let mut out = Vec::with_capacity(levels); @@ -280,220 +322,305 @@ fn gadget_row_scalars(levels: usize, log_basis: u out } -/// Kronecker product of two scalar vectors, producing constant ring elements. -/// Cost: O(1) per pair (just a field multiplication + ring construction). -fn kron_scalars( - left: &[F], - right: &[F], -) -> Vec> { - let mut out = Vec::with_capacity(left.len().saturating_mul(right.len())); - for &l in left { - for &r in right { - out.push(constant_ring(l * r)); +/// Accumulate unreduced polynomial product `a * b` into `poly` (length 2D-1). +fn add_unreduced_product( + poly: &mut [F], + a: &CyclotomicRing, + b: &CyclotomicRing, +) { + if a.is_zero() { + return; + } + let ac = a.coefficients(); + let bc = b.coefficients(); + let is_scalar = ac[1..].iter().all(|c| c.is_zero()); + if is_scalar { + let s = ac[0]; + for k in 0..D { + poly[k] = poly[k] + s * bc[k]; + } + } else { + for t in 0..D { + for s in 0..D { + poly[t + s] = poly[t + s] + ac[t] * bc[s]; + } } } - out } -/// Kronecker product where the right operand is field scalars. -/// Cost: O(D) per pair instead of O(D^2). -fn kron_row_scale( - left: &[CyclotomicRing], - right: &[F], -) -> Vec> { - let mut out = Vec::with_capacity(left.len().saturating_mul(right.len())); - for l in left { - for &r in right { - out.push(l.scale(&r)); +/// Accumulate negated unreduced product `-a * b` into `poly`. +fn sub_unreduced_product( + poly: &mut [F], + a: &CyclotomicRing, + b: &CyclotomicRing, +) { + if a.is_zero() { + return; + } + let ac = a.coefficients(); + let bc = b.coefficients(); + let is_scalar = ac[1..].iter().all(|c| c.is_zero()); + if is_scalar { + let s = ac[0]; + for k in 0..D { + poly[k] = poly[k] - s * bc[k]; + } + } else { + for t in 0..D { + for s in 0..D { + poly[t + s] = poly[t + s] - ac[t] * bc[s]; + } } } - out } -/// Kronecker product of sparse challenges with scalar gadget entries. -/// Cost: O(omega + D) per pair instead of O(D^2). -fn kron_sparse_scale( - left: &[SparseChallenge], - right: &[F], -) -> Vec> { - let mut out = Vec::with_capacity(left.len().saturating_mul(right.len())); - for l in left { - let dense: CyclotomicRing = l.to_dense().expect("valid sparse challenge"); - for &r in right { - out.push(dense.scale(&r)); - } +/// Add scalar * ring_element into the low-D coefficients of `poly`. +/// scalar * ring produces degree D-1, so no high-half contribution. +fn add_scalar_ring_product( + poly: &mut [F], + scalar: &F, + ring: &CyclotomicRing, +) { + for (k, coeff) in ring.coefficients().iter().enumerate() { + poly[k] = poly[k] + *scalar * *coeff; } - out } -fn gadget_block_diag_scalars(blocks: usize, row: &[F]) -> Vec> { - let row_len = row.len(); - let mut rows = Vec::with_capacity(blocks); - for i in 0..blocks { - let mut out = vec![F::zero(); blocks * row_len]; - let start = i * row_len; - out[start..start + row_len].copy_from_slice(row); - rows.push(out); +/// Subtract scalar * ring_element from the low-D coefficients of `poly`. +fn sub_scalar_ring_product( + poly: &mut [F], + scalar: &F, + ring: &CyclotomicRing, +) { + for (k, coeff) in ring.coefficients().iter().enumerate() { + poly[k] = poly[k] - *scalar * *coeff; } - rows } -pub(crate) fn generate_m( - setup: &RingCommitmentSetup, +/// Add sparse_challenge * ring_element as unreduced product into `poly`. +fn add_sparse_ring_product( + poly: &mut [F], + challenge: &SparseChallenge, + ring: &CyclotomicRing, +) { + let dense: CyclotomicRing = challenge.to_dense().expect("valid sparse challenge"); + add_unreduced_product(poly, &dense, ring); +} + +/// Split-eq replacement for `generate_m` + `compute_r_via_poly_division`. +/// +/// Computes `r` such that `M·z = y + (X^D+1)·r` without materializing M or z. +/// Uses split-eq factoring: `kron(left, gadget) · decomposed = left · pre_decomp`. +pub(crate) fn compute_r_split_eq( + setup: &HachiExpandedSetup, opening_point: &RingOpeningPoint, challenges: &[SparseChallenge], -) -> Result>>, HachiError> + w_hat: &[Vec>], + t_hat: &[Vec>], + z_pre: &[CyclotomicRing], + y: &[CyclotomicRing], +) -> Result>, HachiError> where F: FieldCore + CanonicalField, + Cfg: CommitmentConfig, { - let num_blocks = 1usize - .checked_shl(Cfg::R as u32) - .ok_or_else(|| HachiError::InvalidSetup("2^R does not fit usize".to_string()))?; - let block_len = 1usize - .checked_shl(Cfg::M as u32) - .ok_or_else(|| HachiError::InvalidSetup("2^M does not fit usize".to_string()))?; - let w_len = Cfg::DELTA - .checked_mul(num_blocks) - .ok_or_else(|| HachiError::InvalidSetup("w length overflow".to_string()))?; - let t_len = Cfg::DELTA - .checked_mul(Cfg::N_A) - .and_then(|v| v.checked_mul(num_blocks)) - .ok_or_else(|| HachiError::InvalidSetup("t length overflow".to_string()))?; - let z_len = Cfg::TAU - .checked_mul(Cfg::DELTA) - .and_then(|v| v.checked_mul(block_len)) - .ok_or_else(|| HachiError::InvalidSetup("z length overflow".to_string()))?; - let total_cols = w_len - .checked_add(t_len) - .and_then(|v| v.checked_add(z_len)) - .ok_or_else(|| HachiError::InvalidSetup("matrix width overflow".to_string()))?; - - if opening_point.b.len() != num_blocks { - return Err(HachiError::InvalidPointDimension { - expected: num_blocks, - actual: opening_point.b.len(), - }); - } - if opening_point.a.len() != block_len { - return Err(HachiError::InvalidPointDimension { - expected: block_len, - actual: opening_point.a.len(), - }); - } - if challenges.len() != num_blocks { - return Err(HachiError::InvalidSize { - expected: num_blocks, - actual: challenges.len(), - }); - } - if setup.D.len() != Cfg::N_D { - return Err(HachiError::InvalidSize { - expected: Cfg::N_D, - actual: setup.D.len(), - }); - } - if setup.B.len() != Cfg::N_B { - return Err(HachiError::InvalidSize { - expected: Cfg::N_B, - actual: setup.B.len(), - }); - } - if setup.A.len() != Cfg::N_A { - return Err(HachiError::InvalidSize { - expected: Cfg::N_A, - actual: setup.A.len(), - }); - } - if setup.A.first().map(|row| row.len()) != Some(block_len * Cfg::DELTA) { - return Err(HachiError::InvalidSetup("A row width mismatch".to_string())); + let poly_len = 2 * D - 1; + let num_rows = Cfg::N_D + Cfg::N_B + 1 + 1 + Cfg::N_A; + + let w_hat_flat: Vec> = + w_hat.iter().flat_map(|v| v.iter().copied()).collect(); + let t_hat_flat: Vec> = + t_hat.iter().flat_map(|v| v.iter().copied()).collect(); + + let mut result = Vec::with_capacity(num_rows); + + for (row_idx, y_i) in y.iter().enumerate().take(num_rows) { + let mut poly = vec![F::zero(); poly_len]; + + if row_idx < Cfg::N_D { + let d_row = &setup.D[row_idx]; + for (m_ij, z_j) in d_row.iter().zip(w_hat_flat.iter()) { + add_unreduced_product(&mut poly, m_ij, z_j); + } + } else if row_idx < Cfg::N_D + Cfg::N_B { + let b_row = &setup.B[row_idx - Cfg::N_D]; + for (m_ij, z_j) in b_row.iter().zip(t_hat_flat.iter()) { + add_unreduced_product(&mut poly, m_ij, z_j); + } + } else if row_idx == Cfg::N_D + Cfg::N_B { + // row3: b . w_recomp (scalar * ring, degree D-1) + for (i, w_hat_i) in w_hat.iter().enumerate() { + let w_recomp = CyclotomicRing::gadget_recompose_pow2(w_hat_i, Cfg::LOG_BASIS); + add_scalar_ring_product(&mut poly, &opening_point.b[i], &w_recomp); + } + } else if row_idx == Cfg::N_D + Cfg::N_B + 1 { + // row4 w-segment: c . w_recomp (sparse*ring unreduced) + for (i, w_hat_i) in w_hat.iter().enumerate() { + let w_recomp = CyclotomicRing::gadget_recompose_pow2(w_hat_i, Cfg::LOG_BASIS); + add_sparse_ring_product(&mut poly, &challenges[i], &w_recomp); + } + // row4 z-segment: -(a . z_pre_recomp), double-factored + // z_pre_recomp[i] = gadget_recompose(z_pre[i*DELTA..(i+1)*DELTA]) + let block_len = opening_point.a.len(); + for i in 0..block_len { + let start = i * Cfg::DELTA; + let end = start + Cfg::DELTA; + if end <= z_pre.len() { + let z_pre_recomp = + CyclotomicRing::gadget_recompose_pow2(&z_pre[start..end], Cfg::LOG_BASIS); + sub_scalar_ring_product(&mut poly, &opening_point.a[i], &z_pre_recomp); + } + } + } else { + // row5 (N_A rows) + let a_idx = row_idx - (Cfg::N_D + Cfg::N_B + 2); + // t-segment: c . t_recomp[a_idx] (sparse*ring unreduced) + for (i, t_hat_i) in t_hat.iter().enumerate() { + let start = a_idx * Cfg::DELTA; + let end = start + Cfg::DELTA; + if end <= t_hat_i.len() { + let t_recomp = + CyclotomicRing::gadget_recompose_pow2(&t_hat_i[start..end], Cfg::LOG_BASIS); + add_sparse_ring_product(&mut poly, &challenges[i], &t_recomp); + } + } + // z-segment: -(A[a_idx] . z_pre) (ring*ring unreduced) + let a_row = &setup.A[a_idx]; + for (m_ij, z_j) in a_row.iter().zip(z_pre.iter()) { + sub_unreduced_product(&mut poly, m_ij, z_j); + } + } + + let y_coeffs = y_i.coefficients(); + for k in 0..D { + poly[k] = poly[k] - y_coeffs[k]; + } + + // Divide by X^D + 1 + let mut quotient = vec![F::zero(); D]; + for k in (D..poly_len).rev() { + let q = poly[k]; + quotient[k - D] = q; + poly[k - D] = poly[k - D] - q; + } + let coeffs: [F; D] = std::array::from_fn(|k| quotient[k]); + result.push(CyclotomicRing::from_coefficients(coeffs)); } + Ok(result) +} + +/// Split-eq replacement for `generate_m` + `eval_ring_matrix_at`. +/// +/// Computes the field-element evaluations of each M entry at `alpha`, +/// organized as rows of field elements, without materializing M. +pub(crate) fn compute_m_a_streaming( + setup: &HachiExpandedSetup, + opening_point: &RingOpeningPoint, + challenges: &[SparseChallenge], + alpha: &F, +) -> Result>, HachiError> +where + F: FieldCore + CanonicalField, + Cfg: CommitmentConfig, +{ + let layout = setup.seed.layout; + let num_blocks = layout.num_blocks; + let block_len = layout.block_len; + let w_len = Cfg::DELTA * num_blocks; + let t_len = Cfg::DELTA * Cfg::N_A * num_blocks; + let z_len = Cfg::TAU * Cfg::DELTA * block_len; + let total_cols = w_len + t_len + z_len; + let g1 = gadget_row_scalars::(Cfg::DELTA, Cfg::LOG_BASIS); let j1 = gadget_row_scalars::(Cfg::TAU, Cfg::LOG_BASIS); - let row3_w = kron_scalars::(&opening_point.b, &g1); - let row4_w = kron_sparse_scale::(challenges, &g1); - - let ag = kron_scalars::(&opening_point.a, &g1); - let ag_scalars: Vec = ag.iter().map(|r| r.coefficients()[0]).collect(); - let row4_z = kron_scalars::(&ag_scalars, &j1) - .into_iter() - .map(|x| -x) - .collect::>(); - - let g_na = gadget_block_diag_scalars::(Cfg::N_A, &g1); - let row5_mid = g_na - .iter() - .map(|row| kron_sparse_scale::(challenges, row)) - .collect::>(); - let row5_right = setup - .A - .iter() - .map(|row| kron_row_scale(row, &j1).into_iter().map(|x| -x).collect()) - .collect::>>(); - - let zero = CyclotomicRing::::zero(); - let mut rows = Vec::with_capacity(Cfg::N_D + Cfg::N_B + 1usize + 1usize + Cfg::N_A); - - for row in setup.D.iter() { - if row.len() != w_len { - return Err(HachiError::InvalidSetup("D row width mismatch".to_string())); + // Pre-evaluate alpha powers for gadget scalars (already field elements) + // g1 and j1 are already field scalars, so eval_ring_at(constant(g), alpha) = g. + + let mut rows = Vec::with_capacity(Cfg::N_D + Cfg::N_B + 1 + 1 + Cfg::N_A); + + // D rows: setup.D[i] evaluated at alpha, zero-padded + for d_row in setup.D.iter() { + let mut full = vec![F::zero(); total_cols]; + for (j, ring) in d_row.iter().enumerate() { + full[j] = eval_ring_at(ring, alpha); } - let mut full = vec![zero; total_cols]; - full[..w_len].copy_from_slice(row); rows.push(full); } - for row in setup.B.iter() { - if row.len() != t_len { - return Err(HachiError::InvalidSetup("B row width mismatch".to_string())); + // B rows: setup.B[i] evaluated at alpha, in t-segment + for b_row in setup.B.iter() { + let mut full = vec![F::zero(); total_cols]; + for (j, ring) in b_row.iter().enumerate() { + full[w_len + j] = eval_ring_at(ring, alpha); } - let mut full = vec![zero; total_cols]; - full[w_len..w_len + t_len].copy_from_slice(row); rows.push(full); } - let mut row3 = vec![zero; total_cols]; - row3[..w_len].copy_from_slice(&row3_w); - rows.push(row3); + // row3: kron(b, g1) evaluated at alpha -> b[i] * g1[d] (all scalars) + { + let mut full = vec![F::zero(); total_cols]; + for (i, &b_i) in opening_point.b.iter().enumerate() { + for (d, &g) in g1.iter().enumerate() { + full[i * Cfg::DELTA + d] = b_i * g; + } + } + rows.push(full); + } - let mut row4 = vec![zero; total_cols]; - row4[..w_len].copy_from_slice(&row4_w); - row4[w_len + t_len..].copy_from_slice(&row4_z); - rows.push(row4); + // row4: w-segment = kron(c, g1) evaluated at alpha + // z-segment = -kron(kron(a,g1), j1) (all scalars) + { + let mut full = vec![F::zero(); total_cols]; + // w-segment: c[i] evaluated at alpha, times g1[d] + for (i, c) in challenges.iter().enumerate() { + let c_alpha = eval_ring_at(&c.to_dense::().expect("valid challenge"), alpha); + for (d, &g) in g1.iter().enumerate() { + full[i * Cfg::DELTA + d] = c_alpha * g; + } + } + // z-segment: -kron(kron(a,g1), j1) = -(a[i] * g1[d] * j1[t]) + let z_offset = w_len + t_len; + for (i, &a_i) in opening_point.a.iter().enumerate() { + for (d, &g) in g1.iter().enumerate() { + let ag = a_i * g; + for (t, &j) in j1.iter().enumerate() { + let idx = (i * Cfg::DELTA + d) * Cfg::TAU + t; + full[z_offset + idx] = -(ag * j); + } + } + } + rows.push(full); + } - for (mid, right) in row5_mid.into_iter().zip(row5_right.into_iter()) { - let mut row = vec![zero; total_cols]; - row[w_len..w_len + t_len].copy_from_slice(&mid); - row[w_len + t_len..].copy_from_slice(&right); - rows.push(row); + // row5 (N_A rows): t-segment = kron(c, g_na[a_idx]) evaluated at alpha + // z-segment = -kron(A[a_idx], j1) evaluated at alpha + for a_idx in 0..Cfg::N_A { + let mut full = vec![F::zero(); total_cols]; + // t-segment: block-diagonal gadget times challenges + for (i, c) in challenges.iter().enumerate() { + let c_alpha = eval_ring_at(&c.to_dense::().expect("valid challenge"), alpha); + for (d, &g) in g1.iter().enumerate() { + let t_idx = i * (Cfg::N_A * Cfg::DELTA) + a_idx * Cfg::DELTA + d; + full[w_len + t_idx] = c_alpha * g; + } + } + // z-segment: -A[a_idx][k] evaluated at alpha, times j1[t] + let z_offset = w_len + t_len; + let a_row = &setup.A[a_idx]; + for (k, ring) in a_row.iter().enumerate() { + let ring_alpha = eval_ring_at(ring, alpha); + for (t, &j) in j1.iter().enumerate() { + full[z_offset + k * Cfg::TAU + t] = -(ring_alpha * j); + } + } + rows.push(full); } Ok(rows) } -pub(crate) fn generate_z( - w_hat: &[Vec>], - t_hat: &[Vec>], - z_hat: &[CyclotomicRing], -) -> Vec> { - let mut out = Vec::with_capacity( - w_hat.len() - + t_hat.len() - + z_hat.len() - + w_hat.iter().map(|v| v.len()).sum::() - + t_hat.iter().map(|v| v.len()).sum::(), - ); - for w in w_hat { - out.extend(w.iter().copied()); - } - for t in t_hat { - out.extend(t.iter().copied()); - } - out.extend_from_slice(z_hat); - out -} - pub(crate) fn generate_y( v: &[CyclotomicRing], u: &[CyclotomicRing], @@ -529,8 +656,7 @@ where #[cfg(test)] mod tests { use super::*; - use crate::algebra::ring::SparseChallengeConfig; - use crate::algebra::CyclotomicRing; + use crate::algebra::{CyclotomicRing, SparseChallengeConfig}; use crate::protocol::challenges::sparse::sample_sparse_challenges; use crate::protocol::commitment::{HachiCommitmentCore, RingCommitmentScheme}; use crate::protocol::proof::HachiCommitmentHint; @@ -562,7 +688,7 @@ mod tests { } struct Fixture { - setup: RingCommitmentSetup, + setup: HachiProverSetup, commitment_u: Vec>, point: RingOpeningPoint, blocks: Vec>>, @@ -576,7 +702,7 @@ mod tests { >::setup(16).unwrap(); let blocks = sample_blocks(); - let (commitment, s, t_hat) = + let w = >::commit_ring_blocks( &blocks, &setup, ) @@ -587,10 +713,11 @@ mod tests { b: sample_b(), }; + let ring_coeffs: Vec> = + blocks.iter().flat_map(|b| b.iter().copied()).collect(); let hint = HachiCommitmentHint { - s, - t_hat, - ring_coeffs: Vec::new(), + t_hat: w.t_hat, + ring_coeffs, }; let mut transcript = Blake2bTranscript::::new(TRANSCRIPT_SEED); let y_ring = CyclotomicRing::::zero(); @@ -599,7 +726,7 @@ mod tests { &point, &hint, &mut transcript, - &commitment, + &w.commitment, &y_ring, ) .unwrap(); @@ -608,7 +735,7 @@ mod tests { Fixture { setup, - commitment_u: commitment.u.clone(), + commitment_u: w.commitment.u.clone(), point, blocks, quad_eq, @@ -624,7 +751,7 @@ mod tests { let w_hat = f.quad_eq.w_hat().unwrap(); let w_hat_flat: Vec> = w_hat.iter().flat_map(|v| v.iter().copied()).collect(); - let lhs = mat_vec_mul(&f.setup.D, &w_hat_flat); + let lhs = mat_vec_mul(&f.setup.expanded.D, &w_hat_flat); assert_eq!(lhs, f.quad_eq.v(), "Row 1 failed: D · ŵ ≠ v"); } @@ -637,7 +764,7 @@ mod tests { let hint = f.quad_eq.hint().unwrap(); let t_hat_flat: Vec> = hint.t_hat.iter().flat_map(|v| v.iter().copied()).collect(); - let lhs = mat_vec_mul(&f.setup.B, &t_hat_flat); + let lhs = mat_vec_mul(&f.setup.expanded.B, &t_hat_flat); assert_eq!(lhs, f.commitment_u, "Row 2 failed: B · t̂ ≠ u"); } @@ -679,6 +806,14 @@ mod tests { ); } + /// Derive z_hat from z_pre for test assertions. + fn derive_z_hat(z_pre: &[CyclotomicRing]) -> Vec> { + z_pre + .iter() + .flat_map(|z_j| z_j.balanced_decompose_pow2(TAU, LOG_BASIS)) + .collect() + } + /// Row 4: (c^T ⊗ G_1) · ŵ = a^T · G_{2^m} · J · ẑ #[test] fn row4_challenge_fold_w_equals_a_gadget_j_z_hat() { @@ -698,7 +833,8 @@ mod tests { acc + (*c_i * *w_i) }); - let z_recovered = recompose_z_hat(f.quad_eq.z_hat().unwrap()); + let z_hat = derive_z_hat(f.quad_eq.z_pre().unwrap()); + let z_recovered = recompose_z_hat(&z_hat); let rhs = a_transpose_gadget_times_vec(&f.point.a, &z_recovered); assert_eq!(lhs, rhs, "Row 4 failed: (c^T ⊗ G_1)ŵ ≠ a^T G J ẑ"); @@ -719,8 +855,9 @@ mod tests { } } - let z_recovered = recompose_z_hat(f.quad_eq.z_hat().unwrap()); - let rhs = mat_vec_mul(&f.setup.A, &z_recovered); + let z_hat = derive_z_hat(f.quad_eq.z_pre().unwrap()); + let z_recovered = recompose_z_hat(&z_hat); + let rhs = mat_vec_mul(&f.setup.expanded.A, &z_recovered); assert_eq!(lhs, rhs, "Row 5 failed: (c^T ⊗ G_nA)t̂ ≠ A · J · ẑ"); } @@ -739,6 +876,6 @@ mod tests { assert_eq!(hint.t_hat.len(), NUM_BLOCKS); assert!(hint.t_hat.iter().all(|v| v.len() == N_A * DELTA)); - assert_eq!(f.quad_eq.z_hat().unwrap().len(), BLOCK_LEN * DELTA * TAU); + assert_eq!(f.quad_eq.z_pre().unwrap().len(), BLOCK_LEN * DELTA); } } diff --git a/src/protocol/ring_switch.rs b/src/protocol/ring_switch.rs index cb4bc0f9..ef87ed0e 100644 --- a/src/protocol/ring_switch.rs +++ b/src/protocol/ring_switch.rs @@ -4,14 +4,19 @@ //! sumcheck instances by expanding the ring elements into their coefficient //! vectors and setting up the evaluation tables. -use crate::algebra::ring::CyclotomicRing; +use crate::algebra::CyclotomicRing; +use crate::cfg_into_iter; use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; use crate::protocol::commitment::utils::norm::detect_field_modulus; use crate::protocol::commitment::{ - CommitmentConfig, DefaultCommitmentConfig, HachiCommitmentCore, RingCommitment, - RingCommitmentScheme, + CommitmentConfig, HachiCommitmentCore, HachiCommitmentLayout, HachiExpandedSetup, + RingCommitment, RingCommitmentScheme, +}; +use crate::protocol::quadratic_equation::{ + compute_m_a_streaming, compute_r_split_eq, QuadraticEquation, }; -use crate::protocol::quadratic_equation::QuadraticEquation; use crate::protocol::sumcheck::eq_poly::EqPolynomial; use crate::protocol::transcript::labels::{ ABSORB_SUMCHECK_W, CHALLENGE_RING_SWITCH, CHALLENGE_TAU0, CHALLENGE_TAU1, @@ -19,21 +24,22 @@ use crate::protocol::transcript::labels::{ use crate::protocol::transcript::Transcript; use crate::{CanonicalField, FieldCore, FieldSampling}; -/// Output of the ring switch prover, containing everything needed for sumchecks. +/// Output of the ring switch protocol, containing everything needed for sumchecks. pub struct RingSwitchOutput { /// The witness vector w (concatenation of z and r coefficients). pub w: Vec, /// Commitment to w. pub w_commitment: RingCommitment, - /// Evaluation table of w (reordered for sumcheck). - pub w_evals: Vec, + /// Compact evaluation table of w (all entries in [-8, 7], reordered for sumcheck). + /// Populated by the prover; empty on the verifier side. + pub w_evals: Vec, /// Evaluation table of M_alpha(x) (tau1-weighted). pub m_evals_x: Vec, /// Evaluation table of alpha powers (y dimension). pub alpha_evals_y: Vec, - /// Number of upper variable bits in w_evals. + /// Number of upper variable bits. pub num_u: usize, - /// Number of lower variable bits in w_evals. + /// Number of lower variable bits. pub num_l: usize, /// Challenge tau0 for F_0 sumcheck. pub tau0: Vec, @@ -49,28 +55,50 @@ pub struct RingSwitchOutput { /// /// # Errors /// -/// Returns an error if z is missing, commitment fails, or matrix expansion fails. +/// Returns an error if z_pre/w_hat is missing, commitment fails, or matrix expansion fails. pub fn ring_switch_prover( - quad_eq: &QuadraticEquation, + quad_eq: &mut QuadraticEquation, + setup: &HachiExpandedSetup, transcript: &mut T, -) -> Result, HachiError> +) -> Result, HachiError> where F: FieldCore + CanonicalField + FieldSampling, T: Transcript, Cfg: CommitmentConfig, { - let z = quad_eq - .z() - .ok_or_else(|| HachiError::InvalidInput("missing z in prover".to_string()))?; - let r = compute_r_via_poly_division::(quad_eq.m(), z, quad_eq.y()); - let w = build_w_coeffs::(z, &r); - - let w_commitment = commit_w::(&w)?; + let w_hat = quad_eq + .w_hat() + .ok_or_else(|| HachiError::InvalidInput("missing w_hat in prover".to_string()))?; + let z_pre = quad_eq + .z_pre() + .ok_or_else(|| HachiError::InvalidInput("missing z_pre in prover".to_string()))?; + let hint = quad_eq + .hint() + .ok_or_else(|| HachiError::InvalidInput("missing hint in prover".to_string()))?; + let t_hat = &hint.t_hat; + + let r = compute_r_split_eq::( + setup, + quad_eq.opening_point(), + &quad_eq.challenges, + w_hat, + t_hat, + z_pre, + quad_eq.y(), + )?; + let w = build_w_coeffs::(w_hat, t_hat, z_pre, &r); + + let w_commitment = commit_w::(&w)?; transcript.append_serde(ABSORB_SUMCHECK_W, &w_commitment); let alpha: F = transcript.challenge_scalar(CHALLENGE_RING_SWITCH); - let m_a = eval_ring_matrix_at::(quad_eq.m(), &alpha); + let m_a = compute_m_a_streaming::( + setup, + quad_eq.opening_point(), + &quad_eq.challenges, + &alpha, + )?; let m_a_vec = expand_m_a::(&m_a, alpha)?; let m_rows = m_row_count::(); let m_cols = if m_a.is_empty() { @@ -79,7 +107,7 @@ where m_a_vec.len() / m_a.len() }; - let (w_evals, num_u, num_l) = build_w_evals(&w, D); + let (w_evals, num_u, num_l) = build_w_evals_compact::(&w, D)?; let alpha_evals_y = build_alpha_evals_y(alpha, D); let num_sc_vars = num_u + num_l; @@ -112,10 +140,11 @@ where /// Returns an error if matrix expansion fails. pub fn ring_switch_verifier( quad_eq: &QuadraticEquation, + setup: &HachiExpandedSetup, w: &[F], - w_commitment: &RingCommitment, + w_commitment: &RingCommitment, transcript: &mut T, -) -> Result, HachiError> +) -> Result, HachiError> where F: FieldCore + CanonicalField + FieldSampling, T: Transcript, @@ -125,7 +154,12 @@ where let alpha: F = transcript.challenge_scalar(CHALLENGE_RING_SWITCH); - let m_a = eval_ring_matrix_at::(quad_eq.m(), &alpha); + let m_a = compute_m_a_streaming::( + setup, + quad_eq.opening_point(), + &quad_eq.challenges, + &alpha, + )?; let m_a_vec = expand_m_a::(&m_a, alpha)?; let m_rows = m_row_count::(); let m_cols = if m_a.is_empty() { @@ -134,7 +168,9 @@ where m_a_vec.len() / m_a.len() }; - let (w_evals, num_u, num_l) = build_w_evals(w, D); + let num_ring_elems = w.len() / D; + let num_u = num_ring_elems.next_power_of_two().trailing_zeros() as usize; + let num_l = D.trailing_zeros() as usize; let alpha_evals_y = build_alpha_evals_y(alpha, D); let num_sc_vars = num_u + num_l; @@ -148,7 +184,7 @@ where Ok(RingSwitchOutput { w: w.to_vec(), w_commitment: w_commitment.clone(), - w_evals, + w_evals: Vec::new(), m_evals_x, alpha_evals_y, num_u, @@ -160,38 +196,65 @@ where }) } -pub(crate) fn compute_r_via_poly_division( +#[cfg(test)] +pub(crate) fn compute_r_via_poly_division( m: &[Vec>], z: &[CyclotomicRing], y: &[CyclotomicRing], -) -> Vec> { +) -> Result>, HachiError> { let poly_len = 2 * D - 1; - m.iter() + let out = m + .iter() .zip(y.iter()) .map(|(row, y_i)| { - let mut poly = vec![F::zero(); poly_len]; - for (m_ij, z_j) in row.iter().zip(z.iter()) { - if m_ij.is_zero() { - continue; - } - let a = m_ij.coefficients(); - let b = z_j.coefficients(); - - // Detect constant (scalar) ring elements: only a[0] is non-zero. - let is_scalar = a[1..].iter().all(|c| c.is_zero()); - if is_scalar { - let scalar = a[0]; - for s in 0..D { - poly[s] = poly[s] + scalar * b[s]; + let column_contribution = + |m_ij: &CyclotomicRing, z_j: &CyclotomicRing| -> Vec { + let mut local = vec![F::zero(); poly_len]; + if m_ij.is_zero() { + return local; } - } else { - for t in 0..D { + let a = m_ij.coefficients(); + let b = z_j.coefficients(); + let is_scalar = a[1..].iter().all(|c| c.is_zero()); + if is_scalar { + let scalar = a[0]; for s in 0..D { - poly[t + s] = poly[t + s] + a[t] * b[s]; + local[s] = scalar * b[s]; + } + } else { + for t in 0..D { + for s in 0..D { + local[t + s] = local[t + s] + a[t] * b[s]; + } } } + local + }; + + let pointwise_add = |mut a: Vec, b: Vec| -> Vec { + for (ai, bi) in a.iter_mut().zip(b.iter()) { + *ai = *ai + *bi; } - } + a + }; + + #[cfg(feature = "parallel")] + let mut poly = row + .par_iter() + .zip(z.par_iter()) + .fold( + || vec![F::zero(); poly_len], + |acc, (m_ij, z_j)| pointwise_add(acc, column_contribution(m_ij, z_j)), + ) + .reduce(|| vec![F::zero(); poly_len], pointwise_add); + + #[cfg(not(feature = "parallel"))] + let mut poly = row + .iter() + .zip(z.iter()) + .fold(vec![F::zero(); poly_len], |acc, (m_ij, z_j)| { + pointwise_add(acc, column_contribution(m_ij, z_j)) + }); let y_coeffs = y_i.coefficients(); for k in 0..D { poly[k] = poly[k] - y_coeffs[k]; @@ -205,63 +268,65 @@ pub(crate) fn compute_r_via_poly_division( let coeffs: [F; D] = std::array::from_fn(|k| quotient[k]); CyclotomicRing::from_coefficients(coeffs) }) - .collect() + .collect(); + Ok(out) } #[derive(Clone, Copy, Debug)] -struct WCommitmentConfig; - -impl CommitmentConfig for WCommitmentConfig { - const D: usize = DefaultCommitmentConfig::D; - const M: usize = 11; - const R: usize = 0; - const N_A: usize = DefaultCommitmentConfig::N_A; - const N_B: usize = DefaultCommitmentConfig::N_B; - const N_D: usize = DefaultCommitmentConfig::N_D; - const LOG_BASIS: u32 = DefaultCommitmentConfig::LOG_BASIS; - const DELTA: usize = DefaultCommitmentConfig::DELTA; - const TAU: usize = DefaultCommitmentConfig::TAU; - const BETA: u128 = DefaultCommitmentConfig::BETA; - const CHALLENGE_WEIGHT: usize = DefaultCommitmentConfig::CHALLENGE_WEIGHT; +struct WCommitmentConfig { + _cfg: std::marker::PhantomData, } -fn commit_w(w: &[F]) -> Result, HachiError> +impl CommitmentConfig for WCommitmentConfig { + const D: usize = D; + const N_A: usize = Cfg::N_A; + const N_B: usize = Cfg::N_B; + const N_D: usize = Cfg::N_D; + const LOG_BASIS: u32 = Cfg::LOG_BASIS; + const DELTA: usize = Cfg::DELTA; + const TAU: usize = Cfg::TAU; + const CHALLENGE_WEIGHT: usize = Cfg::CHALLENGE_WEIGHT; + + fn commitment_layout(max_num_vars: usize) -> Result { + let alpha = D.trailing_zeros() as usize; + let m_vars = max_num_vars.checked_sub(alpha).ok_or_else(|| { + HachiError::InvalidSetup("max_num_vars is smaller than alpha".to_string()) + })?; + HachiCommitmentLayout::new::(m_vars, 0) + } +} + +fn commit_w(w: &[F]) -> Result, HachiError> where F: FieldCore + CanonicalField + FieldSampling, + Cfg: CommitmentConfig, { - let d = DefaultCommitmentConfig::D; - let block_len = 1usize << WCommitmentConfig::M; + type WCfg = WCommitmentConfig; - let ring_elems: Vec> = w - .chunks(d) + let ring_elems: Vec> = w + .chunks(D) .map(|chunk| { - let coeffs: [F; DefaultCommitmentConfig::D] = + let coeffs: [F; D] = std::array::from_fn(|i| if i < chunk.len() { chunk[i] } else { F::zero() }); CyclotomicRing::from_coefficients(coeffs) }) .collect(); + let block_len = ring_elems.len().next_power_of_two().max(1); let mut padded = ring_elems; - padded.resize( - block_len, - CyclotomicRing::::zero(), - ); - + padded.resize(block_len, CyclotomicRing::::zero()); + let m_vars = block_len.trailing_zeros() as usize; + let max_num_vars = m_vars + D.trailing_zeros() as usize; let blocks = vec![padded]; - let (w_setup, _) = >::setup(WCommitmentConfig::M)?; + let (w_setup, _) = + >>::setup(max_num_vars)?; - let (commitment, _, _) = >::commit_ring_blocks(&blocks, &w_setup)?; + let w = >>::commit_ring_blocks( + &blocks, &w_setup, + )?; - Ok(commitment) + Ok(w.commitment) } pub(crate) fn eval_ring_at(r: &CyclotomicRing, alpha: &F) -> F { @@ -274,20 +339,6 @@ pub(crate) fn eval_ring_at(r: &CyclotomicRing( - v: &[CyclotomicRing], - alpha: &F, -) -> Vec { - v.iter().map(|r| eval_ring_at(r, alpha)).collect() -} - -pub(crate) fn eval_ring_matrix_at( - m: &[Vec>], - alpha: &F, -) -> Vec> { - m.iter().map(|row| eval_ring_vec_at(row, alpha)).collect() -} - pub(crate) fn r_decomp_levels() -> usize { let modulus = detect_field_modulus::(); let bits = 128 - (modulus.saturating_sub(1)).leading_zeros() as usize; @@ -368,25 +419,82 @@ pub(crate) fn expand_m_a(w: &[F], d: usize) -> (Vec, usize, usize) { +/// # Errors +/// +/// Returns an error if `w.len()` is not a multiple of `d`. +pub(crate) fn build_w_evals( + w: &[F], + d: usize, +) -> Result<(Vec, usize, usize), HachiError> { + if d == 0 || w.len() % d != 0 { + return Err(HachiError::InvalidSize { + expected: d, + actual: w.len(), + }); + } let num_l = d.trailing_zeros() as usize; - let num_ring_elems = w.len() / d.max(1); + let num_ring_elems = w.len() / d; let num_u = num_ring_elems.next_power_of_two().trailing_zeros() as usize; let x_len = 1usize << num_u; - let y_len = 1usize << num_l; - let n = x_len * y_len; + let n = x_len << num_l; - let mut evals = vec![F::zero(); n]; - for x in 0..x_len { - for y in 0..y_len { + let evals: Vec = cfg_into_iter!(0..n) + .map(|dst| { + let x = dst & (x_len - 1); + let y = dst >> num_u; let src = y + (x << num_l); if src < w.len() { - let dst = x + (y << num_u); - evals[dst] = w[src]; + w[src] + } else { + F::zero() } - } + }) + .collect(); + Ok((evals, num_u, num_l)) +} + +/// Compact variant of `build_w_evals` returning `Vec`. +/// +/// All entries in `w` must have canonical values in `[-half_b, half_b - 1]` +/// where `half_b = 2^(LOG_BASIS-1)`. This holds when `w` is produced by +/// `build_w_coeffs` (all components go through `balanced_decompose_pow2`). +pub(crate) fn build_w_evals_compact( + w: &[F], + d: usize, +) -> Result<(Vec, usize, usize), HachiError> { + if d == 0 || w.len() % d != 0 { + return Err(HachiError::InvalidSize { + expected: d, + actual: w.len(), + }); } - (evals, num_u, num_l) + let num_l = d.trailing_zeros() as usize; + let num_ring_elems = w.len() / d; + let num_u = num_ring_elems.next_power_of_two().trailing_zeros() as usize; + let x_len = 1usize << num_u; + let n = x_len << num_l; + + let q = (-F::one()).to_canonical_u128() + 1; + let half_q = q / 2; + + let evals: Vec = (0..n) + .map(|dst| { + let x = dst & (x_len - 1); + let y = dst >> num_u; + let src = y + (x << num_l); + if src < w.len() { + let canonical = w[src].to_canonical_u128(); + if canonical <= half_q { + canonical as i8 + } else { + (canonical as i128 - q as i128) as i8 + } + } else { + 0i8 + } + }) + .collect(); + Ok((evals, num_u, num_l)) } pub(crate) fn m_row_count() -> usize { @@ -401,20 +509,20 @@ pub(crate) fn build_m_evals_x( ) -> Vec { let eq_tau1 = EqPolynomial::evals(tau1); let x_len = cols.next_power_of_two(); - let mut m_evals = vec![F::zero(); x_len]; - for x in 0..x_len { - let mut acc = F::zero(); - for i in 0..eq_tau1.len() { - let row_val = if i < rows && x < cols { - m_a_flat[i * cols + x] - } else { - F::zero() - }; - acc = acc + eq_tau1[i] * row_val; - } - m_evals[x] = acc; - } - m_evals + cfg_into_iter!(0..x_len) + .map(|x| { + let mut acc = F::zero(); + for i in 0..eq_tau1.len() { + let row_val = if i < rows && x < cols { + m_a_flat[i * cols + x] + } else { + F::zero() + }; + acc = acc + eq_tau1[i] * row_val; + } + acc + }) + .collect() } pub(crate) fn build_alpha_evals_y(alpha: F, d: usize) -> Vec { @@ -436,7 +544,9 @@ pub(crate) fn sample_tau>( } pub(crate) fn build_w_coeffs( - z: &[CyclotomicRing], + w_hat: &[Vec>], + t_hat: &[Vec>], + z_pre: &[CyclotomicRing], r: &[CyclotomicRing], ) -> Vec { let levels = r_decomp_levels::(); @@ -445,9 +555,119 @@ pub(crate) fn build_w_coeffs() + + t_hat.iter().map(|v| v.len()).sum::() + + z_pre.len() * Cfg::TAU; + let mut out = Vec::with_capacity((z_count + r_hat.len()) * D); + for elem in w_hat_flat + .chain(t_hat_flat) + .chain(z_hat_iter.collect::>().iter()) + .chain(r_hat.iter()) + { out.extend_from_slice(elem.coefficients()); } out } + +#[cfg(test)] +mod tests { + use super::compute_r_via_poly_division; + use crate::algebra::{CyclotomicRing, Fp64}; + use crate::{FieldCore, FromSmallInt}; + + fn compute_r_schoolbook( + m: &[Vec>], + z: &[CyclotomicRing], + y: &[CyclotomicRing], + ) -> Vec> { + let poly_len = 2 * D - 1; + m.iter() + .zip(y.iter()) + .map(|(row, y_i)| { + let mut poly = vec![F::zero(); poly_len]; + for (m_ij, z_j) in row.iter().zip(z.iter()) { + if m_ij.is_zero() { + continue; + } + let a = m_ij.coefficients(); + let b = z_j.coefficients(); + let is_scalar = a[1..].iter().all(|c| c.is_zero()); + if is_scalar { + let scalar = a[0]; + for s in 0..D { + poly[s] = poly[s] + scalar * b[s]; + } + } else { + for t in 0..D { + for s in 0..D { + poly[t + s] = poly[t + s] + a[t] * b[s]; + } + } + } + } + let y_coeffs = y_i.coefficients(); + for k in 0..D { + poly[k] = poly[k] - y_coeffs[k]; + } + let mut quotient = vec![F::zero(); D]; + for k in (D..poly_len).rev() { + let q = poly[k]; + quotient[k - D] = q; + poly[k - D] = poly[k - D] - q; + } + let coeffs: [F; D] = std::array::from_fn(|k| quotient[k]); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect() + } + + #[test] + fn compute_r_matches_schoolbook_reference() { + type F = Fp64<4294967197>; + const D: usize = 64; + + let m: Vec>> = (0..3) + .map(|i| { + (0..4) + .map(|j| { + if (i + j) % 3 == 0 { + let mut coeffs = [F::zero(); D]; + coeffs[0] = F::from_u64((i * 5 + j + 1) as u64); + CyclotomicRing::from_coefficients(coeffs) + } else { + let coeffs = std::array::from_fn(|k| { + F::from_u64((i as u64 * 1000 + j as u64 * 100 + k as u64 + 1) % 97) + }); + CyclotomicRing::from_coefficients(coeffs) + } + }) + .collect() + }) + .collect(); + let z: Vec> = (0..4) + .map(|j| { + let coeffs = + std::array::from_fn(|k| F::from_u64((j as u64 * 37 + k as u64 + 5) % 89)); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect(); + let y: Vec> = (0..3) + .map(|i| { + let coeffs = + std::array::from_fn(|k| F::from_u64((i as u64 * 29 + k as u64 + 7) % 83)); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect(); + + let expected = compute_r_schoolbook(&m, &z, &y); + let got = compute_r_via_poly_division::(&m, &z, &y) + .expect("ring-switch CRT+NTT path should dispatch for D=64"); + assert_eq!(got, expected); + } +} diff --git a/src/protocol/sumcheck/batched_sumcheck.rs b/src/protocol/sumcheck/batched_sumcheck.rs index 15673987..5caa9810 100644 --- a/src/protocol/sumcheck/batched_sumcheck.rs +++ b/src/protocol/sumcheck/batched_sumcheck.rs @@ -12,7 +12,7 @@ use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, SumcheckProof, Uni use crate::error::HachiError; use crate::protocol::transcript::labels; use crate::protocol::transcript::Transcript; -use crate::{CanonicalField, FieldCore}; +use crate::{FieldCore, FromSmallInt}; fn mul_pow_2(x: E, k: usize) -> E { let mut result = x; @@ -33,6 +33,24 @@ fn linear_combination(polys: &[UniPoly], coeffs: &[E]) -> UniPo UniPoly::from_coeffs(result) } +/// Verifier-side output of the batched sumcheck round replay. +/// +/// This carries all transcript-derived values needed for the final oracle check, +/// which is intentionally split out so callers can compute the expected output +/// claim through an external reduction (e.g. Greyhound) before enforcing +/// equality. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct BatchedSumcheckRoundResult { + /// Final claim produced by replaying all sumcheck rounds. + pub output_claim: E, + /// Challenge vector sampled during replay. + pub r_sumcheck: Vec, + /// Front-loaded batching coefficient per verifier instance. + pub batching_coeffs: Vec, + /// Maximum number of rounds among batched instances. + pub max_num_rounds: usize, +} + /// Produce a batched sumcheck proof for multiple instances sharing the same /// variable space, driving the Fiat–Shamir transcript. /// @@ -59,18 +77,22 @@ pub fn prove_batched_sumcheck( mut sample_challenge: S, ) -> Result<(SumcheckProof, Vec), HachiError> where - F: FieldCore + CanonicalField, + F: FieldCore + crate::CanonicalField, T: Transcript, - E: FieldCore + CanonicalField, + E: FieldCore + FromSmallInt, S: FnMut(&mut T) -> E, { - assert!(!instances.is_empty()); + if instances.is_empty() { + return Err(HachiError::InvalidInput( + "no sumcheck instances provided".into(), + )); + } let max_num_rounds = instances .iter() .map(|inst| inst.num_rounds()) .max() - .unwrap(); + .unwrap(); // safe: non-empty checked above // Absorb individual input claims. for inst in instances.iter() { @@ -103,7 +125,7 @@ where let two_inv = E::from_u64(2) .inv() - .expect("2 must be invertible in the field"); + .expect("field characteristic 2 not supported"); let mut round_polys = Vec::with_capacity(max_num_rounds); let mut challenges = Vec::with_capacity(max_num_rounds); @@ -119,8 +141,6 @@ where if active { inst.compute_round_univariate(round - offset, *previous_claim) } else { - // Variable is "dummy" for this instance: polynomial is independent of it, - // so the round univariate is constant with H(0)=H(1)=previous_claim/2. UniPoly::from_coeffs(vec![*previous_claim * two_inv]) } }) @@ -179,10 +199,10 @@ where /// - absorbs each verifier instance's initial claim, /// - re-derives the batching coefficients, /// - computes the batched initial claim, -/// - verifies the proof against the batched claim, -/// - checks that the final output matches the batched expected output claims. +/// - verifies the proof against the batched claim. /// -/// Returns the challenge vector on success. +/// Returns transcript-derived verifier data for the caller to perform the final +/// expected-output equality check. /// /// # Panics /// @@ -190,24 +210,27 @@ where /// /// # Errors /// -/// Returns [`HachiError::InvalidProof`] if the batched output claim does not -/// match the expected value, or propagates per-round verification errors. -pub fn verify_batched_sumcheck( +/// Propagates per-round verification errors. +pub fn verify_batched_sumcheck_rounds( proof: &SumcheckProof, verifiers: Vec<&dyn SumcheckInstanceVerifier>, transcript: &mut T, mut sample_challenge: S, -) -> Result, HachiError> +) -> Result, HachiError> where - F: FieldCore + CanonicalField, + F: FieldCore + crate::CanonicalField, T: Transcript, - E: FieldCore + CanonicalField, + E: FieldCore, S: FnMut(&mut T) -> E, { - assert!(!verifiers.is_empty()); + if verifiers.is_empty() { + return Err(HachiError::InvalidInput( + "no sumcheck instances provided".into(), + )); + } - let max_degree = verifiers.iter().map(|v| v.degree_bound()).max().unwrap(); - let max_num_rounds = verifiers.iter().map(|v| v.num_rounds()).max().unwrap(); + let max_degree = verifiers.iter().map(|v| v.degree_bound()).max().unwrap(); // safe: non-empty + let max_num_rounds = verifiers.iter().map(|v| v.num_rounds()).max().unwrap(); // safe: non-empty // Absorb individual input claims. for v in verifiers.iter() { @@ -239,20 +262,88 @@ where &mut sample_challenge, )?; - // Compute the expected batched output claim from each verifier instance. + Ok(BatchedSumcheckRoundResult { + output_claim, + r_sumcheck, + batching_coeffs, + max_num_rounds, + }) +} + +/// Compute the expected batched output claim from verifier instances and +/// transcript-derived batching data. +/// +/// # Errors +/// +/// Propagates errors from verifier `expected_output_claim` calls. +pub fn compute_batched_expected_output_claim( + verifiers: Vec<&dyn SumcheckInstanceVerifier>, + batching_coeffs: &[E], + max_num_rounds: usize, + r_sumcheck: &[E], +) -> Result { let expected_output_claim: E = verifiers .iter() .zip(batching_coeffs.iter()) .map(|(v, coeff)| { let offset = max_num_rounds - v.num_rounds(); let r_slice = &r_sumcheck[offset..offset + v.num_rounds()]; - v.expected_output_claim(r_slice) * *coeff + v.expected_output_claim(r_slice).map(|val| val * *coeff) }) - .fold(E::zero(), |a, v| a + v); + .try_fold(E::zero(), |a, v| v.map(|val| a + val))?; + Ok(expected_output_claim) +} + +/// Enforce final batched output-claim equality. +/// +/// # Errors +/// +/// Returns an error if `output_claim != expected_output_claim`. +pub fn check_batched_output_claim( + output_claim: E, + expected_output_claim: E, +) -> Result<(), HachiError> { if output_claim != expected_output_claim { return Err(HachiError::InvalidProof); } - Ok(r_sumcheck) + Ok(()) +} + +/// Verify a batched sumcheck proof, including final expected-output equality. +/// +/// This convenience wrapper preserves the previous behavior. Callers that need +/// to inject an external reduction should use [`verify_batched_sumcheck_rounds`] +/// and [`check_batched_output_claim`] directly. +/// +/// # Errors +/// +/// Propagates errors from round verification and output-claim equality check. +pub fn verify_batched_sumcheck( + proof: &SumcheckProof, + verifiers: Vec<&dyn SumcheckInstanceVerifier>, + transcript: &mut T, + mut sample_challenge: S, +) -> Result, HachiError> +where + F: FieldCore + crate::CanonicalField, + T: Transcript, + E: FieldCore, + S: FnMut(&mut T) -> E, +{ + let round_result = verify_batched_sumcheck_rounds::( + proof, + verifiers.clone(), + transcript, + &mut sample_challenge, + )?; + let expected_output_claim = compute_batched_expected_output_claim( + verifiers, + &round_result.batching_coeffs, + round_result.max_num_rounds, + &round_result.r_sumcheck, + )?; + check_batched_output_claim(round_result.output_claim, expected_output_claim)?; + Ok(round_result.r_sumcheck) } diff --git a/src/protocol/sumcheck/eq_poly.rs b/src/protocol/sumcheck/eq_poly.rs index 1b562cd0..353d0830 100644 --- a/src/protocol/sumcheck/eq_poly.rs +++ b/src/protocol/sumcheck/eq_poly.rs @@ -149,7 +149,7 @@ impl EqPolynomial { mod tests { use super::*; use crate::algebra::Fp64; - use crate::{CanonicalField, FieldSampling}; + use crate::{FieldSampling, FromSmallInt}; use rand::rngs::StdRng; use rand::SeedableRng; diff --git a/src/protocol/sumcheck/hachi_sumcheck.rs b/src/protocol/sumcheck/hachi_sumcheck.rs new file mode 100644 index 00000000..f7e1b12a --- /dev/null +++ b/src/protocol/sumcheck/hachi_sumcheck.rs @@ -0,0 +1,548 @@ +//! Fused norm+relation sumcheck prover/verifier for the Hachi PCS. +//! +//! Eliminates the redundant `w_evals` clone by sharing a single `w_table` +//! across both the norm (F_0) and relation (F_α) sumcheck computations. +//! Supports compact `Vec` storage for round 0 (all entries in [-8, 7]), +//! transitioning to `Vec` at half size after the first fold. + +use super::eq_poly::EqPolynomial; +use super::norm_sumcheck::{ + accumulate_affine_range_coeffs, range_check_eval_precomputed, trim_trailing_zeros, + NormRoundKernel, PointEvalPrecomp, RangeAffinePrecomp, +}; +use super::split_eq::GruenSplitEq; +use super::{fold_evals_in_place, multilinear_eval, range_check_eval}; +use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, UniPoly}; +use crate::algebra::CyclotomicRing; +use crate::cfg_into_iter; +use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; +use crate::protocol::ring_switch::eval_ring_at; +use crate::{FieldCore, FromSmallInt}; + +enum WTable { + Compact(Vec), + Full(Vec), +} + +/// Fused norm+relation sumcheck prover. +/// +/// Holds a single `w_table` shared by both sumcheck instances, weighted +/// by `batching_coeff`. The round polynomial is +/// `batching_coeff * norm_round(t) + relation_round(t)`. +pub struct HachiSumcheckProver { + w_table: WTable, + batching_coeff: E, + + // Norm state + split_eq: GruenSplitEq, + round_kernel: NormRoundKernel, + point_precomp: Option>, + range_precomp: Option>, + b: usize, + + // Relation state + alpha_table: Vec, + m_table: Vec, + + num_vars: usize, + relation_claim: E, +} + +impl HachiSumcheckProver { + /// Create a fused norm+relation sumcheck prover. + /// + /// # Panics + /// + /// Panics if table sizes are inconsistent with `num_u` and `num_l`. + #[allow(clippy::too_many_arguments)] + pub fn new( + batching_coeff: E, + w_evals_compact: Vec, + tau0: &[E], + b: usize, + alpha_evals_y: &[E], + m_evals_x: &[E], + num_u: usize, + num_l: usize, + ) -> Self { + let num_vars = num_u + num_l; + let n = 1usize << num_vars; + assert_eq!(w_evals_compact.len(), n); + assert_eq!(tau0.len(), num_vars); + assert_eq!(alpha_evals_y.len(), 1 << num_l); + assert_eq!(m_evals_x.len(), 1 << num_u); + + let x_mask = (1usize << num_u) - 1; + let alpha_table: Vec = cfg_into_iter!(0..n) + .map(|idx| alpha_evals_y[idx >> num_u]) + .collect(); + let m_table: Vec = cfg_into_iter!(0..n) + .map(|idx| m_evals_x[idx & x_mask]) + .collect(); + + let relation_claim = + Self::compute_relation_claim_compact(&w_evals_compact, &alpha_table, &m_table); + + let round_kernel = if b <= 8 { + NormRoundKernel::PointEvalInterpolation + } else { + NormRoundKernel::AffineCoeffComposition + }; + let point_precomp = match round_kernel { + NormRoundKernel::PointEvalInterpolation => Some(PointEvalPrecomp::new(b)), + NormRoundKernel::AffineCoeffComposition => None, + }; + let range_precomp = match round_kernel { + NormRoundKernel::PointEvalInterpolation => None, + NormRoundKernel::AffineCoeffComposition => Some(RangeAffinePrecomp::new(b)), + }; + + Self { + w_table: WTable::Compact(w_evals_compact), + batching_coeff, + split_eq: GruenSplitEq::new(tau0), + round_kernel, + point_precomp, + range_precomp, + b, + alpha_table, + m_table, + num_vars, + relation_claim, + } + } + + fn compute_relation_claim_compact(w_compact: &[i8], alpha_table: &[E], m_table: &[E]) -> E { + w_compact + .iter() + .zip(alpha_table.iter()) + .zip(m_table.iter()) + .fold(E::zero(), |acc, ((&w, &a), &m)| { + acc + E::from_i64(w as i64) * a * m + }) + } + + fn lift_i8(v: i8) -> E { + E::from_i64(v as i64) + } + + fn compute_round_norm_compact(&self, w_compact: &[i8]) -> UniPoly { + let half = w_compact.len() / 2; + + let (e_first, e_second) = self.split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + let first_bits = num_first.trailing_zeros(); + + match self.round_kernel { + NormRoundKernel::PointEvalInterpolation => { + let degree_q = 2 * self.b - 1; + let num_points_q = degree_q + 1; + let range_offsets = &self.point_precomp.as_ref().unwrap().range_offsets; + + let mut q_evals = vec![E::zero(); num_points_q]; + for j in 0..half { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = Self::lift_i8(w_compact[2 * j]); + let w_1 = Self::lift_i8(w_compact[2 * j + 1]); + let delta = w_1 - w_0; + let mut w_t = w_0; + for eval in q_evals.iter_mut() { + *eval = *eval + eq_rem * range_check_eval_precomputed(w_t, range_offsets); + w_t = w_t + delta; + } + } + let q_poly = UniPoly::from_evals(&q_evals); + self.split_eq.gruen_mul(&q_poly) + } + NormRoundKernel::AffineCoeffComposition => { + let range_precomp = self.range_precomp.as_ref().unwrap(); + let num_coeffs_q = range_precomp.degree_q + 1; + let coeff_mix = &range_precomp.coeff_mix; + + let mut q_coeffs = vec![E::zero(); num_coeffs_q]; + for j in 0..half { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = Self::lift_i8(w_compact[2 * j]); + let w_1 = Self::lift_i8(w_compact[2 * j + 1]); + let a = w_1 - w_0; + accumulate_affine_range_coeffs(&mut q_coeffs, coeff_mix, w_0, a, eq_rem); + } + trim_trailing_zeros(&mut q_coeffs); + let q_poly = UniPoly::from_coeffs(q_coeffs); + self.split_eq.gruen_mul(&q_poly) + } + } + } + + fn compute_round_relation_compact(&self, w_compact: &[i8]) -> UniPoly { + let half = w_compact.len() / 2; + let num_points = 3; + + let mut evals = vec![E::zero(); num_points]; + for j in 0..half { + let w_0 = Self::lift_i8(w_compact[2 * j]); + let w_1 = Self::lift_i8(w_compact[2 * j + 1]); + let a_0 = self.alpha_table[2 * j]; + let a_1 = self.alpha_table[2 * j + 1]; + let m_0 = self.m_table[2 * j]; + let m_1 = self.m_table[2 * j + 1]; + for (t, eval) in evals.iter_mut().enumerate() { + let t_e = E::from_u64(t as u64); + let w_t = w_0 + t_e * (w_1 - w_0); + let a_t = a_0 + t_e * (a_1 - a_0); + let m_t = m_0 + t_e * (m_1 - m_0); + *eval = *eval + w_t * a_t * m_t; + } + } + UniPoly::from_evals(&evals) + } + + fn compute_round_norm_full(&self, w_full: &[E]) -> UniPoly { + let half = w_full.len() / 2; + + let (e_first, e_second) = self.split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + let first_bits = num_first.trailing_zeros(); + + match self.round_kernel { + NormRoundKernel::PointEvalInterpolation => { + let degree_q = 2 * self.b - 1; + let num_points_q = degree_q + 1; + let range_offsets = &self.point_precomp.as_ref().unwrap().range_offsets; + + #[cfg(feature = "parallel")] + let q_evals = { + (0..half) + .into_par_iter() + .fold( + || vec![E::zero(); num_points_q], + |mut evals, j| { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = w_full[2 * j]; + let w_1 = w_full[2 * j + 1]; + let delta = w_1 - w_0; + let mut w_t = w_0; + for eval in evals.iter_mut() { + *eval = *eval + + eq_rem * range_check_eval_precomputed(w_t, range_offsets); + w_t = w_t + delta; + } + evals + }, + ) + .reduce( + || vec![E::zero(); num_points_q], + |mut a, b_vec| { + for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { + *ai = *ai + *bi; + } + a + }, + ) + }; + #[cfg(not(feature = "parallel"))] + let q_evals = { + let mut evals = vec![E::zero(); num_points_q]; + for j in 0..half { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = w_full[2 * j]; + let w_1 = w_full[2 * j + 1]; + let delta = w_1 - w_0; + let mut w_t = w_0; + for eval in evals.iter_mut() { + *eval = + *eval + eq_rem * range_check_eval_precomputed(w_t, range_offsets); + w_t = w_t + delta; + } + } + evals + }; + + let q_poly = UniPoly::from_evals(&q_evals); + self.split_eq.gruen_mul(&q_poly) + } + NormRoundKernel::AffineCoeffComposition => { + let range_precomp = self.range_precomp.as_ref().unwrap(); + let num_coeffs_q = range_precomp.degree_q + 1; + let coeff_mix = &range_precomp.coeff_mix; + + #[cfg(feature = "parallel")] + let mut q_coeffs = { + (0..half) + .into_par_iter() + .fold( + || vec![E::zero(); num_coeffs_q], + |mut coeffs, j| { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = w_full[2 * j]; + let w_1 = w_full[2 * j + 1]; + let a = w_1 - w_0; + accumulate_affine_range_coeffs( + &mut coeffs, + coeff_mix, + w_0, + a, + eq_rem, + ); + coeffs + }, + ) + .reduce( + || vec![E::zero(); num_coeffs_q], + |mut a, b_vec| { + for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { + *ai = *ai + *bi; + } + a + }, + ) + }; + #[cfg(not(feature = "parallel"))] + let mut q_coeffs = { + let mut coeffs = vec![E::zero(); num_coeffs_q]; + for j in 0..half { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = w_full[2 * j]; + let w_1 = w_full[2 * j + 1]; + let a = w_1 - w_0; + accumulate_affine_range_coeffs(&mut coeffs, coeff_mix, w_0, a, eq_rem); + } + coeffs + }; + + trim_trailing_zeros(&mut q_coeffs); + let q_poly = UniPoly::from_coeffs(q_coeffs); + self.split_eq.gruen_mul(&q_poly) + } + } + } + + fn compute_round_relation_full(&self, w_full: &[E]) -> UniPoly { + let half = w_full.len() / 2; + let num_points = 3; + + #[cfg(feature = "parallel")] + let round_evals = { + (0..half) + .into_par_iter() + .fold( + || vec![E::zero(); num_points], + |mut evals, j| { + let w_0 = w_full[2 * j]; + let w_1 = w_full[2 * j + 1]; + let a_0 = self.alpha_table[2 * j]; + let a_1 = self.alpha_table[2 * j + 1]; + let m_0 = self.m_table[2 * j]; + let m_1 = self.m_table[2 * j + 1]; + for (t, eval) in evals.iter_mut().enumerate() { + let t_e = E::from_u64(t as u64); + let w_t = w_0 + t_e * (w_1 - w_0); + let a_t = a_0 + t_e * (a_1 - a_0); + let m_t = m_0 + t_e * (m_1 - m_0); + *eval = *eval + w_t * a_t * m_t; + } + evals + }, + ) + .reduce( + || vec![E::zero(); num_points], + |mut a, b| { + for (ai, bi) in a.iter_mut().zip(b.iter()) { + *ai = *ai + *bi; + } + a + }, + ) + }; + #[cfg(not(feature = "parallel"))] + let round_evals = { + let mut evals = vec![E::zero(); num_points]; + for j in 0..half { + let w_0 = w_full[2 * j]; + let w_1 = w_full[2 * j + 1]; + let a_0 = self.alpha_table[2 * j]; + let a_1 = self.alpha_table[2 * j + 1]; + let m_0 = self.m_table[2 * j]; + let m_1 = self.m_table[2 * j + 1]; + for (t, eval) in evals.iter_mut().enumerate() { + let t_e = E::from_u64(t as u64); + let w_t = w_0 + t_e * (w_1 - w_0); + let a_t = a_0 + t_e * (a_1 - a_0); + let m_t = m_0 + t_e * (m_1 - m_0); + *eval = *eval + w_t * a_t * m_t; + } + } + evals + }; + + UniPoly::from_evals(&round_evals) + } + + fn fold_compact_to_full(w_compact: &[i8], r: E) -> Vec { + let half = w_compact.len() / 2; + let mut out = Vec::with_capacity(half); + for j in 0..half { + let w_0 = Self::lift_i8(w_compact[2 * j]); + let w_1 = Self::lift_i8(w_compact[2 * j + 1]); + out.push(w_0 + r * (w_1 - w_0)); + } + out + } +} + +impl SumcheckInstanceProver for HachiSumcheckProver { + fn num_rounds(&self) -> usize { + self.num_vars + } + + fn degree_bound(&self) -> usize { + 2 * self.b + } + + fn input_claim(&self) -> E { + self.relation_claim + } + + fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { + let (norm_poly, relation_poly) = match &self.w_table { + WTable::Compact(w_compact) => { + let norm = self.compute_round_norm_compact(w_compact); + let relation = self.compute_round_relation_compact(w_compact); + (norm, relation) + } + WTable::Full(w_full) => { + let norm = self.compute_round_norm_full(w_full); + let relation = self.compute_round_relation_full(w_full); + (norm, relation) + } + }; + + let max_len = norm_poly.coeffs.len().max(relation_poly.coeffs.len()); + let mut combined = vec![E::zero(); max_len]; + for (i, c) in norm_poly.coeffs.iter().enumerate() { + combined[i] = combined[i] + self.batching_coeff * *c; + } + for (i, c) in relation_poly.coeffs.iter().enumerate() { + combined[i] = combined[i] + *c; + } + UniPoly::from_coeffs(combined) + } + + fn ingest_challenge(&mut self, _round: usize, r: E) { + self.split_eq.bind(r); + + self.w_table = match std::mem::replace(&mut self.w_table, WTable::Full(Vec::new())) { + WTable::Compact(w_compact) => WTable::Full(Self::fold_compact_to_full(&w_compact, r)), + WTable::Full(mut w_full) => { + fold_evals_in_place(&mut w_full, r); + WTable::Full(w_full) + } + }; + + fold_evals_in_place(&mut self.alpha_table, r); + fold_evals_in_place(&mut self.m_table, r); + } +} + +/// Fused norm+relation sumcheck verifier. +pub struct HachiSumcheckVerifier { + batching_coeff: F, + w_evals: Vec, + tau0: Vec, + b: usize, + alpha_evals_y: Vec, + m_evals_x: Vec, + num_u: usize, + num_l: usize, + relation_claim: F, + _marker: std::marker::PhantomData<[F; D]>, +} + +impl HachiSumcheckVerifier { + /// Create a fused verifier for the norm + relation sumcheck. + #[allow(clippy::too_many_arguments)] + pub fn new( + batching_coeff: F, + w_evals: Vec, + tau0: Vec, + b: usize, + alpha_evals_y: Vec, + m_evals_x: Vec, + tau1: Vec, + v: Vec>, + u: Vec>, + y_ring: CyclotomicRing, + alpha: F, + num_u: usize, + num_l: usize, + ) -> Self { + let y_a: Vec = v + .iter() + .chain(u.iter()) + .chain(std::iter::once(&y_ring)) + .map(|r| eval_ring_at(r, &alpha)) + .collect(); + let eq_tau1 = EqPolynomial::evals(&tau1); + let mut relation_claim = F::zero(); + for (i, eq_i) in eq_tau1.iter().enumerate() { + let y_i = if i < y_a.len() { y_a[i] } else { F::zero() }; + relation_claim = relation_claim + *eq_i * y_i; + } + + Self { + batching_coeff, + w_evals, + tau0, + b, + alpha_evals_y, + m_evals_x, + num_u, + num_l, + relation_claim, + _marker: std::marker::PhantomData, + } + } +} + +impl SumcheckInstanceVerifier + for HachiSumcheckVerifier +{ + fn num_rounds(&self) -> usize { + self.num_u + self.num_l + } + + fn degree_bound(&self) -> usize { + 2 * self.b + } + + fn input_claim(&self) -> F { + self.relation_claim + } + + fn expected_output_claim(&self, challenges: &[F]) -> Result { + let eq_val = EqPolynomial::mle(&self.tau0, challenges); + let w_val = multilinear_eval(&self.w_evals, challenges)?; + let norm_oracle = eq_val * range_check_eval(w_val, self.b); + + let (x_challenges, y_challenges) = challenges.split_at(self.num_u); + let alpha_val = multilinear_eval(&self.alpha_evals_y, y_challenges)?; + let m_val = multilinear_eval(&self.m_evals_x, x_challenges)?; + let relation_oracle = w_val * alpha_val * m_val; + + Ok(self.batching_coeff * norm_oracle + relation_oracle) + } +} diff --git a/src/protocol/sumcheck/mod.rs b/src/protocol/sumcheck/mod.rs index 9788b60e..dc824bba 100644 --- a/src/protocol/sumcheck/mod.rs +++ b/src/protocol/sumcheck/mod.rs @@ -1,15 +1,8 @@ -//! Sumcheck core building blocks (univariate messages + proof transcript driver). +//! Sumcheck protocol: traits, proof driver, and concrete instances. //! -//! This module provides: -//! - Univariate polynomials over a field `E` (`UniPoly`). -//! - A compressed univariate representation (`CompressedUniPoly`) that omits the -//! linear term and reconstructs it from the per-round sumcheck hint `g(0)+g(1)`. -//! - A minimal sumcheck proof container (`SumcheckProof`) with a verifier-side -//! transcript driver that returns the derived point and final claimed value. -//! -//! It intentionally does **not** implement a concrete sumcheck prover for any -//! particular oracle/table representation. Higher-level protocols (e.g. Hachi §4.3) -//! should implement the prover logic that constructs each round's univariate `g_i(X)`. +//! Types (`UniPoly`, `CompressedUniPoly`, `SumcheckProof`) live in the +//! [`types`] submodule. Polynomial evaluation utilities (`multilinear_eval`, +//! `fold_evals_in_place`, `range_check_eval`) live in [`crate::algebra::poly`]. //! //! ## Temporary duplication notice (Jolt integration) //! @@ -21,395 +14,19 @@ pub mod batched_sumcheck; pub mod eq_poly; +pub mod hachi_sumcheck; pub mod norm_sumcheck; pub mod relation_sumcheck; pub mod split_eq; +pub mod types; use crate::error::HachiError; -use crate::primitives::serialization::{ - Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, -}; use crate::protocol::transcript::labels; use crate::protocol::transcript::Transcript; -use crate::CanonicalField; use crate::FieldCore; -use std::io::{Read, Write}; - -/// Univariate polynomial in coefficient form: `p(X) = Σ_{i=0}^d coeffs[i] * X^i`. -#[derive(Debug, Clone, PartialEq, Eq)] -pub struct UniPoly { - /// Coefficients from low degree to high degree. - pub coeffs: Vec, -} - -impl UniPoly { - /// Construct from coefficients in increasing-degree order. - pub fn from_coeffs(coeffs: Vec) -> Self { - Self { coeffs } - } - - /// Degree of the polynomial. - /// - /// # Panics - /// - /// Panics if the polynomial has no coefficients. - pub fn degree(&self) -> usize { - self.coeffs - .len() - .checked_sub(1) - .expect("UniPoly must have at least one coefficient") - } - - /// Evaluate at `x` via Horner's method. - pub fn evaluate(&self, x: &E) -> E { - // Horner from highest degree. - let mut acc = E::zero(); - for c in self.coeffs.iter().rev() { - acc = acc * *x + *c; - } - acc - } - - /// Compress this polynomial by omitting the linear coefficient. - /// - /// The verifier can reconstruct/evaluate the missing linear coefficient using - /// the per-round hint `g(0)+g(1)` from the sumcheck protocol. - /// - /// This matches the technique used by Jolt's sumcheck (`CompressedUniPoly`). - pub fn compress(&self) -> CompressedUniPoly { - let coeffs = &self.coeffs; - if coeffs.is_empty() { - return CompressedUniPoly { - coeffs_except_linear_term: Vec::new(), - }; - } - if coeffs.len() == 1 { - return CompressedUniPoly { - coeffs_except_linear_term: vec![coeffs[0]], - }; - } - // Keep coeff[0], drop coeff[1], keep coeff[2..]. - let mut out = Vec::with_capacity(coeffs.len().saturating_sub(1)); - out.push(coeffs[0]); - out.extend_from_slice(&coeffs[2..]); - CompressedUniPoly { - coeffs_except_linear_term: out, - } - } -} - -impl UniPoly { - /// Interpolate from evaluations at equispaced integer points `x = 0, 1, ..., d`. - /// - /// Uses Newton forward-difference interpolation: compute divided differences, - /// then expand via Horner on the nested Newton form. - /// - /// # Panics - /// - /// Panics if any required factorial inverse does not exist (field characteristic - /// must exceed the number of evaluation points). - pub fn from_evals(evals: &[E]) -> Self { - let n = evals.len(); - if n == 0 { - return Self::from_coeffs(vec![]); - } - if n == 1 { - return Self::from_coeffs(vec![evals[0]]); - } - - // Forward differences: delta^k[0] - let mut table = evals.to_vec(); - let mut deltas = vec![table[0]]; - for _ in 1..n { - for j in 0..table.len() - 1 { - table[j] = table[j + 1] - table[j]; - } - table.pop(); - deltas.push(table[0]); - } - - // Divided differences: dd[k] = delta^k / k! - let mut factorial = E::one(); - let mut divided_diffs = vec![deltas[0]]; - for (k, delta_k) in deltas.iter().enumerate().skip(1) { - factorial = factorial * E::from_u64(k as u64); - divided_diffs.push( - *delta_k - * factorial - .inv() - .expect("field characteristic too small for interpolation"), - ); - } - - // Horner expansion of the Newton nested form: - // p(x) = dd[0] + (x-0)(dd[1] + (x-1)(dd[2] + ...)) - let mut coeffs = vec![divided_diffs[n - 1]]; - - for k in (0..n - 1).rev() { - let shift = E::from_u64(k as u64); - let old_len = coeffs.len(); - let mut new_coeffs = vec![E::zero(); old_len + 1]; - - new_coeffs[0] = divided_diffs[k]; - for i in 0..old_len { - new_coeffs[i + 1] = new_coeffs[i + 1] + coeffs[i]; - new_coeffs[i] = new_coeffs[i] - shift * coeffs[i]; - } - - coeffs = new_coeffs; - } - - while coeffs.len() > 1 && coeffs.last().is_some_and(|c| c.is_zero()) { - coeffs.pop(); - } - - Self::from_coeffs(coeffs) - } -} - -impl Valid for UniPoly { - fn check(&self) -> Result<(), SerializationError> { - self.coeffs.check() - } -} - -impl HachiSerialize for UniPoly { - fn serialize_with_mode( - &self, - mut writer: W, - compress: Compress, - ) -> Result<(), SerializationError> { - self.coeffs.serialize_with_mode(&mut writer, compress) - } - - fn serialized_size(&self, compress: Compress) -> usize { - self.coeffs.serialized_size(compress) - } -} - -impl HachiDeserialize for UniPoly { - fn deserialize_with_mode( - mut reader: R, - compress: Compress, - validate: Validate, - ) -> Result { - let coeffs = Vec::::deserialize_with_mode(&mut reader, compress, validate)?; - let out = Self { coeffs }; - if matches!(validate, Validate::Yes) { - out.check()?; - } - Ok(out) - } -} - -/// Compressed univariate polynomial representation omitting the linear term. -/// -/// We store `[c0, c2, c3, ..., cd]`. Given the sumcheck hint `hint = g(0)+g(1)`, -/// the missing linear coefficient is: -/// -/// `c1 = hint - 2*c0 - Σ_{i=2..d} ci`. -#[derive(Debug, Clone, PartialEq, Eq)] -pub struct CompressedUniPoly { - /// Coefficients excluding the linear term: `[c0, c2, c3, ..., cd]`. - pub coeffs_except_linear_term: Vec, -} - -impl CompressedUniPoly { - /// Degree of the underlying uncompressed polynomial. - /// - /// For degree `d`, this stores `d` coefficients (all except the linear term). - pub fn degree(&self) -> usize { - self.coeffs_except_linear_term.len().saturating_sub(1) - } - - fn recover_linear_term(&self, hint: &E) -> E { - if self.coeffs_except_linear_term.is_empty() { - // Treat empty as the zero polynomial. - return E::zero(); - } - - // linear = hint - 2*c0 - Σ_{i>=2} ci - let c0 = self.coeffs_except_linear_term[0]; - let mut linear = *hint - c0 - c0; - for c in self.coeffs_except_linear_term.iter().skip(1) { - linear = linear - *c; - } - linear - } - /// Decompress using `hint = g(0)+g(1)`. - pub fn decompress(&self, hint: &E) -> UniPoly { - if self.coeffs_except_linear_term.is_empty() { - return UniPoly::from_coeffs(Vec::new()); - } - let linear = self.recover_linear_term(hint); - // Always materialize the missing linear coefficient. - // For truly-constant polynomials, the hint forces `linear = 0`, so this is harmless. - let mut coeffs = Vec::with_capacity(self.coeffs_except_linear_term.len() + 1); - coeffs.push(self.coeffs_except_linear_term[0]); - coeffs.push(linear); - coeffs.extend_from_slice(&self.coeffs_except_linear_term[1..]); - UniPoly::from_coeffs(coeffs) - } - - /// Evaluate the uncompressed polynomial at `x`, using `hint = g(0)+g(1)`. - /// - /// This avoids materializing the full coefficient list. - pub fn eval_from_hint(&self, hint: &E, x: &E) -> E { - if self.coeffs_except_linear_term.is_empty() { - return E::zero(); - } - - let linear = self.recover_linear_term(hint); - let mut acc = self.coeffs_except_linear_term[0] + (*x * linear); - - // Add Σ_{i=2..d} c_i * x^i, where stored slice is [c2, c3, ..., cd] - let mut pow = *x * *x; // x^2 - for c in self.coeffs_except_linear_term.iter().skip(1) { - acc = acc + (*c * pow); - pow = pow * *x; - } - acc - } -} - -impl Valid for CompressedUniPoly { - fn check(&self) -> Result<(), SerializationError> { - self.coeffs_except_linear_term.check() - } -} - -impl HachiSerialize for CompressedUniPoly { - fn serialize_with_mode( - &self, - mut writer: W, - compress: Compress, - ) -> Result<(), SerializationError> { - self.coeffs_except_linear_term - .serialize_with_mode(&mut writer, compress) - } - - fn serialized_size(&self, compress: Compress) -> usize { - self.coeffs_except_linear_term.serialized_size(compress) - } -} - -impl HachiDeserialize for CompressedUniPoly { - fn deserialize_with_mode( - mut reader: R, - compress: Compress, - validate: Validate, - ) -> Result { - let coeffs_except_linear_term = - Vec::::deserialize_with_mode(&mut reader, compress, validate)?; - let out = Self { - coeffs_except_linear_term, - }; - if matches!(validate, Validate::Yes) { - out.check()?; - } - Ok(out) - } -} - -/// Sumcheck proof containing one compressed univariate polynomial per round. -#[derive(Debug, Clone, PartialEq, Eq)] -pub struct SumcheckProof { - /// One compressed univariate polynomial per sumcheck round. - pub round_polys: Vec>, -} - -impl Valid for SumcheckProof { - fn check(&self) -> Result<(), SerializationError> { - self.round_polys.check() - } -} - -impl HachiSerialize for SumcheckProof { - fn serialize_with_mode( - &self, - mut writer: W, - compress: Compress, - ) -> Result<(), SerializationError> { - self.round_polys.serialize_with_mode(&mut writer, compress) - } - - fn serialized_size(&self, compress: Compress) -> usize { - self.round_polys.serialized_size(compress) - } -} - -impl HachiDeserialize for SumcheckProof { - fn deserialize_with_mode( - mut reader: R, - compress: Compress, - validate: Validate, - ) -> Result { - let round_polys = - Vec::>::deserialize_with_mode(&mut reader, compress, validate)?; - let out = Self { round_polys }; - if matches!(validate, Validate::Yes) { - out.check()?; - } - Ok(out) - } -} - -impl SumcheckProof { - /// Verifier-side sumcheck transcript driver. - /// - /// This method: - /// - absorbs the per-round prover message (compressed univariate), - /// - samples one challenge per round via `sample_challenge`, - /// - updates the running claim using `eval_from_hint`. - /// - /// It does **not** perform the final oracle check `final_claim == f(r*)`. - /// Callers (e.g. ring-switching) must compute `f(r*)` themselves and compare. - /// - /// # Errors - /// - /// Returns an error if the proof length does not match `num_rounds` or if any - /// per-round polynomial exceeds `degree_bound`. - pub fn verify( - &self, - mut claim: E, - num_rounds: usize, - degree_bound: usize, - transcript: &mut T, - mut sample_challenge: S, - ) -> Result<(E, Vec), HachiError> - where - F: crate::FieldCore + crate::CanonicalField, - T: Transcript, - S: FnMut(&mut T) -> E, - { - if self.round_polys.len() != num_rounds { - return Err(HachiError::InvalidSize { - expected: num_rounds, - actual: self.round_polys.len(), - }); - } - - let mut r = Vec::with_capacity(num_rounds); - for poly in &self.round_polys { - if poly.degree() > degree_bound { - return Err(HachiError::InvalidInput(format!( - "sumcheck round poly degree {} exceeds bound {}", - poly.degree(), - degree_bound - ))); - } - - transcript.append_serde(labels::ABSORB_SUMCHECK_ROUND, poly); - let r_i = sample_challenge(transcript); - r.push(r_i); - - claim = poly.eval_from_hint(&claim, &r_i); - } - - Ok((claim, r)) - } -} +pub use crate::algebra::poly::{fold_evals_in_place, multilinear_eval, range_check_eval}; +pub use types::{CompressedUniPoly, SumcheckProof, UniPoly}; /// Prover-side sumcheck instance interface. /// @@ -459,10 +76,15 @@ pub trait SumcheckInstanceVerifier: Send + Sync { /// Compute the expected final evaluation `f(r_0, ..., r_{n-1})` at the /// challenge point derived during the protocol. - fn expected_output_claim(&self, challenges: &[E]) -> E; + /// + /// # Errors + /// + /// May return an error if internal evaluations fail (e.g., malformed + /// evaluation tables from untrusted proof data). + fn expected_output_claim(&self, challenges: &[E]) -> Result; } -/// Produce a sumcheck proof for a single instance, driving the Fiat–Shamir transcript. +/// Produce a sumcheck proof for a single instance, driving the Fiat-Shamir transcript. /// /// This method: /// - does **not** absorb the initial claim into the transcript (callers should do so), @@ -498,7 +120,6 @@ where for round in 0..num_rounds { let g = instance.compute_round_univariate(round, claim); - // Optional sanity: enforce hint relation in debug builds. debug_assert!( g.evaluate(&E::zero()) + g.evaluate(&E::one()) == claim, "sumcheck round univariate does not match previous claim hint" @@ -517,7 +138,6 @@ where let r_i = sample_challenge(transcript); r.push(r_i); - // Update running claim (this is g(r_i)). claim = compressed.eval_from_hint(&claim, &r_i); instance.ingest_challenge(round, r_i); @@ -567,49 +187,10 @@ where sample_challenge, )?; - let expected = verifier.expected_output_claim(&challenges); + let expected = verifier.expected_output_claim(&challenges)?; if final_claim != expected { return Err(HachiError::InvalidProof); } Ok(challenges) } - -/// Evaluate the range-check polynomial `w · Π_{k=1}^{b−1} (w − k)(w + k)`. -/// -/// This polynomial vanishes exactly when `w ∈ {−(b−1), …, b−1}`. -/// Total degree in `w` is `2b − 1`. -pub fn range_check_eval(w: E, b: usize) -> E { - let mut acc = w; - for k in 1..b { - let k_e = E::from_u64(k as u64); - acc = acc * (w - k_e) * (w + k_e); - } - acc -} - -/// Evaluate a multilinear polynomial (given by boolean-hypercube evaluations in -/// little-endian bit order) at an arbitrary point via iterated folding. -pub fn multilinear_eval(evals: &[E], point: &[E]) -> E { - let mut current = evals.to_vec(); - for &r in point { - let half = current.len() / 2; - let mut next = Vec::with_capacity(half); - for i in 0..half { - next.push(current[2 * i] + r * (current[2 * i + 1] - current[2 * i])); - } - current = next; - } - current[0] -} - -/// Fold an evaluation table by binding its first variable to `r`, halving the -/// table size. -pub(crate) fn fold_evals(evals: &[E], r: E) -> Vec { - let half = evals.len() / 2; - let mut out = Vec::with_capacity(half); - for i in 0..half { - out.push(evals[2 * i] + r * (evals[2 * i + 1] - evals[2 * i])); - } - out -} diff --git a/src/protocol/sumcheck/norm_sumcheck.rs b/src/protocol/sumcheck/norm_sumcheck.rs index 3fd5aa83..db4625cf 100644 --- a/src/protocol/sumcheck/norm_sumcheck.rs +++ b/src/protocol/sumcheck/norm_sumcheck.rs @@ -7,9 +7,140 @@ use super::eq_poly::EqPolynomial; use super::split_eq::GruenSplitEq; -use super::{fold_evals, multilinear_eval, range_check_eval}; +use super::{fold_evals_in_place, multilinear_eval, range_check_eval}; use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, UniPoly}; -use crate::{CanonicalField, FieldCore}; +use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; +use crate::{FieldCore, FromSmallInt}; + +const SMALL_B_POINT_EVAL_MAX: usize = 8; + +#[derive(Clone, Copy, Debug, PartialEq, Eq)] +pub(crate) enum NormRoundKernel { + PointEvalInterpolation, + AffineCoeffComposition, +} + +fn choose_round_kernel(b: usize) -> NormRoundKernel { + if b <= SMALL_B_POINT_EVAL_MAX { + NormRoundKernel::PointEvalInterpolation + } else { + NormRoundKernel::AffineCoeffComposition + } +} + +#[derive(Clone)] +pub(crate) struct RangeAffinePrecomp { + /// `coeff_mix[i][k] = c_{i+k} * binom(i+k, i)`, where + /// `R(w) = sum_m c_m * w^m` is the range-check polynomial. + pub(crate) coeff_mix: Vec>, + pub(crate) degree_q: usize, +} + +impl RangeAffinePrecomp { + pub(crate) fn new(b: usize) -> Self { + assert!(b >= 1, "b must be at least 1"); + let range_coeffs = range_check_coeffs::(b); + let degree_q = range_coeffs.len() - 1; + let small_scalars: Vec = (0..=degree_q + 1).map(|x| E::from_u64(x as u64)).collect(); + let inv_small_scalars: Vec = (0..=degree_q + 1) + .map(|x| { + if x == 0 { + E::zero() + } else { + small_scalars[x] + .inv() + .expect("field characteristic too small for range-check precomputation") + } + }) + .collect(); + let mut coeff_mix = Vec::with_capacity(degree_q + 1); + + for i in 0..=degree_q { + let row_len = degree_q - i + 1; + let mut row = Vec::with_capacity(row_len); + let mut binom_m_i = E::one(); // binom(i, i) + for k in 0..row_len { + let m = i + k; + row.push(range_coeffs[m] * binom_m_i); + if k + 1 < row_len { + let numer = small_scalars[m + 1]; + let denom_inv = inv_small_scalars[k + 1]; + binom_m_i = binom_m_i * numer * denom_inv; + } + } + coeff_mix.push(row); + } + + Self { + coeff_mix, + degree_q, + } + } +} + +#[derive(Clone)] +pub(crate) struct PointEvalPrecomp { + pub(crate) range_offsets: Vec, +} + +impl PointEvalPrecomp { + pub(crate) fn new(b: usize) -> Self { + let range_offsets = (1..b).map(|k| E::from_u64(k as u64)).collect(); + Self { range_offsets } + } +} + +/// Coefficients of `R(w) = w * Π_{k=1}^{b-1}(w-k)(w+k)` in increasing degree order. +fn range_check_coeffs(b: usize) -> Vec { + assert!(b >= 1, "b must be at least 1"); + let mut coeffs = vec![E::zero(), E::one()]; // R(w)=w when b=1 + for k in 1..b { + let k_e = E::from_u64(k as u64); + let k_sq = k_e * k_e; + // Multiply by (w^2 - k^2). + let mut next = vec![E::zero(); coeffs.len() + 2]; + for (idx, c) in coeffs.iter().enumerate() { + next[idx] = next[idx] - *c * k_sq; + next[idx + 2] = next[idx + 2] + *c; + } + coeffs = next; + } + coeffs +} + +pub(crate) fn range_check_eval_precomputed(w: E, range_offsets: &[E]) -> E { + let mut acc = w; + for &k in range_offsets { + acc = acc * (w - k) * (w + k); + } + acc +} + +pub(crate) fn accumulate_affine_range_coeffs( + out_coeffs: &mut [E], + coeff_mix: &[Vec], + w_0: E, + a: E, + scale: E, +) { + let mut a_pow = E::one(); + for (i, row) in coeff_mix.iter().enumerate() { + let mut h_i_w0 = E::zero(); + for coeff in row.iter().rev() { + h_i_w0 = h_i_w0 * w_0 + *coeff; + } + out_coeffs[i] = out_coeffs[i] + scale * a_pow * h_i_w0; + a_pow = a_pow * a; + } +} + +pub(crate) fn trim_trailing_zeros(coeffs: &mut Vec) { + while coeffs.len() > 1 && coeffs.last().is_some_and(|c| c.is_zero()) { + coeffs.pop(); + } +} /// Prover for `F_{0,τ₀}(x,y) = ẽq(τ₀,(x,y)) · w̃(x,y) · range_check(w̃(x,y), b)`. /// @@ -21,29 +152,182 @@ use crate::{CanonicalField, FieldCore}; pub struct NormSumcheckProver { split_eq: GruenSplitEq, w_table: Vec, + round_kernel: NormRoundKernel, + point_precomp: Option>, + range_precomp: Option>, num_vars: usize, b: usize, } -impl NormSumcheckProver { +impl NormSumcheckProver { /// Create a new norm (range-check) sumcheck prover. /// /// # Panics /// /// Panics if `w_evals.len() != 2^tau.len()`. pub fn new(tau: &[E], w_evals: Vec, b: usize) -> Self { + Self::new_with_kernel(tau, w_evals, b, choose_round_kernel(b)) + } + + fn new_with_kernel( + tau: &[E], + w_evals: Vec, + b: usize, + round_kernel: NormRoundKernel, + ) -> Self { let num_vars = tau.len(); assert_eq!(w_evals.len(), 1 << num_vars); + let point_precomp = match round_kernel { + NormRoundKernel::PointEvalInterpolation => Some(PointEvalPrecomp::new(b)), + NormRoundKernel::AffineCoeffComposition => None, + }; + let range_precomp = match round_kernel { + NormRoundKernel::PointEvalInterpolation => None, + NormRoundKernel::AffineCoeffComposition => Some(RangeAffinePrecomp::new(b)), + }; Self { split_eq: GruenSplitEq::new(tau), w_table: w_evals, + round_kernel, + point_precomp, + range_precomp, num_vars, b, } } + + fn compute_round_univariate_point_eval(&self) -> UniPoly { + let half = self.w_table.len() / 2; + let degree_q = 2 * self.b - 1; + let num_points_q = degree_q + 1; + let point_precomp = self + .point_precomp + .as_ref() + .expect("point-eval precomputation must exist"); + let range_offsets = &point_precomp.range_offsets; + + let (e_first, e_second) = self.split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + let first_bits = num_first.trailing_zeros(); + + #[cfg(feature = "parallel")] + let q_evals = { + (0..half) + .into_par_iter() + .fold( + || vec![E::zero(); num_points_q], + |mut evals, j| { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + let delta = w_1 - w_0; + let mut w_t = w_0; + for eval in evals.iter_mut() { + *eval = + *eval + eq_rem * range_check_eval_precomputed(w_t, range_offsets); + w_t = w_t + delta; + } + evals + }, + ) + .reduce( + || vec![E::zero(); num_points_q], + |mut a, b_vec| { + for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { + *ai = *ai + *bi; + } + a + }, + ) + }; + #[cfg(not(feature = "parallel"))] + let q_evals = { + let mut evals = vec![E::zero(); num_points_q]; + for j in 0..half { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + let delta = w_1 - w_0; + let mut w_t = w_0; + for eval in evals.iter_mut() { + *eval = *eval + eq_rem * range_check_eval_precomputed(w_t, range_offsets); + w_t = w_t + delta; + } + } + evals + }; + + let q_poly = UniPoly::from_evals(&q_evals); + self.split_eq.gruen_mul(&q_poly) + } + + fn compute_round_univariate_affine_coeff(&self) -> UniPoly { + let half = self.w_table.len() / 2; + let range_precomp = self + .range_precomp + .as_ref() + .expect("affine-coeff precomputation must exist"); + let num_coeffs_q = range_precomp.degree_q + 1; + + let (e_first, e_second) = self.split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + let first_bits = num_first.trailing_zeros(); + let coeff_mix = &range_precomp.coeff_mix; + + #[cfg(feature = "parallel")] + let q_coeffs = { + (0..half) + .into_par_iter() + .fold( + || vec![E::zero(); num_coeffs_q], + |mut coeffs, j| { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + let a = w_1 - w_0; + accumulate_affine_range_coeffs(&mut coeffs, coeff_mix, w_0, a, eq_rem); + coeffs + }, + ) + .reduce( + || vec![E::zero(); num_coeffs_q], + |mut a, b_vec| { + for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { + *ai = *ai + *bi; + } + a + }, + ) + }; + #[cfg(not(feature = "parallel"))] + let q_coeffs = { + let mut coeffs = vec![E::zero(); num_coeffs_q]; + for j in 0..half { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + let a = w_1 - w_0; + accumulate_affine_range_coeffs(&mut coeffs, coeff_mix, w_0, a, eq_rem); + } + coeffs + }; + + let mut q_coeffs = q_coeffs; + trim_trailing_zeros(&mut q_coeffs); + let q_poly = UniPoly::from_coeffs(q_coeffs); + self.split_eq.gruen_mul(&q_poly) + } } -impl SumcheckInstanceProver for NormSumcheckProver { +impl SumcheckInstanceProver for NormSumcheckProver { fn num_rounds(&self) -> usize { self.num_vars } @@ -57,37 +341,15 @@ impl SumcheckInstanceProver for NormSumcheckPr } fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { - let half = self.w_table.len() / 2; - let degree_q = 2 * self.b - 1; - let num_points_q = degree_q + 1; - let mut q_evals = vec![E::zero(); num_points_q]; - - let (e_first, e_second) = self.split_eq.remaining_eq_tables(); - let num_first = e_first.len(); - let first_bits = num_first.trailing_zeros(); - - for j in 0..half { - let j_low = j & (num_first - 1); - let j_high = j >> first_bits; - let eq_rem = e_first[j_low] * e_second[j_high]; - - let w_0 = self.w_table[2 * j]; - let w_1 = self.w_table[2 * j + 1]; - - for (t, eval) in q_evals.iter_mut().enumerate() { - let t_e = E::from_u64(t as u64); - let w_t = w_0 + t_e * (w_1 - w_0); - *eval = *eval + eq_rem * range_check_eval(w_t, self.b); - } + match self.round_kernel { + NormRoundKernel::PointEvalInterpolation => self.compute_round_univariate_point_eval(), + NormRoundKernel::AffineCoeffComposition => self.compute_round_univariate_affine_coeff(), } - - let q_poly = UniPoly::from_evals(&q_evals); - self.split_eq.gruen_mul(&q_poly) } fn ingest_challenge(&mut self, _round: usize, r: E) { self.split_eq.bind(r); - self.w_table = fold_evals(&self.w_table, r); + fold_evals_in_place(&mut self.w_table, r); } } @@ -99,7 +361,7 @@ pub struct NormSumcheckVerifier { b: usize, } -impl NormSumcheckVerifier { +impl NormSumcheckVerifier { /// Create a new norm (range-check) sumcheck verifier. /// /// # Panics @@ -117,7 +379,7 @@ impl NormSumcheckVerifier { } } -impl SumcheckInstanceVerifier for NormSumcheckVerifier { +impl SumcheckInstanceVerifier for NormSumcheckVerifier { fn num_rounds(&self) -> usize { self.num_vars } @@ -130,10 +392,10 @@ impl SumcheckInstanceVerifier for NormSumcheck E::zero() } - fn expected_output_claim(&self, challenges: &[E]) -> E { + fn expected_output_claim(&self, challenges: &[E]) -> Result { let eq_val = EqPolynomial::mle(&self.tau, challenges); - let w_val = multilinear_eval(&self.w_evals, challenges); - eq_val * range_check_eval(w_val, self.b) + let w_val = multilinear_eval(&self.w_evals, challenges)?; + Ok(eq_val * range_check_eval(w_val, self.b)) } } @@ -143,38 +405,219 @@ mod tests { use crate::algebra::ring::CyclotomicRing; use crate::algebra::Fp64; use crate::primitives::multilinear_evals::DenseMultilinearEvals; - use crate::protocol::ring_switch::build_w_coeffs; + use crate::protocol::ring_switch::r_decomp_levels; use crate::protocol::sumcheck::eq_poly::EqPolynomial; + use crate::protocol::sumcheck::multilinear_eval; use crate::protocol::transcript::labels; use crate::protocol::{ prove_sumcheck, verify_sumcheck, Blake2bTranscript, CommitmentConfig, CommitmentScheme, - DefaultCommitmentConfig, HachiCommitmentScheme, Transcript, + HachiCommitmentScheme, SmallTestCommitmentConfig, Transcript, }; - use crate::{CanonicalField, FieldCore}; + use crate::{FieldCore, FromSmallInt}; + use rand::rngs::StdRng; + use rand::SeedableRng; type F = Fp64<4294967197>; const D: usize = 8; + type Cfg = SmallTestCommitmentConfig; + type Scheme = HachiCommitmentScheme<{ Cfg::D }, Cfg>; + + struct PointEvalReferenceNormSumcheckProver { + split_eq: GruenSplitEq, + w_table: Vec, + num_vars: usize, + b: usize, + } + + impl PointEvalReferenceNormSumcheckProver { + fn new(tau: &[E], w_evals: Vec, b: usize) -> Self { + let num_vars = tau.len(); + assert_eq!(w_evals.len(), 1 << num_vars); + Self { + split_eq: GruenSplitEq::new(tau), + w_table: w_evals, + num_vars, + b, + } + } + } + + impl SumcheckInstanceProver + for PointEvalReferenceNormSumcheckProver + { + fn num_rounds(&self) -> usize { + self.num_vars + } + + fn degree_bound(&self) -> usize { + 2 * self.b + } + + fn input_claim(&self) -> E { + E::zero() + } + + fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { + let half = self.w_table.len() / 2; + let degree_q = 2 * self.b - 1; + let num_points_q = degree_q + 1; + + let (e_first, e_second) = self.split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + let first_bits = num_first.trailing_zeros(); + let b = self.b; + + let mut q_evals = vec![E::zero(); num_points_q]; + for j in 0..half { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + for (t, eval) in q_evals.iter_mut().enumerate() { + let t_e = E::from_u64(t as u64); + let w_t = w_0 + t_e * (w_1 - w_0); + *eval = *eval + eq_rem * range_check_eval(w_t, b); + } + } + + let q_poly = UniPoly::from_evals(&q_evals); + self.split_eq.gruen_mul(&q_poly) + } + + fn ingest_challenge(&mut self, _round: usize, r: E) { + self.split_eq.bind(r); + fold_evals_in_place(&mut self.w_table, r); + } + } fn ring_with_small_coeff(value: u64) -> CyclotomicRing { let coeffs = std::array::from_fn(|_| F::from_u64(value)); CyclotomicRing::from_coefficients(coeffs) } + #[test] + fn norm_sumcheck_runtime_dispatch_matches_reference_kernels() { + let mut rng = StdRng::seed_from_u64(0xC0FFEE); + for (case_idx, b) in [4usize, 8, 16].into_iter().enumerate() { + let case_idx = case_idx as u64; + let num_vars = 6; + let n = 1usize << num_vars; + let w_evals: Vec = (0..n) + .map(|i| F::from_u64((i as u64 * 31 + case_idx * 17) % b as u64)) + .collect(); + let tau: Vec = (0..num_vars) + .map(|_| F::from_u64(rand::Rng::gen_range(&mut rng, 1u64..=257))) + .collect(); + + let mut dispatched = NormSumcheckProver::new(&tau, w_evals.clone(), b); + let mut point_eval = NormSumcheckProver::new_with_kernel( + &tau, + w_evals.clone(), + b, + NormRoundKernel::PointEvalInterpolation, + ); + let mut affine_coeff = NormSumcheckProver::new_with_kernel( + &tau, + w_evals.clone(), + b, + NormRoundKernel::AffineCoeffComposition, + ); + let mut reference = PointEvalReferenceNormSumcheckProver::new(&tau, w_evals, b); + + let mut claim_dispatched = F::zero(); + let mut claim_point = F::zero(); + let mut claim_affine = F::zero(); + let mut claim_reference = F::zero(); + for round in 0..num_vars { + let g_dispatch = dispatched.compute_round_univariate(round, claim_dispatched); + let g_point = point_eval.compute_round_univariate(round, claim_point); + let g_affine = affine_coeff.compute_round_univariate(round, claim_affine); + let g_ref = reference.compute_round_univariate(round, claim_reference); + + assert_eq!( + g_point, g_ref, + "point-eval mismatch for case {case_idx} round {round}" + ); + assert_eq!( + g_affine, g_ref, + "affine-coeff mismatch for case {case_idx} round {round}" + ); + match choose_round_kernel(b) { + NormRoundKernel::PointEvalInterpolation => { + assert_eq!( + g_dispatch, g_point, + "dispatch mismatch for case {case_idx} round {round}" + ); + } + NormRoundKernel::AffineCoeffComposition => { + assert_eq!( + g_dispatch, g_affine, + "dispatch mismatch for case {case_idx} round {round}" + ); + } + } + + assert_eq!( + g_dispatch.evaluate(&F::zero()) + g_dispatch.evaluate(&F::one()), + claim_dispatched, + "dispatched hint mismatch for case {case_idx} round {round}" + ); + assert_eq!( + g_ref.evaluate(&F::zero()) + g_ref.evaluate(&F::one()), + claim_reference, + "reference hint mismatch for case {case_idx} round {round}" + ); + + let r = F::from_u64(rand::Rng::gen_range(&mut rng, 1u64..=257)); + claim_dispatched = g_dispatch.evaluate(&r); + claim_point = g_point.evaluate(&r); + claim_affine = g_affine.evaluate(&r); + claim_reference = g_ref.evaluate(&r); + dispatched.ingest_challenge(round, r); + point_eval.ingest_challenge(round, r); + affine_coeff.ingest_challenge(round, r); + reference.ingest_challenge(round, r); + } + assert_eq!( + claim_dispatched, claim_reference, + "final dispatched claim mismatch for case {case_idx}" + ); + assert_eq!( + claim_point, claim_reference, + "final point claim mismatch for case {case_idx}" + ); + assert_eq!( + claim_affine, claim_reference, + "final affine claim mismatch for case {case_idx}" + ); + } + } + #[test] fn norm_sumcheck_uses_commitment_w_evals() { - let z = vec![ + let z = [ ring_with_small_coeff(1), ring_with_small_coeff(2), ring_with_small_coeff(3), ]; - let r = vec![ring_with_small_coeff(0), ring_with_small_coeff(1)]; - let mut w_evals = build_w_coeffs::(&z, &r); + let r = [ring_with_small_coeff(0), ring_with_small_coeff(1)]; + let levels = r_decomp_levels::(); + let r_hat: Vec> = r + .iter() + .flat_map(|ri| ri.balanced_decompose_pow2(levels, SmallTestCommitmentConfig::LOG_BASIS)) + .collect(); + let mut w_evals: Vec = z + .iter() + .chain(r_hat.iter()) + .flat_map(|elem| elem.coefficients().iter().copied()) + .collect(); let target_len = w_evals.len().next_power_of_two(); w_evals.resize(target_len, F::zero()); let num_vars = target_len.trailing_zeros() as usize; let tau: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); - let b = 1usize << DefaultCommitmentConfig::LOG_BASIS; + let b = 1usize << SmallTestCommitmentConfig::LOG_BASIS; let eq_table = EqPolynomial::evals(&tau); let _claim: F = (0..w_evals.len()) @@ -190,7 +633,7 @@ mod tests { .unwrap(); let oracle = EqPolynomial::mle(&tau, &prover_challenges) - * range_check_eval(multilinear_eval(&w_evals, &prover_challenges), b); + * range_check_eval(multilinear_eval(&w_evals, &prover_challenges).unwrap(), b); assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); let verifier = NormSumcheckVerifier::new(tau, w_evals, b); @@ -206,18 +649,19 @@ mod tests { #[test] fn norm_sumcheck_uses_prove_w_evals() { - let alpha = DefaultCommitmentConfig::D.trailing_zeros() as usize; - let num_vars = DefaultCommitmentConfig::R + DefaultCommitmentConfig::M + alpha; + let alpha = SmallTestCommitmentConfig::D.trailing_zeros() as usize; + let layout = SmallTestCommitmentConfig::commitment_layout(8).unwrap(); + let num_vars = layout.m_vars + layout.r_vars + alpha; let len = 1usize << num_vars; let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); let poly = DenseMultilinearEvals::new_padded(evals); - let setup = HachiCommitmentScheme::setup_prover(num_vars); - let (commitment, hint) = HachiCommitmentScheme::commit(&poly, &setup).unwrap(); + let setup = Scheme::setup_prover(num_vars); + let (commitment, hint) = Scheme::commit(&poly, &setup).unwrap(); let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); let mut prover_transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); - let proof = HachiCommitmentScheme::prove( + let proof = Scheme::prove( &setup, &poly, &opening_point, @@ -234,7 +678,7 @@ mod tests { let tau: Vec = (0..num_sumcheck_vars) .map(|i| F::from_u64((i + 3) as u64)) .collect(); - let b = 1usize << DefaultCommitmentConfig::LOG_BASIS; + let b = 1usize << SmallTestCommitmentConfig::LOG_BASIS; let eq_table = EqPolynomial::evals(&tau); let _claim: F = (0..w_evals.len()) @@ -250,7 +694,7 @@ mod tests { .unwrap(); let oracle = EqPolynomial::mle(&tau, &prover_challenges) - * range_check_eval(multilinear_eval(&w_evals, &prover_challenges), b); + * range_check_eval(multilinear_eval(&w_evals, &prover_challenges).unwrap(), b); assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); let verifier = NormSumcheckVerifier::new(tau, w_evals, b); @@ -263,4 +707,44 @@ mod tests { assert_eq!(prover_challenges, verifier_challenges); } + + #[test] + fn norm_sumcheck_over_ext2() { + use crate::algebra::fields::ext::Ext2; + use crate::algebra::fields::lift::LiftBase; + + type E2 = Ext2; + + let num_vars = 3; + let n = 1usize << num_vars; + let b = 2; + let w_evals_f: Vec = (0..n).map(|i| F::from_u64(i as u64 % b as u64)).collect(); + let tau_f: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); + + let w_evals_e: Vec = w_evals_f.iter().map(|&f| E2::lift_base(f)).collect(); + let tau_e: Vec = tau_f.iter().map(|&f| E2::lift_base(f)).collect(); + + let mut prover = NormSumcheckProver::new(&tau_e, w_evals_e.clone(), b); + + let mut pt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let (proof, prover_challenges, final_claim) = + prove_sumcheck::(&mut prover, &mut pt, |tr| { + E2::lift_base(tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND)) + }) + .unwrap(); + + let oracle = EqPolynomial::mle(&tau_e, &prover_challenges) + * range_check_eval(multilinear_eval(&w_evals_e, &prover_challenges).unwrap(), b); + assert_eq!(final_claim, oracle, "E2 prover final claim != oracle eval"); + + let verifier = NormSumcheckVerifier::new(tau_e, w_evals_e, b); + let mut vt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); + let verifier_challenges = + verify_sumcheck::(&proof, &verifier, &mut vt, |tr| { + E2::lift_base(tr.challenge_scalar(labels::CHALLENGE_SUMCHECK_ROUND)) + }) + .unwrap(); + + assert_eq!(prover_challenges, verifier_challenges); + } } diff --git a/src/protocol/sumcheck/relation_sumcheck.rs b/src/protocol/sumcheck/relation_sumcheck.rs index 44e3c3c2..1f03a09a 100644 --- a/src/protocol/sumcheck/relation_sumcheck.rs +++ b/src/protocol/sumcheck/relation_sumcheck.rs @@ -6,11 +6,15 @@ //! Proves the evaluation relation; sum equals `a = Σ_i ẽq(τ₁,i) · y_i(α)`. use super::eq_poly::EqPolynomial; -use super::{fold_evals, multilinear_eval}; +use super::{fold_evals_in_place, multilinear_eval}; use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, UniPoly}; use crate::algebra::ring::CyclotomicRing; +use crate::cfg_into_iter; +use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; use crate::protocol::ring_switch::eval_ring_at; -use crate::{CanonicalField, FieldCore}; +use crate::{FieldCore, FromSmallInt}; /// Prover for `F_{α,τ₁}(x,y) = w̃(x,y) · α̃(y) · m(x)`. /// @@ -27,7 +31,7 @@ pub struct RelationSumcheckProver { num_vars: usize, } -impl RelationSumcheckProver { +impl RelationSumcheckProver { /// Construct from the three constituent evaluation tables. /// /// - `w_evals`: evaluations of `w̃` over `{0,1}^{num_u + num_l}` (full domain). @@ -53,8 +57,12 @@ impl RelationSumcheckProver { assert_eq!(m_evals_x.len(), 1 << num_u); let x_mask = (1usize << num_u) - 1; - let alpha_table: Vec = (0..n).map(|idx| alpha_evals_y[idx >> num_u]).collect(); - let m_table: Vec = (0..n).map(|idx| m_evals_x[idx & x_mask]).collect(); + let alpha_table: Vec = cfg_into_iter!(0..n) + .map(|idx| alpha_evals_y[idx >> num_u]) + .collect(); + let m_table: Vec = cfg_into_iter!(0..n) + .map(|idx| m_evals_x[idx & x_mask]) + .collect(); Self { w_table: w_evals, @@ -65,7 +73,7 @@ impl RelationSumcheckProver { } } -impl SumcheckInstanceProver for RelationSumcheckProver { +impl SumcheckInstanceProver for RelationSumcheckProver { fn num_rounds(&self) -> usize { self.num_vars } @@ -75,42 +83,90 @@ impl SumcheckInstanceProver for RelationSumche } fn input_claim(&self) -> E { - self.w_table - .iter() - .zip(self.alpha_table.iter()) - .zip(self.m_table.iter()) - .fold(E::zero(), |acc, ((&w, &a), &m)| acc + w * a * m) + #[cfg(feature = "parallel")] + { + self.w_table + .par_iter() + .zip(self.alpha_table.par_iter()) + .zip(self.m_table.par_iter()) + .fold(|| E::zero(), |acc, ((&w, &a), &m)| acc + w * a * m) + .reduce(|| E::zero(), |a, b| a + b) + } + #[cfg(not(feature = "parallel"))] + { + self.w_table + .iter() + .zip(self.alpha_table.iter()) + .zip(self.m_table.iter()) + .fold(E::zero(), |acc, ((&w, &a), &m)| acc + w * a * m) + } } fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { let half = self.w_table.len() / 2; let num_points = 3; // degree 2 → 3 evaluation points - let mut round_evals = vec![E::zero(); num_points]; - - for j in 0..half { - let w_0 = self.w_table[2 * j]; - let w_1 = self.w_table[2 * j + 1]; - let a_0 = self.alpha_table[2 * j]; - let a_1 = self.alpha_table[2 * j + 1]; - let m_0 = self.m_table[2 * j]; - let m_1 = self.m_table[2 * j + 1]; - - for (t, eval) in round_evals.iter_mut().enumerate() { - let t_e = E::from_u64(t as u64); - let w_t = w_0 + t_e * (w_1 - w_0); - let a_t = a_0 + t_e * (a_1 - a_0); - let m_t = m_0 + t_e * (m_1 - m_0); - *eval = *eval + w_t * a_t * m_t; + + #[cfg(feature = "parallel")] + let round_evals = { + (0..half) + .into_par_iter() + .fold( + || vec![E::zero(); num_points], + |mut evals, j| { + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + let a_0 = self.alpha_table[2 * j]; + let a_1 = self.alpha_table[2 * j + 1]; + let m_0 = self.m_table[2 * j]; + let m_1 = self.m_table[2 * j + 1]; + for (t, eval) in evals.iter_mut().enumerate() { + let t_e = E::from_u64(t as u64); + let w_t = w_0 + t_e * (w_1 - w_0); + let a_t = a_0 + t_e * (a_1 - a_0); + let m_t = m_0 + t_e * (m_1 - m_0); + *eval = *eval + w_t * a_t * m_t; + } + evals + }, + ) + .reduce( + || vec![E::zero(); num_points], + |mut a, b| { + for (ai, bi) in a.iter_mut().zip(b.iter()) { + *ai = *ai + *bi; + } + a + }, + ) + }; + #[cfg(not(feature = "parallel"))] + let round_evals = { + let mut evals = vec![E::zero(); num_points]; + for j in 0..half { + let w_0 = self.w_table[2 * j]; + let w_1 = self.w_table[2 * j + 1]; + let a_0 = self.alpha_table[2 * j]; + let a_1 = self.alpha_table[2 * j + 1]; + let m_0 = self.m_table[2 * j]; + let m_1 = self.m_table[2 * j + 1]; + for (t, eval) in evals.iter_mut().enumerate() { + let t_e = E::from_u64(t as u64); + let w_t = w_0 + t_e * (w_1 - w_0); + let a_t = a_0 + t_e * (a_1 - a_0); + let m_t = m_0 + t_e * (m_1 - m_0); + *eval = *eval + w_t * a_t * m_t; + } } - } + evals + }; UniPoly::from_evals(&round_evals) } fn ingest_challenge(&mut self, _round: usize, r: E) { - self.w_table = fold_evals(&self.w_table, r); - self.alpha_table = fold_evals(&self.alpha_table, r); - self.m_table = fold_evals(&self.m_table, r); + fold_evals_in_place(&mut self.w_table, r); + fold_evals_in_place(&mut self.alpha_table, r); + fold_evals_in_place(&mut self.m_table, r); } } @@ -128,7 +184,7 @@ pub struct RelationSumcheckVerifier { num_l: usize, } -impl RelationSumcheckVerifier { +impl RelationSumcheckVerifier { /// Create a new evaluation-relation sumcheck verifier. /// /// # Panics @@ -165,9 +221,7 @@ impl RelationSumcheckVerifier SumcheckInstanceVerifier - for RelationSumcheckVerifier -{ +impl SumcheckInstanceVerifier for RelationSumcheckVerifier { fn num_rounds(&self) -> usize { self.num_u + self.num_l } @@ -194,12 +248,12 @@ impl SumcheckInstanceVerifier acc } - fn expected_output_claim(&self, challenges: &[F]) -> F { + fn expected_output_claim(&self, challenges: &[F]) -> Result { let (x_challenges, y_challenges) = challenges.split_at(self.num_u); - let w_val = multilinear_eval(&self.w_evals, challenges); - let alpha_val = multilinear_eval(&self.alpha_evals_y, y_challenges); - let m_val = multilinear_eval(&self.m_evals_x, x_challenges); - w_val * alpha_val * m_val + let w_val = multilinear_eval(&self.w_evals, challenges)?; + let alpha_val = multilinear_eval(&self.alpha_evals_y, y_challenges)?; + let m_val = multilinear_eval(&self.m_evals_x, x_challenges)?; + Ok(w_val * alpha_val * m_val) } } @@ -213,26 +267,29 @@ mod tests { use crate::protocol::transcript::labels; use crate::protocol::{ prove_sumcheck, verify_sumcheck, Blake2bTranscript, CommitmentConfig, CommitmentScheme, - DefaultCommitmentConfig, HachiCommitmentScheme, Transcript, + HachiCommitmentScheme, SmallTestCommitmentConfig, Transcript, }; - use crate::{CanonicalField, FieldCore}; + use crate::{FieldCore, FromSmallInt}; type F = Fp64<4294967197>; + type Cfg = SmallTestCommitmentConfig; + type Scheme = HachiCommitmentScheme<{ Cfg::D }, Cfg>; #[test] fn relation_sumcheck_uses_prove_w_evals() { - let alpha_bits = DefaultCommitmentConfig::D.trailing_zeros() as usize; - let num_vars = DefaultCommitmentConfig::R + DefaultCommitmentConfig::M + alpha_bits; + let alpha_bits = SmallTestCommitmentConfig::D.trailing_zeros() as usize; + let layout = SmallTestCommitmentConfig::commitment_layout(8).unwrap(); + let num_vars = layout.m_vars + layout.r_vars + alpha_bits; let len = 1usize << num_vars; let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); let poly = DenseMultilinearEvals::new_padded(evals); - let setup = HachiCommitmentScheme::setup_prover(num_vars); - let (commitment, hint) = HachiCommitmentScheme::commit(&poly, &setup).unwrap(); + let setup = Scheme::setup_prover(num_vars); + let (commitment, hint) = Scheme::commit(&poly, &setup).unwrap(); let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); let mut prover_transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); - let proof = HachiCommitmentScheme::prove( + let proof = Scheme::prove( &setup, &poly, &opening_point, @@ -242,17 +299,22 @@ mod tests { ) .unwrap(); - let (alpha, m_a_vec) = - rederive_alpha_and_m_a(&proof, &setup, &opening_point, &commitment).unwrap(); + let (alpha, m_a_vec) = rederive_alpha_and_m_a::( + &proof, + &Scheme::setup_verifier(&setup), + &opening_point, + &commitment, + ) + .unwrap(); - let d = DefaultCommitmentConfig::D; + let d = SmallTestCommitmentConfig::D; assert_eq!(proof.sumcheck_aux.w.len() % d, 0); let w_u = proof.sumcheck_aux.w.len() / d; - let rows = DefaultCommitmentConfig::N_D - + DefaultCommitmentConfig::N_B + let rows = SmallTestCommitmentConfig::N_D + + SmallTestCommitmentConfig::N_B + 1 + 1 - + DefaultCommitmentConfig::N_A; + + SmallTestCommitmentConfig::N_A; assert!(rows > 0); assert_eq!(m_a_vec.len() % rows, 0); let cols = m_a_vec.len() / rows; @@ -317,9 +379,9 @@ mod tests { .unwrap(); let (x_ch, y_ch) = prover_challenges.split_at(num_u); - let oracle = multilinear_eval(&w_evals, &prover_challenges) - * multilinear_eval(&alpha_evals_y, y_ch) - * multilinear_eval(&m_evals_x, x_ch); + let oracle = multilinear_eval(&w_evals, &prover_challenges).unwrap() + * multilinear_eval(&alpha_evals_y, y_ch).unwrap() + * multilinear_eval(&m_evals_x, x_ch).unwrap(); assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); let verifier = RelationSumcheckVerifier::new( diff --git a/src/protocol/sumcheck/split_eq.rs b/src/protocol/sumcheck/split_eq.rs index 1f10dbfe..9ecf7269 100644 --- a/src/protocol/sumcheck/split_eq.rs +++ b/src/protocol/sumcheck/split_eq.rs @@ -23,7 +23,7 @@ use super::eq_poly::EqPolynomial; use super::UniPoly; -use crate::{CanonicalField, FieldCore}; +use crate::FieldCore; /// Split equality polynomial with Gruen scalar accumulation. /// @@ -56,7 +56,7 @@ pub struct GruenSplitEq { } #[allow(non_snake_case)] -impl GruenSplitEq { +impl GruenSplitEq { /// Create a new split-eq from the full challenge vector `τ`. /// /// Precomputes suffix-cached eq tables for two halves of `τ[1..n]`. @@ -151,8 +151,8 @@ impl GruenSplitEq { mod tests { use super::*; use crate::algebra::Fp64; - use crate::protocol::sumcheck::fold_evals; - use crate::FieldSampling; + use crate::protocol::sumcheck::fold_evals_in_place; + use crate::{FieldSampling, FromSmallInt}; use rand::rngs::StdRng; use rand::SeedableRng; @@ -186,7 +186,7 @@ mod tests { } let r = F::sample(&mut rng); - full_eq = fold_evals(&full_eq, r); + fold_evals_in_place(&mut full_eq, r); split_eq.bind(r); } } diff --git a/src/protocol/sumcheck/types.rs b/src/protocol/sumcheck/types.rs new file mode 100644 index 00000000..7fbf4d3b --- /dev/null +++ b/src/protocol/sumcheck/types.rs @@ -0,0 +1,378 @@ +//! Sumcheck data types: univariate polynomials, compressed representation, and proof container. + +use crate::error::HachiError; +use crate::primitives::serialization::{ + Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, +}; +use crate::protocol::transcript::labels; +use crate::protocol::transcript::Transcript; +use crate::FieldCore; +use crate::FromSmallInt; +use std::io::{Read, Write}; + +/// Univariate polynomial in coefficient form: `p(X) = Σ_{i=0}^d coeffs[i] * X^i`. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct UniPoly { + /// Coefficients from low degree to high degree. + pub coeffs: Vec, +} + +impl UniPoly { + /// Construct from coefficients in increasing-degree order. + pub fn from_coeffs(coeffs: Vec) -> Self { + Self { coeffs } + } + + /// Degree of the polynomial (0 for empty or constant). + pub fn degree(&self) -> usize { + self.coeffs.len().saturating_sub(1) + } + + /// Evaluate at `x` via Horner's method. + pub fn evaluate(&self, x: &E) -> E { + let mut acc = E::zero(); + for c in self.coeffs.iter().rev() { + acc = acc * *x + *c; + } + acc + } + + /// Compress this polynomial by omitting the linear coefficient. + /// + /// The verifier can reconstruct/evaluate the missing linear coefficient using + /// the per-round hint `g(0)+g(1)` from the sumcheck protocol. + /// + /// This matches the technique used by Jolt's sumcheck (`CompressedUniPoly`). + pub fn compress(&self) -> CompressedUniPoly { + let coeffs = &self.coeffs; + if coeffs.is_empty() { + return CompressedUniPoly { + coeffs_except_linear_term: Vec::new(), + }; + } + if coeffs.len() == 1 { + return CompressedUniPoly { + coeffs_except_linear_term: vec![coeffs[0]], + }; + } + let mut out = Vec::with_capacity(coeffs.len().saturating_sub(1)); + out.push(coeffs[0]); + out.extend_from_slice(&coeffs[2..]); + CompressedUniPoly { + coeffs_except_linear_term: out, + } + } +} + +impl UniPoly { + /// Interpolate from evaluations at equispaced integer points `x = 0, 1, ..., d`. + /// + /// Uses Newton forward-difference interpolation: compute divided differences, + /// then expand via Horner on the nested Newton form. + /// + /// # Panics + /// + /// Panics if any required factorial inverse does not exist (field characteristic + /// must exceed the number of evaluation points). This is a prover-only + /// function and the condition always holds for Hachi's fields. + pub fn from_evals(evals: &[E]) -> Self { + let n = evals.len(); + if n == 0 { + return Self::from_coeffs(vec![]); + } + if n == 1 { + return Self::from_coeffs(vec![evals[0]]); + } + + let mut table = evals.to_vec(); + let mut deltas = vec![table[0]]; + for _ in 1..n { + for j in 0..table.len() - 1 { + table[j] = table[j + 1] - table[j]; + } + table.pop(); + deltas.push(table[0]); + } + + let mut factorial = E::one(); + let mut divided_diffs = vec![deltas[0]]; + for (k, delta_k) in deltas.iter().enumerate().skip(1) { + factorial = factorial * E::from_u64(k as u64); + divided_diffs.push( + *delta_k + * factorial + .inv() + .expect("field characteristic too small for interpolation"), + ); + } + + let mut coeffs = vec![divided_diffs[n - 1]]; + + for k in (0..n - 1).rev() { + let shift = E::from_u64(k as u64); + let old_len = coeffs.len(); + let mut new_coeffs = vec![E::zero(); old_len + 1]; + + new_coeffs[0] = divided_diffs[k]; + for i in 0..old_len { + new_coeffs[i + 1] = new_coeffs[i + 1] + coeffs[i]; + new_coeffs[i] = new_coeffs[i] - shift * coeffs[i]; + } + + coeffs = new_coeffs; + } + + while coeffs.len() > 1 && coeffs.last().is_some_and(|c| c.is_zero()) { + coeffs.pop(); + } + + Self::from_coeffs(coeffs) + } +} + +impl Valid for UniPoly { + fn check(&self) -> Result<(), SerializationError> { + self.coeffs.check() + } +} + +impl HachiSerialize for UniPoly { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.coeffs.serialize_with_mode(&mut writer, compress) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.coeffs.serialized_size(compress) + } +} + +impl HachiDeserialize for UniPoly { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let coeffs = Vec::::deserialize_with_mode(&mut reader, compress, validate)?; + let out = Self { coeffs }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +/// Compressed univariate polynomial representation omitting the linear term. +/// +/// We store `[c0, c2, c3, ..., cd]`. Given the sumcheck hint `hint = g(0)+g(1)`, +/// the missing linear coefficient is: +/// +/// `c1 = hint - 2*c0 - Σ_{i=2..d} ci`. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct CompressedUniPoly { + /// Coefficients excluding the linear term: `[c0, c2, c3, ..., cd]`. + pub coeffs_except_linear_term: Vec, +} + +impl CompressedUniPoly { + /// Degree of the underlying uncompressed polynomial. + /// + /// `compress()` stores `[c0, c2, ..., cd]` — exactly `d` entries for + /// degree `d >= 2`. For `len <= 1` (degree 0 or 1, which are ambiguous + /// in compressed form) we report 0; this is conservative for the + /// verifier's degree-bound check since `degree_bound >= 2` in practice. + pub fn degree(&self) -> usize { + let len = self.coeffs_except_linear_term.len(); + if len <= 1 { + 0 + } else { + len + } + } + + fn recover_linear_term(&self, hint: &E) -> E { + if self.coeffs_except_linear_term.is_empty() { + return E::zero(); + } + + let c0 = self.coeffs_except_linear_term[0]; + let mut linear = *hint - c0 - c0; + for c in self.coeffs_except_linear_term.iter().skip(1) { + linear = linear - *c; + } + linear + } + + /// Decompress using `hint = g(0)+g(1)`. + pub fn decompress(&self, hint: &E) -> UniPoly { + if self.coeffs_except_linear_term.is_empty() { + return UniPoly::from_coeffs(Vec::new()); + } + let linear = self.recover_linear_term(hint); + let mut coeffs = Vec::with_capacity(self.coeffs_except_linear_term.len() + 1); + coeffs.push(self.coeffs_except_linear_term[0]); + coeffs.push(linear); + coeffs.extend_from_slice(&self.coeffs_except_linear_term[1..]); + UniPoly::from_coeffs(coeffs) + } + + /// Evaluate the uncompressed polynomial at `x`, using `hint = g(0)+g(1)`. + /// + /// This avoids materializing the full coefficient list. + pub fn eval_from_hint(&self, hint: &E, x: &E) -> E { + if self.coeffs_except_linear_term.is_empty() { + return E::zero(); + } + + let linear = self.recover_linear_term(hint); + let mut acc = self.coeffs_except_linear_term[0] + (*x * linear); + + let mut pow = *x * *x; + for c in self.coeffs_except_linear_term.iter().skip(1) { + acc = acc + (*c * pow); + pow = pow * *x; + } + acc + } +} + +impl Valid for CompressedUniPoly { + fn check(&self) -> Result<(), SerializationError> { + self.coeffs_except_linear_term.check() + } +} + +impl HachiSerialize for CompressedUniPoly { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.coeffs_except_linear_term + .serialize_with_mode(&mut writer, compress) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.coeffs_except_linear_term.serialized_size(compress) + } +} + +impl HachiDeserialize for CompressedUniPoly { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let coeffs_except_linear_term = + Vec::::deserialize_with_mode(&mut reader, compress, validate)?; + let out = Self { + coeffs_except_linear_term, + }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +/// Sumcheck proof containing one compressed univariate polynomial per round. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct SumcheckProof { + /// One compressed univariate polynomial per sumcheck round. + pub round_polys: Vec>, +} + +impl Valid for SumcheckProof { + fn check(&self) -> Result<(), SerializationError> { + self.round_polys.check() + } +} + +impl HachiSerialize for SumcheckProof { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + self.round_polys.serialize_with_mode(&mut writer, compress) + } + + fn serialized_size(&self, compress: Compress) -> usize { + self.round_polys.serialized_size(compress) + } +} + +impl HachiDeserialize for SumcheckProof { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let round_polys = + Vec::>::deserialize_with_mode(&mut reader, compress, validate)?; + let out = Self { round_polys }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } +} + +impl SumcheckProof { + /// Verifier-side sumcheck transcript driver. + /// + /// This method: + /// - absorbs the per-round prover message (compressed univariate), + /// - samples one challenge per round via `sample_challenge`, + /// - updates the running claim using `eval_from_hint`. + /// + /// It does **not** perform the final oracle check `final_claim == f(r*)`. + /// Callers (e.g. ring-switching) must compute `f(r*)` themselves and compare. + /// + /// # Errors + /// + /// Returns an error if the proof length does not match `num_rounds` or if any + /// per-round polynomial exceeds `degree_bound`. + pub fn verify( + &self, + mut claim: E, + num_rounds: usize, + degree_bound: usize, + transcript: &mut T, + mut sample_challenge: S, + ) -> Result<(E, Vec), HachiError> + where + F: crate::FieldCore + crate::CanonicalField, + T: Transcript, + S: FnMut(&mut T) -> E, + { + if self.round_polys.len() != num_rounds { + return Err(HachiError::InvalidSize { + expected: num_rounds, + actual: self.round_polys.len(), + }); + } + + let mut r = Vec::with_capacity(num_rounds); + for poly in &self.round_polys { + if poly.degree() > degree_bound { + return Err(HachiError::InvalidInput(format!( + "sumcheck round poly degree {} exceeds bound {}", + poly.degree(), + degree_bound + ))); + } + + transcript.append_serde(labels::ABSORB_SUMCHECK_ROUND, poly); + let r_i = sample_challenge(transcript); + r.push(r_i); + + claim = poly.eval_from_hint(&claim, &r_i); + } + + Ok((claim, r)) + } +} diff --git a/src/protocol/transcript/blake2b.rs b/src/protocol/transcript/hash.rs similarity index 56% rename from src/protocol/transcript/blake2b.rs rename to src/protocol/transcript/hash.rs index c72fba39..cfae7b30 100644 --- a/src/protocol/transcript/blake2b.rs +++ b/src/protocol/transcript/hash.rs @@ -1,22 +1,28 @@ -//! Blake2b transcript implementation for protocol-layer Fiat-Shamir. +//! Generic hash-based transcript for protocol-layer Fiat-Shamir. +//! +//! Parameterised over any `Digest + Clone` hasher, eliminating the +//! near-identical Blake2b and Keccak implementations. use super::Transcript; use crate::primitives::serialization::HachiSerialize; use crate::{CanonicalField, FieldCore}; use blake2::{Blake2b512, Digest}; +use sha3::Keccak256; use std::marker::PhantomData; -/// Blake2b512 transcript with labeled framing. +/// Hash-based transcript with labeled framing. +/// +/// Works with any cryptographic hash that implements `Digest + Clone`. #[derive(Clone)] -pub struct Blake2bTranscript +pub struct HashTranscript where F: FieldCore + CanonicalField + 'static, { - hasher: Blake2b512, + hasher: D, _field: PhantomData, } -impl Blake2bTranscript +impl HashTranscript where F: FieldCore + CanonicalField + 'static, { @@ -28,22 +34,21 @@ where } #[inline] - fn challenge_bytes(&mut self, label: &[u8]) -> [u8; 64] { + fn challenge_and_chain(&mut self, label: &[u8]) -> Vec { self.hasher.update(label); let digest = self.hasher.clone().finalize(); - let mut out = [0u8; 64]; - out.copy_from_slice(digest.as_slice()); - self.hasher.update(out); + let out = digest.to_vec(); + self.hasher.update(&out); out } } -impl Transcript for Blake2bTranscript +impl Transcript for HashTranscript where F: FieldCore + CanonicalField + 'static, { fn new(domain_label: &[u8]) -> Self { - let mut hasher = Blake2b512::new(); + let mut hasher = D::new(); hasher.update(domain_label); Self { hasher, @@ -67,16 +72,32 @@ where } fn challenge_scalar(&mut self, label: &[u8]) -> F { - let bytes = self.challenge_bytes(label); + let bytes = self.challenge_and_chain(label); let mut lo = [0u8; 16]; lo.copy_from_slice(&bytes[..16]); let sampled = u128::from_le_bytes(lo); F::from_canonical_u128_reduced(sampled) } +} - fn reset(&mut self, domain_label: &[u8]) { - let mut hasher = Blake2b512::new(); +impl HashTranscript +where + F: FieldCore + CanonicalField + 'static, +{ + /// Reset transcript state under a new domain label. + /// + /// This is an inherent method (not part of the `Transcript` trait) to + /// discourage use in production protocol code where resetting the + /// Fiat-Shamir chain would be unsound. + pub fn reset(&mut self, domain_label: &[u8]) { + let mut hasher = D::new(); hasher.update(domain_label); self.hasher = hasher; } } + +/// Blake2b512 transcript with labeled framing. +pub type Blake2bTranscript = HashTranscript; + +/// Keccak256 transcript with labeled framing. +pub type KeccakTranscript = HashTranscript; diff --git a/src/protocol/transcript/keccak.rs b/src/protocol/transcript/keccak.rs deleted file mode 100644 index 8fa3855c..00000000 --- a/src/protocol/transcript/keccak.rs +++ /dev/null @@ -1,82 +0,0 @@ -//! Keccak transcript implementation for protocol-layer Fiat-Shamir. - -use super::Transcript; -use crate::primitives::serialization::HachiSerialize; -use crate::{CanonicalField, FieldCore}; -use sha3::{Digest, Keccak256}; -use std::marker::PhantomData; - -/// Keccak256 transcript with labeled framing. -#[derive(Clone)] -pub struct KeccakTranscript -where - F: FieldCore + CanonicalField + 'static, -{ - hasher: Keccak256, - _field: PhantomData, -} - -impl KeccakTranscript -where - F: FieldCore + CanonicalField + 'static, -{ - #[inline] - fn append_bytes_impl(&mut self, label: &[u8], bytes: &[u8]) { - self.hasher.update(label); - self.hasher.update((bytes.len() as u64).to_le_bytes()); - self.hasher.update(bytes); - } - - #[inline] - fn challenge_bytes(&mut self, label: &[u8]) -> [u8; 32] { - self.hasher.update(label); - let digest = self.hasher.clone().finalize(); - let mut out = [0u8; 32]; - out.copy_from_slice(digest.as_slice()); - self.hasher.update(out); - out - } -} - -impl Transcript for KeccakTranscript -where - F: FieldCore + CanonicalField + 'static, -{ - fn new(domain_label: &[u8]) -> Self { - let mut hasher = Keccak256::new(); - hasher.update(domain_label); - Self { - hasher, - _field: PhantomData, - } - } - - fn append_bytes(&mut self, label: &[u8], bytes: &[u8]) { - self.append_bytes_impl(label, bytes); - } - - fn append_field(&mut self, label: &[u8], x: &F) { - self.append_bytes_impl(label, &x.to_canonical_u128().to_le_bytes()); - } - - fn append_serde(&mut self, label: &[u8], s: &S) { - let mut bytes = Vec::new(); - s.serialize_compressed(&mut bytes) - .expect("HachiSerialize should not fail"); - self.append_bytes_impl(label, &bytes); - } - - fn challenge_scalar(&mut self, label: &[u8]) -> F { - let bytes = self.challenge_bytes(label); - let mut lo = [0u8; 16]; - lo.copy_from_slice(&bytes[..16]); - let sampled = u128::from_le_bytes(lo); - F::from_canonical_u128_reduced(sampled) - } - - fn reset(&mut self, domain_label: &[u8]) { - let mut hasher = Keccak256::new(); - hasher.update(domain_label); - self.hasher = hasher; - } -} diff --git a/src/protocol/transcript/mod.rs b/src/protocol/transcript/mod.rs index 7ccd5be9..05434ddb 100644 --- a/src/protocol/transcript/mod.rs +++ b/src/protocol/transcript/mod.rs @@ -1,13 +1,12 @@ //! Protocol transcript contracts and implementations. -mod blake2b; -mod keccak; +mod hash; pub mod labels; +use crate::algebra::fields::lift::ExtField; use crate::{CanonicalField, FieldCore, HachiSerialize}; -pub use blake2b::Blake2bTranscript; -pub use keccak::KeccakTranscript; +pub use hash::{Blake2bTranscript, HashTranscript, KeccakTranscript}; /// Transcript interface for protocol Fiat-Shamir transforms. /// @@ -31,7 +30,21 @@ where /// Derive a challenge scalar under the provided label. fn challenge_scalar(&mut self, label: &[u8]) -> F; +} - /// Reset transcript state under a new domain label. - fn reset(&mut self, domain_label: &[u8]); +/// Sample an extension field challenge by drawing `EXT_DEGREE` base-field +/// challenges and assembling them via `from_base_slice`. +/// +/// When `E = F` (degree 1), this compiles to a single `challenge_scalar` call. +pub fn sample_ext_challenge(tr: &mut T, label: &[u8]) -> E +where + F: FieldCore + CanonicalField, + T: Transcript, + E: ExtField, +{ + E::from_base_slice( + &(0..E::EXT_DEGREE) + .map(|_| tr.challenge_scalar(label)) + .collect::>(), + ) } diff --git a/src/test_utils.rs b/src/test_utils.rs index 2bf775f0..5de0450f 100644 --- a/src/test_utils.rs +++ b/src/test_utils.rs @@ -6,7 +6,7 @@ use crate::algebra::{CyclotomicRing, Fp64}; use crate::protocol::commitment::CommitmentConfig; -use crate::{CanonicalField, FieldCore}; +use crate::{FieldCore, FromSmallInt}; pub type F = Fp64<4294967197>; pub const D: usize = 64; @@ -16,20 +16,23 @@ pub struct TinyConfig; impl CommitmentConfig for TinyConfig { const D: usize = 64; - const M: usize = 1; - const R: usize = 1; const N_A: usize = 2; const N_B: usize = 2; const N_D: usize = 2; const LOG_BASIS: u32 = 4; const DELTA: usize = 9; const TAU: usize = 4; - const BETA: u128 = 1_000_000; const CHALLENGE_WEIGHT: usize = 3; + + fn commitment_layout( + _max_num_vars: usize, + ) -> Result { + crate::protocol::commitment::HachiCommitmentLayout::new::(1, 1) + } } -pub const BLOCK_LEN: usize = 1 << TinyConfig::M; -pub const NUM_BLOCKS: usize = 1 << TinyConfig::R; +pub const BLOCK_LEN: usize = 2; +pub const NUM_BLOCKS: usize = 2; pub const DELTA: usize = TinyConfig::DELTA; pub const LOG_BASIS: u32 = TinyConfig::LOG_BASIS; pub const N_A: usize = TinyConfig::N_A; diff --git a/tests/algebra.rs b/tests/algebra.rs index cbb51aeb..668cacd0 100644 --- a/tests/algebra.rs +++ b/tests/algebra.rs @@ -5,9 +5,13 @@ mod tests { use num_bigint::BigUint; use rand::{rngs::StdRng, SeedableRng}; + use hachi_pcs::algebra::backend::{CrtReconstruct, NttPrimeOps}; use hachi_pcs::algebra::ntt::butterfly::{forward_ntt, inverse_ntt, NttTwiddles}; use hachi_pcs::algebra::poly::Poly; - use hachi_pcs::algebra::tables::{Q32_DATA, Q32_MODULUS, Q32_NUM_PRIMES, Q32_PRIMES}; + use hachi_pcs::algebra::tables::{ + q128_garner, q128_primes, q32_garner, q64_garner, q64_primes, Q128_MODULUS, + Q128_NUM_PRIMES, Q32_MODULUS, Q32_NUM_PRIMES, Q32_PRIMES, Q64_MODULUS, Q64_NUM_PRIMES, + }; use hachi_pcs::algebra::{ pseudo_mersenne_modulus, Pow2Offset128Field, Pow2OffsetPrimeSpec, POW2_OFFSET_MAX, POW2_OFFSET_PRIMES, POW2_OFFSET_TABLE, @@ -19,8 +23,8 @@ mod tests { }; use hachi_pcs::primitives::serialization::SerializationError; use hachi_pcs::{ - CanonicalField, FieldCore, FieldSampling, HachiDeserialize, HachiSerialize, Invertible, - Module, PseudoMersenneField, + CanonicalField, FieldCore, FieldSampling, FromSmallInt, HachiDeserialize, HachiSerialize, + Invertible, Module, PseudoMersenneField, }; const P_159: u128 = 340282366920938463463374607431768211297u128; @@ -439,12 +443,6 @@ mod tests { assert_eq!(a, a); } - #[test] - fn qdata_q_matches_const() { - let q_from_data = Q32_DATA.q_u128().unwrap(); - assert_eq!(q_from_data, Q32_MODULUS as u128); - } - #[test] fn ntt_normalize_in_range() { for prime in &Q32_PRIMES { @@ -460,6 +458,33 @@ mod tests { } } + #[test] + fn csubp_widened_handles_large_negative_i16() { + for &prime in &Q32_PRIMES { + let p = prime.p; + // Values in (-2p, -(2^15 - p)) that previously overflowed in narrow i16 + for &raw in &[-20000i16, -(p + p / 2), -(p + 1000)] { + if raw <= -2 * p || raw >= 0 { + continue; + } + let a = MontCoeff::from_raw(raw); + let reduced = prime.reduce_range(a); + let r = reduced.raw(); + assert!( + r > -p && r < p, + "reduce_range({raw}) = {r} not in (-{p}, {p}) for p={p}" + ); + + let norm = prime.normalize(reduced); + let n = norm.raw(); + assert!( + n >= 0 && n < p, + "normalize(reduce_range({raw})) = {n} not in [0, {p}) for p={p}" + ); + } + } + } + #[test] fn ntt_mul_commutative() { let prime = Q32_PRIMES[0]; @@ -664,18 +689,15 @@ mod tests { #[test] fn ntt_forward_inverse_round_trip() { let prime = Q32_PRIMES[0]; - let tw = NttTwiddles::<64>::compute(prime); + let tw = NttTwiddles::::compute(prime); - // Create a test polynomial in Montgomery form. - let original: [MontCoeff; 64] = + let original: [MontCoeff; 64] = std::array::from_fn(|i| prime.from_canonical((i as i16) % prime.p)); - // Forward then inverse should give back the original. let mut a = original; forward_ntt(&mut a, prime, &tw); inverse_ntt(&mut a, prime, &tw); - // Normalize and compare. for (i, (got, expected)) in a.iter().zip(original.iter()).enumerate() { let got_canon = prime.to_canonical(prime.normalize(*got)); let exp_canon = prime.to_canonical(prime.normalize(*expected)); @@ -689,7 +711,7 @@ mod tests { #[test] fn ntt_forward_inverse_all_primes() { for (pi, prime) in Q32_PRIMES.iter().enumerate() { - let tw = NttTwiddles::<64>::compute(*prime); + let tw = NttTwiddles::::compute(*prime); let original: [_; 64] = std::array::from_fn(|i| prime.from_canonical(((i * (pi + 1)) as i16) % prime.p)); @@ -710,20 +732,213 @@ mod tests { } } + #[test] + fn negacyclic_ntt_mul_matches_schoolbook_single_prime_d8() { + const D: usize = 8; + let prime = Q32_PRIMES[0]; + let tw = NttTwiddles::::compute(prime); + + let a_canon: [i16; D] = std::array::from_fn(|i| ((i as i16 * 7) + 3) % prime.p); + let b_canon: [i16; D] = std::array::from_fn(|i| ((i as i16 * 5) + 11) % prime.p); + + // Schoolbook negacyclic convolution mod p: X^D = -1. + let mut school = [0i16; D]; + for (i, &ai) in a_canon.iter().enumerate() { + for (j, &bj) in b_canon.iter().enumerate() { + let prod = (ai as i64 * bj as i64) % (prime.p as i64); + let idx = i + j; + if idx < D { + school[idx] = ((school[idx] as i64 + prod) % (prime.p as i64)) as i16; + } else { + let k = idx - D; + school[k] = ((school[k] as i64 - prod) % (prime.p as i64)) as i16; + } + } + } + for x in &mut school { + if *x < 0 { + *x = (*x as i64 + prime.p as i64) as i16; + } + } + + let mut a = std::array::from_fn(|i| prime.from_canonical(a_canon[i])); + let mut b = std::array::from_fn(|i| prime.from_canonical(b_canon[i])); + forward_ntt(&mut a, prime, &tw); + forward_ntt(&mut b, prime, &tw); + + let mut c: [_; D] = std::array::from_fn(|i| prime.mul(a[i], b[i])); + inverse_ntt(&mut c, prime, &tw); + + let got: [i16; D] = std::array::from_fn(|i| prime.to_canonical(prime.normalize(c[i]))); + assert_eq!(got, school); + } + + #[test] + fn negacyclic_ntt_forward_matches_manual_evals_d8() { + const D: usize = 8; + let prime = Q32_PRIMES[0]; + let tw = NttTwiddles::::compute(prime); + let p = prime.p as i64; + + fn pow_mod(mut base: i64, mut exp: i64, modulus: i64) -> i64 { + let mut acc = 1i64; + base %= modulus; + while exp > 0 { + if exp & 1 == 1 { + acc = (acc * base) % modulus; + } + base = (base * base) % modulus; + exp >>= 1; + } + acc + } + + // Compute canonical psi (primitive 2D-th root) directly. + let half = (p - 1) / 2; + let exp = (p - 1) / (2 * D as i64); + let mut psi = None; + for a in 2..p { + if pow_mod(a, half, p) == p - 1 { + let cand = pow_mod(a, exp, p); + if pow_mod(cand, D as i64, p) == p - 1 { + psi = Some(cand); + break; + } + } + } + let psi = psi.expect("psi should exist"); + let a_canon: [i16; D] = std::array::from_fn(|i| ((i as i16 * 7) + 3) % prime.p); + + let mut expected = Vec::with_capacity(D); + for k in 0..D { + let alpha = pow_mod(psi, (2 * k + 1) as i64, p); + let mut acc = 0i64; + let mut power = 1i64; + for &ai in &a_canon { + acc = (acc + (ai as i64) * power) % p; + power = (power * alpha) % p; + } + expected.push(acc as i16); + } + expected.sort_unstable(); + + let mut a = std::array::from_fn(|i| prime.from_canonical(a_canon[i])); + forward_ntt(&mut a, prime, &tw); + let mut got: Vec = a + .iter() + .map(|x| prime.to_canonical(prime.normalize(*x))) + .collect(); + got.sort_unstable(); + + assert_eq!(got, expected); + } + + #[test] + fn negacyclic_ntt_mul_matches_schoolbook_single_prime_d64() { + const D: usize = 64; + let prime = Q32_PRIMES[0]; + let tw = NttTwiddles::::compute(prime); + let p = prime.p as i64; + + let a_canon: [i16; D] = std::array::from_fn(|i| ((i as i16 * 7) + 3) % prime.p); + let b_canon: [i16; D] = std::array::from_fn(|i| ((i as i16 * 5) + 11) % prime.p); + + let mut school = [0i16; D]; + for (i, &ai) in a_canon.iter().enumerate() { + for (j, &bj) in b_canon.iter().enumerate() { + let prod = (ai as i64 * bj as i64) % p; + let idx = i + j; + if idx < D { + school[idx] = ((school[idx] as i64 + prod) % p) as i16; + } else { + let k = idx - D; + school[k] = ((school[k] as i64 - prod) % p) as i16; + } + } + } + for x in &mut school { + if *x < 0 { + *x = (*x as i64 + p) as i16; + } + } + + let mut a = std::array::from_fn(|i| prime.from_canonical(a_canon[i])); + let mut b = std::array::from_fn(|i| prime.from_canonical(b_canon[i])); + forward_ntt(&mut a, prime, &tw); + forward_ntt(&mut b, prime, &tw); + + let mut c: [_; D] = std::array::from_fn(|i| prime.reduce_range(prime.mul(a[i], b[i]))); + inverse_ntt(&mut c, prime, &tw); + + let got: [i16; D] = std::array::from_fn(|i| prime.to_canonical(prime.normalize(c[i]))); + assert_eq!(got, school); + } + + #[test] + fn negacyclic_ntt_mul_matches_schoolbook_all_q32_primes_d64() { + const D: usize = 64; + let a_canon: [i16; D] = std::array::from_fn(|i| (i as i16 * 7 + 3)); + let b_canon: [i16; D] = std::array::from_fn(|i| (i as i16 * 5 + 11)); + + for (pi, &prime) in Q32_PRIMES.iter().enumerate() { + let tw = NttTwiddles::::compute(prime); + let p = prime.p as i64; + + let a_mod: [i16; D] = + std::array::from_fn(|i| ((a_canon[i] as i64).rem_euclid(p)) as i16); + let b_mod: [i16; D] = + std::array::from_fn(|i| ((b_canon[i] as i64).rem_euclid(p)) as i16); + + let mut school = [0i16; D]; + for (i, &ai) in a_mod.iter().enumerate() { + for (j, &bj) in b_mod.iter().enumerate() { + let prod = (ai as i64 * bj as i64) % p; + let idx = i + j; + if idx < D { + school[idx] = ((school[idx] as i64 + prod) % p) as i16; + } else { + let k = idx - D; + school[k] = ((school[k] as i64 - prod) % p) as i16; + } + } + } + for x in &mut school { + if *x < 0 { + *x = (*x as i64 + p) as i16; + } + } + + let mut a = std::array::from_fn(|i| prime.from_canonical(a_mod[i])); + let mut b = std::array::from_fn(|i| prime.from_canonical(b_mod[i])); + forward_ntt(&mut a, prime, &tw); + forward_ntt(&mut b, prime, &tw); + + let mut c = [MontCoeff::from_raw(0i16); D]; + for i in 0..D { + c[i] = prime.reduce_range(prime.mul(a[i], b[i])); + } + inverse_ntt(&mut c, prime, &tw); + + let got: [i16; D] = std::array::from_fn(|i| prime.to_canonical(prime.normalize(c[i]))); + assert_eq!(got, school, "prime[{pi}] p={} mismatch", prime.p); + } + } + #[test] fn cyclotomic_ntt_crt_round_trip_q32() { type F = Fp64<{ Q32_MODULUS }>; type R = CyclotomicRing; - type N = CyclotomicCrtNtt; + type N = CyclotomicCrtNtt; - let twiddles: [NttTwiddles<64>; Q32_NUM_PRIMES] = - std::array::from_fn(|k| NttTwiddles::<64>::compute(Q32_PRIMES[k])); + let twiddles: [NttTwiddles; Q32_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::compute(Q32_PRIMES[k])); let coeffs: [F; 64] = std::array::from_fn(|i| F::from_u64(((i as u64 * 17) + 5) % Q32_MODULUS)); let ring = R::from_coefficients(coeffs); let ntt = N::from_ring(&ring, &Q32_PRIMES, &twiddles); - let round_trip = ntt.to_ring(&Q32_PRIMES, &twiddles, &Q32_DATA); + let garner = q32_garner(); + let round_trip = ntt.to_ring(&Q32_PRIMES, &twiddles, &garner); assert_eq!(ring, round_trip); } @@ -732,10 +947,10 @@ mod tests { fn cyclotomic_ntt_reduced_ops_are_stable() { type F = Fp64<{ Q32_MODULUS }>; type R = CyclotomicRing; - type N = CyclotomicCrtNtt; + type N = CyclotomicCrtNtt; - let twiddles: [NttTwiddles<64>; Q32_NUM_PRIMES] = - std::array::from_fn(|k| NttTwiddles::<64>::compute(Q32_PRIMES[k])); + let twiddles: [NttTwiddles; Q32_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::compute(Q32_PRIMES[k])); let a = R::from_coefficients(std::array::from_fn(|i| { F::from_u64(((i as u64 * 3) + 1) % Q32_MODULUS) @@ -751,8 +966,9 @@ mod tests { let back = sum.sub_reduced(&ntt_b, &Q32_PRIMES); assert_eq!(back, ntt_a); + let garner = q32_garner(); let zero_ntt = ntt_a.add_reduced(&ntt_a.neg_reduced(&Q32_PRIMES), &Q32_PRIMES); - let zero_ring = zero_ntt.to_ring(&Q32_PRIMES, &twiddles, &Q32_DATA); + let zero_ring = zero_ntt.to_ring(&Q32_PRIMES, &twiddles, &garner); assert_eq!(zero_ring, R::zero()); } @@ -760,10 +976,10 @@ mod tests { fn backend_path_matches_default_scalar_path() { type F = Fp64<{ Q32_MODULUS }>; type R = CyclotomicRing; - type N = CyclotomicCrtNtt; + type N = CyclotomicCrtNtt; - let twiddles: [NttTwiddles<64>; Q32_NUM_PRIMES] = - std::array::from_fn(|k| NttTwiddles::<64>::compute(Q32_PRIMES[k])); + let twiddles: [NttTwiddles; Q32_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::compute(Q32_PRIMES[k])); let ring = R::from_coefficients(std::array::from_fn(|i| { F::from_u64(((i as u64 * 13) + 9) % Q32_MODULUS) })); @@ -773,15 +989,210 @@ mod tests { N::from_ring_with_backend::(&ring, &Q32_PRIMES, &twiddles); assert_eq!(default_ntt, backend_ntt); - let default_back = default_ntt.to_ring(&Q32_PRIMES, &twiddles, &Q32_DATA); - let backend_back = backend_ntt.to_ring_with_backend::( - &Q32_PRIMES, - &twiddles, - &Q32_DATA, - ); + let garner = q32_garner(); + let default_back = default_ntt.to_ring(&Q32_PRIMES, &twiddles, &garner); + let backend_back = + backend_ntt.to_ring_with_backend::(&Q32_PRIMES, &twiddles, &garner); assert_eq!(default_back, backend_back); } + #[test] + fn crt_ntt_mul_matches_schoolbook_q32() { + type F = Fp64<{ Q32_MODULUS }>; + type R = CyclotomicRing; + type N = CyclotomicCrtNtt; + + let twiddles: [NttTwiddles; Q32_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::compute(Q32_PRIMES[k])); + let garner = q32_garner(); + + let a = R::from_coefficients(std::array::from_fn(|i| { + F::from_u64(((i as u64 * 7) + 3) % Q32_MODULUS) + })); + let b = R::from_coefficients(std::array::from_fn(|i| { + F::from_u64(((i as u64 * 5) + 11) % Q32_MODULUS) + })); + + let schoolbook = a * b; + + let ntt_a = N::from_ring(&a, &Q32_PRIMES, &twiddles); + let ntt_b = N::from_ring(&b, &Q32_PRIMES, &twiddles); + let ntt_prod = ntt_a.pointwise_mul(&ntt_b, &Q32_PRIMES); + let ntt_result: R = ntt_prod.to_ring(&Q32_PRIMES, &twiddles, &garner); + + assert_eq!(schoolbook, ntt_result); + } + + #[test] + fn q128_garner_reconstruct_matches_coeffs_no_ntt() { + type F = Fp128<{ Q128_MODULUS }>; + + let primes = q128_primes(); + let garner = q128_garner(); + + let coeffs: [F; 64] = std::array::from_fn(|i| { + if i < 8 { + F::from_u64((i as u64 * 31) + 7) + } else { + F::zero() + } + }); + + let mut canonical = [[0i32; 64]; Q128_NUM_PRIMES]; + for (k, prime) in primes.iter().enumerate() { + let p = prime.p as u32 as u128; + for (i, c) in coeffs.iter().enumerate() { + canonical[k][i] = (c.to_canonical_u128() % p) as i32; + } + } + + let reconstructed: [F; 64] = + >::reconstruct( + &primes, &canonical, &garner, + ); + + assert_eq!(reconstructed, coeffs); + } + + #[test] + fn q128_prime_ntt_round_trip_per_prime() { + let primes = q128_primes(); + let twiddles: [NttTwiddles; Q128_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::compute(primes[k])); + + // Use the same sparse coefficient pattern as q128_ntt_round_trip, but test + // the per-prime NTT+Montgomery machinery in isolation (no Garner/Fp128). + let residues: [u32; 64] = + std::array::from_fn(|i| if i < 8 { (i as u32 * 31) + 7 } else { 0 }); + + for k in 0..Q128_NUM_PRIMES { + let prime = primes[k]; + let mut limb = [MontCoeff::from_raw(0i32); 64]; + for (i, r) in residues.iter().enumerate() { + let reduced = (*r as i64 % (prime.p as i64)) as i32; + limb[i] = >::from_canonical(prime, reduced); + } + + forward_ntt(&mut limb, prime, &twiddles[k]); + inverse_ntt(&mut limb, prime, &twiddles[k]); + + for (i, r) in residues.iter().enumerate() { + let expected = (*r as i64 % (prime.p as i64)) as i32; + let got = >::to_canonical(prime, limb[i]); + assert_eq!(got, expected, "prime idx={k} coeff idx={i}"); + } + } + } + + #[test] + fn q128_ntt_round_trip() { + type F = Fp128<{ Q128_MODULUS }>; + type R = CyclotomicRing; + type N = CyclotomicCrtNtt; + + let primes = q128_primes(); + let twiddles: [NttTwiddles; Q128_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::compute(primes[k])); + let garner = q128_garner(); + + let coeffs: [F; 64] = std::array::from_fn(|i| { + if i < 8 { + F::from_u64((i as u64 * 31) + 7) + } else { + F::zero() + } + }); + let ring = R::from_coefficients(coeffs); + let ntt = N::from_ring(&ring, &primes, &twiddles); + let round_trip: R = ntt.to_ring(&primes, &twiddles, &garner); + + assert_eq!(ring, round_trip); + } + + #[test] + fn crt_ntt_mul_matches_schoolbook_q128() { + type F = Fp128<{ Q128_MODULUS }>; + type R = CyclotomicRing; + type N = CyclotomicCrtNtt; + + let primes = q128_primes(); + let twiddles: [NttTwiddles; Q128_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::compute(primes[k])); + let garner = q128_garner(); + + let a = R::from_coefficients(std::array::from_fn(|i| { + if i < 8 { + F::from_u64((i as u64 * 7) + 3) + } else { + F::zero() + } + })); + let b = R::from_coefficients(std::array::from_fn(|i| { + if i < 8 { + F::from_u64((i as u64 * 9) + 11) + } else { + F::zero() + } + })); + + let schoolbook = a * b; + + let ntt_a = N::from_ring(&a, &primes, &twiddles); + let ntt_b = N::from_ring(&b, &primes, &twiddles); + let ntt_prod = ntt_a.pointwise_mul(&ntt_b, &primes); + let ntt_result: R = ntt_prod.to_ring(&primes, &twiddles, &garner); + + assert_eq!(schoolbook, ntt_result); + } + + #[test] + fn q64_ntt_round_trip() { + type F = Fp64<{ Q64_MODULUS }>; + type R = CyclotomicRing; + type N = CyclotomicCrtNtt; + + let primes = q64_primes(); + let twiddles: [NttTwiddles; Q64_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::compute(primes[k])); + let garner = q64_garner(); + + let coeffs: [F; 64] = + std::array::from_fn(|i| F::from_u64(((i as u64 * 19) + 3) % Q64_MODULUS)); + let ring = R::from_coefficients(coeffs); + let ntt = N::from_ring(&ring, &primes, &twiddles); + let round_trip: R = ntt.to_ring(&primes, &twiddles, &garner); + + assert_eq!(ring, round_trip); + } + + #[test] + fn crt_ntt_mul_matches_schoolbook_q64() { + type F = Fp64<{ Q64_MODULUS }>; + type R = CyclotomicRing; + type N = CyclotomicCrtNtt; + + let primes = q64_primes(); + let twiddles: [NttTwiddles; Q64_NUM_PRIMES] = + std::array::from_fn(|k| NttTwiddles::compute(primes[k])); + let garner = q64_garner(); + + let a = R::from_coefficients(std::array::from_fn(|i| { + F::from_u64(((i as u64 * 5) + 9) % Q64_MODULUS) + })); + let b = R::from_coefficients(std::array::from_fn(|i| { + F::from_u64(((i as u64 * 17) + 13) % Q64_MODULUS) + })); + + let schoolbook = a * b; + + let ntt_a = N::from_ring(&a, &primes, &twiddles); + let ntt_b = N::from_ring(&b, &primes, &twiddles); + let ntt_prod = ntt_a.pointwise_mul(&ntt_b, &primes); + let ntt_result: R = ntt_prod.to_ring(&primes, &twiddles, &garner); + + assert_eq!(schoolbook, ntt_result); + } + #[test] fn field_sampling_respects_modulus() { type F = Fp32<251>; diff --git a/tests/commitment_contract.rs b/tests/commitment_contract.rs index dc300613..4aaf3822 100644 --- a/tests/commitment_contract.rs +++ b/tests/commitment_contract.rs @@ -6,7 +6,7 @@ use hachi_pcs::protocol::transcript::labels; use hachi_pcs::protocol::{ AppendToTranscript, Blake2bTranscript, CommitmentScheme, StreamingCommitmentScheme, Transcript, }; -use hachi_pcs::{CanonicalField, FieldCore, HachiError, Polynomial}; +use hachi_pcs::{CanonicalField, FieldCore, FromSmallInt, HachiError, Polynomial}; type F = Fp64<4294967197>; diff --git a/tests/hachi_sumcheck.rs b/tests/hachi_sumcheck.rs index 86b843f0..ce33b91b 100644 --- a/tests/hachi_sumcheck.rs +++ b/tests/hachi_sumcheck.rs @@ -10,7 +10,7 @@ use hachi_pcs::protocol::sumcheck::relation_sumcheck::{ use hachi_pcs::protocol::sumcheck::{multilinear_eval, range_check_eval}; use hachi_pcs::protocol::transcript::labels; use hachi_pcs::protocol::{prove_sumcheck, verify_sumcheck, Blake2bTranscript, Transcript}; -use hachi_pcs::{CanonicalField, FieldCore, FieldSampling}; +use hachi_pcs::{FieldCore, FieldSampling, FromSmallInt}; use rand::rngs::StdRng; use rand::SeedableRng; use std::time::Instant; @@ -38,10 +38,9 @@ fn run_f0_e2e(num_u: usize, num_l: usize, b: usize) { // Sanity: prover's final claim matches oracle evaluation. let oracle = EqPolynomial::mle(&tau0, &prover_challenges) - * range_check_eval(multilinear_eval(&w_evals, &prover_challenges), b); + * range_check_eval(multilinear_eval(&w_evals, &prover_challenges).unwrap(), b); assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); - // ---- Verifier ---- let t1 = Instant::now(); let verifier = NormSumcheckVerifier::new(tau0, w_evals, b); let mut vt = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); @@ -147,9 +146,9 @@ fn run_f_alpha_e2e(num_u: usize, num_i: usize) { // Sanity: prover's final claim matches oracle evaluation. let (x_ch, y_ch) = prover_challenges.split_at(num_u); - let oracle = multilinear_eval(&w_evals, &prover_challenges) - * multilinear_eval(&alpha_evals_y, y_ch) - * multilinear_eval(&m_evals_x, x_ch); + let oracle = multilinear_eval(&w_evals, &prover_challenges).unwrap() + * multilinear_eval(&alpha_evals_y, y_ch).unwrap() + * multilinear_eval(&m_evals_x, x_ch).unwrap(); assert_eq!(final_claim, oracle, "prover final claim != oracle eval"); let t1 = Instant::now(); diff --git a/tests/onehot_commitment.rs b/tests/onehot_commitment.rs index f338f266..e3f6c109 100644 --- a/tests/onehot_commitment.rs +++ b/tests/onehot_commitment.rs @@ -1,8 +1,9 @@ #![allow(missing_docs)] +use hachi_pcs::algebra::CyclotomicRing; use hachi_pcs::protocol::commitment::{HachiCommitmentCore, RingCommitmentScheme}; use hachi_pcs::test_utils::*; -use hachi_pcs::{CanonicalField, FieldCore}; +use hachi_pcs::{FieldCore, FromSmallInt}; type Core = HachiCommitmentCore; @@ -18,12 +19,16 @@ fn psetup() -> >::ProverSetup { /// `commit_coeffs`. The optimized impl uses sparse inner Ajtai. /// Both must produce identical (commitment, s_all, t_hat_all). fn assert_onehot_matches_dense(onehot_k: usize, indices: &[usize]) { + let opt_indices: Vec> = indices.iter().map(|&i| Some(i)).collect(); let setup = psetup(); // Optimized sparse path. - let (c_sparse, s_sparse, t_sparse) = - >::commit_onehot(onehot_k, indices, &setup) - .unwrap(); + let w_sparse = >::commit_onehot( + onehot_k, + &opt_indices, + &setup, + ) + .unwrap(); // Reference: materialize the full one-hot vector, pack into ring elements, // and commit via the dense path. @@ -33,20 +38,22 @@ fn assert_onehot_matches_dense(onehot_k: usize, indices: &[usize]) { for (c, &idx) in indices.iter().enumerate() { field_elems[c * onehot_k + idx] = F::from_u64(1); } - let ring_coeffs: Vec> = (0..total_ring) + let ring_coeffs: Vec> = (0..total_ring) .map(|r| { let coeffs: [F; D] = std::array::from_fn(|i| field_elems[r * D + i]); - hachi_pcs::algebra::CyclotomicRing::from_coefficients(coeffs) + CyclotomicRing::from_coefficients(coeffs) }) .collect(); - let (c_dense, s_dense, t_dense) = + let w_dense = >::commit_coeffs(&ring_coeffs, &setup) .unwrap(); - assert_eq!(c_sparse, c_dense, "commitments must match"); - assert_eq!(s_sparse, s_dense, "s_all (decomposed witness) must match"); assert_eq!( - t_sparse, t_dense, + w_sparse.commitment, w_dense.commitment, + "commitments must match" + ); + assert_eq!( + w_sparse.t_hat, w_dense.t_hat, "t_hat_all (decomposed inner output) must match" ); } @@ -124,22 +131,28 @@ fn onehot_k_lt_d_ratio_2() { fn onehot_rejects_non_divisible_k_and_d() { let setup = psetup(); let result = - >::commit_onehot(17, &[0; 4], &setup); + >::commit_onehot(17, &[Some(0); 4], &setup); assert!(result.is_err()); } #[test] fn onehot_rejects_out_of_range_index() { let setup = psetup(); - let result = - >::commit_onehot(64, &[0, 64, 0, 0], &setup); + let result = >::commit_onehot( + 64, + &[Some(0), Some(64), Some(0), Some(0)], + &setup, + ); assert!(result.is_err()); } #[test] fn onehot_rejects_wrong_total_size() { let setup = psetup(); - let result = - >::commit_onehot(64, &[0, 0, 0], &setup); + let result = >::commit_onehot( + 64, + &[Some(0), Some(0), Some(0)], + &setup, + ); assert!(result.is_err()); } diff --git a/tests/ring_commitment_core.rs b/tests/ring_commitment_core.rs index 2fa20bee..4b09501e 100644 --- a/tests/ring_commitment_core.rs +++ b/tests/ring_commitment_core.rs @@ -3,7 +3,8 @@ use hachi_pcs::algebra::CyclotomicRing; use hachi_pcs::error::HachiError; use hachi_pcs::protocol::commitment::{ - CommitmentConfig, DefaultCommitmentConfig, HachiCommitmentCore, RingCommitmentScheme, + CommitmentConfig, HachiCommitmentCore, HachiCommitmentLayout, RingCommitmentScheme, + SmallTestCommitmentConfig, }; use hachi_pcs::test_utils::*; @@ -12,16 +13,17 @@ struct BadDegreeConfig; impl CommitmentConfig for BadDegreeConfig { const D: usize = 32; - const M: usize = 4; - const R: usize = 2; const N_A: usize = 8; const N_B: usize = 4; const N_D: usize = 4; const LOG_BASIS: u32 = 4; const DELTA: usize = 8; const TAU: usize = 4; - const BETA: u128 = 1_000_000; const CHALLENGE_WEIGHT: usize = 3; + + fn commitment_layout(_max_num_vars: usize) -> Result { + HachiCommitmentLayout::new::(4, 2) + } } #[derive(Clone)] @@ -29,16 +31,17 @@ struct BadDigitBudgetConfig; impl CommitmentConfig for BadDigitBudgetConfig { const D: usize = 64; - const M: usize = 4; - const R: usize = 2; const N_A: usize = 8; const N_B: usize = 4; const N_D: usize = 4; const LOG_BASIS: u32 = 32; const DELTA: usize = 5; // 160 > 128 const TAU: usize = 4; - const BETA: u128 = 1_000_000; const CHALLENGE_WEIGHT: usize = 3; + + fn commitment_layout(_max_num_vars: usize) -> Result { + HachiCommitmentLayout::new::(4, 2) + } } #[test] @@ -48,16 +51,19 @@ fn setup_shape_is_consistent() { let (p2, v2) = >::setup(16).unwrap(); - assert_eq!(p1.max_num_vars, 16); - assert_eq!(v1.max_num_vars, 16); - assert_eq!(p2.max_num_vars, 16); - assert_eq!(v2.max_num_vars, 16); - assert_eq!(p1.A.len(), TinyConfig::N_A); - assert_eq!(p1.A[0].len(), (1usize << TinyConfig::M) * TinyConfig::DELTA); - assert_eq!(p1.B.len(), TinyConfig::N_B); + assert_eq!(p1.expanded.seed.max_num_vars, 16); + assert_eq!(v1.expanded.seed.max_num_vars, 16); + assert_eq!(p2.expanded.seed.max_num_vars, 16); + assert_eq!(v2.expanded.seed.max_num_vars, 16); + assert_eq!(p1.expanded.A.len(), TinyConfig::N_A); assert_eq!( - p1.B[0].len(), - TinyConfig::N_A * TinyConfig::DELTA * (1usize << TinyConfig::R) + p1.expanded.A[0].len(), + hachi_pcs::test_utils::BLOCK_LEN * TinyConfig::DELTA + ); + assert_eq!(p1.expanded.B.len(), TinyConfig::N_B); + assert_eq!( + p1.expanded.B[0].len(), + TinyConfig::N_A * TinyConfig::DELTA * hachi_pcs::test_utils::NUM_BLOCKS ); } @@ -67,28 +73,23 @@ fn commit_is_deterministic_and_shape_consistent() { >::setup(16).unwrap(); let blocks = sample_blocks(); - let (c1, s1, t1) = - >::commit_ring_blocks( - &blocks, &psetup, - ) - .unwrap(); - let (c2, s2, t2) = - >::commit_ring_blocks( - &blocks, &psetup, - ) - .unwrap(); - - assert_eq!(c1, c2); - assert_eq!(s1, s2); - assert_eq!(t1, t2); - - let num_blocks = 1usize << TinyConfig::R; - let block_len = 1usize << TinyConfig::M; - assert_eq!(c1.u.len(), TinyConfig::N_B); - assert_eq!(s1.len(), num_blocks); - assert_eq!(t1.len(), num_blocks); - assert!(s1.iter().all(|s| s.len() == block_len * TinyConfig::DELTA)); - assert!(t1 + let w1 = >::commit_ring_blocks( + &blocks, &psetup, + ) + .unwrap(); + let w2 = >::commit_ring_blocks( + &blocks, &psetup, + ) + .unwrap(); + + assert_eq!(w1.commitment, w2.commitment); + assert_eq!(w1.t_hat, w2.t_hat); + + let num_blocks = hachi_pcs::test_utils::NUM_BLOCKS; + assert_eq!(w1.commitment.u.len(), TinyConfig::N_B); + assert_eq!(w1.t_hat.len(), num_blocks); + assert!(w1 + .t_hat .iter() .all(|t| t.len() == TinyConfig::N_A * TinyConfig::DELTA)); } @@ -99,30 +100,24 @@ fn commit_ring_coeffs_matches_block_commitment() { >::setup(16).unwrap(); let blocks = sample_blocks(); - let (c_blocks, s_blocks, t_blocks) = - >::commit_ring_blocks( - &blocks, &psetup, - ) - .unwrap(); - - let num_blocks = 1usize << TinyConfig::R; - let block_len = 1usize << TinyConfig::M; - let mut f_coeffs = Vec::with_capacity(num_blocks * block_len); - for j in 0..block_len { - for block in blocks.iter().take(num_blocks) { - f_coeffs.push(block[j]); - } - } + let wb = >::commit_ring_blocks( + &blocks, &psetup, + ) + .unwrap(); + + // Sequential layout: block 0 elements, then block 1 elements, etc. + let f_coeffs: Vec<_> = blocks + .iter() + .flat_map(|block| block.iter().copied()) + .collect(); - let (c_coeffs, s_coeffs, t_coeffs) = - >::commit_coeffs( - &f_coeffs, &psetup, - ) - .unwrap(); + let wc = >::commit_coeffs( + &f_coeffs, &psetup, + ) + .unwrap(); - assert_eq!(c_blocks, c_coeffs); - assert_eq!(s_blocks, s_coeffs); - assert_eq!(t_blocks, t_coeffs); + assert_eq!(wb.commitment, wc.commitment); + assert_eq!(wb.t_hat, wc.t_hat); } #[test] @@ -130,36 +125,44 @@ fn opening_satisfies_inner_and_outer_equations() { let (psetup, _) = >::setup(16).unwrap(); let blocks = sample_blocks(); - let (commitment, s, t_hat) = - >::commit_ring_blocks( - &blocks, &psetup, - ) - .unwrap(); - - for i in 0..s.len() { - let lhs = mat_vec_mul(&psetup.A, &s[i]); + let w = >::commit_ring_blocks( + &blocks, &psetup, + ) + .unwrap(); + + for (i, block) in blocks.iter().enumerate() { + let s_i = hachi_pcs::protocol::commitment::utils::linear::decompose_block( + block, + TinyConfig::DELTA, + TinyConfig::LOG_BASIS, + ); + let lhs = mat_vec_mul(&psetup.expanded.A, &s_i); let rhs: Vec> = (0..TinyConfig::N_A) .map(|j| { let start = j * TinyConfig::DELTA; let end = start + TinyConfig::DELTA; - CyclotomicRing::gadget_recompose_pow2(&t_hat[i][start..end], TinyConfig::LOG_BASIS) + CyclotomicRing::gadget_recompose_pow2( + &w.t_hat[i][start..end], + TinyConfig::LOG_BASIS, + ) }) .collect(); assert_eq!(lhs, rhs); } let t_hat_flat: Vec> = - t_hat.iter().flat_map(|x| x.iter().copied()).collect(); - let outer = mat_vec_mul(&psetup.B, &t_hat_flat); - assert_eq!(outer, commitment.u); + w.t_hat.iter().flat_map(|x| x.iter().copied()).collect(); + let outer = mat_vec_mul(&psetup.expanded.B, &t_hat_flat); + assert_eq!(outer, w.commitment.u); } #[test] -fn default_config_has_expected_shape() { - assert_eq!(DefaultCommitmentConfig::D, 16); - assert_eq!(1usize << DefaultCommitmentConfig::M, 16); - assert_eq!(1usize << DefaultCommitmentConfig::R, 4); - let delta = DefaultCommitmentConfig::DELTA; +fn small_test_config_has_expected_shape() { + assert_eq!(SmallTestCommitmentConfig::D, 16); + let layout = SmallTestCommitmentConfig::commitment_layout(8).unwrap(); + assert_eq!(layout.block_len, 16); + assert_eq!(layout.num_blocks, 4); + let delta = SmallTestCommitmentConfig::DELTA; assert!(delta > 0); } diff --git a/tests/sparse_challenge.rs b/tests/sparse_challenge.rs index 16eb8ee4..baba7bd3 100644 --- a/tests/sparse_challenge.rs +++ b/tests/sparse_challenge.rs @@ -6,7 +6,7 @@ use hachi_pcs::algebra::Fp64; use hachi_pcs::protocol::challenges::sparse::sparse_challenge_from_transcript; use hachi_pcs::protocol::transcript::labels::DOMAIN_HACHI_PROTOCOL; use hachi_pcs::protocol::transcript::{Blake2bTranscript, Transcript}; -use hachi_pcs::{CanonicalField, FieldCore}; +use hachi_pcs::{FieldCore, FromSmallInt}; type F = Fp64<4294967197>; diff --git a/tests/sumcheck_core.rs b/tests/sumcheck_core.rs index a9c58f28..dcd6486f 100644 --- a/tests/sumcheck_core.rs +++ b/tests/sumcheck_core.rs @@ -2,13 +2,15 @@ use std::time::Instant; +use hachi_pcs::algebra::poly::multilinear_eval; use hachi_pcs::algebra::Fp64; +use hachi_pcs::error::HachiError; use hachi_pcs::protocol::transcript::labels; use hachi_pcs::protocol::{ prove_sumcheck, verify_sumcheck, Blake2bTranscript, CompressedUniPoly, SumcheckInstanceProver, SumcheckInstanceVerifier, SumcheckProof, Transcript, UniPoly, }; -use hachi_pcs::{CanonicalField, FieldCore, FieldSampling}; +use hachi_pcs::{FieldCore, FieldSampling, FromSmallInt}; use rand::rngs::StdRng; use rand::RngCore; use rand::SeedableRng; @@ -86,21 +88,6 @@ fn sumcheck_proof_verifier_driver_is_transcript_deterministic() { assert_eq!(final_claim_1, claim); } -/// Evaluate a multilinear polynomial (given by its boolean-hypercube evaluations -/// in little-endian bit order) at an arbitrary point via iterated folding. -fn multilinear_eval(evals: &[E], point: &[E]) -> E { - let mut current = evals.to_vec(); - for r in point { - let half = current.len() / 2; - let mut next = Vec::with_capacity(half); - for i in 0..half { - next.push(current[2 * i] + *r * (current[2 * i + 1] - current[2 * i])); - } - current = next; - } - current[0] -} - struct DenseSumcheckProver { evals: Vec, num_vars: usize, @@ -127,7 +114,6 @@ impl SumcheckInstanceProver for DenseSumcheckProver { eval_0 = eval_0 + self.evals[2 * i]; eval_1 = eval_1 + self.evals[2 * i + 1]; } - // g(X) = eval_0 + (eval_1 - eval_0) * X (degree 1) UniPoly::from_coeffs(vec![eval_0, eval_1 - eval_0]) } @@ -160,7 +146,7 @@ impl SumcheckInstanceVerifier for DenseSumcheckVerifier { self.claim } - fn expected_output_claim(&self, challenges: &[E]) -> E { + fn expected_output_claim(&self, challenges: &[E]) -> Result { multilinear_eval(&self.evals, challenges) } } @@ -273,7 +259,7 @@ fn e2e_sumcheck_2_pow_20() { assert_eq!(proof.round_polys.len(), num_vars); // Sanity: final claim must equal f evaluated at the challenge point. - let oracle_eval = multilinear_eval(&evals, &prover_challenges); + let oracle_eval = multilinear_eval(&evals, &prover_challenges).unwrap(); assert_eq!(final_claim, oracle_eval); let t1 = Instant::now(); diff --git a/tests/sumcheck_prover_driver.rs b/tests/sumcheck_prover_driver.rs index d309a36d..7ef3ebae 100644 --- a/tests/sumcheck_prover_driver.rs +++ b/tests/sumcheck_prover_driver.rs @@ -47,7 +47,6 @@ impl SumcheckInstanceProver for DenseTableSumcheck { s0 = s0 + self.table[i << 1]; s1 = s1 + self.table[(i << 1) | 1]; } - // g(X) = s0 + (s1 - s0) X UniPoly::from_coeffs(vec![s0, s1 - s0]) } From d5cae31387e4aeea8310fe77060970c40a7521cf Mon Sep 17 00:00:00 2001 From: Quang Dao Date: Tue, 3 Mar 2026 22:00:04 -0800 Subject: [PATCH 4/5] =?UTF-8?q?perf:=20optimize=20proving=20pipeline=20?= =?UTF-8?q?=E2=80=94=20multi-level=20folding,=20i8=20digit=20pipeline,=20N?= =?UTF-8?q?TT=20acceleration=20(#5)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * perf: parallelize commit phase and reduce allocations - Add block-level parallelism to commit_ring_blocks, commit_coeffs, commit_onehot, and commit_mixed via cfg_iter!/cfg_into_iter! - Parallelize vector-to-NTT conversion in mat_vec_mul_precomputed_with_params - Cache CRT+NTT params inside NttMatrixCache, eliminating redundant select_crt_ntt_params calls on every mat-vec multiply - Add balanced_decompose_pow2_into for in-place decomposition, removing per-element Vec allocations in decompose_block/decompose_rows - Add inner_ajtai_onehot_t_only that skips the 16MB s-vector allocation when the caller discards it (commit_onehot, commit_mixed) - Add one-hot and mixed commitment benchmarks to hachi_e2e Made-with: Cursor * chore: remove stale #[allow(non_snake_case)] from setup structs HachiSetupSeed, HachiProverSetup, and HachiVerifierSetup have no uppercase fields — the allows were left over from earlier refactors. Made-with: Cursor * perf: hoist decomposition params to runtime, reduce allocations and cloning Pre-existing change: - Remove rows/cols from matrix domain separator so A matrix is reusable across poly/mega-poly layouts with the same m_vars. New changes: Move delta/tau/log_basis from CommitmentConfig associated constants into HachiCommitmentLayout runtime fields. This decouples decomposition parameters from the config type, allowing them to vary at runtime without monomorphization. All ~50 call sites updated. Eliminate redundant work in the prover hot path: - Flatten w_hat once and reuse in both compute_v and compute_r_split_eq (was flattened separately in each). - Stream z_hat decomposition directly in build_w_coeffs instead of collecting into a temporary Vec. - Skip the unused w.to_vec() clone in ring_switch_verifier output. - Take ownership of ring_opening_point and hint in QuadraticEquation constructors instead of cloning. Reduce stack pressure for large ring elements (8KB at D=512, Fp128): - Add CyclotomicRing::from_slice() to avoid std::array::from_fn intermediaries that create 8KB stack temporaries. - Replace from_fn patterns in process_chunk, reduce_coeffs_to_ring_elements, commit_w, and compute_r_split_eq. Made-with: Cursor * feat: flexible decomposition depth and dual basis mode Move DELTA/TAU/LOG_BASIS out of CommitmentConfig into runtime DecompositionParams (log_basis, log_coeff_bound). Delta and tau are now auto-derived from the coefficient bound, so small-coefficient polynomials (0/1, already range-checked) get proportionally cheaper commitments. Add BasisMode enum (Lagrange / Monomial) as a prove/verify-time parameter. Commitment is basis-agnostic; the mode only changes the tensor-product weights in the opening relation. Made-with: Cursor * fix compute m a streaming to not need padding * refactor: unify polynomial API via HachiPolyOps trait, remove dead code, fix config validation HachiPolyOps trait and implementations: - Add HachiPolyOps trait with 4 operation methods (evaluate_ring, fold_blocks, decompose_fold, commit_inner) replacing raw coefficient access - Add DensePoly for dense ring coefficient vectors - Add OneHotPoly for sparse one-hot polynomials with optimized ops CommitmentScheme refactor: - Parameterize CommitmentScheme (was CommitmentScheme) - Generic commit/prove over P: HachiPolyOps - Rename OpeningProofHint to CommitHint, remove Option wrapper from prove - Remove batch_commit, combine_commitments, combine_hints - Remove StreamingCommitmentScheme trait, HachiChunkState, process_chunk* Dead code removal: - Delete MegaPolyBlock enum and commit_mixed method - Delete inner_ajtai_onehot (keep _t_only variant) - Delete Polynomial trait, MultilinearLagrange trait - Delete DenseMultilinearEvals and multilinear_evals module - Remove all unnecessary #[allow(...)] attributes Proof simplification: - Remove ring_coeffs from HachiCommitmentHint (only t_hat remains) - Update quadratic_equation to use HachiPolyOps methods Config fix: - Remove overly strict delta*log_basis > 128 check in config.rs; balanced_decompose_pow2 already enforces the correct bound (levels*log_basis <= 128+log_basis) Documentation: - Add docs to all public items in test_utils and packed_ext - Remove #[allow(missing_docs)] from parallel, test_utils, packed_ext modules Made-with: Cursor * fix: remove test for deleted delta*log_basis validation The setup_rejects_invalid_digit_budget test asserted the overly strict delta*log_basis > 128 check that was intentionally removed in the previous commit. Delete the test and its BadDigitBudgetConfig. Made-with: Cursor * style: fix formatting in ring_commitment_core.rs Made-with: Cursor * perf: parallelize proving hot paths, eliminate per-proof w-commitment setup Parallelize the three proving bottlenecks (quad_eq, ring_switch, sumcheck) and remove the per-proof matrix generation in commit_w by reusing the main NTT cache. Proving hot-path parallelism: - Parallelize round-0 norm and relation sumcheck via cfg_fold_reduce! macro - Parallelize DensePoly::decompose_fold with parallel fold-reduce over blocks - Parallelize fold_evals_in_place and build_w_evals_compact with cfg_into_iter! - Add cfg_fold_reduce! macro to unify parallel/sequential fold-reduce patterns - Unify compute_round_{norm,relation}_{compact,full} into single generic fns Sumcheck micro-optimizations: - Unroll 3-point relation evaluation to avoid redundant from_u64 conversions and multiply-by-zero/one at evaluation points 0 and 1 - Hoist gadget_recompose_pow2 out of per-row loop in compute_r_split_eq Eliminate per-proof w-commitment setup: - Add w_ring_element_count() and w_commitment_layout() helpers to compute w-commitment matrix dimensions from the main layout - Widen A/B matrices at setup time to max(main, w) column counts so the main NTT cache always covers the w-commitment (required when delta_commit=1, e.g. boolean polynomials) - Rewrite commit_w to take &NttMatrixCache directly, inlining the commit logic with flat_map instead of intermediate Vec> - Remove w_setup field from HachiProverSetup - Add ensure_matrix_shape_ge for >= column checks on widened matrices Naming cleanup: - Rename delta -> num_digits_commit, tau -> num_digits_fold, log_coeff_bound -> log_commit_bound throughout - Add log_open_bound to DecompositionParams for recursive w commitments - Hoist fully qualified paths (std::ops, std::mem, std::iter, crate::protocol::ring_switch::w_commitment_layout) to use statements Made-with: Cursor * perf: profile and accelerate opening proof hot paths Replace D/B-row schoolbook quotient extraction with an NTT-based unreduced quotient path and add targeted tracing spans/timers plus a Perfetto profile example so prover bottlenecks are visible and cheaper to iterate on. Temporarily force the point-eval norm kernel to isolate fused-sumcheck behavior during profiling. Made-with: Cursor * perf: NTT-accelerate A-rows, reduce basis 16→8, fix saturation bug Three optimizations to the proving pipeline: 1. NTT-accelerate A-rows in compute_r_split_eq: use unreduced_quotient_rows_ntt_cached for A*z_pre (O(D log D) instead of O(D^2) schoolbook). Also exploit sparse challenge structure in add_sparse_ring_product (O(weight*D) instead of O(D^2)). 2. Reduce decomposition basis from 16 to 8 (log_basis 4→3): halves the norm sumcheck range-check polynomial degree from 31 to 15, yielding ~4x speedup on the dominant prove-time bottleneck. Soundness is strictly improved (smaller MSIS norm bound). 3. Fix u128 saturation bug in compute_num_digits and r_decomp_levels that caused an incorrect extra decomposition level when b^levels overflows u128. Skip the balanced-range check when levels*log_basis > log_bound, since the digit range is mathematically guaranteed sufficient for b >= 4. Also: replace hardcoded LOG_BASIS const with log_basis() function derived from TinyConfig, fuse decompose+sparse-mul in decompose_fold to i32 arithmetic, and add balanced_decompose_pow2_i8 variant. Net result: prove time 4.76s → 1.57s (3.0x speedup) at num_vars=19. Made-with: Cursor * perf: i8 digit pipeline for w_hat — bypass Fp128 for small decomposed digits Store w_hat/w_hat_flat as [i8; D] instead of CyclotomicRing, eliminating redundant field arithmetic on values in [-b/2, b/2). - Add balanced_decompose_pow2_i8 and gadget_recompose_pow2_i8 - Add CyclotomicCrtNtt::from_i8_with_params / from_i8_cyclic for direct i8 → CRT+NTT conversion (skips Fp128 centering) - Add mat_vec_mul_ntt_cached_i8 and unreduced_quotient_rows_ntt_cached_i8 - Change QuadraticEquation w_hat/w_hat_flat types + all consumers - Simplify build_w_coeffs to write i8 digits directly as field elements Made-with: Cursor * perf(poly): optimize range_check_eval and fold_evals_in_place range_check_eval: precompute w² and use (w²−k²) instead of (w−k)(w+k), saving one multiply per factor. fold_evals_in_place: fold in-place with truncate() instead of allocating a new Vec, removing the rayon dependency from this function. Made-with: Cursor * refactor(sumcheck): centralize and optimize norm sumcheck computation Extract duplicated norm round polynomial logic from NormSumcheckProver and HachiSumcheckProver into shared compute_norm_round_poly() and compute_norm_round_poly_compact() functions. Optimizations: - Flat contiguous storage for RangeAffinePrecomp (coeff_mix_flat + row_offsets) - Precomputed small-integer LUT (h_i(w_0)) for round-0 compact accumulation - Native i128 range-check evaluation path for b <= 10 - Precomputed squared offsets in PointEvalPrecomp - Make choose_round_kernel public with env var override and b-threshold dispatch Made-with: Cursor * feat(protocol): multi-level recursive folding proof Replace single-shot proof with recursive multi-level folding. Instead of sending the full w vector after one round of quad_eq → ring_switch → sumcheck, the prover now recursively commits to w and opens it via the same protocol until w is small enough to send directly. Key changes: - HachiProof now holds Vec + final_w instead of flat fields - Remove SumcheckAux; each level carries a w_eval claim instead - Extract prove_one_level / verify_one_level from monolithic prove/verify - Folding stops via should_stop_folding heuristic (MIN_W_LEN_FOR_FOLDING, MIN_SHRINK_RATIO) - QuadraticEquation takes explicit layout parameter for per-level configs - ring_switch exports WCommitmentConfig for recursive w-openings - D matrix widened to max(layout, w_layout) for shared setup - HachiSumcheckVerifier gains w_val_override for intermediate levels Made-with: Cursor * chore(examples): update profile example for multi-level proofs and A/B kernel testing - Extract run_prove() helper for reuse across kernel configs - Add A/B test mode (HACHI_AB_TEST=1) to compare affine_coeff vs point_eval - Update layout from (6,4) to (8,8) - Report multi-level proof stats (levels, final_w length, proof size) - Set 64 MiB rayon stack size Made-with: Cursor * style: remove section banners and hoist mid-function use statement - Remove redundant section banner comments in proof.rs and commitment_scheme.rs - Move choose_round_kernel import from function body to top-level in hachi_sumcheck.rs Made-with: Cursor * perf(algebra): use bitwise ops for balanced digit decomposition Replace rem_euclid(b) with bitwise AND and division with right shift in CyclotomicRing digit decomposition (decompose_balanced, decompose_balanced_digit_planes, decompose_balanced_i8) and DensePoly commit_with_setup. Valid since b is always a power of two. Made-with: Cursor * perf: store t_hat as i8 digit planes, cache w_folded to skip recompose Switch t_hat storage from Vec>> to Vec> throughout the commitment and proving pipeline. Decomposed digits are bounded by log_basis (typically 3), so i8 is sufficient and avoids carrying full field-element ring elements through commit, ring-switch, and serialization. Key changes: - CommitWitness and HachiCommitmentHint now hold [i8; D] digit planes - New i8 variants: decompose_block_i8, decompose_rows_i8, mat_vec_mul_ntt_cached_i8, gadget_recompose_pow2_i8 - HachiPolyOps::commit_blocks returns [i8; D] digit planes - QuadraticEquation caches w_folded (pre-decomposition folded ring elements) so compute_r_split_eq avoids a gadget_recompose roundtrip - Precomputed idx/sign lookup tables for sparse challenge multiplication - Custom i8 serialization for HachiCommitmentHint - Remove bogus debug_assert constraining ring degree D<=128 in build_w_evals_compact (was checking log2(D) but message said log_basis) Made-with: Cursor * perf: optimize hot paths in commit/prove pipeline - Hoist NTT conversions out of per-row quotient loops (crt_ntt, linear) - Precompute c_alpha in compute_m_a_streaming (quadratic_equation) - Compact alpha/m tables with variable-specific folding (sumcheck) - Eliminate t_hat_flat rematerialization and zero_t_hat clones (commit, ring_switch, hachi_poly_ops) - Merge duplicate w-eval passes (ring_switch, commitment_scheme) - Clean up fully qualified paths (linear, relation_sumcheck, hachi_poly_ops) Made-with: Cursor * feat(algebra): add wide unreduced accumulators and fused shift-accumulate Add Fp32x2i32, Fp64x4i32, Fp128x8i32 types that split field elements into 16-bit limbs in i32 slots for carry-free SIMD-friendly addition. Overflow budget ~32k signed adds before reduction. Add shift_accumulate_into / shift_sub_into / mul_by_monomial_sum_into on CyclotomicRing for fused negacyclic shift + accumulate without temporary ring allocations. Make field offset constants C public. Made-with: Cursor * refactor(protocol): per-matrix NttSlotCache, fused one-hot commit, bench stack fix Replace monolithic NttMatrixCache with per-matrix NttSlotCache, removing HachiPreparedSetup and MatrixSlot enum. HachiProverSetup now holds three independent NttSlotCache instances (A, B, D). Simplify dispatch macros in linear.rs to operate on a single slot. Add CommitCache associated type to HachiPolyOps trait. Wire one-hot commit path to use fused mul_by_monomial_sum_into, eliminating temporary allocations. Fix pre-existing benchmark stack overflow by configuring rayon with a 64MB thread stack (matching examples/profile.rs). Made-with: Cursor * feat(commit): column-tiled A matvec for cache-efficient commitment Add mat_vec_mul_ntt_tiled_i8 and mat_vec_mul_ntt_tiled_single_i8 that tile the NTT matrix columns into L2-sized chunks (~400 cols). Each rayon thread owns one tile and iterates over all blocks, so the matrix is loaded from DRAM exactly once. Ring coefficients are decomposed on-the-fly per tile to avoid full digit materialization. All call sites (commit, commit_coeffs, commit_onehot, ring_switch, quadratic_equation, HachiPolyOps::commit_inner) updated to use the tiled API. Reduces total DRAM traffic ~25x for large traces. Made-with: Cursor * refactor: promote TWO_INV and ZERO to const associated items on FieldCore Hoists two_inv from a trait method to a compile-time constant, and adds const ZERO so extension fields (Fp2, Fp4) can build their TWO_INV without runtime calls. Deduplicates CrtNttParamSet computation across A/B/D caches. Made-with: Cursor * refactor: remove two_inv parameters now that TWO_INV is a const Functions and macros no longer thread two_inv through call chains; they reference F::TWO_INV directly. Also removes the runtime computation in batched_sumcheck. Made-with: Cursor * feat(commit): stub HachiSerialize for HachiProverSetup Add Valid + HachiSerialize impls for HachiProverSetup that return an error on serialize (NTT caches are runtime artifacts). Needed by downstream wrappers that require the trait bound. Made-with: Cursor * perf: fuse hot loops, eliminate allocations, cheaper CRT reduction - mul_by_sparse: use shift_accumulate_into/shift_sub_into for ±1 coeffs - inverse NTT: fuse d_inv and psi_inv trailing passes into one loop - CRT conversion: replace __modti3 (i128 % i128) with split i64 arithmetic - Fp128 sqr_raw: 3 widening muls instead of 4 via squaring symmetry - decompose_block_i8: add _into variant, reuse buffer across tiles - sumcheck: fuse norm+relation into single pass over w_table - ring_switch: fuse expand_m_a+build_m_evals_x, rayon::join parallel phases - ring_switch: build_w_evals_dual uses unzip instead of triple allocation - quadratic_equation: hoist scratch allocations out of row loop Made-with: Cursor * feat: wide ring accumulators with NEON SIMD for one-hot commitment Introduce carry-free wide accumulators (Fp32x2i32, Fp64x4i32, Fp128x8i32) that defer modular reduction during one-hot commitment, yielding 69x faster commit for sparse witnesses. Key changes: - AdditiveGroup trait decoupling additive ops from full FieldCore - WideCyclotomicRing for carry-free ring accumulation - HasWide / ReduceTo traits for type-level wide ↔ canonical dispatch - NEON SIMD backends for Fp64x4i32 and Fp128x8i32 with scalar fallback - inner_ajtai_onehot_wide replaces inner_ajtai_onehot_t_only - Profile example now covers both dense and one-hot paths Made-with: Cursor * refactor: drop "_tiled" suffix from mat-vec functions Tiling is an internal optimization detail, not an API distinction. The tiled versions are the only production path; non-tiled variants exist only as #[cfg(test)] reference implementations. Made-with: Cursor * refactor: rename Fp128CommitmentConfig, hoist inline qualified path - Drop "Production" prefix from ProductionFp128CommitmentConfig - Hoist crate::algebra::fields::LiftBase to use statement in sparse_challenge.rs Made-with: Cursor * feat: pack final_w as balanced digits, use Vec throughout prover Represent the prover's witness vector w as Vec instead of Vec throughout the folding pipeline. Introduces PackedDigits to bit-pack the final-level w into log_basis bits per element, reducing proof size by ~32x. Cleans up import hygiene in profile example and proof module. Made-with: Cursor * perf: use const digit lookup table for i8-to-field conversion Add const fn digit_lut to Fp128 and FromSmallInt trait for precomputing balanced-digit-to-field-element tables. Replaces per-element from_i64 calls with indexed loads in the three hot prover loops (commit_w, build_w_evals_dual, dense_poly_from_w). Made-with: Cursor * perf: add DigitMontLut for i8 mat-vec kernels, clean up imports Add a precomputed Montgomery lookup table (DigitMontLut) for balanced digit values {-8..7}, replacing per-coefficient from_canonical calls in the i8→CRT+NTT conversion hot path. Wire it into mat_vec_mul_ntt_i8, mat_vec_mul_ntt_single_i8, and unreduced_quotient_rows_ntt_cached_i8. Also: merge duplicate NTT butterfly imports, remove duplicated doc comment on from_ring_cyclic, export DigitMontLut through ring/algebra modules, apply cargo fmt. Made-with: Cursor * perf: NEON SIMD kernels, decompose_fold optimization, explicit layout API Add AArch64 NEON SIMD for NTT butterflies, pointwise multiply-accumulate, and add-reduce (neon.rs). Dispatch from butterfly.rs and linear.rs with runtime feature check and scalar fallback. Optimize DensePoly::decompose_fold with two-phase restructure: K=3 interleaved carry chains for ILP on decomposition, then NEON rotate-and-add scatter (decompose_fold_neon.rs). ~2x speedup on compute_z_pre. Optimize OneHotPoly::decompose_fold by replacing O(omega*D) mul_by_sparse with direct sparse scatter O(omega*|nonzero_coeffs|). ~22x speedup. Thread explicit HachiCommitmentLayout through commit/prove/verify instead of computing from setup internally. Add OneHotIndex trait for generic onehot indices. Profile now uses OneHotPoly end-to-end for the onehot path. Clean up imports: hoist qualified crate::algebra::ntt::neon paths, move test-function use statements to module scope. Made-with: Cursor * perf: unreduced accumulation for sumcheck, fused compact round-0 loop Introduce HasUnreducedOps trait with MulU64Accum / ProductAccum types for Fp64, Fp128, and Fp2, enabling widening multiplies that defer reduction until after accumulation. Key changes: - Fuse norm + relation computation into a single pass for compact (Round 0) via compute_round_compact_fused, using split pos/neg MulU64Accum for the relation and i128/LUT arithmetic for the norm. - Sparse integer representation for affine-coeff precomputation (SparseCoeffEntry) with batched x4 kernel (compute_entry_coeffs_x4). - Two-level inner/outer ProductAccum accumulation for affine-coeff kernel, both compact and full-field paths. - Optimize fold_compact_to_full to use mul_u64_unreduced for r * delta. - Parallelize OneHotPoly::evaluate_ring, fold_blocks, decompose_fold. - Add FromSmallInt::from_i128 default method. Made-with: Cursor * perf: two-level ProductAccum for full-field affine-coeff kernel Upgrade the WTable::Full + AffineCoeffComposition path in HachiSumcheckProver to use two-level ProductAccum accumulation (outer loop over e_second, inner mul_to_product_accum, single reduction per j_high block), matching the standalone norm_sumcheck.rs implementation. Also fix multilinear_eval_small missing FromSmallInt bound, switch commitment_scheme w_eval to use w_evals_field (w_evals is moved), and add missing doc on ScaleI32 trait method. Made-with: Cursor * style: rustfmt formatting for poly.rs and hachi_sumcheck.rs Made-with: Cursor * fix(ci): use compound assignment operators to satisfy clippy Made-with: Cursor * chore: remove docs/ and paper/ from tracked files Backed up to quang/temp-docs branch. Files remain on disk. Made-with: Cursor * fix(ci): implement assign traits and fix all clippy assign_op_pattern lints Add MulAssign for Fp128, and AddAssign/SubAssign/MulAssign for all PackedNeon types. Convert all x = x op y patterns to x op= y across benches, tests, and lib. Made-with: Cursor * fix(ci): add assign traits to NoPacking, AVX2/AVX512 packed types, Fp32, Fp64 NoPacking (x86_64 fallback) was missing AddAssign/SubAssign/MulAssign, causing CI failures on the GitHub runner. Add assign traits uniformly across all packed backends and scalar field types. Fix remaining assign_op_pattern lints in benches and tests. Made-with: Cursor * fix(ci): fix no-default-features clippy — unused var, dead code, rayon gate - Allow unused rel_combine (only used in parallel reduce combiner) - Allow dead_code on add_ntt_into (only used in parallel + aarch64) - Gate rayon::ThreadPoolBuilder behind cfg(feature = "parallel") - Fix remaining assign_op_pattern in norm_sumcheck bench Made-with: Cursor --- .gitignore | 2 + Cargo.lock | 115 +- Cargo.toml | 5 + benches/field_arith.rs | 44 +- benches/hachi_e2e.rs | 253 ++- benches/norm_sumcheck.rs | 6 +- docs/FIELD_EMBEDDINGS_SUPERNEO_VS_HACHI.md | 698 --------- docs/FIELD_OPS_PERF.md | 237 --- docs/HACHI_DIGEST.md | 1362 ----------------- docs/SUPERNEO_DIGEST.md | 271 ---- docs/TRANSCRIPT_COMMITMENT_COMPAT_SPEC.md | 106 -- examples/profile.rs | 295 ++++ paper/fri-binius.pdf | Bin 819617 -> 0 bytes paper/greyhound.pdf | Bin 557273 -> 0 bytes paper/hachi.pdf | Bin 678598 -> 0 bytes paper/labrador.pdf | Bin 569118 -> 0 bytes paper/standards/NIST.FIPS.203.pdf | Bin 1252341 -> 0 bytes paper/standards/NIST.FIPS.204.pdf | Bin 3291746 -> 0 bytes paper/superneo.pdf | Bin 740185 -> 0 bytes src/algebra/backend/scalar.rs | 2 +- src/algebra/fields/ext.rs | 105 +- src/algebra/fields/fp128.rs | 114 +- src/algebra/fields/fp32.rs | 40 +- src/algebra/fields/fp64.rs | 40 +- src/algebra/fields/mod.rs | 6 +- src/algebra/fields/packed.rs | 23 +- src/algebra/fields/packed_avx2.rs | 65 +- src/algebra/fields/packed_avx512.rs | 65 +- src/algebra/fields/packed_ext.rs | 6 + src/algebra/fields/packed_neon.rs | 65 +- src/algebra/fields/wide.rs | 1238 +++++++++++++++ src/algebra/mod.rs | 4 +- src/algebra/module.rs | 4 +- src/algebra/ntt/butterfly.rs | 218 ++- src/algebra/ntt/mod.rs | 2 + src/algebra/ntt/neon.rs | 1001 ++++++++++++ src/algebra/poly.rs | 86 +- src/algebra/ring/crt_ntt_repr.rs | 241 ++- src/algebra/ring/cyclotomic.rs | 472 +++++- src/algebra/ring/mod.rs | 4 +- src/algebra/ring/sparse_challenge.rs | 7 +- src/lib.rs | 13 +- src/parallel.rs | 18 + src/primitives/arithmetic.rs | 74 +- src/primitives/mod.rs | 1 - src/primitives/multilinear_evals.rs | 155 -- src/primitives/poly.rs | 57 +- src/protocol/commitment/commit.rs | 501 +++--- src/protocol/commitment/config.rs | 291 +++- src/protocol/commitment/mod.rs | 12 +- src/protocol/commitment/onehot.rs | 189 ++- src/protocol/commitment/scheme.rs | 145 +- src/protocol/commitment/utils/crt_ntt.rs | 118 +- src/protocol/commitment/utils/linear.rs | 616 +++++++- src/protocol/commitment/utils/matrix.rs | 11 +- src/protocol/commitment/utils/mod.rs | 2 +- src/protocol/commitment_scheme.rs | 1142 +++++++------- .../hachi_poly_ops/decompose_fold_neon.rs | 143 ++ src/protocol/hachi_poly_ops/mod.rs | 740 +++++++++ src/protocol/mod.rs | 16 +- src/protocol/opening_point.rs | 27 +- src/protocol/proof.rs | 364 ++++- src/protocol/quadratic_equation.rs | 652 ++++---- src/protocol/ring_switch.rs | 517 +++++-- src/protocol/sumcheck/batched_sumcheck.rs | 18 +- src/protocol/sumcheck/eq_poly.rs | 2 +- src/protocol/sumcheck/hachi_sumcheck.rs | 788 ++++++---- src/protocol/sumcheck/mod.rs | 18 +- src/protocol/sumcheck/norm_sumcheck.rs | 854 ++++++++--- src/protocol/sumcheck/relation_sumcheck.rs | 124 +- src/protocol/sumcheck/split_eq.rs | 4 +- src/protocol/sumcheck/types.rs | 8 +- src/test_utils.rs | 89 +- tests/commitment_contract.rs | 226 ++- tests/onehot_commitment.rs | 11 +- tests/ring_commitment_core.rs | 96 +- tests/sparse_challenge.rs | 4 +- tests/sumcheck_core.rs | 4 +- tests/sumcheck_prover_driver.rs | 4 +- 79 files changed, 9724 insertions(+), 5532 deletions(-) delete mode 100644 docs/FIELD_EMBEDDINGS_SUPERNEO_VS_HACHI.md delete mode 100644 docs/FIELD_OPS_PERF.md delete mode 100644 docs/HACHI_DIGEST.md delete mode 100644 docs/SUPERNEO_DIGEST.md delete mode 100644 docs/TRANSCRIPT_COMMITMENT_COMPAT_SPEC.md create mode 100644 examples/profile.rs delete mode 100644 paper/fri-binius.pdf delete mode 100644 paper/greyhound.pdf delete mode 100644 paper/hachi.pdf delete mode 100644 paper/labrador.pdf delete mode 100644 paper/standards/NIST.FIPS.203.pdf delete mode 100644 paper/standards/NIST.FIPS.204.pdf delete mode 100644 paper/superneo.pdf create mode 100644 src/algebra/fields/wide.rs create mode 100644 src/algebra/ntt/neon.rs delete mode 100644 src/primitives/multilinear_evals.rs create mode 100644 src/protocol/hachi_poly_ops/decompose_fold_neon.rs create mode 100644 src/protocol/hachi_poly_ops/mod.rs diff --git a/.gitignore b/.gitignore index bd04f281..dff37f8b 100644 --- a/.gitignore +++ b/.gitignore @@ -5,3 +5,5 @@ .urs PUBLISH_CHECKLIST.md + +profile_traces/ diff --git a/Cargo.lock b/Cargo.lock index e184f5cc..fa36fad0 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -477,6 +477,8 @@ dependencies = [ "sha3", "thiserror", "tracing", + "tracing-chrome", + "tracing-subscriber", ] [[package]] @@ -559,18 +561,48 @@ dependencies = [ "cpufeatures", ] +[[package]] +name = "lazy_static" +version = "1.5.0" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "bbd2bcb4c963f2ddae06a2efc7e9f3591312473c50c6685e1f298068316e66fe" + [[package]] name = "libc" version = "0.2.177" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "2874a2af47a2325c2001a6e6fad9b16a53b802102b528163885171cf92b15976" +[[package]] +name = "log" +version = "0.4.29" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "5e5032e24019045c762d3c0f28f5b6b8bbf38563a65908389bf7978758920897" + +[[package]] +name = "matchers" +version = "0.2.0" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "d1525a2a28c7f4fa0fc98bb91ae755d1e2d1505079e05539e35bc876b5d65ae9" +dependencies = [ + "regex-automata", +] + [[package]] name = "memchr" version = "2.7.6" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "f52b00d39961fc5b2736ea853c9cc86238e165017a493d1d5c8eac6bdc4cc273" +[[package]] +name = "nu-ansi-term" +version = "0.50.3" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "7957b9740744892f114936ab4a57b3f487491bbeafaf8083688b16841a4240e5" +dependencies = [ + "windows-sys", +] + [[package]] name = "num-bigint" version = "0.4.6" @@ -831,6 +863,21 @@ dependencies = [ "keccak", ] +[[package]] +name = "sharded-slab" +version = "0.1.7" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "f40ca3c46823713e0d4209592e8d6e826aa57e928f09752619fc696c499637f6" +dependencies = [ + "lazy_static", +] + +[[package]] +name = "smallvec" +version = "1.15.1" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "67b1b7a3b5fe4f1376887184045fcf45c69e92af734b7aaddc05fb777b6fbd03" + [[package]] name = "subtle" version = "2.6.1" @@ -879,6 +926,15 @@ dependencies = [ "syn 2.0.110", ] +[[package]] +name = "thread_local" +version = "1.1.9" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "f60246a4944f24f6e018aa17cdeffb7818b76356965d03b07d6a9886e8962185" +dependencies = [ + "cfg-if", +] + [[package]] name = "tinytemplate" version = "1.2.1" @@ -891,9 +947,9 @@ dependencies = [ [[package]] name = "tracing" -version = "0.1.41" +version = "0.1.44" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "784e0ac535deb450455cbfa28a6f0df145ea1bb7ae51b821cf5e7927fdcfbdd0" +checksum = "63e71662fa4b2a2c3a26f570f037eb95bb1f85397f3cd8076caed2f026a6d100" dependencies = [ "pin-project-lite", "tracing-attributes", @@ -902,22 +958,63 @@ dependencies = [ [[package]] name = "tracing-attributes" -version = "0.1.30" +version = "0.1.31" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "81383ab64e72a7a8b8e13130c49e3dab29def6d0c7d76a03087b3cf71c5c6903" +checksum = "7490cfa5ec963746568740651ac6781f701c9c5ea257c58e057f3ba8cf69e8da" dependencies = [ "proc-macro2", "quote", "syn 2.0.110", ] +[[package]] +name = "tracing-chrome" +version = "0.7.2" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "bf0a738ed5d6450a9fb96e86a23ad808de2b727fd1394585da5cdd6788ffe724" +dependencies = [ + "serde_json", + "tracing-core", + "tracing-subscriber", +] + [[package]] name = "tracing-core" -version = "0.1.34" +version = "0.1.36" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "db97caf9d906fbde555dd62fa95ddba9eecfd14cb388e4f491a66d74cd5fb79a" +dependencies = [ + "once_cell", + "valuable", +] + +[[package]] +name = "tracing-log" +version = "0.2.0" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "b9d12581f227e93f094d3af2ae690a574abb8a2b9b7a96e7cfe9647b2b617678" +checksum = "ee855f1f400bd0e5c02d150ae5de3840039a3f54b025156404e34c23c03f47c3" dependencies = [ + "log", "once_cell", + "tracing-core", +] + +[[package]] +name = "tracing-subscriber" +version = "0.3.22" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "2f30143827ddab0d256fd843b7a66d164e9f271cfa0dde49142c5ca0ca291f1e" +dependencies = [ + "matchers", + "nu-ansi-term", + "once_cell", + "regex-automata", + "sharded-slab", + "smallvec", + "thread_local", + "tracing", + "tracing-core", + "tracing-log", ] [[package]] @@ -932,6 +1029,12 @@ version = "1.0.22" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "9312f7c4f6ff9069b165498234ce8be658059c6728633667c526e27dc2cf1df5" +[[package]] +name = "valuable" +version = "0.1.1" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "ba73ea9cf16a25df0c8caa16c51acb937d5712a8429db78a3ee29d5dcacd3a65" + [[package]] name = "version_check" version = "0.9.5" diff --git a/Cargo.toml b/Cargo.toml index ab91eead..a364070e 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -50,6 +50,11 @@ criterion = { version = "0.5", features = ["html_reports"] } num-bigint = "0.4.6" ark-bn254 = { git = "https://github.com/a16z/arkworks-algebra", branch = "dev/twist-shout", features = ["scalar_field"] } ark-ff = { git = "https://github.com/a16z/arkworks-algebra", branch = "dev/twist-shout" } +tracing-chrome = "0.7" +tracing-subscriber = { version = "0.3", features = ["env-filter", "registry"] } + +[[example]] +name = "profile" [[bench]] name = "ring_ntt" diff --git a/benches/field_arith.rs b/benches/field_arith.rs index c3b04578..e5f07f25 100644 --- a/benches/field_arith.rs +++ b/benches/field_arith.rs @@ -132,7 +132,7 @@ fn bench_mul_only(c: &mut Criterion) { b.iter(|| { let mut acc = F13::one(); for x in inputs_f13.iter() { - acc = acc * *x; + acc *= *x; } black_box(acc) }) @@ -143,7 +143,7 @@ fn bench_mul_only(c: &mut Criterion) { let mut acc = F13::one(); for _ in 0..8 { for x in inputs_f13.iter() { - acc = acc * *x; + acc *= *x; } } black_box(acc) @@ -154,7 +154,7 @@ fn bench_mul_only(c: &mut Criterion) { b.iter(|| { let mut sum = F13::zero(); for pair in inputs_f13.chunks_exact(2) { - sum = sum + pair[0] * pair[1]; + sum += pair[0] * pair[1]; } black_box(sum) }) @@ -164,7 +164,7 @@ fn bench_mul_only(c: &mut Criterion) { b.iter(|| { let mut acc = F2p18p1::one(); for x in inputs_f2p18p1.iter() { - acc = acc * *x; + acc *= *x; } black_box(acc) }) @@ -174,7 +174,7 @@ fn bench_mul_only(c: &mut Criterion) { b.iter(|| { let mut acc = F2p54m1::one(); for x in inputs_f2p54m1.iter() { - acc = acc * *x; + acc *= *x; } black_box(acc) }) @@ -347,7 +347,7 @@ fn bench_inv(c: &mut Criterion) { b.iter(|| { let mut acc = F13::one(); for x in inputs.iter() { - acc = acc * x.inv_or_zero(); + acc *= x.inv_or_zero(); } black_box(acc) }) @@ -500,7 +500,7 @@ fn bench_packed_fp128_backend(c: &mut Criterion) { let mut out = lhs.clone(); b.iter(|| { for (dst, src) in out.iter_mut().zip(rhs.iter()) { - *dst = *dst + *src; + *dst += *src; } black_box(out[0]) }) @@ -511,7 +511,7 @@ fn bench_packed_fp128_backend(c: &mut Criterion) { let mut out = packed_lhs.clone(); b.iter(|| { for (dst, src) in out.iter_mut().zip(packed_rhs.iter()) { - *dst = *dst + *src; + *dst += *src; } black_box(out[0].extract(0)) }) @@ -522,7 +522,7 @@ fn bench_packed_fp128_backend(c: &mut Criterion) { b.iter(|| { let mut acc = F::one(); for x in scalar_latency_inputs.iter() { - acc = acc * *x; + acc *= *x; } black_box(acc) }) @@ -533,7 +533,7 @@ fn bench_packed_fp128_backend(c: &mut Criterion) { b.iter(|| { let mut acc = PF::broadcast(F::one()); for x in packed_latency_inputs.iter() { - acc = acc * *x; + acc *= *x; } black_box(acc.extract(0)) }) @@ -548,7 +548,7 @@ fn bench_packed_fp128_backend(c: &mut Criterion) { let mut acc: Vec = lanes.iter().map(|(a, b)| *a * *b).collect(); for _ in 0..throughput_iters { for (acc_i, lane) in acc.iter_mut().zip(lanes.iter()) { - *acc_i = *acc_i * lane.0; + *acc_i *= lane.0; } } black_box(acc[0]) @@ -564,7 +564,7 @@ fn bench_packed_fp128_backend(c: &mut Criterion) { let mut acc: Vec = lanes.iter().map(|(a, b)| *a * *b).collect(); for _ in 0..throughput_iters { for (acc_i, lane) in acc.iter_mut().zip(lanes.iter()) { - *acc_i = *acc_i * lane.0; + *acc_i *= lane.0; } } black_box(acc[0].extract(0)) @@ -582,13 +582,13 @@ fn bench_packed_fp128_backend(c: &mut Criterion) { for (acc_i, lane) in acc.iter_mut().zip(lanes.iter()) { let (x, y) = *lane; for _ in 0..mix_muls { - *acc_i = *acc_i * x; + *acc_i *= x; } for _ in 0..mix_adds { - *acc_i = *acc_i + y; + *acc_i += y; } for _ in 0..mix_subs { - *acc_i = *acc_i - x; + *acc_i -= x; } } } @@ -607,13 +607,13 @@ fn bench_packed_fp128_backend(c: &mut Criterion) { for (acc_i, lane) in acc.iter_mut().zip(lanes.iter()) { let (x, y) = *lane; for _ in 0..mix_muls { - *acc_i = *acc_i * x; + *acc_i *= x; } for _ in 0..mix_adds { - *acc_i = *acc_i + y; + *acc_i += y; } for _ in 0..mix_subs { - *acc_i = *acc_i - x; + *acc_i -= x; } } } @@ -649,7 +649,7 @@ fn bench_fp32_fp64_mul(c: &mut Criterion) { b.iter(|| { let mut acc = <$ty>::one(); for x in $inputs.iter() { - acc = acc * *x; + acc *= *x; } black_box(acc) }) @@ -813,7 +813,7 @@ fn bench_accumulator_pattern(c: &mut Criterion) { let b_s = black_box(&inputs_b_u64[..n]); let mut acc = F::zero(); for i in 0..n { - acc = acc + a_s[i] * F::from_u64(b_s[i]); + acc += a_s[i] * F::from_u64(b_s[i]); } black_box(acc) }) @@ -848,7 +848,7 @@ fn bench_accumulator_pattern(c: &mut Criterion) { let b_s = black_box(&inputs_b_f[..n]); let mut acc = F::zero(); for i in 0..n { - acc = acc + a_s[i] * b_s[i]; + acc += a_s[i] * b_s[i]; } black_box(acc) }) @@ -1389,7 +1389,7 @@ fn bench_packed_sumcheck_mix(c: &mut Criterion) { let p_v = black_box(&poly_p); acc = <$packing>::broadcast(<$field>::zero()); for i in 0..e.len() { - acc = acc + e[i] * p_v[i]; + acc += e[i] * p_v[i]; } black_box(acc) }) diff --git a/benches/hachi_e2e.rs b/benches/hachi_e2e.rs index d21b2f3f..3d34f911 100644 --- a/benches/hachi_e2e.rs +++ b/benches/hachi_e2e.rs @@ -1,19 +1,22 @@ #![allow(missing_docs)] -use criterion::{black_box, criterion_group, criterion_main, BenchmarkId, Criterion}; +use criterion::{black_box, criterion_group, BenchmarkId, Criterion}; +use hachi_pcs::algebra::poly::multilinear_eval; use hachi_pcs::algebra::Fp128; use hachi_pcs::error::HachiError; -use hachi_pcs::primitives::multilinear_evals::DenseMultilinearEvals; -use hachi_pcs::protocol::commitment::{HachiCommitmentLayout, ProductionFp128CommitmentConfig}; +use hachi_pcs::protocol::commitment::{ + DecompositionParams, Fp128CommitmentConfig, HachiCommitmentLayout, +}; use hachi_pcs::protocol::commitment_scheme::HachiCommitmentScheme; +use hachi_pcs::protocol::hachi_poly_ops::{DensePoly, OneHotPoly}; use hachi_pcs::protocol::transcript::Blake2bTranscript; use hachi_pcs::protocol::CommitmentConfig; -use hachi_pcs::{CommitmentScheme, FromSmallInt, Polynomial, Transcript}; +use hachi_pcs::{BasisMode, CommitmentScheme, FromSmallInt, Transcript}; use std::time::Duration; type F = Fp128<0xfffffffffffffffffffffffffffffeed>; -const D: usize = ProductionFp128CommitmentConfig::D; +const D: usize = Fp128CommitmentConfig::D; macro_rules! bench_config { ($name:ident, M = $m:expr, R = $r:expr) => { @@ -21,18 +24,19 @@ macro_rules! bench_config { struct $name; impl CommitmentConfig for $name { const D: usize = D; - const N_A: usize = ProductionFp128CommitmentConfig::N_A; - const N_B: usize = ProductionFp128CommitmentConfig::N_B; - const N_D: usize = ProductionFp128CommitmentConfig::N_D; - const LOG_BASIS: u32 = ProductionFp128CommitmentConfig::LOG_BASIS; - const DELTA: usize = ProductionFp128CommitmentConfig::DELTA; - const TAU: usize = ProductionFp128CommitmentConfig::TAU; - const CHALLENGE_WEIGHT: usize = ProductionFp128CommitmentConfig::CHALLENGE_WEIGHT; + const N_A: usize = Fp128CommitmentConfig::N_A; + const N_B: usize = Fp128CommitmentConfig::N_B; + const N_D: usize = Fp128CommitmentConfig::N_D; + const CHALLENGE_WEIGHT: usize = Fp128CommitmentConfig::CHALLENGE_WEIGHT; + + fn decomposition() -> DecompositionParams { + Fp128CommitmentConfig::decomposition() + } fn commitment_layout( _max_num_vars: usize, ) -> Result { - HachiCommitmentLayout::new::($m, $r) + HachiCommitmentLayout::new::($m, $r, &Self::decomposition()) } } }; @@ -43,30 +47,29 @@ bench_config!(CfgNv14, M = 6, R = 4); bench_config!(CfgNv18, M = 8, R = 6); bench_config!(CfgNv20, M = 8, R = 8); +type Scheme = HachiCommitmentScheme; + fn num_vars() -> usize { let alpha = Cfg::D.trailing_zeros() as usize; let layout = Cfg::commitment_layout(0).expect("benchmark layout"); layout.m_vars + layout.r_vars + alpha } -fn make_poly(nv: usize) -> DenseMultilinearEvals { +fn make_dense_poly(nv: usize) -> DensePoly { let len = 1usize << nv; let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); - DenseMultilinearEvals::new_padded(evals) + DensePoly::from_field_evals(nv, &evals).unwrap() } fn opening_point(nv: usize) -> Vec { (0..nv).map(|i| F::from_u64((i + 2) as u64)).collect() } -fn bench_phases(c: &mut Criterion, label: &str) -where - HachiCommitmentScheme: CommitmentScheme, -{ - type S = HachiCommitmentScheme; +fn bench_phases(c: &mut Criterion, label: &str) { let nv = num_vars::(); - let poly = make_poly(nv); + let poly = make_dense_poly(nv); let pt = opening_point(nv); + let layout = Cfg::commitment_layout(nv).expect("benchmark layout"); let mut group = c.benchmark_group(format!("hachi/{label}/nv{nv}")); if nv >= 18 { @@ -75,62 +78,78 @@ where } group.bench_function("setup", |b| { - b.iter(|| black_box( as CommitmentScheme>::setup_prover(black_box(nv)))) + b.iter(|| { + black_box( as CommitmentScheme>::setup_prover( + black_box(nv), + )) + }) }); - let setup = as CommitmentScheme>::setup_prover(nv); + let setup = as CommitmentScheme>::setup_prover(nv); group.bench_function("commit", |b| { b.iter(|| { black_box( - as CommitmentScheme>::commit(black_box(&poly), black_box(&setup)) - .unwrap(), + as CommitmentScheme>::commit( + black_box(&poly), + black_box(&setup), + black_box(&layout), + ) + .unwrap(), ) }) }); - let (commitment, hint) = as CommitmentScheme>::commit(&poly, &setup).unwrap(); + let (commitment, hint) = + as CommitmentScheme>::commit(&poly, &setup, &layout).unwrap(); group.bench_function("prove", |b| { b.iter(|| { let mut transcript = Blake2bTranscript::::new(b"bench"); black_box( - as CommitmentScheme>::prove( + as CommitmentScheme>::prove( black_box(&setup), black_box(&poly), black_box(&pt), - Some(hint.clone()), + hint.clone(), &mut transcript, black_box(&commitment), + BasisMode::Lagrange, + black_box(&layout), ) .unwrap(), ) }) }); - let verifier_setup = as CommitmentScheme>::setup_verifier(&setup); - let opening = poly.evaluate(&pt); + let verifier_setup = as CommitmentScheme>::setup_verifier(&setup); + let evals: Vec = (0..(1usize << nv)).map(|i| F::from_u64(i as u64)).collect(); + let opening = multilinear_eval(&evals, &pt).unwrap(); let mut prover_transcript = Blake2bTranscript::::new(b"bench"); - let proof = as CommitmentScheme>::prove( + let proof = as CommitmentScheme>::prove( &setup, &poly, &pt, - Some(hint), + hint, &mut prover_transcript, &commitment, + BasisMode::Lagrange, + &layout, ) .unwrap(); group.bench_function("verify", |b| { b.iter(|| { let mut transcript = Blake2bTranscript::::new(b"bench"); - as CommitmentScheme>::verify( + as CommitmentScheme>::verify( black_box(&proof), black_box(&verifier_setup), &mut transcript, black_box(&pt), black_box(&opening), black_box(&commitment), + BasisMode::Lagrange, + black_box(&layout), ) .unwrap(); }) @@ -138,25 +157,165 @@ where group.bench_function(BenchmarkId::new("e2e", nv), |b| { b.iter(|| { - let (cm, h) = as CommitmentScheme>::commit(&poly, &setup).unwrap(); + let (cm, h) = + as CommitmentScheme>::commit(&poly, &setup, &layout).unwrap(); let mut pt_tr = Blake2bTranscript::::new(b"bench"); - let pf = as CommitmentScheme>::prove( + let pf = as CommitmentScheme>::prove( &setup, &poly, &pt, - Some(h), + h, &mut pt_tr, &cm, + BasisMode::Lagrange, + &layout, ) .unwrap(); let mut vt_tr = Blake2bTranscript::::new(b"bench"); - as CommitmentScheme>::verify( + as CommitmentScheme>::verify( &pf, &verifier_setup, &mut vt_tr, &pt, &opening, &cm, + BasisMode::Lagrange, + &layout, + ) + .unwrap(); + black_box(()) + }) + }); + + group.finish(); +} + +fn bench_onehot_phases(c: &mut Criterion, label: &str) { + let nv = num_vars::(); + let layout = Cfg::commitment_layout(nv).expect("benchmark layout"); + let total_ring = layout.num_blocks * layout.block_len; + let onehot_k = D; + let num_chunks = total_ring; + + let indices: Vec> = (0..num_chunks).map(|i| Some(i % onehot_k)).collect(); + + let onehot_poly = + OneHotPoly::::new(onehot_k, indices.clone(), layout.r_vars, layout.m_vars).unwrap(); + + let dense_evals: Vec = { + let mut evals = vec![F::from_u64(0); total_ring * D]; + for (ci, opt_idx) in indices.iter().enumerate() { + if let Some(idx) = opt_idx { + evals[ci * onehot_k + idx] = F::from_u64(1); + } + } + evals + }; + let dense_poly = DensePoly::::from_field_evals(nv, &dense_evals).unwrap(); + let pt = opening_point(nv); + + let setup = as CommitmentScheme>::setup_prover(nv); + + let mut group = c.benchmark_group(format!("hachi_onehot/{label}/nv{nv}")); + if nv >= 18 { + group.sample_size(10); + group.measurement_time(Duration::from_secs(30)); + } + + group.bench_function("commit_onehot", |b| { + b.iter(|| { + black_box( + as CommitmentScheme>::commit( + black_box(&onehot_poly), + black_box(&setup), + black_box(&layout), + ) + .unwrap(), + ) + }) + }); + + let (commitment, hint) = + as CommitmentScheme>::commit(&onehot_poly, &setup, &layout).unwrap(); + + group.bench_function("prove", |b| { + b.iter(|| { + let mut transcript = Blake2bTranscript::::new(b"bench"); + black_box( + as CommitmentScheme>::prove( + black_box(&setup), + black_box(&dense_poly), + black_box(&pt), + hint.clone(), + &mut transcript, + black_box(&commitment), + BasisMode::Lagrange, + black_box(&layout), + ) + .unwrap(), + ) + }) + }); + + let verifier_setup = as CommitmentScheme>::setup_verifier(&setup); + let opening = multilinear_eval(&dense_evals, &pt).unwrap(); + let mut prover_transcript = Blake2bTranscript::::new(b"bench"); + let proof = as CommitmentScheme>::prove( + &setup, + &dense_poly, + &pt, + hint.clone(), + &mut prover_transcript, + &commitment, + BasisMode::Lagrange, + &layout, + ) + .unwrap(); + + group.bench_function("verify", |b| { + b.iter(|| { + let mut transcript = Blake2bTranscript::::new(b"bench"); + as CommitmentScheme>::verify( + black_box(&proof), + black_box(&verifier_setup), + &mut transcript, + black_box(&pt), + black_box(&opening), + black_box(&commitment), + BasisMode::Lagrange, + black_box(&layout), + ) + .unwrap(); + }) + }); + + group.bench_function(BenchmarkId::new("e2e", nv), |b| { + b.iter(|| { + let (cm, h) = + as CommitmentScheme>::commit(&onehot_poly, &setup, &layout) + .unwrap(); + let mut pt_tr = Blake2bTranscript::::new(b"bench"); + let pf = as CommitmentScheme>::prove( + &setup, + &dense_poly, + &pt, + h, + &mut pt_tr, + &cm, + BasisMode::Lagrange, + &layout, + ) + .unwrap(); + let mut vt_tr = Blake2bTranscript::::new(b"bench"); + as CommitmentScheme>::verify( + &pf, + &verifier_setup, + &mut vt_tr, + &pt, + &opening, + &cm, + BasisMode::Lagrange, + &layout, ) .unwrap(); black_box(()) @@ -178,12 +337,28 @@ fn bench_nv18(c: &mut Criterion) { fn bench_nv20(c: &mut Criterion) { bench_phases::(c, "fp128_p275"); } +fn bench_onehot_nv14(c: &mut Criterion) { + bench_onehot_phases::(c, "fp128_p275"); +} criterion_group!( hachi_benches, bench_nv10, bench_nv14, bench_nv18, - bench_nv20 + bench_nv20, + bench_onehot_nv14, ); -criterion_main!(hachi_benches); + +fn main() { + #[cfg(feature = "parallel")] + rayon::ThreadPoolBuilder::new() + .stack_size(64 * 1024 * 1024) + .build_global() + .ok(); + + hachi_benches(); + criterion::Criterion::default() + .configure_from_args() + .final_summary(); +} diff --git a/benches/norm_sumcheck.rs b/benches/norm_sumcheck.rs index 655d6cab..266bc880 100644 --- a/benches/norm_sumcheck.rs +++ b/benches/norm_sumcheck.rs @@ -78,7 +78,7 @@ impl SumcheckInstanceProver for BaselineNormSumc for (t, eval) in evals.iter_mut().enumerate() { let t_e = E::from_u64(t as u64); let w_t = w_0 + t_e * (w_1 - w_0); - *eval = *eval + eq_rem * range_check_eval(w_t, b); + *eval += eq_rem * range_check_eval(w_t, b); } evals }, @@ -87,7 +87,7 @@ impl SumcheckInstanceProver for BaselineNormSumc || vec![E::zero(); num_points_q], |mut a, b_vec| { for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { - *ai = *ai + *bi; + *ai += *bi; } a }, @@ -105,7 +105,7 @@ impl SumcheckInstanceProver for BaselineNormSumc for (t, eval) in q_evals.iter_mut().enumerate() { let t_e = E::from_u64(t as u64); let w_t = w_0 + t_e * (w_1 - w_0); - *eval = *eval + eq_rem * range_check_eval(w_t, b); + *eval += eq_rem * range_check_eval(w_t, b); } } q_evals diff --git a/docs/FIELD_EMBEDDINGS_SUPERNEO_VS_HACHI.md b/docs/FIELD_EMBEDDINGS_SUPERNEO_VS_HACHI.md deleted file mode 100644 index 90b631c2..00000000 --- a/docs/FIELD_EMBEDDINGS_SUPERNEO_VS_HACHI.md +++ /dev/null @@ -1,698 +0,0 @@ -# Field embeddings in SuperNeo vs Hachi (math-first notes) - -This note focuses **only** on the math in the two papers: - -- `docs/superneo.pdf` (“Neo and SuperNeo: Post-quantum folding with pay-per-bit costs over small fields”) -- `paper/hachi.pdf` (“Hachi: Efficient Lattice-Based Multilinear Polynomial Commitments over Extension Fields”) - -The shared theme is: lattice commitments naturally live over **cyclotomic rings**, but we want the *interactive proof logic* (sum-check, norm checks, etc.) to live over a **(small) field or a small extension field**. Both works build *embeddings/reductions* that let you: - -- commit in a ring/module world (Ajtai/Module-SIS commitments), while -- proving the needed algebraic statements using field arithmetic, and -- keeping norms under control (for binding) and enabling linear-combination/folding operations. - ---- - -## 1) Common background and notation (as used in SuperNeo) - -SuperNeo sets up a base field \(F = \mathbb{F}_q\), an extension field \(K/F\) of minimal degree such that \(1/|K| = \mathrm{negl}(\lambda)\), and a cyclotomic ring - -\[ -R_F := F[X]/(\Phi(X)), \quad R_K := K[X]/(\Phi(X)), -\] - -where \(\Phi(X)\) is an \(\eta\)-th cyclotomic polynomial of degree \(d\). It explicitly treats - -\[ -F \subseteq R_F \subseteq R_K, \qquad F \subseteq K -\] - -as nested substructures (SuperNeo, Def. 1; `docs/superneo.pdf`, p. 19–20: “-- 19 of 60 --”, “-- 20 of 60 --”). - -Two coefficient maps show up everywhere: - -- coefficient vector: \(\mathrm{cf}(a)\in F^d\) for \(a\in R_F\), -- constant term: \(\mathrm{ct}(a)\in F\) for \(a\in R_F\), - -and similarly over \(R_K\) (SuperNeo, Def. 2; `docs/superneo.pdf`, p. 20: “-- 20 of 60 --”). - -### 1.1 What I mean by the “Gram operator” in this note - -Fix: - -- an \(F\)-basis \(\{e_0,\dots,e_{d-1}\}\) of the \(F\)-vector space \(R_F\) (most often \(e_i = X^i\), the coefficient basis), and -- a bilinear form \(B: R_F\times R_F \to F\). - -Typical examples in these papers are: - -- \(B(u,v)=\mathrm{ct}(u\cdot v)\) (SuperNeo’s constant-term functional), possibly with an automorphism inserted, or -- \(B(u,v)=\mathrm{Tr}_H(u\cdot \sigma_{-1}(v))\) (Hachi’s trace-to-subfield functional). - -Then the **Gram matrix** of \(B\) in the basis \(\{e_i\}\) is the \(d\times d\) matrix -\[ -G_{ij} := B(e_i,e_j). -\] -This matrix encodes the pairing: -if \(u=\sum_i a_i e_i\) and \(v=\sum_j b_j e_j\), then -\[ -B(u,v) = a^\top\, G\, b. -\] - -The corresponding **Gram operator** is just the linear map \(g: F^d\to F^d\) given by -\[ -g(b) := G\,b, -\] -so that \(B(u,v)=a^\top g(b)\). - -When SuperNeo says “there exists a linear transform \(T\) such that \(\mathrm{ct}(T(a)\cdot b)=\langle a,b\rangle\)” (Thm. 3), -one way to interpret it is: choose a bilinear form \(B_0(u,v)=\mathrm{ct}(u\cdot v)\) (or a close variant), write down its Gram matrix \(G\) in the coefficient basis, and take \(T = G^{-{\top}}\). This makes the pairing become the standard dot product in coordinates. - ---- - -## 2) What “field embedding” means in SuperNeo (the core problem) - -### 2.1 The Ajtai-commitment mismatch - -Ajtai/Module-SIS style commitments are *ring-module* commitments: - -- Commit to \(z \in R_F^n\) via a linear map \(c = A z\) over \(R_F\). - -But CCS witnesses (and CCS arithmetic) are naturally vectors over \(F\). So you need a map: - -\[ -\iota: F^{N} \longrightarrow R_F^n -\] - -that is compatible with: - -- **norm constraints** (binding only holds for “small-norm” openings), -- **field constraint checking** via sum-check over \(F\) or \(K\), -- **folding** (random linear combinations of commitments and claims). - -SuperNeo frames this as “embed field vectors (CCS witnesses) into the ring vectors that Ajtai commitments operate over” and calls out that the embedding must preserve **norm bounds** and an **evaluation homomorphism** needed for sum-check-based folding (SuperNeo, §1.2; `docs/superneo.pdf`, p. 5–6: “-- 5 of 60 --”, “-- 6 of 60 --”). - -### 2.2 What went wrong before (NTT embedding) - -Prior lattice folding used an NTT/SIMD isomorphism that maps ring elements into a product of extension fields; this makes field-constraint checking look “ring-native”, but: - -- the NTT map is **not norm-preserving**, so small bit-width witnesses become arbitrary-norm ring elements, -- the commitment must then decompose regardless of bit-width ⇒ **no pay-per-bit**, -- packing efficiency is limited by the factor \(t\) in \(F_{q^t}\) (SuperNeo, §1.2.1; `docs/superneo.pdf`, p. 6–7: “-- 6 of 60 --”, “-- 7 of 60 --”). - ---- - -## 3) SuperNeo’s key innovation: *norm-preserving embeddings + evaluation homomorphism* - -SuperNeo’s abstract summarizes the core as: - -> “two new norm-preserving embeddings of field vectors into ring vectors that respect an evaluation homomorphism required for folding” -(`docs/superneo.pdf`, p. 1: “-- 1 of 60 --”). - -The paper describes both a “Neo embedding” (SIMD-friendly) and a “SuperNeo embedding” (general, non-SIMD), and then focuses the rest of the paper on SuperNeo (see `docs/superneo.pdf`, p. 10–11: “-- 10 of 60 --”, “-- 11 of 60 --”). - -### 3.1 Neo embedding (high level: “coefficients-as-SIMD lanes”) - -Neo’s embedding idea: pack **\(d\) field vectors** \(z^{(1)},\dots,z^{(d)}\in F^n\) into the **coefficient slots** of a ring vector \(z \in R_F^n\), so the coefficient matrix \(\mathrm{cf}(z)\in F^{d\times n}\) literally equals those \(d\) vectors (SuperNeo, §1.2.2 “Contribution 1”; `docs/superneo.pdf`, p. 8–10: “-- 8 of 60 --”, “-- 9 of 60 --”, “-- 10 of 60 --”). - -Key consequences: - -- **norm-preserving**: small field entries ⇒ small ring coefficients ⇒ binding is aligned with bit-width. -- **optimal SIMD packing**: achieves \(d\cdot n\) field elements per length-\(n\) ring vector (under a SIMD constraint system). -- **evaluation homomorphism for folding**: if you fold commitments with a *short ring* challenge \(\delta\in R_F\), the embedded evaluation claims can be folded consistently by embedding the \(d\) field evaluations as a ring element \(y=\sum_i y^{(i)}X^{i-1}\) (SuperNeo, p. 9: “-- 9 of 60 --”). - -But Neo still needs SIMD constraints: “the same constraint system must be applied to all \(d\) underlying field vectors” (SuperNeo, p. 10: “-- 10 of 60 --”). - -### 3.2 SuperNeo embedding (formal: coefficient embedding of **one** length-\(d n_R\) vector) - -SuperNeo removes SIMD by embedding a **single** long field vector \(z\in F^{n_F}\) where \(n_F = d\cdot n_R\), by chunking it into \(n_R\) blocks of length \(d\), and mapping each block to one ring element’s coefficient vector. - -This is defined formally as “Coefficient Embedding” (SuperNeo, §5, Def. 7; `docs/superneo.pdf`, p. 23: “-- 23 of 60 --”): - -- element: \(v\in F^d \mapsto \mathbf{v}\in R_F\) with \(\mathrm{cf}(\mathbf{v})=v\) -- vector: \(z\in F^{d n_R}\mapsto \mathbf{z}\in R_F^{n_R}\) by splitting into \(d\)-sized blocks -- matrix: \(M\in F^{m\times d n_R}\mapsto \mathbf{M}\in R_F^{m\times n_R}\) row-wise. - -**Why this matters:** - -- **optimal packing without SIMD**: you pack \(d\cdot n_R\) field elements into \(n_R\) ring elements. -- **norm-preserving**: the committed object’s coefficients are exactly the witness entries. -- **field-native checks become possible**: you can write constraints directly over the underlying field vector \(z\) and use sum-check over \(F\) or \(K\). - -### 3.3 The nontrivial part: lifting *field* products to *ring* products while keeping folding linear - -SuperNeo’s obstacle is: commitments/folding live over the ring, but sum-check outputs **field** multilinear evaluation claims like - -\[ -M z \;\widetilde{}\; (r) \in K -\] - -for some random \(r\), and folding wants to take ring-linear combinations \(z'' = z + \delta z'\) with \(\delta \in R_F\) and have the **claims** fold “the same way”. - -SuperNeo’s main embedding tool is Section 5 “Embedding products with evaluation homomorphism”: - -1. Use a cyclotomic **inner-product automorphism trick** to turn coefficient inner products into ring constant terms. - -SuperNeo states an “Inner Product Transform” (Thm. 3; `docs/superneo.pdf`, p. 23: “-- 23 of 60 --”): - -> there exists a linear transform \(\bar{\cdot}: F^d \to F^d\) such that for all \(a,b\in F^d\), -> \[ -> \mathrm{ct}(\overline{a}\cdot \mathbf{b}) = \langle a,b\rangle. -> \] - -Conceptually: cyclotomic rings have many Galois automorphisms (e.g. “conjugation” \(X\mapsto X^{-1}\)), and by applying an appropriate automorphism/linear transform to one operand, the constant coefficient of a ring product recovers a dot product of coefficient vectors. (SuperNeo explicitly attributes this to “(Galois, conjugation, or inner product) automorphism trick” in §1.2.2; `docs/superneo.pdf`, p. 10–11: “-- 10 of 60 --”, “-- 11 of 60 --”.) - -2. Extend this transform blockwise to vectors/matrices (Def. 8; `docs/superneo.pdf`, p. 23: “-- 23 of 60 --”). - -3. Obtain a **matrix-vector product transform** (Thm. 4; `docs/superneo.pdf`, p. 23–24: “-- 23 of 60 --”, “-- 24 of 60 --”): - -> For \(M\in F^{m\times n_F}\), \(z\in F^{n_F}\), -> \[ -> M z = \mathrm{ct}(\overline{M}\,\mathbf{z}), -> \] -> i.e. the field product equals the vector of constant terms of a ring product. - -4. Lift this to evaluation claims and prove the **evaluation homomorphism** (Thm. 5; `docs/superneo.pdf`, p. 24: “-- 24 of 60 --”): - -Roughly: if you linearly combine committed ring vectors with ring scalars \(\rho_i\in R_F\), then the lifted ring-evaluation objects combine linearly as well, and constant terms track the underlying field evaluations. - -This is the formal engine that makes “field-native sum-check + ring-linear folding” composable. - -### 3.3.1 Explicit inner-product transforms for two cyclotomics you care about - -SuperNeo’s Theorem 3 is an *existence* statement: there is a linear map \(T: F^d \to F^d\) (write \(T(a)=\bar a\)) such that for all \(a,b\in F^d\), - -\[ -\mathrm{ct}(\mathbf{\bar a}\cdot \mathbf{b}) = \langle a,b\rangle -\] - -where \(\mathbf{v}\in R_F\) denotes the coefficient embedding of \(v\in F^d\). - -Below are **concrete closed forms** for \(T\) in two important special cases. - -#### (A) Power-of-two cyclotomic: \(\Phi(X)=X^d+1\) (negacyclic ring) - -Let \(R_F = F[X]/(X^d+1)\), and write -\(a(X)=\sum_{i=0}^{d-1} a_i X^i\), \(b(X)=\sum_{i=0}^{d-1} b_i X^i\). - -Define \(\bar a(X)\) by the coefficient rule: - -- \(\bar a_0 := a_0\) -- for \(i=1,\dots,d-1\): \(\bar a_i := -a_{d-i}\) - -Equivalently, -\[ -\bar a(X)=a_0 - \sum_{i=1}^{d-1} a_i X^{d-i}. -\] - -Then in \(R_F\), -\[ -\mathrm{ct}(\bar a(X)\,b(X)) = \sum_{i=0}^{d-1} a_i b_i. -\] - -Reason (one-line): the term \((-a_i X^{d-i})(b_i X^i)=-a_i b_i X^d\) contributes \(+a_i b_i\) to the constant term since \(X^d=-1\); other cross-terms cannot reduce to constants without leaving a nonzero power of \(X\). - -This is exactly the classical “conjugation/inversion automorphism” trick specialized to \(X^d+1\). - -#### (B) Trinomial cyclotomic: \(\Phi_{81}(X)=X^{54}+X^{27}+1\) - -Let \(R_F = F[X]/(X^{54}+X^{27}+1)\) (so \(d=54\)). Write -\(a(X)=\sum_{i=0}^{53} a_i X^i\), \(b(X)=\sum_{i=0}^{53} b_i X^i\). - -One valid “inner product transform” \(T(a)=\bar a\) with -\(\mathrm{ct}(\bar a(X)\,b(X))=\sum_i a_i b_i\) -is: - -- \(\bar a_0 := a_0\) -- for \(i=1,\dots,26\): \(\bar a_i := -(a_{27-i} + a_{54-i})\) -- for \(i=27,\dots,53\): \(\bar a_i := -a_{54-i}\) - -(indices are in \(\{0,\dots,53\}\)). - -Notable features: - -- **extremely sparse**: each output coefficient depends on at most 2 input coefficients, -- **\(O(d)\)** time with only adds + sign flips, matching SuperNeo’s efficiency remark for power-of-two / trinomial cyclotomics. - ---- - -### 3.4 Why this is the “field-embedding innovation” (in one sentence) - -SuperNeo’s innovation on the embedding side is: - -- **embed a single field witness vector into ring coefficients in a norm-preserving way**, and -- **systematically lift field matrix products/evaluations to ring expressions whose constant terms recover the field values**, so that -- **ring-linear folding preserves the field evaluation claims** (evaluation homomorphism), - -thereby enabling a HyperNova-like folding architecture where *sum-check and norm checks run over \(K\)* rather than over the ring, while commitments still live over \(R_F\). - ---- - -## 4) What “field embedding” means in Hachi (the PCS perspective) - -Hachi is not a folding scheme; it is a **multilinear PCS**. But the verification bottleneck is similar: classic lattice PCS machinery lives in cyclotomic rings \(R_q = \mathbb{Z}_q[X]/(X^d+1)\), whereas sum-check is naturally over a field. - -Hachi’s abstract states its two embedding/reduction ideas (Hachi, Abstract; `paper/hachi.pdf`, p. 1: “-- 1 of 33 --”): - -1. **Ring-switching + sum-check**: integrate Greyhound with ring-switching so the verifier avoids ring multiplication. -2. **Generic reduction (extension field → ring)**: convert evaluation proofs over \( \mathbb{F}_{q^k}\) into statements over cyclotomic rings \(R_q\). - -### 4.1 Embedding extension fields inside cyclotomic rings (fixed rings under automorphisms) - -In Hachi’s technical overview (Hachi, §1.3; `paper/hachi.pdf`, p. 4–5: “-- 4 of 33 --”, “-- 5 of 33 --”), it identifies finite fields \( \mathbb{F}_{q^k}\) *inside* \(R_q\) using fixed subrings under a subgroup of the Galois group: - -- Let \(R = \mathbb{Z}[X]/(X^d+1)\) and \(R_q = R/(q)\) with \(d=2^\alpha\). -- For automorphisms \(\sigma_i: X\mapsto X^i\), define the fixed ring - \[ - R_q^H := \{x\in R_q : \forall \sigma\in H,\;\sigma(x)=x\}. - \] - -Then (Lemma 1, informal; `paper/hachi.pdf`, p. 5: “-- 5 of 33 --”): - -> for suitable \(q\) (notably \(q\equiv 5\pmod 8\)) and \(k\mid d/2\), there exists \(H\) such that \(R_q^H\) is a **subfield** of \(R_q\) isomorphic to \(\mathbb{F}_{q^k}\). - -This is a literal *field embedding into the ring*: \(\mathbb{F}_{q^k}\hookrightarrow R_q\) realized as a fixed subring. - -### 4.2 Inner products via trace + automorphisms (a close cousin of SuperNeo’s transform) - -Hachi then uses a trace map \(\mathrm{Tr}_H:R_q\to R_q^H\) and an automorphism (notably \(\sigma_{-1}\)) to turn ring products into **field inner products** (Theorem 1, informal; `paper/hachi.pdf`, p. 5: “-- 5 of 33 --”): - -> there exists a bijection \(\psi:(R_q^H)^{d/k}\to R_q\) such that -> \[ -> \mathrm{Tr}_H\big(\psi(a)\cdot \sigma_{-1}(\psi(b))\big) = (d/k)\cdot \langle a,b\rangle. -> \] - -This is structurally very similar to SuperNeo’s “inner product transform → constant term” idea, except Hachi uses: - -- a **trace to a subfield** \(R_q^H \cong \mathbb{F}_{q^k}\), -- whereas SuperNeo phrases it as a **linear transform** on coefficient vectors whose ring-product constant term recovers the dot product. - -### 4.3 Ring-switching: from ring equations to extension-field equations (so the verifier stays field-native) - -Hachi’s “ring switching and sum-check over extension fields” overview (Hachi, §1.3; `paper/hachi.pdf`, p. 6–7: “-- 6 of 33 --”, “-- 7 of 33 --”) sketches: - -- lift a relation over \(R_q\) to an identity over \(\mathbb{Z}_q[X]\) with an explicit multiple of \((X^d+1)\), -- sample \(\alpha \leftarrow \mathbb{F}_{q^k}\) and substitute \(X=\alpha\), -- reducing the ring relation to a **field inner product / sum-check-type claim** over \(\mathbb{F}_{q^k}\), -- then run sum-check over the field and recurse. - -This is the PCS analogue of “avoid ring operations during sum-check”: Hachi’s verifier can avoid cyclotomic ring multiplications even though the underlying assumption/commitments are lattice/ring-based. - ---- - -## 5) Same vs different (embedding viewpoint) - -### 5.1 The same (high-level mathematical pattern) - -- **Cyclotomic rings + automorphisms are the bridge.** - - SuperNeo: an automorphism/linear transform makes \(\mathrm{ct}(\bar{a}\cdot b)\) become \(\langle a,b\rangle\) (SuperNeo Thm. 3; `docs/superneo.pdf`, p. 23: “-- 23 of 60 --”). - - Hachi: trace + automorphisms make \(\mathrm{Tr}_H(\psi(a)\cdot \sigma_{-1}(\psi(b)))\) become \(\langle a,b\rangle\) (Hachi Thm. 1; `paper/hachi.pdf`, p. 5: “-- 5 of 33 --”). - -- **Field-native sum-check is the goal.** - - SuperNeo explicitly targets “field-native arithmetic” where “sum-check and norm checks run purely over a small field” (SuperNeo Abstract; `docs/superneo.pdf`, p. 1: “-- 1 of 60 --”). - - Hachi’s verifier similarly reduces to sum-check over \(\mathbb{F}_{q^k}\) after ring switching (Hachi §1.3; `paper/hachi.pdf`, p. 6–7: “-- 6 of 33 --”, “-- 7 of 33 --”). - -- **Linearity matters.** - Both constructions rely on the fact that the commitment operation is linear in the ring/module, and they build embeddings/reductions so the *claimed evaluations* transform linearly under the same combinations (SuperNeo Thm. 5; `docs/superneo.pdf`, p. 24: “-- 24 of 60 --”). - -### 5.2 The different (what each paper is optimizing for) - -- **Direction of “embedding”:** - - **SuperNeo**: embeds *field witnesses* into *ring vectors* to make Ajtai commitments “pay-per-bit” and folding-friendly. - - **Hachi**: embeds *extension-field evaluation statements* into *ring statements* (and back), to make PCS verification fast via sum-check. - -- **Primary object being preserved:** - - **SuperNeo**: preserves **norm** (for binding/pay-per-bit) *and* preserves **evaluation homomorphism** (for folding). - - **Hachi**: preserves the **truth of evaluation claims** (over \(\mathbb{F}_{q^k}\)) when translated into ring relations; norm constraints are handled via sum-check after ring switching. - -- **Ring family emphasis:** - - **Hachi**’s core ring is explicitly power-of-two cyclotomic \(X^d+1\) (Hachi Abstract; `paper/hachi.pdf`, p. 1: “-- 1 of 33 --”). - - **SuperNeo** broadens to more general cyclotomics to support fields like Goldilocks without “full splitting” issues, and explicitly mentions supporting trinomials in parameter sets (SuperNeo intro + parameters discussion; `docs/superneo.pdf`, p. 1–4 and later “concrete parameters” sections). - -- **Protocol role:** - - **SuperNeo** needs an embedding compatible with **folding** (random linear combination of instances/commitments). - - **Hachi** needs a reduction compatible with **PCS recursion and verifier-time reduction** (ring switching + sum-check). - -### 5.3 Are the embeddings “the same”, mathematically? - -It depends what you mean by “same”. There are two distinct layers: - -- **Layer 1: the raw embedding map(s) \(F^{dn}\to R_F^n\) vs \(F_{q^k}\to R_q\)** - These are **not the same functions**. - - SuperNeo’s core embedding is literally the **coefficient embedding** (Def. 7 in their §5), i.e. *place field coordinates into ring coefficients* (`docs/superneo.pdf`, “Definition 7”; see the quote range in this repo at lines 1222–1238 of the extracted text). - - Hachi’s key “field embedding” is to realize \(F_{q^k}\) as a **fixed subfield** \(R_q^H \subseteq R_q\), then use a **basis-dependent bijection** \(\psi:(R_q^H)^{d/k}\to R_q\) (`paper/hachi.pdf`, lines 290–300 in the extracted text). - -- **Layer 2: the algebraic *mechanism* (automorphisms/trace giving inner products, and linearity of evaluations)** - At this layer, they are **the same underlying idea**: both are exploiting a canonical bilinear pairing on cyclotomic rings derived from Galois automorphisms (e.g. \(\sigma_{-1}\)) plus a linear functional (constant term or trace). - - SuperNeo packages it as “there exists a linear transform \(T\) so that \(\mathrm{ct}(T(a)\cdot b)=\langle a,b\rangle\)” (Thm. 3). - - Hachi packages it as “there exists a bijection \(\psi\) so that \(\mathrm{Tr}_H(\psi(a)\cdot\sigma_{-1}(\psi(b)))=(d/k)\langle a,b\rangle\)” (Thm. 1). - -Concretely: SuperNeo’s \(T\) is (mathematically) the **inverse Gram operator** of the ring’s trace/constant-term pairing *expressed in the coefficient basis*. Hachi’s \(\psi\) is a **choice of basis** that identifies \(R_q\) as a free module over a subfield \(R_q^H\cong F_{q^k}\), so that the same pairing looks like a scaled dot product over that subfield. - -So the correct crisp statement is: - -- **Not identical as maps** (different domains/codomains and different basis choices), but -- **equivalent in the sense that both instantiate the same cyclotomic “automorphism + linear functional = inner product” backbone**, just presented in different coordinates. - ---- - -## 6) Practical mental model (how to read both papers through one lens) - -Both papers can be read as building “interfaces” between three layers: - -1. **Ring/module commitment layer** (Ajtai / Module-SIS commitments) -2. **Field arithmetic layer** (sum-check, equality tests, low-degree checks) -3. **Embedding/reduction layer** (the math glue) - -SuperNeo’s embedding layer is primarily: - -- coefficient embedding \(F^{d n_R} \leftrightarrow R_F^{n_R}\), -- inner-product transform + constant-term extraction, -- evaluation homomorphism for ring-linear combinations. - -Hachi’s embedding layer is primarily: - -- fixed-field embedding \( \mathbb{F}_{q^k} \cong R_q^H \subseteq R_q\), -- trace + automorphisms for inner products, -- ring-switching by evaluation \(X=\alpha\) to move verifier work into \( \mathbb{F}_{q^k}\). - -If you want a single phrase: - -> **SuperNeo**: “make folding happen over small fields even though commitments live over rings.” -> **Hachi**: “make PCS verification happen over extension fields even though commitments live over rings.” - - ---- - -## 7) SuperNeo's bilinear form, explicitly identified - -SuperNeo's Theorem 3 states existence of a linear transform \(T\) but never identifies it as a Galois automorphism. Here we close that gap. - -### 7.1 Claim: \(T = \sigma_{-1}\) for \(\Phi(X) = X^d + 1\) - -In \(R_q = F_q[X]/(X^d+1)\), we have \(X^d = -1\), so \(X^{-1} = -X^{d-1}\). The automorphism \(\sigma_{-1}: X \mapsto X^{-1}\) acts on monomials as: - -\[ -\sigma_{-1}(X^0) = 1, \qquad \sigma_{-1}(X^i) = X^{-i} = -X^{d-i} \;\text{ for } 1 \le i \le d-1. -\] - -So on a polynomial \(a(X) = \sum_i a_i X^i\): - -\[ -\sigma_{-1}(a) = a_0 - \sum_{i=1}^{d-1} a_i\, X^{d-i}. -\] - -This is *exactly* the transform \(\bar{a}(X)\) from §3.3.1(A). - -### 7.2 Why the Gram matrix is the identity - -Consider the bilinear form \(B(a,b) = \mathrm{ct}(\sigma_{-1}(a)\cdot b)\) in the monomial basis \(\{1, X, \dots, X^{d-1}\}\). The Gram matrix is: - -\[ -G_{ij} = \mathrm{ct}\big(X^{j-i} \bmod (X^d+1)\big). -\] - -For \(j = i\): \(\mathrm{ct}(1) = 1\). - -For \(j \ne i\): the exponent \(j-i\) satisfies \(-(d-1) \le j-i \le d-1\) and \(j-i \ne 0\). -- If \(j > i\): \(\mathrm{ct}(X^{j-i}) = 0\) since \(1 \le j-i \le d-1\). -- If \(j < i\): \(X^{j-i} = X^{j-i+d}\cdot X^{-d} = -X^{d+j-i}\) where \(1 \le d+j-i \le d-1\), so \(\mathrm{ct}(-X^{d+j-i}) = 0\). - -Therefore \(G = I\) (the identity matrix). This means: - -\[ -\mathrm{ct}(\sigma_{-1}(a)\cdot b) = \mathrm{cf}(a)^\top\, I\, \mathrm{cf}(b) = \langle \mathrm{cf}(a),\,\mathrm{cf}(b)\rangle. -\] - -No Gram correction is needed. The pairing \((\sigma_{-1}, \mathrm{ct})\) gives the standard dot product directly. - -### 7.3 For the trinomial \(\Phi_{81}(X) = X^{54}+X^{27}+1\), the Gram matrix is NOT the identity - -Here \(X^{81} = 1\) but \(X^{27} \ne 1\) in \(R_F\). So \(X^{-27} = X^{54} = -X^{27}-1\), which gives: - -\[ -\mathrm{ct}(X^{-27}) = \mathrm{ct}(-X^{27}-1) = -1. -\] - -The Gram matrix \(G_{ij} = \mathrm{ct}(X^{j-i} \bmod \Phi_{81})\) therefore has off-diagonal entries \(G_{i,\,i+27} = -1\) (and their transposes). The inner-product transform for the trinomial (§3.3.1(B)) is \(T = G^{-1}\circ \sigma_{-1}\), which is why its formula involves sums like \(-(a_{27-i}+a_{54-i})\) rather than a simple sign flip. - -### 7.4 Bottom line - -SuperNeo's bilinear form is: - -\[ -B_{\mathrm{SuperNeo}}(a,b) = \mathrm{ct}\big(\sigma_{-1}(a)\cdot b\big) \in F_q. -\] - -Hachi's bilinear form is: - -\[ -B_{\mathrm{Hachi}}(a,b) = \mathrm{Tr}_H\big(a\cdot \sigma_{-1}(b)\big) \in R_q^H \cong \mathbb{F}_{q^k}. -\] - -Same involution \(\sigma_{-1}\). Different linear functional (\(\mathrm{ct}\) vs \(\mathrm{Tr}_H\)). Different target (\(F_q\) vs \(\mathbb{F}_{q^k}\)). - ---- - -## 8) Classification of non-degenerate bilinear forms on cyclotomic rings - -### 8.1 The general template - -For a cyclotomic ring \(R_q = F_q[X]/(\Phi(X))\) of degree \(d\), with Galois group \(\mathrm{Gal} = (\mathbb{Z}/\eta\mathbb{Z})^\times\) acting by \(\sigma_i: X\mapsto X^i\), the general bilinear form from an automorphism + linear functional is: - -\[ -B_{\sigma,\lambda}(a,b) = \lambda\big(a\cdot \sigma(b)\big) -\] - -where \(\sigma \in \mathrm{Gal}\) and \(\lambda: R_q \to T\) is a linear functional into some target \(T\). - -### 8.2 When is this non-degenerate? (Frobenius algebra theory) - -\(R_q = F_q[X]/(\Phi(X))\) is a **Frobenius algebra** over \(F_q\) (since cyclotomic polynomials are squarefree). This gives a clean classification: - -**Theorem (Frobenius classification)**: A linear functional \(\lambda: R_q \to F_q\) makes the bilinear form \(B(a,b) = \lambda(a\cdot b)\) non-degenerate if and only if \(\lambda\) is a **generating functional**, meaning the induced map \(R_q \to R_q^\vee\) (sending \(a\) to the functional \(b\mapsto \lambda(ab)\)) is an isomorphism. - -Moreover: **the set of all generating functionals is \(\{\lambda(g\,\cdot\,{-}) : g \in R_q^\times\}\)**. Once you have one non-degenerate form, all others come from pre-multiplying by a unit. - -For the form \(B_{\sigma,\lambda}(a,b)=\lambda(a\cdot\sigma(b))\), non-degeneracy reduces to: \(\lambda\circ(\text{mult by }\sigma(\cdot))\) is generating. Since \(\sigma\) is an automorphism (hence maps units to units), \(B_{\sigma,\lambda}\) is non-degenerate iff \(\lambda\) is generating. - -### 8.3 Complete menu of linear functionals - -The dual space \(R_q^\vee = \mathrm{Hom}_{F_q}(R_q, F_q)\) is \(d\)-dimensional. Here are the "natural" families: - -#### (A) Coefficient extraction: \(\mathrm{ct}_j(a) = [X^j](a)\) - -Target: \(F_q\). There are \(d\) such functionals (one per coefficient index \(j\)). - -\(\mathrm{ct} = \mathrm{ct}_0\) is the constant term. For \(\Phi = X^d+1\) with \(\sigma_{-1}\), the Gram matrix of \(\mathrm{ct}_0\) is the identity (§7.2). Other \(\mathrm{ct}_j\) give non-degenerate forms too, but with permuted/signed Gram matrices. - -*Generating?* Yes for many cyclotomics including \(X^d+1\). Can fail for pathological factorizations. - -#### (B) Absolute trace: \(\mathrm{Tr}_{R_q/F_q}(a) = \sum_{\sigma\in\mathrm{Gal}} \sigma(a)\) - -Target: \(F_q\). This is the canonical choice from algebraic number theory. - -*Generating?* Always yes for separable algebras (which cyclotomic rings are). - -Relation to \(\mathrm{ct}\): since both are generating, \(\mathrm{Tr}(a) = \mathrm{ct}(g\cdot a)\) for some explicit unit \(g\in R_q^\times\) (related to the "different ideal" of the cyclotomic extension). - -#### (C) Relative/partial trace: \(\mathrm{Tr}_H(a) = \sum_{\sigma\in H}\sigma(a) \in R_q^H\) - -Target: \(R_q^H \cong \mathbb{F}_{q^k}\) (the fixed subfield under a subgroup \(H \subseteq \mathrm{Gal}\)). - -This is what Hachi uses. The key upgrade: the target is an extension field \(\mathbb{F}_{q^k}\), not just \(F_q\). You get an \(\mathbb{F}_{q^k}\)-valued bilinear form, which means inner products live natively in the sumcheck domain. - -*Generating?* As a map \(R_q \to R_q^H\), yes: the induced \(R_q^H\)-bilinear form on \(R_q\) (viewed as a free \(R_q^H\)-module of rank \(d/k\)) is non-degenerate. - -Trace tower: \(\mathrm{Tr}_{R_q/F_q} = \mathrm{Tr}_{R_q^H/F_q}\circ \mathrm{Tr}_H\). So the relative trace "refines" the absolute trace. - -#### (D) Evaluation at a root: \(\mathrm{ev}_\zeta(a) = a(\zeta)\) for \(\zeta\) a root of \(\Phi\) in some \(\mathbb{F}_{q^t}\) - -Target: \(\mathbb{F}_{q^t}\). - -*Generating?* If \(\Phi\) is irreducible over \(F_q\) (so \(R_q \cong \mathbb{F}_{q^d}\)), every nonzero functional is generating. If \(\Phi\) factors, \(\mathrm{ev}_\zeta\) projects onto one CRT slot and annihilates the others, so it is **not** generating. - -**Fatal for norms**: the evaluation map is equivalent to NTT, which is not norm-preserving. This is exactly the problem SuperNeo identifies with prior approaches (§2.2). - -#### (E) CRT-slot projection: \(\pi_s: R_q \twoheadrightarrow \mathbb{F}_{q^t}\) - -When \(\Phi = \prod_i \phi_i\) factors over \(F_q\) (each \(\phi_i\) irreducible of degree \(t\)), \(R_q \cong \prod_i \mathbb{F}_{q^t}\). The projection \(\pi_s\) onto one factor is: - -Target: \(\mathbb{F}_{q^t}\). - -*Generating?* **No** --- it annihilates the other factors. - -**Same norm problem as (D)**: the CRT isomorphism is an NTT-like map. - -#### (F) Arbitrary \(F_q\)-linear combinations of the above - -Any \(\lambda = \sum_j c_j \,\mathrm{ct}_j\) for scalars \(c_j \in F_q\) gives a functional. It is generating iff the associated element \(g = \sum_j c_j X^j \in R_q\) is a unit. - -### 8.4 Practical takeaway - -If you want **norm preservation**, you must stay in "coefficient-land" (functionals A, B, C, F). Evaluation-based functionals (D, E) destroy norms. - -If you want **extension-field-valued inner products** (for native sumcheck over \(\mathbb{F}_{q^k}\)), the only natural coefficient-land option is **(C) the relative trace** \(\mathrm{Tr}_H\). - ---- - -## 9) The evaluation homomorphism (SuperNeo Theorem 5), spelled out - -This is the key property that makes SuperNeo's folding work. The paper states it abstractly; here is the fully explicit version. - -### 9.1 Setup - -Fix: -- Base field \(F = \mathbb{F}_q\), extension \(K = \mathbb{F}_{q^2}\) (or any extension with \(1/|K| = \mathrm{negl}(\lambda)\)). -- Cyclotomic ring \(R_F = F[X]/(\Phi(X))\), \(R_K = K[X]/(\Phi(X))\), degree \(d\). -- A CCS matrix \(M \in F^{m\times n_F}\) with \(n_F = d\cdot n_R\). -- Witness vectors \(z_1, \dots, z_\ell \in F^{n_F}\), coefficient-embedded as \(\mathbf{z}_i \in R_F^{n_R}\). -- Folding challenges \(\rho_1, \dots, \rho_\ell \in C \subset R_F\) (short ring elements). -- An evaluation point \(r \in K^{\log m}\) (from a prior sumcheck round). -- Any \(R_F\)-module homomorphisms \(L: R_F^{n_R}\to C\) (commitment) and \(\mathrm{Lin}: R_F^{n_R}\to R_F^{n_{R,\mathrm{in}}}\) (input extraction). - -### 9.2 Per-instance "lifted" claims - -For each instance \(i\in[\ell]\), define three objects: - -- **Commitment**: \(c_i := L(\mathbf{z}_i) \in C\) (Ajtai commitment of the ring vector). -- **Input**: \(x_i := \mathrm{Lin}(\mathbf{z}_i) \in R_F^{n_{R,\mathrm{in}}}\) (public input part). -- **Lifted evaluation**: \(y_i := \overline{M}\,\widetilde{\mathbf{z}_i}(r) \in R_K\) (apply the transformed matrix \(\overline{M}\) to the multilinear extension of the ring vector \(\mathbf{z}_i\), evaluated at \(r\)). - -The lifted evaluation \(y_i\) is a **ring element in \(R_K\)** (not a field element in \(K\)). Its constant term recovers the field-level evaluation (by Theorem 4 / Remark 2): - -\[ -\mathrm{ct}(y_i) = M\,\widetilde{z_i}(r) \in K. -\] - -In other words: \(y_i\) has \(d\) coefficients in \(K\); the constant coefficient is the "real" field evaluation; the other \(d-1\) coefficients carry extra information that is needed for folding consistency. - -### 9.3 The evaluation homomorphism (Theorem 5) - -**Statement**: Define the folded objects: - -\[ -\mathbf{z} := \sum_{i\in[\ell]} \rho_i\,\mathbf{z}_i \in R_F^{n_R}, \quad -c := \sum_{i\in[\ell]} \rho_i\, c_i \in C, \quad -x := \sum_{i\in[\ell]} \rho_i\, x_i \in R_F^{n_{R,\mathrm{in}}}, -\quad -y := \sum_{i\in[\ell]} \rho_i\, y_i \in R_K. -\] - -Then **all three of the following hold simultaneously**: - -1. **Commitment homomorphism**: \(c = L(\mathbf{z})\). -2. **Lifted-evaluation homomorphism**: \(y = \overline{M}\,\widetilde{\mathbf{z}}(r)\). -3. **Field-evaluation consistency**: \(\mathrm{ct}(y) = M\,\widetilde{z}(r) \in K\) where \(z = \sum_i \rho_i z_i \in F^{n_F}\). - -(1) holds because \(L\) is \(R_F\)-linear. (2) holds because multilinear extension is \(K\)-linear and matrix multiplication is \(R_K\)-linear. (3) follows from applying \(\mathrm{ct}\) to (2) and invoking Theorem 4. - -### 9.4 Why ring-level claims are essential (the subtle point) - -The folding challenge \(\rho_i \in R_F\) is a **ring** scalar, not a field scalar. At the field level, multiplying by \(\rho_i\) acts on the coefficient vector \(z_i \in F^{n_F}\) by **convolution** (polynomial multiplication scrambles coefficients), not by coordinate-wise scaling. - -This means: -- **At the field level**: after folding, the individual CCS constraints \(Mz = 0\) do NOT hold in any simple sense. The "meaning" of the folded witness as a CCS satisfier is lost. -- **At the ring level**: the commitment, lifted evaluation claims, and input extraction all fold cleanly. The accumulator stores \((c, x, r, y)\) as ring-level objects. - -This is why SuperNeo's accumulator relation is **CE (CCS Evaluation)**, not CCS itself: it stores ring-level evaluation claims \(y_j \in R_K\), and the decider checks them by opening the commitment and verifying ring-level equalities. The \(\mathrm{ct}\) extraction (field-level check) happens only once, at decision time. - -### 9.5 Contrast with Hachi - -Hachi does not need an "evaluation homomorphism" in SuperNeo's sense because Hachi does not fold multiple instances. Instead: - -- Hachi's protocol reduces a *single* opening claim by splitting the coefficient table into blocks, folding with a sparse ring challenge \(c\), and then using ring-switching + sumcheck. -- The analogue of "linearity under ring multiplication" in Hachi is the fold relations (Eq. (18)--(19)): \(a^\top G_{2^m} z = (c^\top\otimes G_1)\hat{w}\) and \(Az = (c^\top\otimes G_{n_A})\hat{t}\), which are linear in the sparse challenge \(c\). - -Both papers exploit the same algebraic fact (ring multiplication is \(R_F\)-linear), but for different protocol purposes: folding (SuperNeo) vs opening reduction (Hachi). - ---- - -## 10) Unified embedding framework (best of both worlds) - -### 10.1 The core observation - -The two bilinear forms use the **same involution** \(\sigma_{-1}\) and differ only in the "readout functional": - -| | SuperNeo | Hachi | -|---|---|---| -| Form | \(\mathrm{ct}(\sigma_{-1}(a)\cdot b)\) | \(\mathrm{Tr}_H(\sigma_{-1}(a)\cdot b)\) | -| Target | \(F_q\) | \(\mathbb{F}_{q^k}\) | -| Gram (for \(X^d+1\)) | \(I\) (identity) | Non-trivial (absorbed into \(\psi\)) | - -These are **compatible**: they use the same product \(\sigma_{-1}(a)\cdot b\) in \(R_q\) and differ only in what you project onto. The trace tower connects them: - -\[ -\mathrm{Tr}_{R_q/F_q} = \mathrm{Tr}_{\mathbb{F}_{q^k}/F_q} \circ \mathrm{Tr}_H. -\] - -### 10.2 The unified pairing abstraction - -**Definition (Cyclotomic Pairing).** Given: -- cyclotomic ring \(R_q\) of degree \(d\), -- a subfield \(S \cong \mathbb{F}_{q^k}\) realized as \(R_q^H \subseteq R_q\) (or \(S = F_q\) as the trivial case \(k=1\)), -- the involution \(\sigma_{-1} \in \mathrm{Aut}(R_q)\), -- the relative trace \(\mathrm{Tr}_H: R_q \to S\), - -define the **level-\(k\) pairing**: - -\[ -B_k(a,b) := \mathrm{Tr}_H\big(\sigma_{-1}(a)\cdot b\big) \in S \cong \mathbb{F}_{q^k}. -\] - -Special cases: -- **\(k = 1\)** (\(H = \mathrm{Gal}\), \(S = F_q\)): \(B_1\) is (up to unit scaling) the absolute-trace pairing. Closely related to SuperNeo's \(\mathrm{ct}\)-based form. -- **\(k = d\)** (\(H = \{1\}\), \(S = R_q\)): \(B_d(a,b) = \sigma_{-1}(a)\cdot b\) (the ring product itself, no projection). -- **\(1 < k < d\)** (\(H\) a proper subgroup): Hachi's setting. \(B_k\) is an \(\mathbb{F}_{q^k}\)-valued non-degenerate bilinear form on the free \(\mathbb{F}_{q^k}\)-module \(R_q \cong \mathbb{F}_{q^k}^{d/k}\). - -### 10.3 Combined embedding pipeline - -``` -Field witness z ∈ F_q^{d·n_R} - │ coefficient embedding (SuperNeo Def. 7, norm-preserving) - ▼ -Ring vector z ∈ R_q^{n_R} ← ‖z‖_∞ preserved - │ Ajtai commit: c = Az - ▼ -Commitment c ∈ R_q^κ - │ - ├── MODE A (SuperNeo-style folding): - │ Use B_1: ct(σ_{-1}(a)·b) = ⟨cf(a), cf(b)⟩ ∈ F_q - │ → sumcheck over K = F_{q²}, fold with ρ ∈ R_F, track ring-level claims y ∈ R_K - │ - └── MODE B (Hachi-style PCS opening): - Use B_k: Tr_H(σ_{-1}(a)·b) ∈ F_{q^k} - → ring-switch at α ∈ F_{q^k}, sumcheck over F_{q^k}, recurse on smaller instance -``` - -The committed object \(\mathbf{z}\in R_q^{n_R}\) is the same in both modes. The choice of functional only affects how you read out inner products and run the interactive proof. - -### 10.4 What you gain - -| Property | SuperNeo alone | Hachi alone | Unified | -|---|---|---|---| -| Norm-preserving embedding | Yes | N/A (PCS, not CCS) | Yes | -| Pay-per-bit commitments | Yes | No | Yes | -| Extension-field inner products | No (\(\mathrm{ct}\to F_q\)) | Yes (\(\mathrm{Tr}_H\to \mathbb{F}_{q^k}\)) | Yes | -| Sumcheck natively over \(\mathbb{F}_{q^k}\) | No (needs \(K\) externally) | Yes | Yes | -| Power-of-two cyclotomics | Supported | Required | Supported | -| General cyclotomics (trinomials) | Supported | Not discussed | Supported (Gram \(\ne I\)) | - -### 10.5 The Gram cost of switching from \(\mathrm{ct}\) to \(\mathrm{Tr}_H\) - -For \(\Phi = X^d+1\) with \(\sigma_{-1}\): -- \(\mathrm{ct}\): Gram = \(I\). No correction needed. Beautifully simple. -- \(\mathrm{Tr}_H\): Gram \(\ne I\). Hachi absorbs this into the packing map \(\psi:(R_q^H)^{d/k}\to R_q\) (Theorem 2, Eq. (8)). - -If you use \(\mathrm{Tr}_H\) instead of \(\mathrm{ct}\), you need: -- the packing map \(\psi\) (one \(O(d)\) linear map per block), -- its inverse \(\psi^{-1}\) (for verification). - -Both are explicit, \(O(d)\)-time, and defined once per parameter set. The Galois subgroup \(H\) and the map \(\psi\) are static public data. - -### 10.6 When you would want each mode - -- **Folding** (SuperNeo-style IVC) with pay-per-bit: use \(\mathrm{ct}\) mode. The evaluation homomorphism (§9) works cleanly because the Gram is trivial. -- **PCS opening** (Hachi-style recursive reduction): switch to \(\mathrm{Tr}_H\) mode when you need ring-switching at \(\alpha \in \mathbb{F}_{q^k}\). -- **Hybrid fold-then-open**: fold in \(\mathrm{ct}\) mode (accumulating ring-level claims), then at the end, open the accumulated commitment using \(\mathrm{Tr}_H\) mode for efficient PCS verification. - -The handoff between modes is seamless because the committed object \(\mathbf{z}\in R_q^{n_R}\) is the same either way. diff --git a/docs/FIELD_OPS_PERF.md b/docs/FIELD_OPS_PERF.md deleted file mode 100644 index 13a90846..00000000 --- a/docs/FIELD_OPS_PERF.md +++ /dev/null @@ -1,237 +0,0 @@ -# Field Operations Performance - -Benchmark results for scalar and packed (SIMD) field arithmetic across -platforms. All numbers are **element throughput** (median) reported by -`criterion` over 4096-element arrays (`cargo bench --bench field_arith`). - -## Prime selection - -All primes (except M31) are pseudo-Mersenne: `q = 2^k − c` where `c` is -the **smallest positive offset** such that `q` is prime and `q ≡ 5 -(mod 8)`. The congruence `q ≡ 5 (mod 8)` is required so that the -cyclotomic ring `Z_q[X]/(X^d + 1)` splits fully via NTT when `d` is a -power of two (equivalently, `−1` is a quadratic residue but not a quartic -residue mod `q`). - -The constraint `q ≡ 5 (mod 8)` forces `c ≡ 2^k − 5 (mod 8)`: - -| k mod 8 | required c mod 8 | examples | -|---------|------------------|----------| -| 0 | 3 | k=24,32,40,48,56,64,128 | -| 6 | 1 | k=30 | -| 7 | 2 | k=31 | - -For each `k`, smaller candidates were checked and found composite. For -instance at `k = 31` (`c ≡ 3 mod 8`): `2^31 − 3 = 5 × 429496729`, -`2^31 − 11 = 3 × 715827879`, so the first prime is `2^31 − 19`. - -**M31** (`2^31 − 1`, Mersenne prime, `q ≡ 7 mod 8`) is included for -comparison with plonky3 even though it does not satisfy `q ≡ 5 (mod 8)`. - -## Primes benchmarked - -| Label | Modulus | Offset | Rust type | SIMD width | -|-------|---------|--------|-----------|------------| -| fp32_24b | `2^24 − 3` | 3 | `Fp32` | AVX-512: 16, AVX2: 8, NEON: 4 | -| fp32_30b | `2^30 − 35` | 35 | `Fp32` | AVX-512: 16, AVX2: 8, NEON: 4 | -| fp32_31b | `2^31 − 19` | 19 | `Fp32` | AVX-512: 16, AVX2: 8, NEON: 4 | -| fp32_m31 | `2^31 − 1` | 1 | `Fp32` | AVX-512: 16, AVX2: 8, NEON: 4 | -| fp32_32b | `2^32 − 99` | 99 | `Fp32` | AVX-512: 16, AVX2: 8, NEON: 4 | -| fp64_40b | `2^40 − 195` | 195 | `Fp64` | AVX-512: 8, AVX2: 4, NEON: 2 | -| fp64_48b | `2^48 − 59` | 59 | `Fp64` | AVX-512: 8, AVX2: 4, NEON: 2 | -| fp64_56b | `2^56 − 27` | 27 | `Fp64` | AVX-512: 8, AVX2: 4, NEON: 2 | -| fp64_64b | `2^64 − 59` | 59 | `Fp64` | AVX-512: 8, AVX2: 4, NEON: 2 | -| fp128 | `2^128 − 275` | 275 | `Fp128` | AVX-512: 8 (SoA), AVX2: 4 (SoA), NEON: 2 (SoA) | - ---- - -## AMD Zen 5 (Ryzen 9950X / leopard) - -Backend: **AVX-512** (16-wide Fp32, 8-wide Fp64, 8-wide Fp128 SoA with -vectorized add/sub and scalar-per-lane mul). -`RUSTFLAGS='-C target-cpu=native'`, nightly toolchain. - -### Scalar (`throughput/`) - -| Field | mul | add | -|-------|-----|-----| -| fp32_24b | 1.224 Gelem/s | 2.050 Gelem/s | -| fp32_30b | 1.220 Gelem/s | 2.026 Gelem/s | -| fp32_31b | 1.212 Gelem/s | 1.866 Gelem/s | -| fp32_m31 | 1.355 Gelem/s | 1.993 Gelem/s | -| fp32_32b | 1.219 Gelem/s | 1.955 Gelem/s | -| fp64_40b | 1.018 Gelem/s | 2.074 Gelem/s | -| fp64_48b | 1.021 Gelem/s | 2.073 Gelem/s | -| fp64_56b | 0.945 Gelem/s | 2.060 Gelem/s | -| fp64_64b | 0.927 Gelem/s | 1.840 Gelem/s | -| fp128 | 0.452 Gelem/s | 1.127 Gelem/s | - -### Packed (`packed_throughput/`) - -| Field | mul | add | sub | -|-------|-----|-----|-----| -| fp32_24b | 5.362 Gelem/s | 12.76 Gelem/s | 12.74 Gelem/s | -| fp32_30b | 6.145 Gelem/s | 13.53 Gelem/s | 13.55 Gelem/s | -| fp32_31b | 6.187 Gelem/s | 13.53 Gelem/s | 13.54 Gelem/s | -| fp32_m31 | 6.943 Gelem/s | 13.56 Gelem/s | 13.50 Gelem/s | -| fp32_32b | 6.785 Gelem/s | 13.02 Gelem/s | 12.66 Gelem/s | -| fp64_40b | 1.961 Gelem/s | 5.847 Gelem/s | 5.861 Gelem/s | -| fp64_48b | 1.942 Gelem/s | 5.852 Gelem/s | 5.853 Gelem/s | -| fp64_56b | 1.937 Gelem/s | 5.847 Gelem/s | 5.796 Gelem/s | -| fp64_64b | 1.742 Gelem/s | 5.278 Gelem/s | 5.760 Gelem/s | -| fp128 | 0.284 Gelem/s | 2.314 Gelem/s | 3.175 Gelem/s | - -### Packed speedup over scalar - -| Field | mul | add | -|-------|-----|-----| -| fp32_24b | **4.4x** | **6.2x** | -| fp32_30b | **5.0x** | **6.7x** | -| fp32_31b | **5.1x** | **7.3x** | -| fp32_m31 | **5.1x** | **6.8x** | -| fp32_32b | **5.6x** | **6.7x** | -| fp64_40b | **1.9x** | **2.8x** | -| fp64_48b | **1.9x** | **2.8x** | -| fp64_56b | **2.0x** | **2.8x** | -| fp64_64b | **1.9x** | **2.9x** | -| fp128 | **0.6x** | **2.1x** | - -### Sumcheck MACC (`packed_sumcheck_mix/`) - -`acc += eq[i] * poly[i]` loop (dominant inner loop in sumcheck provers). - -| Field | MACC | % of pure mul | -|-------|------|---------------| -| fp32_24b | 4.764 Gelem/s | 89% | -| fp32_30b | 5.352 Gelem/s | 87% | -| fp32_31b | 5.351 Gelem/s | 86% | -| fp32_m31 | 6.097 Gelem/s | 88% | -| fp32_32b | 3.409 Gelem/s | 50% | -| fp64_40b | 1.488 Gelem/s | 76% | -| fp64_48b | 1.492 Gelem/s | 77% | -| fp64_56b | 1.491 Gelem/s | 77% | -| fp64_64b | 1.141 Gelem/s | 65% | -| fp128 | 0.323 Gelem/s | 114% | - ---- - -## Apple M4 Pro (macOS / aarch64) - -Backend: **NEON** (4-wide Fp32, 2-wide Fp64, 2-wide Fp128 SoA). -`RUSTFLAGS='-C target-cpu=native'`, nightly toolchain. - -### Scalar (`throughput/`) - -| Field | mul | add | -|-------|-----|-----| -| fp32_24b | 1.129 Gelem/s | 1.426 Gelem/s | -| fp32_30b | 1.133 Gelem/s | 1.425 Gelem/s | -| fp32_31b | 1.043 Gelem/s | 1.433 Gelem/s | -| fp32_m31 | 1.319 Gelem/s | 1.435 Gelem/s | -| fp32_32b | 1.135 Gelem/s | 1.423 Gelem/s | -| fp64_40b | 0.871 Gelem/s | 1.446 Gelem/s | -| fp64_48b | 0.886 Gelem/s | 1.385 Gelem/s | -| fp64_56b | 0.891 Gelem/s | 1.442 Gelem/s | -| fp64_64b | 0.923 Gelem/s | 1.443 Gelem/s | -| fp128 | 0.444 Gelem/s | 0.938 Gelem/s | - -### Packed (`packed_throughput/`) - -| Field | mul | add | sub | -|-------|-----|-----|-----| -| fp32_24b | 3.717 Gelem/s | 5.272 Gelem/s | 5.278 Gelem/s | -| fp32_30b | 3.719 Gelem/s | 5.281 Gelem/s | 5.275 Gelem/s | -| fp32_31b | 3.719 Gelem/s | 5.283 Gelem/s | 5.268 Gelem/s | -| fp32_m31 | 3.720 Gelem/s | 5.263 Gelem/s | 5.263 Gelem/s | -| fp32_32b | 2.524 Gelem/s | 5.296 Gelem/s | 5.253 Gelem/s | -| fp64_40b | 1.253 Gelem/s | 2.648 Gelem/s | 2.645 Gelem/s | -| fp64_48b | 1.254 Gelem/s | 2.650 Gelem/s | 2.643 Gelem/s | -| fp64_56b | 1.255 Gelem/s | 2.632 Gelem/s | 2.650 Gelem/s | -| fp64_64b | 1.399 Gelem/s | 2.639 Gelem/s | 2.602 Gelem/s | -| fp128 | 0.480 Gelem/s | 1.724 Gelem/s | 2.107 Gelem/s | - -### Packed speedup over scalar - -| Field | mul | add | -|-------|-----|-----| -| fp32_24b | **3.3x** | **3.7x** | -| fp32_30b | **3.3x** | **3.7x** | -| fp32_31b | **3.6x** | **3.7x** | -| fp32_m31 | **2.8x** | **3.7x** | -| fp32_32b | **2.2x** | **3.7x** | -| fp64_40b | **1.4x** | **1.8x** | -| fp64_48b | **1.4x** | **1.9x** | -| fp64_56b | **1.4x** | **1.8x** | -| fp64_64b | **1.5x** | **1.8x** | -| fp128 | **1.1x** | **1.8x** | - -### Sumcheck MACC (`packed_sumcheck_mix/`) - -| Field | MACC | % of pure mul | -|-------|------|---------------| -| fp32_24b | 2.652 Gelem/s | 71% | -| fp32_30b | 2.660 Gelem/s | 72% | -| fp32_31b | 2.662 Gelem/s | 72% | -| fp32_m31 | 2.661 Gelem/s | 72% | -| fp32_32b | 1.991 Gelem/s | 79% | -| fp64_40b | 0.990 Gelem/s | 79% | -| fp64_48b | 0.991 Gelem/s | 79% | -| fp64_56b | 0.993 Gelem/s | 79% | -| fp64_64b | 0.795 Gelem/s | 57% | -| fp128 | 0.450 Gelem/s | 94% | - ---- - -## Notes - -### Zen 5 AVX-512 observations - -- **Fp32 add/sub** saturate at ~13–13.5 Gelem/s, close to 1 cycle per - 16-wide vector at 5 GHz. -- **M31 is the fastest Fp32 prime** for packed mul (6.94 Gelem/s) and - sumcheck MACC (6.10 Gelem/s), because `C = 1` minimizes the reduction - chain. -- **Fp32 mul** is latency-bound by the 2-fold Solinas reduction chain - (~18 cycles per vector). -- **Fp64 sub-word** primes (40b, 48b, 56b) show nearly identical packed - mul throughput (~1.94 Gelem/s), since the vectorized schoolbook - multiply + Solinas reduction dominates regardless of bit-width. -- **Fp64 64b** is slower than sub-word variants due to multi-stage - overflow tracking in the Solinas reduction. -- **Fp32 32b sumcheck MACC** drops to 50% of pure mul, the worst ratio, - because the carry-based add correction creates additional dependencies - in the `acc += eq * poly` loop. -- **Fp128** packed backend now uses SoA layout (8-wide) with vectorized - add/sub via `__m512i`. Add improved **2.1x** (1.13 → 2.31 Gelem/s), - sub improved **2.4x** (1.34 → 3.18 Gelem/s). Mul remains scalar - per-lane and regressed 0.6x (0.45 → 0.28 Gelem/s) due to SoA - pack/unpack overhead. Sumcheck MACC is -7% (0.35 → 0.32 Gelem/s); - MACC exceeds pure-mul throughput (114%) because the accumulation loop - avoids the SoA store overhead that the throughput benchmark incurs. - -### M4 Pro NEON observations - -- **NEON is 4-wide for Fp32, 2-wide for Fp64/Fp128**, so maximum - speedup is 4x and 2x respectively (vs 16x/8x for AVX-512). -- **Fp32 packed mul** is uniform at ~3.72 Gelem/s for all sub-word - primes (24b–31b, including M31), unlike Zen 5 where M31 is notably - faster. The 4-wide NEON `vmull_u32` + reduction is the bottleneck. -- **Fp32 32b packed mul** drops to 2.52 Gelem/s (carry-based path). -- **Fp64 packed mul** ~1.25 Gelem/s for all sub-word primes, ~1.40 - for 64b — the 64b prime is *faster* on NEON, opposite to Zen 5. -- **Fp128 packed add** 1.72 Gelem/s = **1.8x** scalar speedup; sub - 2.11 Gelem/s = **2.2x**, both close to the theoretical 2x from - 2-wide `uint64x2_t`. Mul 0.48 Gelem/s ≈ **1.1x** (scalar per-lane). -- **Sumcheck MACC** is 71–72% of pure mul for sub-word Fp32, 79% for - Fp64 sub-word, and 94% for Fp128 — higher than Zen 5 ratios. - -### Reduction strategy by field width - -| Field | Reduction method | -|-------|-----------------| -| Fp32, BITS ≤ 31 | `min(t, t−P)` — single unsigned compare + blend | -| Fp32, BITS = 32 | carry-based: detect overflow, conditionally add `C`, then subtract `P` if `≥ P` | -| Fp64, BITS ≤ 62 | 2-fold Solinas in u64: `(lo & mask) + c * (lo >> k)`, repeat | -| Fp64, BITS = 64 | vectorized schoolbook 64×64→128 + multi-stage Solinas with overflow tracking | -| Fp128 add/sub | vectorized 128-bit add/sub with carry/borrow propagation via `__m512i` | -| Fp128 mul | scalar per-lane: 9-limb Solinas via u64 decomposition | diff --git a/docs/HACHI_DIGEST.md b/docs/HACHI_DIGEST.md deleted file mode 100644 index c0d0328b..00000000 --- a/docs/HACHI_DIGEST.md +++ /dev/null @@ -1,1362 +0,0 @@ -# Hachi Digest (for side-by-side comparison with SuperNeo) - -This file captures the parts of `paper/hachi.pdf` that are most actionable for understanding Hachi’s **parameterization** and **protocol shape**, in a compact AI-readable format. - -Primary source: `paper/hachi.pdf` (“Hachi: Efficient Lattice-Based Multilinear Polynomial Commitments over Extension Fields”). - -## Canonical parameter tuples (from paper) - -The paper gives a concrete benchmark parameter set (ℓ = 30) in Figure 9 and uses it to estimate proof size (~55KB) in §5.2. - -```yaml -hachi_parameter_tuples: - - id: l30_benchmark_first_round - witness_num_vars_ell: 30 - base_field: - q: 4294967197 # ~2^32, prime (paper Fig. 9) - ring_coeffs: "Z_q (aka F_q)" - extension_field_for_sumcheck: - k: 4 - field: "F_{q^4}" # paper §5.1, §5.4 - cyclotomic_ring: - phi: "X^d + 1" - alpha: 10 - d: 1024 - ring: "R_q = Z_q[X]/(X^d + 1)" - split_and_fold_params: - m: 10 - r: 10 - commitment_matrices_heights: - nA: 1 - nB: 1 - nD: 1 - decomposition_and_challenges: - decomposition_base_b: 16 - delta: 8 # decomposition length (Fig. 9) - tau: 4 # expansion factor for decomposing z (Fig. 9) - omega_L1: 16 - c_nonzero_coeffs_in_challenge: 16 - norm_bounds: - z_Linf_bound: 30583 - next_witness_Linf_bound: 8 - next_round_witness: - size: 226 - proof_size_estimate: - first_round_sumcheck: "~7.3KB" - adaptation_overhead: "~4.8KB" - greyhound_subproof: "~43KB" - total: "~55.1KB" - timings_reported: - verify_ms_server: 227 # paper §5.2 narrative (first round), plus Fig. 8 context - verify_ms_server_greyhound: 130 # cited as Greyhound estimate in §5.2 narrative -``` - -Notes: - -- The paper’s 55.1KB estimate is explicitly derived in §5.2 (“To conclude, the total evaluation proof can be estimated to be 7.3 + 4.8 + 43 KB = 55.1KB.”). -- This tuple is the “Hachi + compose with Greyhound” estimate for ℓ = 30, not “Hachi alone forever”; Hachi’s design explicitly allows switching to Greyhound/LaBRADOR at small witness sizes. - -## Exact counts (from the paper’s concrete section) - -- Total explicit concrete parameter tables in the paper: **1** (Figure 9; ℓ = 30). -- Concrete benchmark variable counts shown: **3** (ℓ ∈ {26, 28, 30} in Figure 8 timings), but only ℓ = 30 is fully parameterized in Figure 9. -- Unique cyclotomic family used: **1** (`X^d + 1` with `d` power of two). - -## What Hachi suggests (for its purpose) - -High-level message (from the abstract + technical overview): - -- Use **sum-check** to get fast verification, but avoid doing sum-check “over the ring”. -- Use **ring switching** (evaluate at a random α in an extension field) so that the verifier’s checks are field-native and do not require expensive \(R_q\) multiplication. -- Use a **generic reduction** to convert evaluation proofs over extension fields \(F_{q^k}\) into equivalent ring statements over \(R_q\), enabling extension-field evaluation support for lattice PCS. - -Concrete implication (paper §5.3–§5.4): - -- Hachi can pick **larger ring dimensions** (e.g. \(d=1024\)) than Greyhound’s typical \(d=64\) and still keep verification efficient; larger \(d\) helps commitment time (fewer ring mults, NTT-friendly structure) and enables very sparse challenges. - -## Fit into this repo design (easy vs harder) - -- Easy fit (already aligned): - - Hachi’s core ring family is power-of-two cyclotomic \(R_q = Z_q[X]/(X^d+1)\), which matches this repo’s existing algebra/ring direction. -- Harder pieces (protocol-level, not yet fully implemented here): - - Ring switching pipeline (lifting ring equations to \(Z_q[X]\), evaluate at random α in \(F_{q^k}\), sum-check over \(F_{q^k}\)). - - The “compose with Greyhound” handoff (treating the reduced witness as a short ring instance for an existing PCS/proof system). - -## Notation glossary (from `paper/hachi.pdf`) - -Hachi’s paper reuses common lattice-proof-system symbols; here are the ones that tend to confuse on first read. - -### Base objects - -- **\(q\)**: prime modulus; base ring/field is \(Z_q\) (paper treats \(Z_q\) and \(F_q\) interchangeably). -- **\(d = 2^\alpha\)**: cyclotomic ring dimension (power of two). -- **\(\alpha\)**: shorthand for \(\log_2 d\) (used heavily in §3’s “variable count after transformation” formulas). -- **\(R\)**: integer cyclotomic ring \(Z[X]/(X^d+1)\). -- **\(R_q\)**: cyclotomic ring mod \(q\): \(Z_q[X]/(X^d+1)\). -- **\(F_{q^k}\)**: extension field used to run sum-check with negligible soundness error. -- **\(\kappa\)**: shorthand for \(\log_2 k\) when \(k\) is a power of two (this is the \(\kappa\) used in §3.2 and in the “\(\ell-\alpha+\kappa\)” variable-count formulas). -- **\(\sigma_i\)**: Galois automorphism \(X \mapsto X^i\) on \(R\) / \(R_q\) (with \(i\in (\mathbb{Z}/2d\mathbb{Z})^\times\)). -- **\(R_q^H\)**: fixed ring under a subgroup \(H\) of automorphisms; becomes a subfield isomorphic to \(F_{q^k}\) under conditions (Lemma 1 informal in §1.3). -- **\(\mathrm{Tr}_H\)**: trace map \(R_q \to R_q^H\). -- **\(\psi\)**: an efficiently computable bijection \((R_q^H)^{d/k} \to R_q\) used to turn trace-of-product into inner products (Theorem 1 informal in §1.3). - -### Multilinear polynomials / sizes - -- **\(\ell\)**: number of variables of the multilinear polynomial (so witness length is \(2^\ell\)). -- **\(L := 2^\ell\)**: number of coefficients / evaluation-table length. - -### Split-and-fold / decomposition parameters (Figure 9) - -The paper uses **\(m, r\)** as “folding parameters” (they are *not* the same \(m\) as “#constraints” in SuperNeo’s CCS section). - -- **\(m, r\)**: split-and-fold parameters controlling the shape of the quadratic relation after one reduction step. -- **\(b\)**: decomposition base (e.g. 16 in Fig. 9). -- **\(\delta\)**: decomposition length for base witness (e.g. 8 in Fig. 9; essentially \(\lceil \log_b q\rceil\) in spirit). -- **\(\tau\)**: expansion factor / extra length parameter for decomposing intermediate vectors (e.g. 4 in Fig. 9). -- **\(\omega\)**: \(\ell_1\)-norm bound on a sparse challenge (Fig. 9). -- **\(c\)**: number of nonzero coefficients in a sparse challenge polynomial (Fig. 9). - -### Commitment matrix “heights” (Figure 9) - -Hachi uses commitment matrices \(A,B,D\) (not the same “Ajtai A” notation as in SuperNeo). - -- **\(n_A, n_B, n_D\)**: heights (row counts) of the corresponding commitment matrices in the composed relation (Fig. 9 uses all 1). - -## Protocol overview (what is proved, and what is sent) - -This is an end-to-end walkthrough of the **full Hachi protocol**, in the order it’s built in `paper/hachi.pdf`. - -### What Hachi is (PCS statement + design goal, **field-first**) - -The digest previously jumped straight to the §4 “ring PCS statement”. That is **not the full picture**: the paper’s *natural* PCS interface is the usual one where the **witness coefficients are in the base field** \(Z_q \cong F_q\) but the **evaluation point is in an extension field** \(F_{q^k}\) (because sumcheck / batching wants negligible soundness error). - -Concretely, the “true” opening statement the paper starts from (Intro + §3.2) is: - -- **Witness polynomial (true witness)**: \(f \in Z_q^{\le 1}[X_1,\dots,X_\ell]\) (equivalently \(F_q^{\le1}[\cdot]\)), with coefficient table \((f_i)_{i\in\{0,1\}^\ell}\subset Z_q\). -- **Claim (extension-field point/value)**: for a public point \(x=(x_1,\dots,x_\ell)\in F_{q^k}^\ell\), prove \(f(x)=y\in F_{q^k}\). - -Hachi is engineered so that the verifier’s heavy checking runs as **sumcheck over \(F_{q^k}\)** (fast), while commitments / Module-SIS structure remain over the cyclotomic ring \(R_q = Z_q[X]/(X^d+1)\). - -### Step 0 (paper §3.2 → §3.1): the missing “embedding” step (from **\(F_q\)-witness @ \(F_{q^k}\)-point** to a ring statement) - -The paper’s §3 is exactly the bridge from the “true” statement above to the §4 ring PCS statement. - -#### 0.A (paper §3.2): reduce **\(f\in Z_q[\cdot]\)** at **\(x\in F_{q^k}^\ell\)** to one evaluation over \(F_{q^k}\) - -Assume \(k\) is a power of two and write \(k = 2^\kappa\) (this \(\kappa\) is the one used in §3). Split variables into the first \(\kappa\) and the remaining \(\ell-\kappa\). The evaluation can be rewritten (paper Eq. (11)) as: - -\[ -y \;=\;\sum_{i\in\{0,1\}^\kappa}\Big(\prod_{t=1}^{\kappa} x_t^{i_t}\Big)\cdot y_i, -\quad\text{where}\quad -y_i \;:=\; f_{i}(\,x_{\kappa+1},\dots,x_\ell\,)\in F_{q^k}. -\] - -So the prover can send the \(k=2^\kappa\) *partial evaluations* \((y_i)_i\) (and the verifier checks the recombination); what remains is to prove each \(y_i\) is well-formed. - -Paper detail (§3.2, right after Eq. (11)): the verifier can compute \(y_{0\ldots 0}\) from the claimed \(y\) and the other \(y_i\), so in principle only **\(k-1\)** of the partial evaluations need to be transmitted. - -To make that “prove all \(y_i\)” look like **one** extension-field evaluation, §3.2 defines \(F_{q^k} := F_q[Z]/\varphi(Z)\) and builds an \((\ell-\kappa)\)-variate multilinear polynomial \(f' \in F_{q^k}[X_{\kappa+1},\dots,X_\ell]\) by *embedding* the \(k\) slices \((f_i)_i\) into the \(F_q\)-basis \(1,Z,Z^2,\dots,Z^{k-1}\) (paper §3.2): - -\[ -f'(X_{\kappa+1},\dots,X_\ell) -:=\sum_{i\in\{0,1\}^\kappa} -f_i(X_{\kappa+1},\dots,X_\ell)\cdot Z^{\sum_{t=1}^{\kappa} i_t 2^{t-1}}. -\] - -Then \(f'(x_{\kappa+1},\dots,x_\ell)=\sum_i y_i\cdot Z^{(\cdot)}\) holds as an algebraic identity. - -**Critical caveat (security / binding):** it is **not** generally sound to claim that “proving the single packed value \(f'(x_{\kappa+1},\dots,x_\ell)\)” suffices to prove that *each* \(y_i\) is correct, because the coefficients \(y_i\) live in \(F_{q^k}\) (not in the ground field \(F_q\)). - -Concretely, the linear map - -\[ -(y_i)_{i\in\{0,1\}^\kappa}\in (F_{q^k})^{2^\kappa} -\;\longmapsto\; -\sum_i y_i \cdot Z^{(\cdot)} \in F_{q^k} -\] - -is **\(F_{q^k}\)-linear** and therefore has a large kernel whenever \(2^\kappa>1\). So many distinct tuples \((y_i)_i\) produce the *same* packed sum. A toy example for \(k=2\) (basis \(\{1,Z\}\)): the two different pairs \((y_0,y_1)\) and \((y_0+Z,\; y_1-1)\) satisfy - -\[ -(y_0+Z) + (y_1-1)\cdot Z \;=\; y_0 + y_1\cdot Z, -\] - -so the packed value alone does not pin down \(y_0,y_1\). - -This is exactly the “basis is only independent over the ground field” pitfall called out in `paper/fri-binius.pdf`, where they explain that a basis \((\beta_v)\) is linearly independent over \(K\) but **not** over its extension \(L\); hence basis-combining \(L\)-valued claims is insecure. See the strawman discussion around Figure 1 in: - -- `paper/fri-binius.pdf` §1.3 “Ring-Switching”, “A strawman approach”, Figure 1, and the paragraph beginning “While this protocol is complete, it’s not secure.” (pages 4–6 in this PDF copy). - -**How to fix (high-level, sumcheck-style):** you must reduce the “\(y_i\) are well-formed” constraints into **ground-field (\(F_q\)) constraints** before basis-combining / packing them. - -The standard way (as in Fri-Binius ring-switching) is: - -1. **Basis-decompose each \(y_i\) over \(F_q\)**: write \(y_i = \sum_{u=0}^{k-1} y_{u,i}\,Z^u\) with \(y_{u,i}\in F_q\). -2. Also basis-decompose the extension-field weights (the equality-polynomial weights / monomial weights) into \(F_q\) coefficients. -3. Check the resulting family of \(F_q\)-valued equalities “slice-wise” (over the \(u\) index), and then **batch them with an additional sumcheck** so the verifier only pays polylog overhead. - -After this extra sumcheck layer pins down the \(F_q\)-slices, packing becomes injective again (because it is now combining **\(F_q\)-vectors** against an \(F_q\)-basis), and the reduction from “many partial claims” to “one packed claim” becomes sound. - -##### 0.A.1 Concrete “extra sumcheck” shape (Fri-Binius Eq. (12) style), and how many rounds it costs - -This subsection spells out the *exact* reason the extra sumcheck has \(\ell\) rounds (and how it fits the objects already in §3.2). - -Let \(K:=F_q\) and \(L:=F_{q^k}\), and assume \(k=2^\kappa\) for some \(\kappa\) (as in §3.2). Fix a \(K\)-basis \((\beta_u)_{u\in\{0,1\}^\kappa}\) of \(L\) (in §3.2 the paper chooses \(1,Z,\dots,Z^{k-1}\), which is just one such basis). - -The goal is to prove the family of claims (paper after Eq. (11)): - -\[ -\forall v\in\{0,1\}^\kappa:\quad -y_v \stackrel{?}{=} f_v(x_{\kappa+1},\dots,x_\ell)\in L, -\] - -where \(f_v\in K^{\le1}[X_{\kappa+1},\dots,X_\ell]\) is the “slice” of \(f\) with the first \(\kappa\) variables fixed to \(v\). - -The unsafe step is to basis-combine these \(L\)-valued equalities directly. The safe replacement is to basis-decompose everything so the equalities become \(K\)-valued first. - -1) **Basis-decompose the prover’s \(L\)-claims**: for each \(v\in\{0,1\}^\kappa\), write - -\[ -y_v = \sum_{u\in\{0,1\}^\kappa} y_{u,v}\,\beta_u, -\quad\text{with } y_{u,v}\in K. -\] - -2) **Expand \(f_v(x_{\kappa+1},\dots,x_\ell)\) as a \(K\)-weighted sum.** Let \(\ell':=\ell-\kappa\) and index \(w\in\{0,1\}^{\ell'}\). Then - -\[ -f_v(x_{\kappa+1},\dots,x_\ell) -= -\sum_{w\in\{0,1\}^{\ell'}} -\mathrm{eq}(x_{\kappa+1},\dots,x_\ell;\,w)\cdot f(v,w), -\] - -where \(f(v,w)\in K\) is the \((v,w)\) Lagrange coefficient of \(f\), and \(\mathrm{eq}(\cdot;\,w)\in L\) is the multilinear equality indicator value. - -3) **Basis-decompose the (public) weights**: for each \(w\), decompose the \(L\)-element \(\mathrm{eq}(x_{\kappa+1},\dots,x_\ell;\,w)\) in the same basis: - -\[ -\mathrm{eq}(x_{\kappa+1},\dots,x_\ell;\,w) -= -\sum_{u\in\{0,1\}^\kappa} A_{w,u}\,\beta_u, -\quad\text{with } A_{w,u}\in K, -\] - -where the \(A_{w,u}\) are deterministically computable from the public point \((x_{\kappa+1},\dots,x_\ell)\) and the chosen basis. - -4) **Now each coordinate is a \(K\)-statement**: equating coefficients of \(\beta_u\) yields the family of \(K\)-equalities - -\[ -\forall u,v\in\{0,1\}^\kappa:\quad -y_{u,v} \stackrel{?}{=} \sum_{w\in\{0,1\}^{\ell'}} A_{w,u}\cdot f(v,w). -\] - -5) **Pack the \(f(v,w)\) table into one \(L\)-multilinear** (this is the same “packing” idea as §3.2, but applied to a \(K\)-table so it is information-preserving): - -\[ -f'(w) := \sum_{v\in\{0,1\}^\kappa} f(v,w)\,\beta_v \in L, -\] - -so \(f'\) has \(\ell'=\ell-\kappa\) variables over \(L\). - -6) **Batch and sumcheck.** Define the combined \(L\)-valued claims (these are the secure analog of the strawman’s linear combination step): - -\[ -\hat y_u := \sum_{v\in\{0,1\}^\kappa} y_{u,v}\,\beta_v \in L. -\] - -Then the \(K\)-equalities above imply the \(L\)-equalities - -\[ -\forall u\in\{0,1\}^\kappa:\quad -\hat y_u \stackrel{?}{=} \sum_{w\in\{0,1\}^{\ell'}} A_{w,u}\cdot f'(w). -\] - -Finally, batch over \(u\) with a random point \(r''\in L^\kappa\) and apply sumcheck to the identity - -\[ -\sum_{u\in\{0,1\}^\kappa} \mathrm{eq}(u;\,r'')\cdot \hat y_u -\stackrel{?}{=} -\sum_{w\in\{0,1\}^{\ell'}} -\Big(\sum_{u\in\{0,1\}^\kappa}\mathrm{eq}(u;\,r'')\cdot A_{w,u}\Big)\cdot f'(w). -\] - -This is exactly the structural form of Fri-Binius Eq. (12). The sum ranges over \((u,w)\in\{0,1\}^\kappa\times\{0,1\}^{\ell'}\), so the sumcheck has **\(\kappa+\ell'=\ell\) rounds**, i.e. it costs **\(+\kappa=\log_2 k\)** more rounds than a hypothetical scheme that only needed to open \(f'\) (which has \(\ell'\) variables). - -Asymptotically, prover time for this added sumcheck is linear in the domain size \(2^{\kappa+\ell'}=2^\ell\) (times poly\((\ell,k)\) factors), i.e. \(\Theta(2^\ell)\) field operations in \(L\) for the sumcheck layer, plus one opening of the \(L\)-PCS on \(f'\) at the final point. - -#### 0.B (paper §3.1): embed \(F_{q^k}\) inside \(R_q\) and turn extension-field inner products into trace statements over \(R_q\) - -Now treat the remaining claim as an evaluation over \(F_{q^k}\) (equivalently over the subfield \(R_q^H \cong F_{q^k}\) from Lemma 5). §3.1 then provides: - -- **A subfield of \(R_q\)**: for \(q \equiv 5 \pmod 8\) and \(k\mid d/2\), define \(H=\langle\sigma^{-1},\sigma^{4k+1}\rangle\subset\mathrm{Aut}(R)\). Then the fixed ring \(R_q^H\) is a field and \(R_q^H \cong F_{q^k}\). (Lemma 5.) -- **A packing bijection** \(\psi:(R_q^H)^{d/k}\to R_q\). (Eq. (8), Theorem 2.) -- **A trace/inner-product identity** (Theorem 2): - - \[ - \mathrm{Tr}_H\big(\psi(a)\cdot \sigma^{-1}(\psi(b))\big) \;=\; \frac{d}{k}\cdot \langle a,b\rangle, - \quad a,b \in (R_q^H)^{d/k}. - \] - -Concretely (paper around Eq. (10)), pick \(\alpha:=\log_2 d\) and split the \(\ell\) variables into an “outer” prefix of length \(\ell-\alpha+\kappa\) and an “inner” suffix of length \(\alpha-\kappa\). Write indices as \(i\in\{0,1\}^{\ell-\alpha+\kappa}\) and \(j\in\{0,1\}^{\alpha-\kappa}\). Define: - -- **Packed coefficient blocks**: \(F_i := \psi\big((f_{i\parallel j})_{j\in\{0,1\}^{\alpha-\kappa}}\big)\in R_q\). -- **Packed monomial block at the suffix**: - - \[ - v := \psi\Big(\big(\prod_{t=1}^{\alpha-\kappa} x_{\ell-\alpha+\kappa+t}^{\,j_t}\big)_{j\in\{0,1\}^{\alpha-\kappa}}\Big)\in R_q. - \] - -Then the extension-field evaluation is reduced to checking a **single trace equation** in \(R_q\) involving: - -\[ -Y \;:=\; \sum_{i\in\{0,1\}^{\ell-\alpha+\kappa}} -\Big(\prod_{t=1}^{\ell-\alpha+\kappa} x_t^{i_t}\Big)\cdot F_i -\;\in\; R_q, -\] - -namely \(\mathrm{Tr}_H\big(Y\cdot \sigma^{-1}(v)\big)=\tfrac{d}{k}\,y\). The prover sends this single ring element \(Y\). - -What remains is to prove that \(Y\) is well-formed, i.e. that it is *exactly* the evaluation of the \((\ell-\alpha+\kappa)\)-variate ring polynomial \(F := (F_i)_i \in R_q^{\le 1}[X_1,\dots,X_{\ell-\alpha+\kappa}]\) at the point \((x_1,\dots,x_{\ell-\alpha+\kappa})\) (viewing those \(x_t\) as elements of the subfield \(R_q^H\subset R_q\)). This is the “smaller multilinear evaluation claim over \(R_q\)” that becomes the input to the §4 core PCS. - -### Step 1 (paper §4): the internal ring PCS statement Hachi actually proves - -After §3’s transformation, Hachi reduces extension-field evaluation claims to the §4 “core” ring PCS statement: - -- **Witness polynomial (ring core)**: \(f \in R_q^{\le 1}[X_1,\dots,X_{\ell'}]\) with coefficients in \(R_q\) (this \(f\) is the reduced ring polynomial constructed in Step 0.B; i.e., it is the \(F := (F_i)_i\) from above, just returning to the paper’s §4 notation), -- **Claim**: for a public point \(x\in R_q^{\ell'}\) (in the reduction flow, typically \(x\in (R_q^H)^{\ell'}\subset R_q^{\ell'}\)), prove \(f(x)=u\in R_q\), - -where (per §3.2) \(\ell' = \ell - \alpha\) in the important special case “coefficients in \(Z_q\), point in \(F_{q^k}\)”, with \(d=2^\alpha\). - -From here on, we are *inside* §4. The paper continues to write the ring instance as \(\ell\)-variate; in digest notation, you can read the \(\ell\) used in Steps A/B/C below as \(\ell'\) (the post-§3 reduced variable count). - -### Step A (paper §4.1): Commit to the coefficient table (inner + outer commitments) - -Hachi’s commitment structure is Greyhound-style: it commits to the coefficient table in blocks using two Ajtai commitments. - -Split \(\ell = m + r\) with \(m \approx r\). Define the block slices \(f_i^\top := (f_{i\|j})_{j\in\{0,1\}^m}\in R_q^{2^m}\) for each outer index \(i\in\{0,1\}^r\). (This is the “\(f_i\)” notation right below Equation (12).) - -Commitment construction (Equations (13)–(14)): - -- **Decompose each slice**: \(s_i := G^{-1}_{2^m}(f_i)\in R_q^{2^m\delta}\), where \(\delta=\lceil \log_b q\rceil\). (Eq. (13).) -- **Inner Ajtai commit**: \(t_i := A s_i \in R_q^{n_A}\) for all \(i\in[2^r]\). -- **Decompose the inner commit**: \(\hat t_i := G^{-1}_{n_A}(t_i)\). -- **Outer Ajtai commit**: stack all \(\hat t_i\) and commit: - - \(u := B[\hat t_1;\dots;\hat t_{2^r}] \in R_q^{n_B}\). (Eq. (14).) - -So: - -- **Commitment** is \(u \in R_q^{n_B}\). -- **Opening witness** (conceptually) is \((s_i,\hat t_i)_i\). -- Knowledge/binding is phrased in terms of “weak openings” (definition right after Eq. (14), Lemma 7). - -### Step B (paper §4.2): Reduce “open \(f(x)=u\)” to “prove knowledge of short vectors satisfying a public linear system” - -This is the core reduction pipeline of Hachi’s opening proof. - -#### B.0. Descriptive names for the “hat” variables (implementation-minded) - -The paper uses “hats” (\(\hat{\cdot}\)) for **digit-decomposed** objects (small coefficients), and uses a few single-letter vectors that are easy to lose track of. Here is a naming map that matches the paper’s definitions in §4.1–§4.2 and is meant to be used as docstring text during implementation. - -- **\(s_i\)** = **block_digits** (digits of the \(i\)-th coefficient block): - - \(s_i = G^{-1}_{2^m}(f_i)\). (Eq. (13).) - - Shape: vector of ring elements, length \(2^m\cdot\delta\). - -- **\(t_i\)** = **inner_commitment_block_i** (Ajtai commit of the \(i\)-th block digits): - - \(t_i := A s_i \in R_q^{n_A}\). - -- **\(\hat t_i\)** = **inner_commitment_digits_block_i** (digits of \(t_i\)): - - \(\hat t_i := G^{-1}_{n_A}(t_i)\). - -- **\(u\)** = **outer_commitment** (the actual PCS commitment output): - - \(u := B[\hat t_1;\dots;\hat t_{2^r}] \in R_q^{n_B}\). (Eq. (14).) - -- **\(w_i\)** = **block_partial_eval_i** (block \(i\)’s contribution after plugging the “\(a\)” half of the opening point): - - \(w_i := a^\top G_{2^m} s_i \in R_q\). (Defined right before Eq. (16).) - -- **\(\hat w_i\)** = **block_partial_eval_digits_i** (digits of \(w_i\)): - - \(\hat w_i := G^{-1}_1(w_i) \in R_q^\delta\). - -- **\(v\)** = **aux_commitment_to_block_partials** (commitment to all \(\hat w_i\)): - - \(v := D\hat w \in R_q^{n_D}\). (Eq. (16).) - -- **\(c\)** = **fold_challenge_vector** (short/sparse ring challenge used to fold blocks): - - \(c=(c_1,\dots,c_{2^r})\in C^{2^r}\), with \(\|c_i\|_1\le \omega\). - -- **\(z\)** = **folded_block_digits** (folded witness over block digits): - - \(z := \sum_{i=1}^{2^r} c_i s_i\). (Eq. (18)/(19) discussion.) - - This is the key “compress all blocks into one witness” object. - -- **\(\hat z\)** = **folded_block_digits_redecomposed** (extra decomposition of \(z\) after coefficient growth): - - \(\hat z := J^{-1}_{2^m}(z)\), where \(J\) is the gadget matrix sized for \(\tau\) digits (so \(\hat z\) has length \(2^m\cdot\delta\cdot\tau\)). (Right after Eq. (20).) - -- **\(r\)** = **modulus_quotient_witness** / **slack_witness** (ring-switching quotient): - - \(Mz = y + (X^d+1)\cdot r\) over \(Z_q[X]\). (§4.3.) - - In the “real” protocol, \(r\) is digit-decomposed as \(r=\sum_u b^u r_u\) and the prover commits to the digit vectors \(r_u\). (See §4.3 and our C.2.1.) - -#### B.1. Rewrite evaluation as a bilinear form (Eq. (12)) - -Define the monomial vectors from the evaluation point \(x\): - -- \(b^\top := (x_1^{i_1}\cdots x_r^{i_r})_{i\in\{0,1\}^r}\in R_q^{2^r}\) -- \(a^\top := (x_{r+1}^{j_1}\cdots x_\ell^{j_m})_{j\in\{0,1\}^m}\in R_q^{2^m}\) - -Then the evaluation can be written as Equation (12), which motivates everything that follows. - -#### B.2. Introduce intermediate values \(w_i\) and commit to them (Eq. (16)) - -Using the decomposed slices \(s_i\), Equation (15) rewrites the opening equation using \(s_i\). - -Define the intermediate ring elements: - -- \(w_i := a^\top G_{2^m} s_i \in R_q\). (Defined right before Eq. (16).) - -Then: - -- \(u = b^\top w\). (Eq. (17).) - -The prover also commits to \(w\) using another Ajtai-style commitment (Eq. (16)): - -- decompose \(w_i\) to \(\hat w_i := G^{-1}_1(w_i)\in R_q^\delta\), -- stack \(\hat w := (\hat w_1,\dots,\hat w_{2^r})\), -- compute **\(v := D \hat w \in R_q^{n_D}\)**. (Eq. (16).) - -This is the first prover message in Figure 3: - -- **P → V**: send \(v\). - -#### B.3. Fold all the \(s_i\) using a short challenge vector \(c\) (Eqs. (18)–(19)) - -The verifier samples a short/sparse challenge vector: - -- **V → P**: \(c=(c_1,\dots,c_{2^r}) \leftarrow C^{2^r}\), where \(C \subset \{c\in R_q : \|c\|_1 \le \omega\}\). (See the paragraph introducing \(c\).) - -The prover folds the witness: - -- \(z := \sum_{i=1}^{2^r} c_i s_i \in R_q^{2^m\delta}\). (Immediately after defining \(c\).) - -Two crucial linear identities then hold: - -- \(a^\top G_{2^m} z = (c^\top \otimes G_1)\hat w\). (Eq. (18).) -- \(A z = (c^\top \otimes G_{n_A})\hat t\). (Eq. (19).) - -These relate the folded witness \(z\) to the already-committed objects \(\hat w,\hat t\). - -#### B.4. Decompose \(z\) further and form one big “unstructured linear relation” (Eq. (20)) - -Because coefficients of \(z\) are larger, the prover further decomposes \(z\) using another gadget matrix \(J\): - -- pick a bound \(\beta\) on \(\|z\|_\infty\), define \(\tau:=\lceil \log_b \beta\rceil\), -- compute \(\hat z := J^{-1}_{2^m}(z)\in R_q^{2^m\delta\tau}\). - -At this point, the prover’s remaining task becomes: - -> prove knowledge of a short vector \((\hat w,\hat t,\hat z)\) satisfying a public linear system over \(R_q\). (Eq. (20).) - -Equation (20) is exactly that public linear system: - -- it includes the matrices \(D,B,A\), -- it includes the evaluation-derived vectors \(a,b\), -- it includes the verifier challenge \(c\), -- and it enforces: (i) consistency with the commitments \(u,v\), (ii) the opening equation, and (iii) the fold relations (18)–(19). - -##### B.4.1 Eq. (20) rewritten as a list of constraints (no hats, descriptive meaning) - -Mentally, Eq. (20) is just a *bundling* of several checks into one linear system \(M_{\text{big}}\cdot \text{witness} = \text{statement}\). Written as explicit constraints, the prover is proving existence of **small** objects: - -- **`block_partial_eval_digits`** = \(\hat w\) -- **`inner_commitment_digits`** = \(\hat t\) -- **`folded_block_digits_redecomposed`** = \(\hat z\) (and implicitly \(z = J\hat z\)) - -such that all of the following hold: - -1. **Aux-commitment consistency (ties \(\hat w\) to the sent commitment \(v\))**: - - \(D\hat w = v\). (Eq. (16).) - -2. **Main commitment consistency (ties \(\hat t\) to the sent commitment \(u\))**: - - \(B\hat t = u\). (Eq. (14).) - -3. **Evaluation equation (ties the claimed opening value \(u\) to the partials \(w\))**: - - If \(w := G_{2^r}\hat w\) then \(b^\top w = u\). (Eq. (17).) - -4. **Fold-consistency: partial-eval folding matches the folded witness \(z\)**: - - Let \(z := J\hat z\) (so \(z\) is the “recomposed” folded block-digits witness). - - Then \(a^\top G_{2^m} z = (c^\top\otimes G_1)\hat w\). (Eq. (18).) - -5. **Fold-consistency: inner-commitment folding matches the same folded witness \(z\)**: - - \(A z = (c^\top\otimes G_{n_A})\hat t\). (Eq. (19).) - -6. **Smallness/range constraints (coefficient bounds)**: - - Coefficients of \(\hat w,\hat t,\hat z\) lie in the intended digit ranges (bounded by the gadget decomposition), and the protocol’s range-check machinery in §4.3 ultimately enforces these via the \(H_0\) constraint. - -Figure 3 shows this “conceptual protocol”, ending with the prover *sending* \((\hat w,\hat t,\hat z)\), but the paper immediately notes: - -- in the **final scheme**, the prover does not send these in the clear; instead it proves knowledge of them. - -### Step C (paper §4.3): Prove the unstructured linear relation + coefficient smallness via ring switching + sumcheck over \(F_{q^k}\) - -This is the main verifier-efficiency trick: transform ring relations into field relations (via evaluation at a random \(\alpha\)), then apply sumcheck over \(F_{q^k}\). - -#### C.1. The generic linear relation they want to prove - -They define: - -- \(R^{\mathrm{lin}}_{q,d,n,\mu,b}\): given public \(M\in R_q^{n\times \mu}\), \(y\in R_q^n\), prove knowledge of \(z\in R_q^\mu\) such that \(Mz=y\) and \(\|z\|_\infty \le b-1\). - -Eq. (20) is an instance of this relation (with \(z=(\hat w,\hat t,\hat z)\)). - -#### C.2. Ring switching (Figure 4): lift equality in \(R_q\) to an identity in \(Z_q[X]\), then evaluate at random \(\alpha\) - -Because \(R_q = Z_q[X]/(X^d+1)\), the ring equation \(Mz=y\) holds iff there exists a “slack” polynomial vector \(r\) such that (paper §4.3, “Ring switching.”): - -- \(Mz = y + (X^d+1)\cdot r\) over \(Z_q[X]\). - -##### C.2.1 Critical “hidden detail”: \(r\) is gadget-decomposed, and the protocol commits to the digits - -The paper explicitly notes that **both \(z\) and \(r\)** are prover witnesses, and while the verifier ultimately needs a check involving \(r\), the prover *does not* want to commit to a large-\(q\) object and then range-check it “as-is”. - -So, for “notation and implementation simplicity”, Hachi performs a base-\(b\) gadget decomposition of the quotient witness \(r\) (paper §4.3): - -- \(r = \sum_u b^u \cdot r_u\), -- the prover commits to \((z, r_1, \dots, r_{\log_b(q)})\) instead of \((z,r)\), -- and the prover proves \(\|r_u\|_\infty \le b-1\) for every digit-vector \(r_u\). - -The paper then says it **omits the subscript \(u\)** from this point on, and that to incorporate this in the sumcheck view, “we can modify the multilinear extension correspondingly.” - -Concretely, the “real” linear constraint is: - -\[ -Mz = y + (X^d+1)\cdot \sum_u b^u r_u \quad\text{over } Z_q[X], -\] - -and the “real” smallness constraints are: - -\[ -\|z\|_\infty \le b-1 -\quad\text{and}\quad -\|r_u\|_\infty \le b-1 \ \forall u. -\] - -Protocol idea (Figure 4): - -- **P → V**: commit to \((z,r)\): \(t := \mathrm{Com}(z,r)\). (In the “real” protocol: commit to \((z,(r_u)_u)\) as above; the paper keeps writing \((z,r)\) after omitting the digit index.) -- **V → P**: sample \(\alpha \leftarrow F_{q^k}\). -- Reduce to checking the *field* equations: - - \(M(\alpha)z(\alpha) = y(\alpha) + (\alpha^d+1)r(\alpha)\) over \(F_{q^k}\). (Figure 4.) - -Soundness of this “evaluate at random \(\alpha\)” step is formalized as \(2d\)-special soundness (Lemma 9), reflecting degree \(\le 2d-1\). - -They also need to enforce that the witness coefficients are genuinely in \(Z_q\) and small (not arbitrary in \(F_{q^k}\)), and they fold those checks into the next “sumcheck view”. - -#### C.3. Represent the constraints as multilinear polynomials and batch them (Eqs. (21)–(23), Figure 5) - -This is where the **full constraint system** (including the range check) is spelled out in the paper. - -##### C.3.1 The witness polynomial \(\tilde w\) (Eq. (21)) - -The prover’s committed witness for sumcheck is a multilinear polynomial \(\tilde w\) that encodes coefficient tables. - -**Important:** because of §4.3’s hidden gadget decomposition \(r=\sum_u b^u r_u\), the *real* committed witness should be thought of as encoding coefficient tables of: - -- the vector of polynomials \(z\), and -- all digit-vectors \(r_u\), - -not just a single undigitized \(r\). The paper immediately omits the digit index \(u\) and keeps writing \((z,r)\); this is why Eq. (21) below only has one \(r\). - -The paper defines a multilinear polynomial \(e_w\) (same role as \(\tilde w\) in our prose) as: - -- \(e_w(u,\ell) = z_{u,\ell}\) if \(u \le \mu\), -- \(e_w(u,\ell) = r_{u-\mu,\ell}\) if \(\mu < u \le \mu+n\). (Eq. (21).) - -Here \(u\) and \(\ell\) are treated as binary strings indexing \([\,\mu+n\,]\) and \([\,d\,]\). - -To “incorporate the gadget decomposition” in the exact same shape, one natural flattened encoding is: - -- let \(\delta := \lceil \log_b(q)\rceil\) be the number of digits, -- treat the committed table as indexed by \([\,\mu + n\cdot \delta\,]\times[\,d\,]\), -- keep \(e_w(u,\ell)=z_{u,\ell}\) for \(u\in[\mu]\), -- and set \(e_w(\mu + u'\cdot n + i,\ell) := (r_{u'})_{i,\ell}\) for digit index \(u'\in[\delta]\) and row index \(i\in[n]\). - -With this flattening, the “range check” constraints apply to **every** coordinate of \(z\) and **every** coordinate of every digit vector \(r_{u'}\). - -##### C.3.1.1 Digit-aware \(e_{M_\alpha}\): the fully expanded constraint coefficient function - -The paper’s simplified definition (after Eq. (21)) encodes the linear constraint at \(\alpha\) by defining a public function \(e_{M_\alpha}(i,u)\) that (informally) gives the coefficient multiplying the polynomial \(w_u(\alpha)\) inside row \(i\). - -Once you flatten the digit vectors \((r_{u'})_{u'\in[\delta]}\) into the witness index \(u\in[\,\mu+n\delta\,]\), the *literal* digit-aware version is: - -- Let \(u\in[\,\mu+n\delta\,]\). -- Define the “decoded” witness coordinate \(W_u(\alpha)\) by: - - for \(1 \le u \le \mu\): \(W_u(\alpha) := z_u(\alpha)\), - - for \(\mu + (u'-1)n + i\) with \(u'\in[\delta]\) and \(i\in[n]\): \(W_{\mu + (u'-1)n + i}(\alpha) := (r_{u'})_i(\alpha)\). - -Then define: - -\[ -e^{\text{dig}}_{M_\alpha}(i,u) := -\begin{cases} -M_{i,u}(\alpha) & \text{if } 1 \le u \le \mu, \\ --\,b^{u'-1}\cdot(\alpha^d+1) & \text{if } u = \mu + (u'-1)n + i \text{ for some } u'\in[\delta], \\ -0 & \text{otherwise.} -\end{cases} -\] - -With this explicit \(e^{\text{dig}}_{M_\alpha}\), the digitized ring-switch check for each row \(i\in[n]\) is exactly: - -\[ -\sum_{u=1}^{\mu+n\delta} e^{\text{dig}}_{M_\alpha}(i,u)\cdot W_u(\alpha) \;=\; y_i(\alpha). -\] - -This is just the statement: - -\[ -\sum_{j=1}^{\mu} M_{i,j}(\alpha)\,z_j(\alpha)\;-\;(\alpha^d+1)\sum_{u'=1}^{\delta} b^{u'-1}\,(r_{u'})_i(\alpha) \;=\; y_i(\alpha), -\] - -which is equivalent to the “real” lifted identity \(Mz = y + (X^d+1)\sum_{u'}b^{u'-1}r_{u'}\) after evaluation at \(X=\alpha\). - -##### C.3.2 The two *literal* constraints before batching (paper right before Eq. (22)/(23)) - -For a fixed ring-switch challenge \(\alpha\in F_{q^k}\), the verifier wants to enforce: - -1. **Linear constraints (ring switching at \(\alpha\))**: for each row \(i\in[n]\), - - \[ - \sum_{u=1}^{\mu+n} e_{M_\alpha}(i,u)\cdot \sum_{\ell} e_w(u,\ell)\cdot e_\alpha(\ell)\;=\;y_i(\alpha), - \] - - where \(e_\alpha(\ell)=\alpha^\ell\) and \(e_{M_\alpha}(i,u)\) is the public multilinear encoding of \(M(\alpha)\) plus the extra \(-(\alpha^d+1)\) term on the \(r\)-coordinates. (This is the first bullet list item under Figure 5 in the paper.) - - With the hidden gadget decomposition \(r=\sum_u b^u r_u\), the same constraint is enforced except the right-hand side becomes \(y_i(\alpha) + (\alpha^d+1)\sum_u b^u r_{i,u}(\alpha)\). In the “\(e_{M_\alpha}\cdot e_w\)” encoding, this is handled by: - - - expanding \(e_w\) to include all digit-vectors \((r_u)_u\) (as described in C.3.1), and - - modifying the \(-(\alpha^d+1)\) part of \(e_{M_\alpha}\) to include the appropriate digit weights \(-b^u(\alpha^d+1)\) on the digit blocks. - -2. **Smallness / range constraints (this is the “range check”)**: for *every* coordinate \((u,\ell)\), - - \[ - P_b\big(e_w(u,\ell)\big) = 0 - \quad\text{where}\quad - P_b(T) := \prod_{t=-(b-1)}^{b-1}(T-t). - \] - - The paper writes this explicitly as the vanishing product: - \(e_w(u,\ell)\cdot(e_w(u,\ell)-1)\cdot(e_w(u,\ell)+1)\cdots(e_w(u,\ell)-b+1)\cdot(e_w(u,\ell)+b-1)=0\). - -This is **not optional**: it is exactly how Hachi enforces that the coefficients the prover is claiming for \(z\) (and the \(r\)-side witness they commit) are small integers (embedded into \(F_{q^k}\)), i.e. a range/membership proof via a root-check polynomial. - -##### C.3.3 Batching with equality polynomials: the exact \(H_\alpha\) and \(H_0\) (Eqs. (22)–(23)) - -Let the multilinear equality polynomial be: - -- \(e_{eq}(t,i) = \prod_j (t_j i_j + (1-t_j)(1-i_j))\). - -Then the paper defines: - -- **Linear constraint batch** \(H_\alpha(t)\) (Eq. (22)): - - \[ - H_\alpha(t) := - \sum_{i\in[n]} e_{eq}(t,i)\cdot - \Big(\sum_{u,\ell} e_{M_\alpha}(i,u)\cdot e_w(u,\ell)\cdot e_\alpha(\ell) - y_i(\alpha)\Big). - \] - -- **Smallness/range batch** \(H_0(t)\) (Eq. (23)): - - \[ - H_0(t) := - \sum_{u,\ell} e_{eq}\big(t,(u,\ell)\big)\cdot P_b\big(e_w(u,\ell)\big). - \] - -The goal is to prove both are **identically zero polynomials**, which they reduce (Figure 5) to random-point checks: - -- **V → P**: send random points \(\tau_0,\tau_1\), -- prove \(H_0(\tau_0)=0\) and \(H_\alpha(\tau_1)=0\). - -#### C.4. Use sumcheck to prove the remaining batched sums (Figure 6) - -After fixing \(\tau_0,\tau_1\), they rewrite \(H_0(\tau_0)\) and \(H_\alpha(\tau_1)\) as sums over \((u,\ell)\) of polynomials \(F_{0,\tau_0}\) and \(F_{\alpha,\tau_1}\), and then apply **sumcheck** over \(F_{q^k}\) (discussion right after Eq. (23)). - -Figure 6 gives the “single-round view” of sumcheck: prover sends univariate \(g_i\), verifier sends random challenge scalars \(a_i\), and in the end the verifier reduces everything to checking an evaluation of the witness polynomial \(\tilde w\) at one final random point. - -Crucially, the sumcheck ends in: - -- a **final evaluation claim** of the committed \(\tilde w\) at a random point \(r^\*\), -- plus the requirement to prove this evaluation is consistent with the commitment \(t\). - -That “prove the evaluation claim for \(\tilde w\)” is exactly where recursion happens: you invoke the PCS again on the smaller committed object. - -##### C.4.1 Full message flow (Figure 7), spelled out - -Figure 7 in the paper is the full composition of Figures 4, 5, and 6. Written as an explicit transcript skeleton: - -- **P → V**: \(t := \mathrm{Com}(z,r)\). (In the “real” protocol: \(t := \mathrm{Com}(z,(r_u)_u)\) with \(r=\sum_u b^u r_u\).) -- **V → P**: sample challenges: - - \(\alpha \leftarrow F_{q^k}\), - - \(\tau_0 \leftarrow F_{q^k}^{\log(\mu)+\log(d)}\), - - \(\tau_1 \leftarrow F_{q^k}^{\log(n)}\). -- **P ↔ V (sumcheck)**: run sumcheck to prove \(H_0(\tau_0)=0\) and \(H_\alpha(\tau_1)=0\): - - in each sumcheck round, **P → V** sends a univariate polynomial \(g_i(X_i)\), - - and **V → P** responds with a random scalar challenge \(a_i \leftarrow F_{q^k}\). (Figure 6.) -- **P → V (final opening)**: open the commitment \(t\) at the final point determined by \((a_1,\dots,a_\ell)\) to provide the needed value(s) of \(\tilde w\). -- **V (final checks)**: - - evaluate the public multilinear extensions (notably \(e_{M_\alpha}\) / \(e_\alpha\)) at the same final point, - - and check the final sumcheck identities (Figure 6’s last-round checks). - -### Step D (paper §3 + §5): recursion shape and concrete proof-size accounting - -Recursion shape (high-level): - -- One invocation reduces the big opening proof into opening proofs for **smaller** committed objects (smaller \(\ell\), smaller coefficient domains after decomposition, and evaluation points living in \(F_{q^k}\)). -- Eventually, Hachi suggests switching to different sub-proofs when the witness is small (paper discusses both switching to LaBRADOR/JL and composing with Greyhound). - -Concrete proof-size estimate for \(\ell=30\) (paper §5.2): - -- Sumcheck for the first round: ~7.3KB. -- “Adaptation + Greyhound subproof” gives total ~55.1KB for an evaluation proof. - -This is the explicit estimate in §5.2: - -- first-round sumcheck: \(7.3\)KB, -- plus preparation/adaptation \(4.8\)KB, -- plus Greyhound evaluation subproof \(43\)KB, -- total \(7.3 + 4.8 + 43 = 55.1\)KB. - -#### D.1 What the “adaptation to Greyhound” actually means (paper §4.5, §5.2) - -When the witness becomes small enough, Hachi can stop running its own §4.3 ring-switch + sumcheck recursion and instead reduce the remaining claim into a **Greyhound-native** opening proof. - -The key shape (paper §4.5 and the concrete instantiation in §5.2) is: - -- you end up with an evaluation claim where the verifier has reduced everything to checking that a committed multilinear object \(\tilde w\) evaluates correctly at a random point; -- the prover groups / “packs” the needed coefficients into extension-field elements, and then uses the §3 embedding machinery (the \(\psi\) map and trace identity) to turn the remaining check into a ring statement supported by Greyhound. - -In the concrete accounting, the additional prover communication for this handoff is bounded as (Equation (28) in the paper excerpted in §4.5): - -- \((k-1)\cdot k \cdot \log q\) bits for the sent partial evaluations \((y_i)\), plus -- \(d'\cdot \log q\) bits for sending one ring element \(p\in R'_{q}\) (where \(d'\) is the Greyhound ring dimension, e.g. \(d'=64\) in §5.2). - -This is why §5.2 reports the “adaptation overhead” as small (~0.3KB for the non-commitment part), and then adds the cost to **commit** to the new Greyhound witness element(s). - -### Message flow summary (first / dominant round) - -If you want a “wire-format mental model” aligned to Figures 3–6, the dominant first round contains: - -- **Ring commitments**: the main commitment \(u\in R_q^{n_B}\) (Eq. (14)) and the auxiliary commitment \(v\in R_q^{n_D}\) (Eq. (16)). -- **Ring challenge**: short/sparse \(c\in C^{2^r}\) used to fold the opening witness (Eq. (18)–(19)). -- **Field challenge**: \(\alpha\in F_{q^k}\) for ring switching (Figure 4), and random points \(\tau_0,\tau_1\) (Figure 5). -- **Sumcheck transcript**: univariate polynomials \(g_i\) and challenge scalars \(a_i\) (Figure 6), ending in a point \(r^\*\) and an evaluation value \(\tilde w(r^\*)\). -- **Opening proof(s)**: recursive PCS openings that prove the claimed evaluations of the committed \(\tilde w\) values match the commitments. - -## Implementation-oriented PCS flow spec (what we need before coding) - -This section re-states the end-to-end PCS as a **software spec**: what the prover/verifier compute, what objects exist (and their “witness” roles), and what must be pinned down *before* we implement §4.3 “witness table embedding” or the ring-switch sumcheck instances. - -### E.0 The key mental model: “stacked linear relation” → “ring switch” → “sumcheck” → “new opening claim” - -The paper explains §4.3 in the simplified setting \(Mz=y\) for \(z\in R_q^\mu\). In the actual PCS opening proof, §4.2 produces exactly such a relation, but with: - -- a **stacked witness vector** \(z\) that bundles multiple unknowns (notably \(\hat w,\hat t,\hat z\) from Eq. (20)), and -- a stacked statement \(y\) and matrix \(M\) derived from public matrices \(A,B,D\), the opening point \(x\) (via \(a,b\)), the claimed opening value, and the verifier challenge \(c\). - -Once the prover and verifier agree on that concrete \((M,y)\), §4.3 proceeds as: - -1. **Ring switching introduces a quotient witness** \(r\) such that: - - \[ - Mz = y + (X^d+1)\cdot r \quad \text{over } Z_q[X]. - \] - -2. **Digitize the quotient witness** \(r = \sum_{u'=0}^{\delta-1} b^{u'} r_{u'}\) and range-check each digit block. -3. Encode the (digitized) coefficient tables of \((z,(r_{u'})_{u'})\) into one multilinear object \(\tilde w\) (paper Eq. (21), with the digit index omitted in the paper’s notation). -4. Prove the linear and range constraints by sumcheck, which ends in an evaluation claim \(\tilde w(r^\*)\) at a random point \(r^\*\). -5. **Recursion boundary**: the next PCS subproblem is “open the commitment to \(\tilde w\) at point \(r^\*\)”. - -### E.1 What the prover’s “witness” is after the first interaction rounds (ring switching + sumcheck) - -If by “after the first rounds” you mean “after the verifier samples \(\alpha,\tau_0,\tau_1\) and sumcheck begins”, then the prover’s relevant witnesses are: - -- **The stacked linear-relation witness** \(z\) from §4.2 (Eq. (20)’s unknown vector; in the paper’s naming, this is \((\hat w,\hat t,\hat z)\) with the implicit recomposition \(z := J\hat z\)). -- **The ring-switch quotient witness digits** \((r_{u'})_{u'\in[\delta]}\) satisfying: - - \[ - Mz - y = (X^d+1)\sum_{u'} b^{u'} r_{u'}. - \] - -These are not sent directly. Instead they are **committed** and then accessed *only* through: - -- evaluations of the committed multilinear object \(\tilde w\) during sumcheck, and finally -- one PCS opening of \(\tilde w\) at the final sumcheck point \(r^\*\). - -So the short answer is: - -> After ring switching starts, the “PCS witness” (for the next recursion layer) is the committed multilinear polynomial \(\tilde w\) that encodes the coefficient table of the stacked witness \(z\) and the digitized quotient witness \((r_{u'})_{u'}\). Sumcheck reduces everything to opening \(\tilde w\) at one random point \(r^\*\). - -### E.2 What “witness table embedding” (Eq. (21)) really must encode in the full PCS (not the simplified \(Mz=y\) story) - -Eq. (21) defines \(e_w(u,\ell)\) in the simplified \((z,r)\) notation. For implementation, the important points are: - -- The “\(z\)” rows are not just “some vector”; in the PCS they are the **stacked unknowns** of Eq. (20), i.e. the prover’s hidden objects that tie together: - - the main commitment \(u\), - - the aux commitment \(v\), - - the opening equation, - - the fold identities (18)–(19), - - and the redecomposition via \(J\). -- The “\(r\)” rows are not optional: they are the **quotient witness** for the lifted equation over \(Z_q[X]\), and in the real protocol are digitized as \((r_{u'})_{u'}\) and range-checked. - -In other words, the witness-table encoder we build should take as input: - -- the stacked witness vector (call it `linear_relation_witness` instead of paper’s `z`), and -- the digitized quotient witness blocks `quotient_digits` (instead of paper’s `r`), - -and output a padded, evaluation-form multilinear object \(\tilde w\). - -### E.3 Why the PoC’s “next witness” contains “extra quotient terms” (and why they don’t contradict the paper) - -The PoC does not implement §4.3 for a single abstract relation \(Mz=y\). It already constructs (a variant of) Eq. (20)’s **stacked linear system**, which bundles multiple constraints. - -Each lifted constraint row contributes its own quotient polynomial(s) when you rewrite it as: - -\[ -\text{(row LHS)} - \text{(row RHS)} = (X^d+1)\cdot r_i(X), -\] - -so the PoC ends up with several quotient vectors (for several different stacked sub-constraints), and it concatenates them into the “next witness table” before padding to a power of two. - -This is an implementation manifestation of the same principle the paper uses: - -- §4.2 stacks many checks into one linear system (Eq. (20)), -- §4.3 introduces quotient witnesses for that system when lifted to \(Z_q[X]\), -- §4.3 then commits to a single coefficient-table object \(\tilde w\) representing *all* witness coordinates and *all* quotient-digit coordinates. - -So: seeing “more quotient chunks” in a prototype is expected whenever you expand the simplified \(Mz=y\) exposition into the concrete PCS relation. - -### E.4 Concrete “before we code” checklist (MVP up through §4.3) - -To avoid implementing §4.3 machinery “in the dark”, we should pin down the following concrete spec items first. - -#### E.4.1 Fix the exact stacked linear relation produced by §4.2 - -We need a concrete `LinearRelationInstance` spec with: - -- **Public statement**: - - the stacked matrix \(M\in R_q^{n\times \mu}\), - - the stacked right-hand side \(y\in R_q^n\), - - and the coefficient smallness parameters (base \(b\), digit length \(\delta\), and any redecomposition \(\tau\) where relevant). -- **Witness semantics**: - - what each coordinate of the stacked witness vector means (e.g., slices corresponding to \(\hat w,\hat t,\hat z\)), - - and which coordinates are subject to the range-check polynomial \(P_b\). - -Without this, we cannot correctly define how many “\(z\) rows” Eq. (21) has (the paper’s \(\mu\)). - -#### E.4.2 Fix the quotient witness structure introduced by ring switching - -For the chosen \((M,y)\), ring switching requires: - -- the quotient witness vector \(r\in (Z_q[X]_{ idx\) to become “evaluations on the hypercube”. - -This is the “witness table embedding” deliverable: it is the object whose commitment is opened at the end of sumcheck (Figure 6 / Figure 7). - -#### E.4.4 Fix the public multilinear encodings needed by §4.3 constraints - -To define \(H_\alpha\) and \(H_0\) (Eqs. (22)–(23)), we need: - -- `AlphaPowers`: the table \(e_\alpha(\ell)=\alpha^\ell\), -- `LinearCoeffEncoding`: the digit-aware coefficient function \(e^{dig}_{M_\alpha}(i,u)\) (i.e., how \(M(\alpha)\) and \(-(\alpha^d+1)\cdot b^{u'}\) are encoded), -- and the equality polynomials \(e_{eq}\) used for batching. - -#### E.4.5 Fix how sumcheck’s final oracle check becomes a PCS opening claim - -Our sumcheck core deliberately stops at “here is the final point \(r^\*\)”; the ring-switch module must: - -- compute the expected final value using the public parts, and -- reduce to a **single opening claim** of the committed \(\tilde w\) at \(r^\*\). - -This is exactly where the PCS prover/verifier “open-check” logic plugs in (currently stubbed in this repo). - -## Modulus switching / cross-prime sumcheck (Jolt-motivated extension; not in the Hachi paper) - -This section sketches how to adapt the Hachi “ring switch \(\to\) sumcheck” pipeline to the setting where: - -- **Commitments** are over a *small* prime field / ring modulus \(q\) (e.g. \(\approx 2^{32}\)), because that makes commitment-time arithmetic and NTT/CRT layouts fast. -- **Sumcheck / arithmetization** must run over a *large* prime field \(F_{q'}\) (e.g. 128-bit prime), because the application (e.g. Jolt) requires characteristic large enough to avoid wrap-around in \(u64\cdot u64\) accumulation. - -This is *similar in spirit* to §3’s extension-field story, but **strictly harder**: there is no field embedding \(F_q \hookrightarrow F_{q'}\) that preserves addition/multiplication mod the prime, so we must explicitly control an **integer lift** via range checks. - -### F.0 Target statement (“foreign-field opening”) - -Let \(q\) be a small prime, \(q'\) a large prime, and let \(f\) be an \(\ell\)-variate multilinear with **small coefficients**, ideally bits: - -\[ -f \in F_q^{\le 1}[X_1,\dots,X_\ell],\quad f_i \in \{0,1\}\subset F_q. -\] - -We commit to the coefficient table \((f_i)_{i\in\{0,1\}^\ell}\) using the Hachi/Greyhound-style commitment core over \(R_q\) (or over \(F_q\) as the \(d=1\) special case). - -The opening claim we want to support is over the **large prime field**: - -\[ -\text{given } x\in F_{q'}^\ell,\ y\in F_{q'},\ \text{prove } f(x)=y\ \text{(interpreting the coefficients as small integers in }F_{q'}\text{).} -\] - -Because the coefficients are in \(\{0,1\}\), there is a canonical injection \(\iota:\{0,1\}\to F_{q'}\) (map to the same integers). The only remaining job is to enforce that the committed coefficients are indeed in \(\{0,1\}\) (bitness) and that every algebraic check is performed with respect to this integer lift. - -#### F.0.1 Important clarification: this is **not** “digit-decompose \(x,y\)” - -It is tempting to think “we have an evaluation claim \(f(x)=y\) in the large field \(F_{q'}\), so we should decompose \(x\) and \(y\) into base-\(b\) digits and prove digit-wise subclaims.” That is **not** what the modulus-switching reduction does, and it generally does not work (polynomial evaluation does not decompose into independent digit evaluations). - -Instead: - -- The evaluation point \(x\in F_{q'}^\ell\) and claimed value \(y\in F_{q'}\) are already *native* to the field where Jolt runs sumcheck. There is typically no reason to decompose them. -- The lift issue arises because the **committed objects** live over the *small* modulus \(q\) (i.e. values are only defined modulo \(q\)), while the verifier wants to check equations **inside \(F_{q'}\)**. - -So the purpose of \(\mathrm{lift}_q\) is to assign a **canonical integer meaning** to committed mod-\(q\) values (made unambiguous by range constraints like “bitness”), so those values can be interpreted inside \(F_{q'}\). - -Warm-up (scalar version). For integers \(\tilde A,\tilde B\in Z\), the statement “\(A=B\) in \(Z_q\)” is exactly: - -\[ -\tilde A \equiv \tilde B \pmod q -\quad\Longleftrightarrow\quad -\exists s\in Z:\ \tilde A - \tilde B = q\cdot s. -\] - -The \(q\cdot s\) term is the “modulus switching slack”. The ring/polynomial version in F.1 is the same idea applied coefficient-wise (and with an additional cyclotomic slack \((X^d+1)\cdot r\) for the ring quotient). - -#### F.0.2 How this plugs into Hachi’s six core constraints (B.4.1) in the Jolt Stage-8 setting - -Jolt Stage 8 asks the PCS to prove openings of the form “\(P(\mathbf r)=v\)” where both the point \(\mathbf r\) and value \(v\) live in the **Jolt field** \(F\) (in your target case, \(F=F_{q'}\)). See: - -- `../jolt/jolt-core/src/poly/opening_proof.rs`: `pub type Opening = (OpeningPoint<..., F>, F);` -- `../jolt/jolt-core/src/zkvm/prover.rs`: Stage 8 calls `PCS::prove(..., &opening_point.r, ...)` where `opening_point.r` is a vector of field challenges. - -Hachi’s Step B constraints (the six items in B.4.1) are written as equalities over the **ring** \(R_q\). To use a Hachi-style PCS under Jolt’s interface, we keep the *same witness objects* \((\hat w,\hat t,\hat z,\dots)\) and the *same logical constraints*, but we do **not** expect the verifier to check them natively in \(R_q\) (and we cannot even form the “\(a,b\in R_q\) from the opening point” parts when \(\mathbf r\in F_{q'}^\ell\)). - -Instead, the PCS opening proof checks these constraints **after ring switching**, i.e. after applying an evaluation map - -\[ -\mathrm{ev}_\alpha: R_q \to F_{q'} -\] - -at a random \(\alpha\in F_{q'}\) (and including the modulus-switch slack \(q\cdot s\) to make “mod \(q\)” equalities meaningful in \(F_{q'}\)). - -Concretely: - -- Constraints **(1), (2), and the purely ring-linear parts** of (4),(5) are still “ring equations”, but they are verified in \(F_{q'}\) by checking \(\mathrm{ev}_\alpha(\text{LHS}-\text{RHS})=0\) (with quotient witnesses for \((X^d+1)\) and \(q\) as in F.1). -- Constraints **(3)–(5)** are the ones that *mention the evaluation point* (via the monomial vectors \(a,b\)) and therefore must be interpreted in the **field**: - - compute \(a,b\) directly from the Stage-8 opening point \(\mathbf r\in F_{q'}^\ell\), - - treat unknown ring elements like \(w_i\in R_q\) only through their field images \(w_i(\alpha):=\mathrm{ev}_\alpha(w_i)\in F_{q'}\), - - and enforce the same algebraic equalities (Eq. (17)–(19)) in \(F_{q'}\). - -So the “generalization to account for \(q'\)” is not “change a few constraints while keeping the rest in \(q\)”; it is: - -> keep the constraint *structure*, but **move their verification domain** from \(R_q\) to \(F_{q'}\) via ring switching (plus a \(q\cdot s\) slack), because Stage 8’s statement lives in \(F_{q'}\). - -#### F.0.3 Why you cannot keep the *entire* opening proof “purely in \(F_q/R_q\)” under Jolt’s interface - -Under Jolt, the opening point \(\mathbf r\) is sampled as transcript challenges in the **same field as the sumchecks**, i.e. \(\mathbf r\in F_{q'}^m\) (see `OpeningPoint<..., F>` in `../jolt/jolt-core/src/poly/opening_proof.rs`). - -Any PCS that plugs into Stage 8 must therefore convince the verifier of a statement that is *parameterized by* these \(F_{q'}\) elements: - -\[ -P(\mathbf r)=v\quad\text{for }\mathbf r,v\in F_{q'}. -\] - -If a verifier refuses to do any \(F_{q'}\) arithmetic, it cannot even *evaluate the public weights* (equality polynomials) at \(\mathbf r\), nor can it check the final identity that defines “evaluation at \(\mathbf r\)”. The only way around this would be to represent every \(F_{q'}\) element (including \(\mathbf r\), \(v\), and all derived weights) as **non-native data** over \(F_q\) (e.g. base-\(b\) limbs) and then prove that these limbs satisfy the mod-\(q'\) arithmetic via additional quotient/carry constraints. - -That “all-\(F_q\) verification” route is a different, much heavier design: it is essentially a SNARK for \(F_{q'}\) arithmetic implemented over \(F_q\), and it introduces digit/carry constraints for every multiplication/addition in the opening protocol. This is *not* what Hachi’s ring switching is optimizing for. - -So the realistic design space is: - -- commitments / witness representation over \(F_q\) / \(R_q\) for performance, -- but verifier-side checking (sumcheck challenges, equality weights, and final identities) in \(F_{q'}\). - -#### F.0.4 Recursion / “next folding steps” in the cross-prime setting - -In Hachi, the “recursion boundary” is: sumcheck reduces a large set of constraints to **one new opening claim** for a committed multilinear object (the \(\tilde w\) table). The next layer repeats the same pattern on a smaller witness. - -In the cross-prime Stage-8 adaptation: - -- the **commitment domain stays** \(F_q/R_q\) at every layer (you keep committing to digitized tables over the small modulus), -- the **opening points stay** in \(F_{q'}\) at every layer, because they are derived from sumcheck challenges / transcript in \(F_{q'}\), -- and the verifier continues to check constraints in \(F_{q'}\) via ring switching (evaluation at \(\alpha\in F_{q'}\) plus the \((X^d+1)\cdot r\) and \(q\cdot s\) quotient witnesses). - -So “continuing in \(F_{q'}\)” does not mean “switch commitments to \(q'\)”; it means the *interactive checking algebra* (sumcheck, batching, evaluation weights) remains in the Jolt field where the statement is expressed. - -#### F.0.5 One full “folding/recursion step” of the adapted PCS (clean, end-to-end) - -This subsection gives a clean one-layer view: how we go from **one opening claim at point \(\mathbf r\in F_{q'}^m\)** to **a smaller opening claim at a new point \(\mathbf r^\*\in F_{q'}^{m'}\)**, and why that output is amenable to repeating the same procedure. - -We describe this as a PCS protocol (what Stage 8 wants), independent of Jolt’s earlier stages. - -##### Inputs (statement) and commitment domain - -- **Commitment domain** (small): commitments are to coefficient tables over \(F_q\) (or ring elements over \(R_q\)) using Hachi’s §4.1 Ajtai-style structure. -- **Opening statement domain** (large): the opening point \(\mathbf r\) and claimed value \(v\) are in \(F_{q'}\) (Jolt’s `JoltField`). - -So the opening statement is: - -\[ -\text{Given commitment } C \text{ to a multilinear table } P,\ \text{and public } \mathbf r\in F_{q'}^m,\ v\in F_{q'},\ \text{prove } P(\mathbf r)=v. -\] - -Here \(P(\mathbf r)\) is defined by interpreting the committed coefficients as integers (via \(\mathrm{lift}_q\)) and reducing them into \(F_{q'}\); for bit/one-hot tables, this interpretation is canonical. - -##### Step 1 (Hachi Step B “split-and-fold”): reduce evaluation to a structured linear relation witness - -This step is unchanged in *spirit* from Hachi: we rewrite “\(P(\mathbf r)=v\)” into a small set of algebraic constraints involving intermediate witnesses (partial evaluations, decomposed digits, and folded combinations). - -The key point in the two-field setting is typing: - -- any time the original §4.2 constraints multiply “point-derived scalars” into witness quantities, those scalars are in \(F_{q'}\) and we interpret the witness quantities through their images in \(F_{q'}\) (via ring switching in Step 2), rather than trying to multiply \(F_{q'}\) scalars by \(R_q\) elements directly. - -Operationally, the prover still constructs the same witness objects (\(\hat w,\hat t,\hat z\), folded \(z\), etc.) and commits to the same ring elements (\(u,v\), etc.). The verifier will not check the ring equations directly; it will check their *ring-switched* images in Step 2. - -##### Step 2 (Hachi Step C generalized): ring switching + modulus switching to get field-native constraints - -The verifier samples a random \(\alpha\leftarrow F_{q'}\) and defines the evaluation map: - -\[ -\mathrm{ev}_\alpha: R_q \to F_{q'} -\] - -as “lift coefficients to integers (per chosen \(\mathrm{lift}_q\)), then evaluate the polynomial at \(X=\alpha\) in \(F_{q'}\)”. - -Now take each ring equation from the Step B constraint set (the six constraints in B.4.1) and convert it into a field equation at \(\alpha\) by: - -1. lifting it from \(R_q\) to \(Z[X]\) with a cyclotomic quotient witness \(r\) (as in the paper), and -2. adding a modulus quotient witness \(s\) so that “mod \(q\) equality” becomes an *integer* equality plus a \(q\cdot s\) slack (Section F.1). - -After evaluating at \(X=\alpha\), every check becomes an identity in \(F_{q'}\) involving: - -- public scalars derived from \(\mathbf r\) (equality weights / monomial vectors), -- the prover’s unknowns only through \(\mathrm{ev}_\alpha(\cdot)\), -- and the quotient witnesses \(r(\alpha), s(\alpha)\). - -##### Step 3 (Hachi §4.3 sumcheck): batch all constraints and reduce to one oracle evaluation - -Exactly as in Hachi, we encode the relevant coefficient tables into one committed multilinear object \(\tilde w\) (“witness table embedding”), except that in the cross-prime setting \(\tilde w\) must encode the extra modulus quotient witness \(s\) as well as \(r\). - -Then we define batched constraint polynomials (the analogs of \(H_\alpha\) and \(H_0\)), and run sumcheck over **\(F_{q'}\)** (not over \(R_q\)). The sumcheck transcript produces a final random point: - -\[ -\mathbf r^\* \in F_{q'}^{m'} -\] - -and reduces verification to a **single evaluation claim** of the committed witness-table multilinear: - -\[ -\tilde w(\mathbf r^\*) = v^\*\in F_{q'}. -\] - -##### Step 4 (recursion boundary): output a smaller opening claim of the same type - -This is the crucial “amenable to further folding” point: - -- The new claim “\(\tilde w(\mathbf r^\*)=v^\*\)” has the **same shape** as the original opening claim, just on a different committed multilinear and a different point. -- The commitment to \(\tilde w\) is again over the **small modulus domain** (it is built from digitized tables over \(F_q/R_q\)). -- The opening point \(\mathbf r^\*\) is again in the **large field** \(F_{q'}\), because it is derived from the sumcheck challenges (and thus from the Jolt transcript). - -Therefore, we can repeat the same 4-step pipeline on \(\tilde w\): - -\[ -P(\mathbf r)=v -\ \leadsto\ -\tilde w(\mathbf r^\*)=v^\* -\ \leadsto\ -\tilde w^{(2)}(\mathbf r^{\*\*})=v^{\*\*} -\ \leadsto\ \cdots -\] - -and eventually hand off to a base PCS / small-instance prover once the witness table is small enough (exactly the same “stop recursion when small” design choice as Hachi’s §5 composition discussion). - -#### F.0.6 Option B (for comparison): decompose the \(F_{q'}\) opening point/value and prove everything over \(F_q/R_q\) - -This subsection works out the alternative you asked for: **avoid doing any verifier arithmetic in \(F_{q'}\)** by representing all \(F_{q'}\) elements (the opening point \(\mathbf r\) and claimed value \(v\), plus all derived weights) as *digits/limbs* over the small field. - -This is not “ring switching”; it is **non-native (foreign-field) arithmetic**: we simulate mod-\(q'\) arithmetic inside a proof system whose native arithmetic is mod-\(q\). - -##### Why this is a different interface than Jolt Stage 8 - -In Jolt, Stage 8’s opening statement is parameterized by an actual \(\mathbf r\in F_{q'}^m\) sampled from the transcript (see `OpeningPoint<..., F>`). - -Option B instead treats \(\mathbf r\) and \(v\) as **public limb vectors over \(F_q\)**. To plug this into Jolt unchanged, you would need to either: - -- change Jolt’s transcript/challenges to live in the small field (not compatible with the stated “char \(> u64\cdot u64\)” requirement), or -- keep \(\mathbf r\in F_{q'}\) as usual but additionally provide a limb decomposition of \(\mathbf r\) and then **prove inside the PCS** that those limbs reconstruct the same \(\mathbf r\) (which reintroduces \(F_{q'}\) operations unless you also non-natively model the transcript). - -So Option B is best viewed as a “theoretical comparison point”, not a drop-in Stage-8 replacement. - -##### Representation: limbs for \(F_{q'}\) elements - -Fix a radix \(B=2^t\) (e.g. \(B=2^{16}\) so limbs fit comfortably under a 32-bit-ish \(q\)), and let - -\[ -L := \left\lceil \log_B(q') \right\rceil -\] - -be the limb count (for a 128-bit prime and \(B=2^{16}\), \(L\approx 8\)). - -We represent a field element \(a\in F_{q'}\) by an integer representative \(\tilde a\in[0,q')\) (canonical lift mod \(q'\)) and a limb decomposition: - -\[ -\tilde a = \sum_{j=0}^{L-1} a_j B^j,\quad a_j\in\{0,1,\dots,B-1\}. -\] - -All limbs \(a_j\) are then encoded as small elements of \(F_q\) (and range-checked to lie in \([0,B)\)). - -##### Non-native arithmetic constraints (core gadget) - -To simulate \(F_{q'}\) arithmetic, every operation becomes an integer identity plus a \(q'\)-multiple slack: - -- **Addition**: to enforce \(c \equiv a+b \pmod{q'}\), prove - - \[ - \tilde a + \tilde b - \tilde c = q'\cdot k - \] - - for some integer \(k\) (with \(k\in\{0,1\}\) if \(\tilde a,\tilde b,\tilde c\in[0,q')\)). - -- **Multiplication**: to enforce \(c \equiv a\cdot b \pmod{q'}\), prove - - \[ - \tilde a\cdot \tilde b - \tilde c = q'\cdot k - \] - - for some integer \(k\) with \(0 \le k < q'\). - -In practice, you do not materialize \(\tilde a\) as a single huge integer; you enforce these identities **in base \(B\) with carries**: - -- introduce carry variables \(u_t\) so that the schoolbook convolution of limbs matches the target limbs, -- and range-check carries so that “equality mod \(q\)” implies “equality over integers” (no wrap-around) at the limb level. - -Cost model: one non-native multiplication of two \(L\)-limb numbers costs - -\[ -\Theta(L^2)\ \text{small-field multiplications} \quad + \quad \Theta(L)\ \text{carry/range constraints}. -\] - -##### How to prove an opening claim \(P(\mathbf r)=v\) using Option B - -Let \(P\) be a multilinear polynomial committed over \(F_q\) (or \(R_q\)) whose coefficients are small integers (bits/one-hot is the cleanest case). - -Public input for Option B: - -- limb decompositions of each coordinate \(r_i\in F_{q'}\) (so \(\tilde r_i=\sum_j r_{i,j}B^j\)), -- limb decomposition of \(v\in F_{q'}\), -- and the modulus \(q'\) itself (public constant). - -Prover witness: - -- limb decompositions for all intermediate \(F_{q'}\) values needed to evaluate \(P\) at \(\mathbf r\), -- plus all carry/quotient witnesses for the modular reduction constraints above. - -Then enforce, inside the proof system over \(F_q/R_q\): - -1. **Range**: every limb is in \([0,B)\) (bitness is the special case \(B=2\)). -2. **Recomposition**: the limb vectors correspond to integers in \([0,q')\) (often implemented by providing a quotient \(t\) such that \(\sum_j a_jB^j = \tilde a + q' t\) and constraining \(\tilde a CE(b,L)^(K+k) -- - | - Π_RLC - | - CE(B,L) - | - Π_DEC - | - next accumulator: CE(b,L)^k -``` - -### What the prover sends in each sub-protocol - -Below is the communication “payload” you should have in mind (Fiat–Shamir makes verifier randomness transcript-derived, but sizes are the same). - -#### Π_CCS (paper §7.3) - -Prover payload: - -- **Sum-check transcript over \(K\)** for \(\log m\) rounds (one univariate polynomial per round; degree is small in typical CCS, e.g. R1CS-like \(u=2\)). -- **Oracle answers after sum-check**: for every claim \(i\in[K+k]\) and every matrix \(j\in[t]\), send - \[ - y'_{i,j} = \bar M_j \tilde z_i(r') \in R_K. - \] - -Rule of thumb: the \(y'_{i,j}\) payload dominates. - -#### Π_RLC (paper §7.4) - -This is just random linear combination using \(\rho_i\in C\): - -\[ -c := \sum_i \rho_i c_i,\quad y_j := \sum_i \rho_i y_{i,j},\quad z := \sum_i \rho_i z_i. -\] - -Prover payload: essentially **nothing new** (the reduction is “algebraic bookkeeping”; in FS the \(\rho_i\) come from the transcript). - -#### Π_DEC (paper §7.5) - -Prover payload: - -- Decompose \(z\) into digits \((z_1,\dots,z_k)=\mathrm{split}_b(z)\). -- Send **\(k\) new commitments** \(c_i = L(z_i)\). -- Send **\(k\cdot t\)** new lifted evaluations \(y_{i,j} = \bar M_j \tilde z_i(r)\in R_K\). - -### Proof size accounting (symbolic, per fold step) - -Let: - -- commitment output be \(c\in R_F^\kappa\) (Ajtai: \(\kappa\) ring elements over \(R_F\)), -- each lifted evaluation be one ring element in \(R_K\) (degree \(d\) over \(K\)), -- \(\ell := \log m\) be the sum-check arity. - -Then per fold step, prover sends approximately: - -- **Π\_CCS**: - - sum-check: \(O(\ell)\) field elements in \(K\), - - evaluations: \((K+k)\cdot t\) ring elements in \(R_K\). -- **Π\_DEC**: - - commitments: \(k\cdot \kappa\) ring elements in \(R_F\), - - evaluations: \(k\cdot t\) ring elements in \(R_K\). - -Total (dominant terms): - -\[ -\text{#}(R_K\text{-elements}) \approx (K+k)t + kt = (K+2k)t, -\] -\[ -\text{#}(R_F\text{-elements}) \approx k\kappa, -\] -plus a small \(\tilde O(\log m)\) number of \(K\)-field elements from sum-check. - -To convert to bytes for appendix parameter sets where \(K=\mathbb{F}_{q^2}\) and \(q\) is 61–64 bits: - -- 1 \(F\)-element ≈ 8 bytes -- 1 \(K\)-element ≈ 16 bytes -- 1 \(R_F\)-element ≈ \(d\cdot 8\) bytes -- 1 \(R_K\)-element ≈ \(d\cdot 16\) bytes -- 1 commitment \(c\in R_F^\kappa\) ≈ \(\kappa\cdot d\cdot 8\) bytes - -So a back-of-the-envelope fold proof byte size is: - -\[ -\approx (K+2k)t\cdot(d\cdot 16)\;+\;k\kappa\cdot(d\cdot 8)\;+\;\tilde O(\log m)\cdot 16. -\] - -## Exact counts - -- Total concrete field/cyclotomic tuples in SuperNeo appendix: **3** -- Unique base fields in those tuples: **3** -- Unique cyclotomic polynomials in those tuples: **2** - - `X^64 + 1` - - `X^54 + X^27 + 1` -- Strict Solinas-only tuples (`q = 2^x - 2^y + 1`): **2 / 3** - - Goldilocks (`2^64 - 2^32 + 1`) - - Mersenne61 (`2^61 - 1 = 2^61 - 2^1 + 1`) -- Non-Solinas tuple: **1 / 3** - - Almost-Goldilocks (`2^64 - 2^32 - 31`) - -## What SuperNeo suggests (for their purpose) - -- Keep sum-check and norm-check over a small field (or small extension), not over ring arithmetic. -- Do not restrict to only power-of-two cyclotomics (`X^d + 1`); using broader cyclotomics can unlock better field compatibility. -- For Goldilocks/M61, the paper uses a trinomial cyclotomic (`X^54 + X^27 + 1`) instead of `X^d + 1`. -- They explicitly discuss why power-of-two cyclotomics are problematic for some small fields (full splitting / security issues in prior designs). - -## Fit into Hachi design (easy vs harder) - -- Easy fit now: - - Almost-Goldilocks-like setup with `d = 64` and `X^64 + 1` is structurally close to Hachi's current ring form. -- Requires refactor: - - Goldilocks and M61 with `X^54 + X^27 + 1` do not match the current hardcoded negacyclic `X^D + 1` shape. - -## Minimal integration plan into current architecture - -1. Add a cyclotomic profile abstraction (`CyclotomicProfile`) that defines modulus polynomial behavior. -2. Keep current profile as `Negacyclic` (`X^D + 1`) for existing NTT/CRT path. -3. Add a `Trinomial54` profile (`X^54 + X^27 + 1`) for SuperNeo-style field/ring experiments. -4. Keep backend split: - - current CRT+NTT backend for `Negacyclic` only, - - coefficient-domain backend first for `Trinomial54` (no forced NTT dependency). -5. Add explicit domain aliases for profile-bound rings so APIs remain clear (`CoeffDomain`). - -## Practical implication if we insist on Solinas-only fields - -- Within SuperNeo's concrete options, we still have **2 viable Solinas choices**: - - Goldilocks + `X^54 + X^27 + 1` - - M61 + `X^54 + X^27 + 1` -- If we also insist on power-of-two cyclotomics only (`X^d + 1`), SuperNeo's concrete Solinas count drops to **0**. diff --git a/docs/TRANSCRIPT_COMMITMENT_COMPAT_SPEC.md b/docs/TRANSCRIPT_COMMITMENT_COMPAT_SPEC.md deleted file mode 100644 index 03fceb7a..00000000 --- a/docs/TRANSCRIPT_COMMITMENT_COMPAT_SPEC.md +++ /dev/null @@ -1,106 +0,0 @@ -# Transcript and Commitment Compatibility Spec (Hachi Core) - -This document specifies Hachi's protocol-layer transcript and commitment interfaces. - -## Scope - -- Applies to Hachi core (`src/protocol/*`). -- Uses **Hachi-native** transcript labels and ordering. -- Does **not** wire Hachi into Jolt in this phase. -- Any future cross-system interop (for example Jolt-facing adaptation) must be handled by an adapter layer outside core label definitions. - -## Transcript Contract - -Hachi protocol transcripts implement: - -- `new(domain_label)` -- `append_bytes(label, bytes)` -- `append_field(label, x)` -- `append_serde(label, s)` -- `challenge_scalar(label)` -- `reset(domain_label)` - -Current core implementations: - -- `Blake2bTranscript` (Blake2b-512) -- `KeccakTranscript` (Keccak-256, matching Jolt's `sha3` crate usage) - -### Byte Framing - -All absorbed bytes use deterministic framing: - -- `label || len_le64 || bytes` - -This framing is applied uniformly for raw bytes, fields, and serializable protocol objects. - -### Field Encoding - -- Field elements are encoded through canonical representatives (little-endian `u128` bytes). -- Challenge derivation maps transcript digest bytes into field elements via canonical reduction. - -### Label Namespace - -All labels are defined in `src/protocol/transcript/labels.rs` and are Hachi-native. - -Reserved core labels include: - -- Domain label: `hachi/protocol` -- Commitment phase (§4.1): commitment -- Reduction phase (§4.2): evaluation-claims + linear-relation challenge -- Ring-switch phase (§4.3): ring-switch-message + ring-switch challenge -- Sumcheck phase (§4.3): sumcheck-round + sumcheck-round challenge -- Recursion stop phase (§4.5): stop-condition + stop-condition challenge - -Forbidden in Hachi core transcript constants: - -- Dory label literals (for example `vmv_c`, `beta`, `alpha`, `gamma`, `final_e1`, `final_e2`, `d`) - -## Commitment Contract - -Hachi protocol commitment interfaces include: - -- `CommitmentScheme` -- `StreamingCommitmentScheme` -- `AppendToTranscript` - -The commitment layer defines: - -- setup split (`setup_prover`, `setup_verifier`) -- commitment/opening APIs (`commit`, `prove`, `verify`) -- homomorphic combination APIs (`combine_commitments`, `combine_hints`) -- optional streaming/chunked path for large inputs -- label-directed transcript absorption (`AppendToTranscript` call sites choose event labels) - -## Determinism Requirements - -- Prover and verifier must absorb the same labeled byte sequence in the same order. -- Transcript challenges must be reproducible for identical input schedules. -- Commitment/proof objects absorbed via `append_serde` must use deterministic `HachiSerialize` encoding. - -## Test Requirements - -Tests should enforce: - -- Transcript replay determinism (same schedule => same challenges). -- Label/order sensitivity (different labels/order => diverging challenges). -- Framing stability. -- No Dory-label leakage in Hachi label constants/schedules. -- Commitment/hint combination algebraic sanity. - -## Deferred Integration Note - -Integration into Jolt is a separate, deferred phase tracked in `HACHI_PROGRESS.md`. -When started, an adapter should translate between external transcript conventions and Hachi core interfaces without changing Hachi-native core labels. - -## Deferred Adapter Contract (Design Only) - -`JoltToHachiTranscript` is deferred, but its expected behavior is fixed now: - -- Owns a mutable reference to a Jolt transcript object. -- Implements Hachi `Transcript` by forwarding absorption/challenge calls. -- Performs label translation at the boundary (Jolt-side naming to Hachi-side API events). -- Never mutates or extends Hachi core label constants. -- Maintains deterministic call ordering: prover and verifier adapter paths must replay identical absorb/challenge sequences. -- Supports domain initialization and explicit reset semantics. - -This adapter lives outside Hachi core protocol modules and is not part of this phase's implementation. diff --git a/examples/profile.rs b/examples/profile.rs new file mode 100644 index 00000000..d29c6fe0 --- /dev/null +++ b/examples/profile.rs @@ -0,0 +1,295 @@ +#![allow(missing_docs)] + +use hachi_pcs::algebra::poly::multilinear_eval; +use hachi_pcs::algebra::Fp128; +use hachi_pcs::error::HachiError; +use hachi_pcs::primitives::serialization::Compress; +use hachi_pcs::protocol::commitment::{ + DecompositionParams, Fp128CommitmentConfig, HachiCommitmentLayout, +}; +use hachi_pcs::protocol::commitment_scheme::HachiCommitmentScheme; +use hachi_pcs::protocol::hachi_poly_ops::{DensePoly, OneHotPoly}; +use hachi_pcs::protocol::proof::HachiProof; +use hachi_pcs::protocol::sumcheck::norm_sumcheck::choose_round_kernel; +use hachi_pcs::protocol::transcript::Blake2bTranscript; +use hachi_pcs::protocol::CommitmentConfig; +use hachi_pcs::{ + BasisMode, CanonicalField, CommitmentScheme, FromSmallInt, HachiSerialize, Transcript, +}; +use rand::rngs::StdRng; +use rand::{Rng, SeedableRng}; +use std::env; +use std::fs; +use std::time::{Instant, SystemTime, UNIX_EPOCH}; +use tracing_chrome::ChromeLayerBuilder; +use tracing_subscriber::prelude::*; + +type F = Fp128<0xfffffffffffffffffffffffffffffeed>; + +const D: usize = Fp128CommitmentConfig::D; + +#[derive(Clone, Copy, Debug)] +struct ProfileCfg; +impl CommitmentConfig for ProfileCfg { + const D: usize = D; + const N_A: usize = Fp128CommitmentConfig::N_A; + const N_B: usize = Fp128CommitmentConfig::N_B; + const N_D: usize = Fp128CommitmentConfig::N_D; + const CHALLENGE_WEIGHT: usize = Fp128CommitmentConfig::CHALLENGE_WEIGHT; + + fn decomposition() -> DecompositionParams { + Fp128CommitmentConfig::decomposition() + } + + fn commitment_layout(max_num_vars: usize) -> Result { + match (env::var("HACHI_M_VARS"), env::var("HACHI_R_VARS")) { + (Ok(m_str), Ok(r_str)) => { + let m: usize = m_str.parse().expect("HACHI_M_VARS must be a number"); + let r: usize = r_str.parse().expect("HACHI_R_VARS must be a number"); + eprintln!(" [layout] override: m_vars={m}, r_vars={r}"); + HachiCommitmentLayout::new::(m, r, &Self::decomposition()) + } + _ => Fp128CommitmentConfig::commitment_layout(max_num_vars), + } + } +} + +type Scheme = HachiCommitmentScheme; + +fn run_prove( + label: &str, + setup: &>::ProverSetup, + poly: &DensePoly, + pt: &[F], + opening: F, + layout: &HachiCommitmentLayout, +) { + let t0 = Instant::now(); + let (commitment, hint) = + >::commit(poly, setup, layout).unwrap(); + eprintln!("[{label}] commit: {:.3}s", t0.elapsed().as_secs_f64()); + + let t0 = Instant::now(); + let mut prover_transcript = Blake2bTranscript::::new(b"profile"); + let proof = >::prove( + setup, + poly, + pt, + hint, + &mut prover_transcript, + &commitment, + BasisMode::Lagrange, + layout, + ) + .unwrap(); + eprintln!("[{label}] prove: {:.3}s", t0.elapsed().as_secs_f64()); + print_proof_summary(label, &proof); + + let t0 = Instant::now(); + let verifier_setup = >::setup_verifier(setup); + let mut verifier_transcript = Blake2bTranscript::::new(b"profile"); + >::verify( + &proof, + &verifier_setup, + &mut verifier_transcript, + pt, + &opening, + &commitment, + BasisMode::Lagrange, + layout, + ) + .unwrap(); + eprintln!("[{label}] verify: {:.3}s", t0.elapsed().as_secs_f64()); +} + +fn print_proof_summary(label: &str, proof: &HachiProof) { + eprintln!( + "[{label}] levels: {}, proof size: {} bytes", + proof.levels.len(), + proof.size() + ); + for (i, lp) in proof.levels.iter().enumerate() { + let w_comm_size = lp.w_commitment.serialized_size(Compress::No); + let sc_size = lp.sumcheck_proof.serialized_size(Compress::No); + eprintln!( + "[{label}] L{i}: w_commitment={} ring elems ({} bytes), sumcheck={} bytes", + lp.w_commitment.u.len(), + w_comm_size, + sc_size, + ); + } + eprintln!( + "[{label}] final_w: {} elems, {} bits/elem, packed {} bytes", + proof.final_w.num_elems, + proof.final_w.bits_per_elem, + proof.final_w.serialized_size(Compress::No), + ); +} + +fn run_prove_onehot( + label: &str, + setup: &>::ProverSetup, + onehot_poly: &OneHotPoly, + pt: &[F], + opening: F, + layout: &HachiCommitmentLayout, +) { + let t0 = Instant::now(); + let (commitment, hint) = + >::commit(onehot_poly, setup, layout).unwrap(); + eprintln!( + "[{label}] onehot commit: {:.3}s", + t0.elapsed().as_secs_f64() + ); + + let t0 = Instant::now(); + let mut prover_transcript = Blake2bTranscript::::new(b"profile"); + let proof = >::prove( + setup, + onehot_poly, + pt, + hint, + &mut prover_transcript, + &commitment, + BasisMode::Lagrange, + layout, + ) + .unwrap(); + eprintln!("[{label}] prove: {:.3}s", t0.elapsed().as_secs_f64()); + print_proof_summary(label, &proof); + + let t0 = Instant::now(); + let verifier_setup = >::setup_verifier(setup); + let mut verifier_transcript = Blake2bTranscript::::new(b"profile"); + >::verify( + &proof, + &verifier_setup, + &mut verifier_transcript, + pt, + &opening, + &commitment, + BasisMode::Lagrange, + layout, + ) + .unwrap(); + eprintln!("[{label}] verify: {:.3}s", t0.elapsed().as_secs_f64()); +} + +fn main() { + #[cfg(feature = "parallel")] + rayon::ThreadPoolBuilder::new() + .stack_size(64 * 1024 * 1024) + .build_global() + .ok(); + + let trace_dir = "profile_traces"; + fs::create_dir_all(trace_dir).ok(); + + let log_basis = ProfileCfg::decomposition().log_basis; + let b = 1u32 << log_basis; + + let alpha = D.trailing_zeros() as usize; + let nv: usize = match (env::var("HACHI_M_VARS"), env::var("HACHI_R_VARS")) { + (Ok(m_str), Ok(r_str)) => { + let m: usize = m_str.parse().expect("HACHI_M_VARS must be a number"); + let r: usize = r_str.parse().expect("HACHI_R_VARS must be a number"); + m + r + alpha + } + _ => env::var("HACHI_NUM_VARS") + .ok() + .and_then(|s| s.parse().ok()) + .unwrap_or(25), + }; + + let timestamp = SystemTime::now() + .duration_since(UNIX_EPOCH) + .unwrap() + .as_secs(); + let trace_file = format!("{trace_dir}/hachi_nv{nv}_b{b}_{timestamp}.json"); + + let (chrome_layer, _guard) = ChromeLayerBuilder::new() + .include_args(true) + .file(&trace_file) + .build(); + + tracing_subscriber::registry().with(chrome_layer).init(); + + eprintln!("Perfetto trace will be written to: {trace_file}"); + eprintln!("Open at https://ui.perfetto.dev/"); + eprintln!("num_vars = {nv}, b = {b}"); + + let mut rng = StdRng::seed_from_u64(0xbeef_cafe); + + let len = 1usize << nv; + let evals: Vec = (0..len) + .map(|_| F::from_canonical_u128_reduced(rng.gen::())) + .collect(); + let poly = DensePoly::::from_field_evals(nv, &evals).unwrap(); + let pt: Vec = (0..nv) + .map(|_| F::from_canonical_u128_reduced(rng.gen::())) + .collect(); + + let opening = multilinear_eval(&evals, &pt).unwrap(); + + let t0 = Instant::now(); + let setup = >::setup_prover(nv); + eprintln!("setup: {:.3}s", t0.elapsed().as_secs_f64()); + + let ab_mode = env::var("HACHI_AB_TEST").unwrap_or_default(); + + let layout = ProfileCfg::commitment_layout(nv).expect("layout"); + + if ab_mode == "1" { + eprintln!("\n=== A/B TEST: running both kernels ===\n"); + + env::set_var("HACHI_NORM_KERNEL", "affine_coeff"); + eprintln!("--- kernel: affine_coeff ---"); + run_prove("affine", &setup, &poly, &pt, opening, &layout); + + env::set_var("HACHI_NORM_KERNEL", "point_eval"); + eprintln!("\n--- kernel: point_eval ---"); + run_prove("point", &setup, &poly, &pt, opening, &layout); + + env::remove_var("HACHI_NORM_KERNEL"); + } else { + eprintln!( + "kernel: {:?} (set HACHI_AB_TEST=1 to compare both)", + choose_round_kernel(b as usize) + ); + run_prove("default", &setup, &poly, &pt, opening, &layout); + } + + eprintln!("\n--- one-hot commit path ---"); + let total_ring = layout.num_blocks * layout.block_len; + let onehot_k = D; + + let indices: Vec> = (0..total_ring) + .map(|_| Some(rng.gen_range(0..onehot_k))) + .collect(); + let onehot_poly = + OneHotPoly::::new(onehot_k, indices.clone(), layout.r_vars, layout.m_vars).unwrap(); + + let onehot_evals: Vec = { + let mut evals = vec![F::from_u64(0); total_ring * onehot_k]; + for (ci, opt_idx) in indices.iter().enumerate() { + if let Some(idx) = opt_idx { + evals[ci * onehot_k + idx] = F::from_u64(1); + } + } + evals + }; + let onehot_pt: Vec = (0..nv) + .map(|_| F::from_canonical_u128_reduced(rng.gen::())) + .collect(); + let opening_oh = multilinear_eval(&onehot_evals, &onehot_pt).unwrap(); + run_prove_onehot( + "onehot", + &setup, + &onehot_poly, + &onehot_pt, + opening_oh, + &layout, + ); + + eprintln!("\nDone. Trace saved to {trace_file}"); +} diff --git a/paper/fri-binius.pdf b/paper/fri-binius.pdf deleted file mode 100644 index 9f19074d66d9ee6b30f56a40fe780acb9cac8c5e..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 819617 zcma&MQ?;Gw(ZsKo^PKyF)+lpda zEYpds3Dv1|nP9sQP+&W+m(oy*@U?aF&;se_b0>pml?3eLJ0?moE}+kx11u z3Ds+{YxI3|x7ZXsV*h=5J-waK?~Pj#GA&di*W9+npi(k4TNKSYEu<>2Z1%v|rgOz+ zS?REHYoq=AF4Un{cPt6sYSXN1u-|eVYP0OPzf^fKRb8EJTU^;ECV0qCW@I=6gu6d;huRE|8;7frc?=QA)p>&+urBN^XdNMR7m6%)cqDF~rMwQyqU=oakl= zHi9-U!_rUtH@}R7g-QR|Afe3lErn4i`D|2b5G*41+hn_Q+Cq0nO`)75ijA(B^Ms0b zs>qb<)OSGpqt$k!1m@@U*ACu!Oo<#uHjm!m6_>AN*!{%tmb5{;u$6zpcB#Yb7I!j) zO7gefxq?__35uV<(US*sI@nld_Ff{xfR~w^D0Yx^YQJugL9OZV>9fxMrt^0jWQo~C zKsqd3!LSNi@4)VEzbKlA!&S+m?Tt3*)*x`S>Tpv&QA(%v!ee?@3OFL&(wAhfbT;^@ zaXYW{mVNzi-S)~7FFfV#`pW8DTD8cZy9T#*FI~bksQ|h^?M7nbLM7*5OikgCK!{hoO~K<41zJof!Ti;*)D)5Ry&>P)l!pEYD?hZCn`*laciH z$KjAPHu#J=x|(IW$f*0DRN4t|oOJO8tV1E8Ej8M{BEEfuLjwHdy#OYV_z*QI-B<@y 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zUQHVK!{j?bxkDqr8pa$uCxx1E#+*X;3HVPtiAFWOD^8MUMsFL2a%jBb)&yMl{{^fh zNt|Ve3{4BmU6b0leHl;SwW4(WGTwj^S}y<@Dtjgk-6f)xJ8Pf(E=Dm=c58Tlq%R{> zwRZ0y(^l!?!2JCh0<5sI&S(<#xahHlS*XxXZVTr2#K`q%L< zB?qxQUG=)t%?;cl)d!Ug_SH;+R%|<7OqsQ*ZCzyt?G3;8Ol1fw>4H8NC{&<#1tJhu zaXw}jFjXkONKDsjLnz+44>Moa#9v!h_-`h3GgEYybPsN5Y$k26US!mF?^hr=#^c}5 zl%V?m9EQ7NW4*YIgNs*#Us!qWrS>%|?&c_f>+;nM-kpF`>uBocqF}jria`CnMS+l8 zgLglw9!$9LZnFppwf(nIu~*MxOf7+W$iq-=I++6<6{jBd&I}QA`ZRB6<1j0*Tcu=_RDOXQH&7(9_ViZBq)S$ zY-BeC9bp`xHd%^oUG{ea{rES3KC(nEpT@neMeSh+?PdD>d83y1qnFJ-KDfTQ?x%G` zIH4N!--{%K)j0-jAnp7$3INEj6N#_sXdRK1WkG12>G4UR_ozGbP=^R_j7=%+cFf9u zi~|_Za~%-YMfzn7ao698_gioPg%gs0Qp^*~Q^}=jcUrSIA9zp CrtReconstruct for let mut result = F::from_i64(v[0]); let mut partial_prod = F::from_i64(primes[0].p.to_i64()); for i in 1..K { - result = result + F::from_i64(v[i]) * partial_prod; + result += F::from_i64(v[i]) * partial_prod; if i + 1 < K { partial_prod = partial_prod * F::from_i64(primes[i].p.to_i64()); } diff --git a/src/algebra/fields/ext.rs b/src/algebra/fields/ext.rs index c341b6fa..b46cbbf9 100644 --- a/src/algebra/fields/ext.rs +++ b/src/algebra/fields/ext.rs @@ -1,10 +1,11 @@ //! Quadratic and quartic extension fields. +use super::wide::{AccumPair, HasUnreducedOps}; use crate::algebra::module::VectorModule; use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; -use crate::{FieldCore, FieldSampling, FromSmallInt}; +use crate::{AdditiveGroup, FieldCore, FieldSampling, FromSmallInt}; /// `Fp2Config` with non-residue = -1. /// @@ -34,7 +35,7 @@ impl Fp2Config for TwoNr { use rand_core::RngCore; use std::io::{Read, Write}; use std::marker::PhantomData; -use std::ops::{Add, Mul, Neg, Sub}; +use std::ops::{Add, AddAssign, Mul, Neg, Sub, SubAssign}; /// Parameters for an `Fp2` quadratic extension over base field `F`. pub trait Fp2Config { @@ -142,6 +143,18 @@ impl> Neg for Fp2 { Self::new(-self.c0, -self.c1) } } +impl> AddAssign for Fp2 { + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} +impl> SubAssign for Fp2 { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} impl> Mul for Fp2 { type Output = Self; fn mul(self, rhs: Self) -> Self::Output { @@ -213,11 +226,15 @@ impl> HachiDeserialize for Fp2 { } } -impl> FieldCore for Fp2 { - fn zero() -> Self { - Self::new(F::zero(), F::zero()) - } +impl> AdditiveGroup for Fp2 { + const ZERO: Self = Self { + c0: F::ZERO, + c1: F::ZERO, + _cfg: PhantomData, + }; +} +impl> FieldCore for Fp2 { fn one() -> Self { Self::new(F::one(), F::zero()) } @@ -242,6 +259,12 @@ impl> FieldCore for Fp2 { let inv_n = self.norm().inv()?; Some(Self::new(self.c0 * inv_n, (-self.c1) * inv_n)) } + + const TWO_INV: Self = Self { + c0: F::TWO_INV, + c1: F::ZERO, + _cfg: PhantomData, + }; } impl> FieldSampling for Fp2 { @@ -260,6 +283,46 @@ impl> FromSmallInt for Fp2< } } +impl> HasUnreducedOps for Fp2 { + type MulU64Accum = AccumPair; + type ProductAccum = AccumPair; + + #[inline] + fn mul_u64_unreduced(self, small: u64) -> AccumPair { + AccumPair( + self.c0.mul_u64_unreduced(small), + self.c1.mul_u64_unreduced(small), + ) + } + + #[inline] + fn mul_to_product_accum(self, other: Self) -> AccumPair { + // Karatsuba: (c0 + c1·u)(d0 + d1·u) = (c0·d0 + NR·c1·d1) + (c0·d1 + c1·d0)·u + let v0 = self.c0.mul_to_product_accum(other.c0); + let v1 = self.c1.mul_to_product_accum(other.c1); + let cross = (self.c0 + self.c1).mul_to_product_accum(other.c0 + other.c1); + + let nr_v1 = if C::IS_NEG_ONE { -v1 } else { v1 + v1 }; + AccumPair(v0 + nr_v1, cross - v0 - v1) + } + + #[inline] + fn reduce_mul_u64_accum(accum: AccumPair) -> Self { + Self::new( + F::reduce_mul_u64_accum(accum.0), + F::reduce_mul_u64_accum(accum.1), + ) + } + + #[inline] + fn reduce_product_accum(accum: AccumPair) -> Self { + Self::new( + F::reduce_product_accum(accum.0), + F::reduce_product_accum(accum.1), + ) + } +} + /// Parameters for an `Fp4` quadratic extension over `Fp2`. pub trait Fp4Config> { /// Non-residue `NR2` in `Fp2` such that `v^2 = NR2`. @@ -359,6 +422,18 @@ impl, C4: Fp4Config> Neg for Fp4, C4: Fp4Config> AddAssign for Fp4 { + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} +impl, C4: Fp4Config> SubAssign for Fp4 { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} impl, C4: Fp4Config> Mul for Fp4 { type Output = Self; fn mul(self, rhs: Self) -> Self::Output { @@ -433,11 +508,15 @@ impl, C4: Fp4Config> HachiDeserial } } -impl, C4: Fp4Config> FieldCore for Fp4 { - fn zero() -> Self { - Self::new(Fp2::zero(), Fp2::zero()) - } +impl, C4: Fp4Config> AdditiveGroup for Fp4 { + const ZERO: Self = Self { + c0: Fp2::ZERO, + c1: Fp2::ZERO, + _cfg: PhantomData, + }; +} +impl, C4: Fp4Config> FieldCore for Fp4 { fn one() -> Self { Self::new(Fp2::one(), Fp2::zero()) } @@ -460,6 +539,12 @@ impl, C4: Fp4Config> FieldCore for let inv_n = self.norm().inv()?; Some(Self::new(self.c0 * inv_n, (-self.c1) * inv_n)) } + + const TWO_INV: Self = Self { + c0: Fp2::TWO_INV, + c1: Fp2::ZERO, + _cfg: PhantomData, + }; } impl, C4: Fp4Config> FieldSampling diff --git a/src/algebra/fields/fp128.rs b/src/algebra/fields/fp128.rs index 99f3fc5b..78531bdc 100644 --- a/src/algebra/fields/fp128.rs +++ b/src/algebra/fields/fp128.rs @@ -11,7 +11,7 @@ //! `Prime128M13M4P0` denotes `p = 2^128 − 2^13 − 2^4 + 2^0`. use std::io::{Read, Write}; -use std::ops::{Add, Mul, Neg, Sub}; +use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign}; use rand_core::RngCore; @@ -19,7 +19,8 @@ use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; use crate::{ - CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, PseudoMersenneField, + AdditiveGroup, CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, + PseudoMersenneField, }; /// Pack two u64 limbs into `[lo, hi]`. @@ -62,7 +63,7 @@ impl Eq for Fp128

{} impl Fp128

{ /// Offset `c = 2^128 − p`. Validated at compile time. - const C: u128 = { + pub const C: u128 = { let c = 0u128.wrapping_sub(P); assert!(P != 0, "modulus must be nonzero"); assert!(P & 1 == 1, "modulus must be odd"); @@ -74,7 +75,8 @@ impl Fp128

{ ); c }; - const C_LO: u64 = Self::C as u64; + /// Low 64 bits of `C` (always equals `C` since `C < 2^64`). + pub const C_LO: u64 = Self::C as u64; /// +1 means `C = 2^a + 1`, -1 means `C = 2^a - 1`, 0 means generic. const C_SHIFT_KIND: i8 = { let c = Self::C_LO; @@ -129,6 +131,33 @@ impl Fp128

{ to_u128(self.0) } + /// Const-evaluable `from_i64`. Embeds a small signed integer into `Fp`. + pub const fn from_i64_const(val: i64) -> Self { + if val >= 0 { + Self(from_u128(val as u128)) + } else { + Self(Self::sub_raw( + pack(0, 0), + from_u128(val.unsigned_abs() as u128), + )) + } + } + + /// Const-evaluable lookup table for balanced digits in `[-b/2, b/2)` + /// where `b = 2^log_basis`. Requires `log_basis <= 4`. + pub const fn digit_lut(log_basis: u32) -> [Self; 16] { + assert!(log_basis > 0 && log_basis <= 4); + let b = 1u32 << log_basis; + let half_b = (b / 2) as i64; + let mut lut = [Self(pack(0, 0)); 16]; + let mut i = 0u32; + while i < b { + lut[i as usize] = Self::from_i64_const(i as i64 - half_b); + i += 1; + } + lut + } + #[inline(always)] fn add_raw(a: [u64; 2], b: [u64; 2]) -> [u64; 2] { let (s, carry) = to_u128(a).overflowing_add(to_u128(b)); @@ -141,7 +170,7 @@ impl Fp128

{ } #[inline(always)] - fn sub_raw(a: [u64; 2], b: [u64; 2]) -> [u64; 2] { + const fn sub_raw(a: [u64; 2], b: [u64; 2]) -> [u64; 2] { let (diff, borrow) = to_u128(a).overflowing_sub(to_u128(b)); from_u128(if borrow { diff.wrapping_add(P) } else { diff }) } @@ -209,9 +238,33 @@ impl Fp128

{ Self::reduce_4(r0, r1, r2, r3) } + #[inline(always)] + fn sqr_wide(self) -> [u64; 4] { + let (a0, a1) = (self.0[0], self.0[1]); + let (p00_lo, p00_hi) = mul64_wide(a0, a0); + let (p01_lo, p01_hi) = mul64_wide(a0, a1); + let (p11_lo, p11_hi) = mul64_wide(a1, a1); + + let row1 = p00_hi as u128 + (p01_lo as u128) * 2; + let r0 = p00_lo; + let r1 = row1 as u64; + let carry1 = (row1 >> 64) as u64; + + let row2 = (p01_hi as u128) * 2 + p11_lo as u128 + carry1 as u128; + let r2 = row2 as u64; + let carry2 = (row2 >> 64) as u64; + + let row3 = p11_hi as u128 + carry2 as u128; + let r3 = row3 as u64; + debug_assert_eq!(row3 >> 64, 0); + + [r0, r1, r2, r3] + } + #[inline(always)] fn sqr_raw(a: [u64; 2]) -> [u64; 2] { - Self::mul_raw(a, a) + let [r0, r1, r2, r3] = Self(a).sqr_wide(); + Self::reduce_4(r0, r1, r2, r3) } /// Squaring, equivalent to `self * self`. @@ -225,7 +278,7 @@ impl Fp128

{ let mut acc = Self::one(); while exp > 0 { if (exp & 1) == 1 { - acc = acc * base; + acc *= base; } base = Self(Self::sqr_raw(base.0)); exp >>= 1; @@ -643,6 +696,27 @@ impl Neg for Fp128

{ } } +impl AddAssign for Fp128

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for Fp128

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for Fp128

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl<'a, const P: u128> Add<&'a Self> for Fp128

{ type Output = Self; #[inline] @@ -722,11 +796,11 @@ impl HachiDeserialize for Fp128

{ } } -impl FieldCore for Fp128

{ - fn zero() -> Self { - Self(pack(0, 0)) - } +impl AdditiveGroup for Fp128

{ + const ZERO: Self = Self(pack(0, 0)); +} +impl FieldCore for Fp128

{ fn one() -> Self { Self(pack(1, 0)) } @@ -743,6 +817,11 @@ impl FieldCore for Fp128

{ Some(inv) } } + + const TWO_INV: Self = { + let v = (P >> 1) + 1; + Self(pack(v as u64, (v >> 64) as u64)) + }; } impl Invertible for Fp128

{ @@ -778,12 +857,11 @@ impl FromSmallInt for Fp128

{ } fn from_i64(val: i64) -> Self { - if val >= 0 { - Self::from_u64(val as u64) - } else { - // unsigned_abs avoids overflow for i64::MIN. - -Self::from_u64(val.unsigned_abs()) - } + Self::from_i64_const(val) + } + + fn digit_lut(log_basis: u32) -> [Self; 16] { + Self::digit_lut(log_basis) } } @@ -957,7 +1035,7 @@ mod tests { carry = (sum >> 64) as u64; } assert_eq!(carry, 0); - expected = expected + a * F::from_u64(b); + expected += a * F::from_u64(b); } assert_eq!(F::solinas_reduce(&acc), expected); diff --git a/src/algebra/fields/fp32.rs b/src/algebra/fields/fp32.rs index 9be1b7b3..77419476 100644 --- a/src/algebra/fields/fp32.rs +++ b/src/algebra/fields/fp32.rs @@ -4,7 +4,7 @@ //! Uses Solinas-style two-fold reduction: the offset `c` and fold point `k` //! are computed at compile time from the const-generic modulus `P`. -use std::ops::{Add, Mul, Neg, Sub}; +use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign}; use rand_core::RngCore; @@ -12,7 +12,8 @@ use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; use crate::{ - CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, PseudoMersenneField, + AdditiveGroup, CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, + PseudoMersenneField, }; use std::io::{Read, Write}; @@ -29,7 +30,7 @@ impl Fp32

{ const BITS: u32 = 32 - P.leading_zeros(); /// Offset `c = 2^k − P`. - const C: u32 = { + pub const C: u32 = { let c = if Self::BITS == 32 { 0u32.wrapping_sub(P) } else { @@ -152,7 +153,7 @@ impl Fp32

{ let mut acc = Self::one(); while exp > 0 { if (exp & 1) == 1 { - acc = acc * base; + acc *= base; } base = base.square(); exp >>= 1; @@ -218,6 +219,27 @@ impl Neg for Fp32

{ } } +impl AddAssign for Fp32

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for Fp32

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for Fp32

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl<'a, const P: u32> Add<&'a Self> for Fp32

{ type Output = Self; #[inline] @@ -288,11 +310,11 @@ impl HachiDeserialize for Fp32

{ } } -impl FieldCore for Fp32

{ - fn zero() -> Self { - Self(0) - } +impl AdditiveGroup for Fp32

{ + const ZERO: Self = Self(0); +} +impl FieldCore for Fp32

{ fn one() -> Self { Self(if P > 1 { 1 } else { 0 }) } @@ -309,6 +331,8 @@ impl FieldCore for Fp32

{ Some(inv) } } + + const TWO_INV: Self = Self((P as u64).div_ceil(2) as u32); } impl Invertible for Fp32

{ diff --git a/src/algebra/fields/fp64.rs b/src/algebra/fields/fp64.rs index 8b81218e..5e88ec5b 100644 --- a/src/algebra/fields/fp64.rs +++ b/src/algebra/fields/fp64.rs @@ -4,7 +4,7 @@ //! Uses Solinas-style two-fold reduction. For `c = 2^a ± 1` the fold //! multiply is replaced by shift+add/sub, saving a u128 widening multiply. -use std::ops::{Add, Mul, Neg, Sub}; +use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign}; use rand_core::RngCore; @@ -12,7 +12,8 @@ use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; use crate::{ - CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, PseudoMersenneField, + AdditiveGroup, CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, + PseudoMersenneField, }; use std::io::{Read, Write}; @@ -31,7 +32,7 @@ impl Fp64

{ const BITS: u32 = 64 - P.leading_zeros(); /// Offset `c = 2^k − P`. - const C: u64 = { + pub const C: u64 = { let c = if Self::BITS == 64 { 0u64.wrapping_sub(P) } else { @@ -254,7 +255,7 @@ impl Fp64

{ let mut acc = Self::one(); while exp > 0 { if (exp & 1) == 1 { - acc = acc * base; + acc *= base; } base = base.square(); exp >>= 1; @@ -322,6 +323,27 @@ impl Neg for Fp64

{ } } +impl AddAssign for Fp64

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for Fp64

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for Fp64

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl<'a, const P: u64> Add<&'a Self> for Fp64

{ type Output = Self; #[inline] @@ -392,11 +414,11 @@ impl HachiDeserialize for Fp64

{ } } -impl FieldCore for Fp64

{ - fn zero() -> Self { - Self(0) - } +impl AdditiveGroup for Fp64

{ + const ZERO: Self = Self(0); +} +impl FieldCore for Fp64

{ fn one() -> Self { Self(if P > 1 { 1 } else { 0 }) } @@ -413,6 +435,8 @@ impl FieldCore for Fp64

{ Some(inv) } } + + const TWO_INV: Self = Self((P as u128).div_ceil(2) as u64); } impl Invertible for Fp64

{ diff --git a/src/algebra/fields/mod.rs b/src/algebra/fields/mod.rs index 85cf56d0..90ff6c91 100644 --- a/src/algebra/fields/mod.rs +++ b/src/algebra/fields/mod.rs @@ -18,12 +18,12 @@ pub mod packed_avx2; target_feature = "avx512dq" ))] pub mod packed_avx512; -#[allow(missing_docs)] pub mod packed_ext; #[cfg(all(target_arch = "aarch64", target_feature = "neon"))] pub mod packed_neon; pub mod pseudo_mersenne; pub(crate) mod util; +pub mod wide; pub use ext::{Ext2, Ext4, Fp2, Fp2Config, Fp4, Fp4Config, NegOneNr, TwoNr, UnitNr}; pub use fp128::{ @@ -41,3 +41,7 @@ pub use pseudo_mersenne::{ Pow2Offset56Field, Pow2Offset64Field, Pow2OffsetPrimeSpec, POW2_OFFSET_IMPLEMENTED_MAX_BITS, POW2_OFFSET_MAX, POW2_OFFSET_PRIMES, POW2_OFFSET_TABLE, }; +pub use wide::{ + AccumPair, Fp128MulU64Accum, Fp128ProductAccum, Fp128x8i32, Fp32x2i32, Fp64ProductAccum, + Fp64x4i32, HasUnreducedOps, HasWide, ReduceTo, +}; diff --git a/src/algebra/fields/packed.rs b/src/algebra/fields/packed.rs index eaf15ab2..6da7917b 100644 --- a/src/algebra/fields/packed.rs +++ b/src/algebra/fields/packed.rs @@ -2,7 +2,7 @@ use crate::algebra::fields::{Fp128, Fp32, Fp64}; use crate::FieldCore; -use core::ops::{Add, Mul, Sub}; +use core::ops::{Add, AddAssign, Mul, MulAssign, Sub, SubAssign}; /// Array-like packed values over a scalar type. pub trait PackedValue: 'static + Copy + Send + Sync { @@ -121,6 +121,27 @@ impl Mul for NoPacking { } } +impl AddAssign for NoPacking { + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for NoPacking { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for NoPacking { + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl PackedField for NoPacking { type Scalar = T; diff --git a/src/algebra/fields/packed_avx2.rs b/src/algebra/fields/packed_avx2.rs index 95468959..c29685e2 100644 --- a/src/algebra/fields/packed_avx2.rs +++ b/src/algebra/fields/packed_avx2.rs @@ -7,7 +7,7 @@ use crate::algebra::fields::{Fp128, Fp32, Fp64}; use core::arch::x86_64::*; use core::fmt; use core::mem::transmute; -use core::ops::{Add, Mul, Sub}; +use core::ops::{Add, AddAssign, Mul, MulAssign, Sub, SubAssign}; /// Duplicate high 32 bits of each 64-bit lane into the low 32 bits. /// Uses the float `movehdup` instruction which runs on port 5 (doesn't compete @@ -240,6 +240,27 @@ impl PackedValue for PackedFp32Avx2

{ } } +impl AddAssign for PackedFp32Avx2

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for PackedFp32Avx2

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for PackedFp32Avx2

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl PackedField for PackedFp32Avx2

{ type Scalar = Fp32

; @@ -485,6 +506,27 @@ impl PackedValue for PackedFp64Avx2

{ } } +impl AddAssign for PackedFp64Avx2

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for PackedFp64Avx2

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for PackedFp64Avx2

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl PackedField for PackedFp64Avx2

{ type Scalar = Fp64

; @@ -691,6 +733,27 @@ impl PackedValue for PackedFp128Avx2

{ } } +impl AddAssign for PackedFp128Avx2

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for PackedFp128Avx2

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for PackedFp128Avx2

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl PackedField for PackedFp128Avx2

{ type Scalar = Fp128

; diff --git a/src/algebra/fields/packed_avx512.rs b/src/algebra/fields/packed_avx512.rs index 1102ac95..343c1dfc 100644 --- a/src/algebra/fields/packed_avx512.rs +++ b/src/algebra/fields/packed_avx512.rs @@ -9,7 +9,7 @@ use crate::FieldCore; use core::arch::x86_64::*; use core::fmt; use core::mem::transmute; -use core::ops::{Add, Mul, Sub}; +use core::ops::{Add, AddAssign, Mul, MulAssign, Sub, SubAssign}; #[inline(always)] unsafe fn movehdup_epi32_512(x: __m512i) -> __m512i { @@ -251,6 +251,27 @@ impl PackedValue for PackedFp32Avx512

{ } } +impl AddAssign for PackedFp32Avx512

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for PackedFp32Avx512

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for PackedFp32Avx512

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl PackedField for PackedFp32Avx512

{ type Scalar = Fp32

; @@ -475,6 +496,27 @@ impl PackedValue for PackedFp64Avx512

{ } } +impl AddAssign for PackedFp64Avx512

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for PackedFp64Avx512

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for PackedFp64Avx512

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl PackedField for PackedFp64Avx512

{ type Scalar = Fp64

; @@ -653,6 +695,27 @@ impl PackedValue for PackedFp128Avx512

{ } } +impl AddAssign for PackedFp128Avx512

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for PackedFp128Avx512

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for PackedFp128Avx512

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl PackedField for PackedFp128Avx512

{ type Scalar = Fp128

; diff --git a/src/algebra/fields/packed_ext.rs b/src/algebra/fields/packed_ext.rs index 5bf061d9..9725b598 100644 --- a/src/algebra/fields/packed_ext.rs +++ b/src/algebra/fields/packed_ext.rs @@ -15,7 +15,9 @@ use core::ops::{Add, Mul, Sub}; /// /// If `PF` has width `W`, this represents `W` parallel `Fp2` values. pub struct PackedFp2, PF: PackedField> { + /// Degree-0 coefficient (packed across SIMD lanes). pub c0: PF, + /// Degree-1 coefficient (packed across SIMD lanes). pub c1: PF, _marker: std::marker::PhantomData (F, C)>, } @@ -37,6 +39,7 @@ impl, PF: PackedField> std::fmt::Debug } impl, PF: PackedField> PackedFp2 { + /// Create a `PackedFp2` from its two packed coefficients. #[inline] pub fn new(c0: PF, c1: PF) -> Self { Self { @@ -158,7 +161,9 @@ pub struct PackedFp4< C4: Fp4Config, PF: PackedField, > { + /// Low half (`Fp2` coefficient 0). pub c0: PackedFp2, + /// High half (`Fp2` coefficient 1). pub c1: PackedFp2, _marker: std::marker::PhantomData C4>, } @@ -203,6 +208,7 @@ where C4: Fp4Config, PF: PackedField, { + /// Create a `PackedFp4` from its two `PackedFp2` halves. #[inline] pub fn new(c0: PackedFp2, c1: PackedFp2) -> Self { Self { diff --git a/src/algebra/fields/packed_neon.rs b/src/algebra/fields/packed_neon.rs index a50f73a0..e76c1ed2 100644 --- a/src/algebra/fields/packed_neon.rs +++ b/src/algebra/fields/packed_neon.rs @@ -11,7 +11,7 @@ use core::arch::aarch64::{ }; use core::fmt; use core::mem::transmute; -use core::ops::{Add, Mul, Sub}; +use core::ops::{Add, AddAssign, Mul, MulAssign, Sub, SubAssign}; /// Number of packed `Fp128` lanes in this backend. pub const WIDTH: usize = 2; @@ -315,6 +315,27 @@ impl Mul for PackedFp128Neon

{ } } +impl AddAssign for PackedFp128Neon

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for PackedFp128Neon

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for PackedFp128Neon

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl PackedField for PackedFp128Neon

{ type Scalar = Fp128

; @@ -530,6 +551,27 @@ impl PackedValue for PackedFp32Neon

{ } } +impl AddAssign for PackedFp32Neon

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for PackedFp32Neon

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for PackedFp32Neon

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl PackedField for PackedFp32Neon

{ type Scalar = Fp32

; @@ -708,6 +750,27 @@ impl PackedValue for PackedFp64Neon

{ } } +impl AddAssign for PackedFp64Neon

{ + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +impl SubAssign for PackedFp64Neon

{ + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +impl MulAssign for PackedFp64Neon

{ + #[inline] + fn mul_assign(&mut self, rhs: Self) { + *self = *self * rhs; + } +} + impl PackedField for PackedFp64Neon

{ type Scalar = Fp64

; diff --git a/src/algebra/fields/wide.rs b/src/algebra/fields/wide.rs new file mode 100644 index 00000000..e160f3d1 --- /dev/null +++ b/src/algebra/fields/wide.rs @@ -0,0 +1,1238 @@ +//! Wide unreduced field accumulators for carry-free signed addition. +//! +//! Each type splits a canonical field element into 16-bit limbs stored in +//! `i32` slots. Addition and negation are element-wise i32 ops — no carry +//! propagation, no modular reduction. Reduction back to canonical form +//! happens once after accumulation via [`reduce`](Fp128x8i32::reduce). +//! +//! The i32 overflow budget is `i32::MAX / u16::MAX ≈ 32,769` signed +//! additions before any limb can overflow. + +use std::ops::{Add, AddAssign, Neg, Sub, SubAssign}; + +use crate::{AdditiveGroup, CanonicalField, FieldCore}; + +use super::fp128::Fp128; +use super::fp32::Fp32; +use super::fp64::Fp64; + +/// Wide unreduced accumulator for `Fp32`: 2 × i32 limbs (16-bit data each). +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +#[repr(C)] +pub struct Fp32x2i32(pub [i32; 2]); + +impl Fp32x2i32 { + /// Returns the zero accumulator. + #[inline] + pub fn zero() -> Self { + ::ZERO + } +} + +impl From> for Fp32x2i32 { + #[inline] + fn from(x: Fp32

) -> Self { + let v = x.0; + Self([(v & 0xFFFF) as i32, (v >> 16) as i32]) + } +} + +impl Fp32x2i32 { + /// Multiply every limb by a small signed scalar. + /// + /// Safe when `|small| * max_limb_magnitude` fits in i32. After `From`, + /// limbs are in `[0, 0xFFFF]`, so `|small| ≤ 32_767` is safe for a single + /// product. For accumulation of `k` scaled values, require + /// `k * |small| * 0xFFFF < i32::MAX`, i.e. roughly `k * |small| < 32_768`. + #[inline] + pub fn scale_i32(self, small: i32) -> Self { + Self([self.0[0] * small, self.0[1] * small]) + } + + /// Reduce back to canonical `Fp32

`. + /// + /// Carry-propagates the i32 limbs into a signed value, normalizes to + /// `[0, p)`, and returns the canonical field element. + #[inline] + pub fn reduce(self) -> Fp32

{ + let [l0, l1] = self.0; + // Carry-propagate: value = l0 + l1 * 2^16 + let wide = l0 as i64 + (l1 as i64) * (1i64 << 16); + // Normalize to [0, p) + let p = P as i64; + let normalized = ((wide % p) + p) % p; + Fp32::from_canonical_u32(normalized as u32) + } +} + +impl Add for Fp32x2i32 { + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + Self([self.0[0] + rhs.0[0], self.0[1] + rhs.0[1]]) + } +} + +impl AddAssign for Fp32x2i32 { + #[inline] + fn add_assign(&mut self, rhs: Self) { + self.0[0] += rhs.0[0]; + self.0[1] += rhs.0[1]; + } +} + +impl Sub for Fp32x2i32 { + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + Self([self.0[0] - rhs.0[0], self.0[1] - rhs.0[1]]) + } +} + +impl SubAssign for Fp32x2i32 { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + self.0[0] -= rhs.0[0]; + self.0[1] -= rhs.0[1]; + } +} + +impl Neg for Fp32x2i32 { + type Output = Self; + #[inline] + fn neg(self) -> Self { + Self([-self.0[0], -self.0[1]]) + } +} + +/// Wide unreduced accumulator for `Fp64`: 4 × i32 limbs (16-bit data each). +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +#[repr(C)] +pub struct Fp64x4i32(pub [i32; 4]); + +impl Fp64x4i32 { + /// Returns the zero accumulator. + #[inline] + pub fn zero() -> Self { + ::ZERO + } +} + +impl From> for Fp64x4i32 { + #[inline] + fn from(x: Fp64

) -> Self { + let v = x.0; + Self([ + (v & 0xFFFF) as i32, + ((v >> 16) & 0xFFFF) as i32, + ((v >> 32) & 0xFFFF) as i32, + ((v >> 48) & 0xFFFF) as i32, + ]) + } +} + +impl Fp64x4i32 { + /// Multiply every limb by a small signed scalar. See [`Fp32x2i32::scale_i32`]. + #[inline] + pub fn scale_i32(self, small: i32) -> Self { + Self([ + self.0[0] * small, + self.0[1] * small, + self.0[2] * small, + self.0[3] * small, + ]) + } + + /// Reduce back to canonical `Fp64

`. + #[inline] + pub fn reduce(self) -> Fp64

{ + let [l0, l1, l2, l3] = self.0; + // Carry-propagate: value = l0 + l1*2^16 + l2*2^32 + l3*2^48 + let wide = l0 as i128 + + (l1 as i128) * (1i128 << 16) + + (l2 as i128) * (1i128 << 32) + + (l3 as i128) * (1i128 << 48); + let p = P as i128; + let normalized = ((wide % p) + p) % p; + Fp64::

::from_canonical_u64(normalized as u64) + } +} + +#[cfg(target_arch = "aarch64")] +impl Add for Fp64x4i32 { + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + unsafe { + use std::arch::aarch64::*; + let a = vld1q_s32(self.0.as_ptr()); + let b = vld1q_s32(rhs.0.as_ptr()); + let mut out = [0i32; 4]; + vst1q_s32(out.as_mut_ptr(), vaddq_s32(a, b)); + Self(out) + } + } +} + +#[cfg(target_arch = "aarch64")] +impl AddAssign for Fp64x4i32 { + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +#[cfg(target_arch = "aarch64")] +impl Sub for Fp64x4i32 { + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + unsafe { + use std::arch::aarch64::*; + let a = vld1q_s32(self.0.as_ptr()); + let b = vld1q_s32(rhs.0.as_ptr()); + let mut out = [0i32; 4]; + vst1q_s32(out.as_mut_ptr(), vsubq_s32(a, b)); + Self(out) + } + } +} + +#[cfg(target_arch = "aarch64")] +impl SubAssign for Fp64x4i32 { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +#[cfg(target_arch = "aarch64")] +impl Neg for Fp64x4i32 { + type Output = Self; + #[inline] + fn neg(self) -> Self { + unsafe { + use std::arch::aarch64::*; + let a = vld1q_s32(self.0.as_ptr()); + let mut out = [0i32; 4]; + vst1q_s32(out.as_mut_ptr(), vnegq_s32(a)); + Self(out) + } + } +} + +#[cfg(not(target_arch = "aarch64"))] +impl Add for Fp64x4i32 { + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + Self([ + self.0[0] + rhs.0[0], + self.0[1] + rhs.0[1], + self.0[2] + rhs.0[2], + self.0[3] + rhs.0[3], + ]) + } +} + +#[cfg(not(target_arch = "aarch64"))] +impl AddAssign for Fp64x4i32 { + #[inline] + fn add_assign(&mut self, rhs: Self) { + self.0[0] += rhs.0[0]; + self.0[1] += rhs.0[1]; + self.0[2] += rhs.0[2]; + self.0[3] += rhs.0[3]; + } +} + +#[cfg(not(target_arch = "aarch64"))] +impl Sub for Fp64x4i32 { + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + Self([ + self.0[0] - rhs.0[0], + self.0[1] - rhs.0[1], + self.0[2] - rhs.0[2], + self.0[3] - rhs.0[3], + ]) + } +} + +#[cfg(not(target_arch = "aarch64"))] +impl SubAssign for Fp64x4i32 { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + self.0[0] -= rhs.0[0]; + self.0[1] -= rhs.0[1]; + self.0[2] -= rhs.0[2]; + self.0[3] -= rhs.0[3]; + } +} + +#[cfg(not(target_arch = "aarch64"))] +impl Neg for Fp64x4i32 { + type Output = Self; + #[inline] + fn neg(self) -> Self { + Self([-self.0[0], -self.0[1], -self.0[2], -self.0[3]]) + } +} + +/// Wide unreduced accumulator for `Fp128`: 8 × i32 limbs (16-bit data each). +/// +/// On AVX2, one element fits a single 256-bit YMM register. On NEON, it +/// spans two 128-bit Q registers. All arithmetic is carry-free element-wise +/// i32 operations. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +#[repr(C)] +pub struct Fp128x8i32(pub [i32; 8]); + +impl Fp128x8i32 { + /// Returns the zero accumulator. + #[inline] + pub fn zero() -> Self { + ::ZERO + } +} + +impl From> for Fp128x8i32 { + #[inline] + fn from(x: Fp128

) -> Self { + let lo = x.0[0]; + let hi = x.0[1]; + Self([ + (lo & 0xFFFF) as i32, + ((lo >> 16) & 0xFFFF) as i32, + ((lo >> 32) & 0xFFFF) as i32, + ((lo >> 48) & 0xFFFF) as i32, + (hi & 0xFFFF) as i32, + ((hi >> 16) & 0xFFFF) as i32, + ((hi >> 32) & 0xFFFF) as i32, + ((hi >> 48) & 0xFFFF) as i32, + ]) + } +} + +impl Fp128x8i32 { + /// Multiply every limb by a small signed scalar. See [`Fp32x2i32::scale_i32`]. + #[inline] + pub fn scale_i32(self, small: i32) -> Self { + Self([ + self.0[0] * small, + self.0[1] * small, + self.0[2] * small, + self.0[3] * small, + self.0[4] * small, + self.0[5] * small, + self.0[6] * small, + self.0[7] * small, + ]) + } + + /// Reduce back to canonical `Fp128

`. + /// + /// Carry-propagates the 8 × i32 limbs into unsigned u64 limbs, then + /// applies Solinas reduction. + #[inline] + pub fn reduce(self) -> Fp128

{ + let limbs = self.0; + + // Carry-propagate from low to high, accumulating into i64 slots. + // Each i32 limb can be in [-32769*65535, 32769*65535] ≈ ±2^31. + // After propagation, each 16-bit "digit" is in [0, 65535] and we + // may have a signed residual in the top that overflows 128 bits. + let mut carry: i64 = 0; + let mut digits = [0u16; 8]; + for i in 0..8 { + let v = limbs[i] as i64 + carry; + // Arithmetic right-shift to propagate sign correctly + digits[i] = (v & 0xFFFF) as u16; + carry = v >> 16; + } + + // Reassemble into u64 limbs + let lo = digits[0] as u64 + | (digits[1] as u64) << 16 + | (digits[2] as u64) << 32 + | (digits[3] as u64) << 48; + let hi = digits[4] as u64 + | (digits[5] as u64) << 16 + | (digits[6] as u64) << 32 + | (digits[7] as u64) << 48; + + // p = 2^128 - c, so 2^128 ≡ c (mod p). + // value = lo + hi*2^64 + carry*2^128 ≡ lo + hi*2^64 + carry*c (mod p). + let c = Fp128::

::C_LO; + if carry == 0 { + Fp128::

::from_canonical_u128_reduced(lo as u128 | (hi as u128) << 64) + } else if carry > 0 { + Fp128::

::solinas_reduce(&[lo, hi, carry as u64]) + } else { + // carry < 0: value = base - |carry|*c. + let neg_carry = (-carry) as u64; + let sub = neg_carry as u128 * c as u128; + let base = lo as u128 | (hi as u128) << 64; + if base >= sub { + Fp128::

::from_canonical_u128_reduced(base - sub) + } else { + let diff = sub - base; + Fp128::

::from_canonical_u128_reduced(P - diff) + } + } + } +} + +#[cfg(target_arch = "aarch64")] +impl Add for Fp128x8i32 { + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + unsafe { + use std::arch::aarch64::*; + let a0 = vld1q_s32(self.0.as_ptr()); + let a1 = vld1q_s32(self.0.as_ptr().add(4)); + let b0 = vld1q_s32(rhs.0.as_ptr()); + let b1 = vld1q_s32(rhs.0.as_ptr().add(4)); + let mut out = [0i32; 8]; + vst1q_s32(out.as_mut_ptr(), vaddq_s32(a0, b0)); + vst1q_s32(out.as_mut_ptr().add(4), vaddq_s32(a1, b1)); + Self(out) + } + } +} + +#[cfg(target_arch = "aarch64")] +impl AddAssign for Fp128x8i32 { + #[inline] + fn add_assign(&mut self, rhs: Self) { + *self = *self + rhs; + } +} + +#[cfg(target_arch = "aarch64")] +impl Sub for Fp128x8i32 { + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + unsafe { + use std::arch::aarch64::*; + let a0 = vld1q_s32(self.0.as_ptr()); + let a1 = vld1q_s32(self.0.as_ptr().add(4)); + let b0 = vld1q_s32(rhs.0.as_ptr()); + let b1 = vld1q_s32(rhs.0.as_ptr().add(4)); + let mut out = [0i32; 8]; + vst1q_s32(out.as_mut_ptr(), vsubq_s32(a0, b0)); + vst1q_s32(out.as_mut_ptr().add(4), vsubq_s32(a1, b1)); + Self(out) + } + } +} + +#[cfg(target_arch = "aarch64")] +impl SubAssign for Fp128x8i32 { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + *self = *self - rhs; + } +} + +#[cfg(target_arch = "aarch64")] +impl Neg for Fp128x8i32 { + type Output = Self; + #[inline] + fn neg(self) -> Self { + unsafe { + use std::arch::aarch64::*; + let a0 = vld1q_s32(self.0.as_ptr()); + let a1 = vld1q_s32(self.0.as_ptr().add(4)); + let mut out = [0i32; 8]; + vst1q_s32(out.as_mut_ptr(), vnegq_s32(a0)); + vst1q_s32(out.as_mut_ptr().add(4), vnegq_s32(a1)); + Self(out) + } + } +} + +#[cfg(not(target_arch = "aarch64"))] +impl Add for Fp128x8i32 { + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + Self([ + self.0[0] + rhs.0[0], + self.0[1] + rhs.0[1], + self.0[2] + rhs.0[2], + self.0[3] + rhs.0[3], + self.0[4] + rhs.0[4], + self.0[5] + rhs.0[5], + self.0[6] + rhs.0[6], + self.0[7] + rhs.0[7], + ]) + } +} + +#[cfg(not(target_arch = "aarch64"))] +impl AddAssign for Fp128x8i32 { + #[inline] + fn add_assign(&mut self, rhs: Self) { + self.0[0] += rhs.0[0]; + self.0[1] += rhs.0[1]; + self.0[2] += rhs.0[2]; + self.0[3] += rhs.0[3]; + self.0[4] += rhs.0[4]; + self.0[5] += rhs.0[5]; + self.0[6] += rhs.0[6]; + self.0[7] += rhs.0[7]; + } +} + +#[cfg(not(target_arch = "aarch64"))] +impl Sub for Fp128x8i32 { + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + Self([ + self.0[0] - rhs.0[0], + self.0[1] - rhs.0[1], + self.0[2] - rhs.0[2], + self.0[3] - rhs.0[3], + self.0[4] - rhs.0[4], + self.0[5] - rhs.0[5], + self.0[6] - rhs.0[6], + self.0[7] - rhs.0[7], + ]) + } +} + +#[cfg(not(target_arch = "aarch64"))] +impl SubAssign for Fp128x8i32 { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + self.0[0] -= rhs.0[0]; + self.0[1] -= rhs.0[1]; + self.0[2] -= rhs.0[2]; + self.0[3] -= rhs.0[3]; + self.0[4] -= rhs.0[4]; + self.0[5] -= rhs.0[5]; + self.0[6] -= rhs.0[6]; + self.0[7] -= rhs.0[7]; + } +} + +#[cfg(not(target_arch = "aarch64"))] +impl Neg for Fp128x8i32 { + type Output = Self; + #[inline] + fn neg(self) -> Self { + Self([ + -self.0[0], -self.0[1], -self.0[2], -self.0[3], -self.0[4], -self.0[5], -self.0[6], + -self.0[7], + ]) + } +} + +impl AdditiveGroup for Fp32x2i32 { + const ZERO: Self = Self([0; 2]); +} + +impl AdditiveGroup for Fp64x4i32 { + const ZERO: Self = Self([0; 4]); +} + +impl AdditiveGroup for Fp128x8i32 { + const ZERO: Self = Self([0; 8]); +} + +/// Accumulator for `Fp64 × u64` products (also used for `Fp64 × Fp64`). +/// +/// Each product is ≤ 128 bits, split into two u64 halves stored as u128 slots. +/// Headroom: 2^64 additions per slot before overflow. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct Fp64ProductAccum(pub [u128; 2]); + +impl Fp64ProductAccum { + /// Reduce accumulated products to a canonical `Fp64

`. + #[inline] + pub fn reduce(self) -> Fp64

{ + let [s0, s1] = self.0; + // s0 = Σ lo_i, s1 = Σ hi_i; value = s0 + s1 * 2^64 + let a = Fp64::

::solinas_reduce(s0); + let b = Fp64::

::solinas_reduce(s1); + let shift = Fp64::

::solinas_reduce(1u128 << 64); + let b_shifted = Fp64::

::solinas_reduce(b.mul_wide_u64(shift.to_limbs())); + a + b_shifted + } +} + +impl From> for Fp64ProductAccum { + #[inline] + fn from(x: Fp64

) -> Self { + Self([x.to_limbs() as u128, 0]) + } +} + +impl AdditiveGroup for Fp64ProductAccum { + const ZERO: Self = Self([0; 2]); +} + +impl Add for Fp64ProductAccum { + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + Self([self.0[0] + rhs.0[0], self.0[1] + rhs.0[1]]) + } +} +impl AddAssign for Fp64ProductAccum { + #[inline] + fn add_assign(&mut self, rhs: Self) { + self.0[0] += rhs.0[0]; + self.0[1] += rhs.0[1]; + } +} +impl Sub for Fp64ProductAccum { + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + Self([ + self.0[0].wrapping_sub(rhs.0[0]), + self.0[1].wrapping_sub(rhs.0[1]), + ]) + } +} +impl SubAssign for Fp64ProductAccum { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + self.0[0] = self.0[0].wrapping_sub(rhs.0[0]); + self.0[1] = self.0[1].wrapping_sub(rhs.0[1]); + } +} +impl Neg for Fp64ProductAccum { + type Output = Self; + #[inline] + fn neg(self) -> Self { + Self([self.0[0].wrapping_neg(), self.0[1].wrapping_neg()]) + } +} + +/// Accumulator for `Fp128 × u64` products. +/// +/// Each `mul_wide_u64` produces 3 u64 limbs; stored as `[u128; 3]`. +/// Headroom: 2^64 additions per slot. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct Fp128MulU64Accum(pub [u128; 3]); + +impl Fp128MulU64Accum { + /// Reduce to canonical `Fp128

`. + #[inline] + pub fn reduce(self) -> Fp128

{ + let [s0, s1, s2] = self.0; + let c0 = s0 >> 64; + let r0 = s0 as u64; + let t1 = s1 + c0; + let r1 = t1 as u64; + let c1 = t1 >> 64; + let t2 = s2 + c1; + let r2 = t2 as u64; + let r3 = (t2 >> 64) as u64; + Fp128::

::solinas_reduce(&[r0, r1, r2, r3]) + } +} + +impl From> for Fp128MulU64Accum { + #[inline] + fn from(x: Fp128

) -> Self { + let [lo, hi] = x.to_limbs(); + Self([lo as u128, hi as u128, 0]) + } +} + +impl AdditiveGroup for Fp128MulU64Accum { + const ZERO: Self = Self([0; 3]); +} + +impl Add for Fp128MulU64Accum { + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + Self([ + self.0[0] + rhs.0[0], + self.0[1] + rhs.0[1], + self.0[2] + rhs.0[2], + ]) + } +} +impl AddAssign for Fp128MulU64Accum { + #[inline] + fn add_assign(&mut self, rhs: Self) { + self.0[0] += rhs.0[0]; + self.0[1] += rhs.0[1]; + self.0[2] += rhs.0[2]; + } +} +impl Sub for Fp128MulU64Accum { + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + Self([ + self.0[0].wrapping_sub(rhs.0[0]), + self.0[1].wrapping_sub(rhs.0[1]), + self.0[2].wrapping_sub(rhs.0[2]), + ]) + } +} +impl SubAssign for Fp128MulU64Accum { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + self.0[0] = self.0[0].wrapping_sub(rhs.0[0]); + self.0[1] = self.0[1].wrapping_sub(rhs.0[1]); + self.0[2] = self.0[2].wrapping_sub(rhs.0[2]); + } +} +impl Neg for Fp128MulU64Accum { + type Output = Self; + #[inline] + fn neg(self) -> Self { + Self([ + self.0[0].wrapping_neg(), + self.0[1].wrapping_neg(), + self.0[2].wrapping_neg(), + ]) + } +} + +/// Accumulator for `Fp128 × Fp128` products. +/// +/// Each `mul_wide` produces 4 u64 limbs; stored as `[u128; 4]`. +/// Headroom: 2^64 additions per slot. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct Fp128ProductAccum(pub [u128; 4]); + +impl Fp128ProductAccum { + /// Reduce to canonical `Fp128

`. + #[inline] + pub fn reduce(self) -> Fp128

{ + let [s0, s1, s2, s3] = self.0; + let c0 = s0 >> 64; + let r0 = s0 as u64; + let t1 = s1 + c0; + let r1 = t1 as u64; + let c1 = t1 >> 64; + let t2 = s2 + c1; + let r2 = t2 as u64; + let c2 = t2 >> 64; + let t3 = s3 + c2; + let r3 = t3 as u64; + let r4 = (t3 >> 64) as u64; + Fp128::

::solinas_reduce(&[r0, r1, r2, r3, r4]) + } +} + +impl From> for Fp128ProductAccum { + #[inline] + fn from(x: Fp128

) -> Self { + let [lo, hi] = x.to_limbs(); + Self([lo as u128, hi as u128, 0, 0]) + } +} + +impl AdditiveGroup for Fp128ProductAccum { + const ZERO: Self = Self([0; 4]); +} + +impl Add for Fp128ProductAccum { + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + Self([ + self.0[0] + rhs.0[0], + self.0[1] + rhs.0[1], + self.0[2] + rhs.0[2], + self.0[3] + rhs.0[3], + ]) + } +} +impl AddAssign for Fp128ProductAccum { + #[inline] + fn add_assign(&mut self, rhs: Self) { + self.0[0] += rhs.0[0]; + self.0[1] += rhs.0[1]; + self.0[2] += rhs.0[2]; + self.0[3] += rhs.0[3]; + } +} +impl Sub for Fp128ProductAccum { + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + Self([ + self.0[0].wrapping_sub(rhs.0[0]), + self.0[1].wrapping_sub(rhs.0[1]), + self.0[2].wrapping_sub(rhs.0[2]), + self.0[3].wrapping_sub(rhs.0[3]), + ]) + } +} +impl SubAssign for Fp128ProductAccum { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + self.0[0] = self.0[0].wrapping_sub(rhs.0[0]); + self.0[1] = self.0[1].wrapping_sub(rhs.0[1]); + self.0[2] = self.0[2].wrapping_sub(rhs.0[2]); + self.0[3] = self.0[3].wrapping_sub(rhs.0[3]); + } +} +impl Neg for Fp128ProductAccum { + type Output = Self; + #[inline] + fn neg(self) -> Self { + Self([ + self.0[0].wrapping_neg(), + self.0[1].wrapping_neg(), + self.0[2].wrapping_neg(), + self.0[3].wrapping_neg(), + ]) + } +} + +/// Pair accumulator for extension fields. +/// +/// Wraps two base-field accumulators `(c0, c1)` component-wise. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct AccumPair(pub A, pub A); + +impl AdditiveGroup for AccumPair { + const ZERO: Self = Self(A::ZERO, A::ZERO); +} + +impl Add for AccumPair { + type Output = Self; + #[inline] + fn add(self, rhs: Self) -> Self { + Self(self.0 + rhs.0, self.1 + rhs.1) + } +} +impl AddAssign for AccumPair { + #[inline] + fn add_assign(&mut self, rhs: Self) { + self.0 += rhs.0; + self.1 += rhs.1; + } +} +impl Sub for AccumPair { + type Output = Self; + #[inline] + fn sub(self, rhs: Self) -> Self { + Self(self.0 - rhs.0, self.1 - rhs.1) + } +} +impl SubAssign for AccumPair { + #[inline] + fn sub_assign(&mut self, rhs: Self) { + self.0 -= rhs.0; + self.1 -= rhs.1; + } +} +impl Neg for AccumPair { + type Output = Self; + #[inline] + fn neg(self) -> Self { + Self(-self.0, -self.1) + } +} + +/// Reduce a wide unreduced accumulator back to a canonical field element. +pub trait ReduceTo { + /// Carry-propagate and reduce to a canonical field element. + fn reduce(self) -> F; +} + +impl ReduceTo> for Fp32x2i32 { + #[inline] + fn reduce(self) -> Fp32

{ + Fp32x2i32::reduce::

(self) + } +} + +impl ReduceTo> for Fp64x4i32 { + #[inline] + fn reduce(self) -> Fp64

{ + Fp64x4i32::reduce::

(self) + } +} + +impl ReduceTo> for Fp128x8i32 { + #[inline] + fn reduce(self) -> Fp128

{ + Fp128x8i32::reduce::

(self) + } +} + +/// Multi-level unreduced multiplication hierarchy. +/// +/// Provides `field × u64` and `field × field` widening multiplies that return +/// accumulator types supporting carry-free addition. Reduction back to a +/// canonical field element happens once after accumulation. +pub trait HasUnreducedOps: FieldCore { + /// Accumulator for `self × u64` products (narrower than full product). + type MulU64Accum: AdditiveGroup; + /// Accumulator for `self × self` products. + type ProductAccum: AdditiveGroup; + + /// Widening `self × small` with no reduction. + fn mul_u64_unreduced(self, small: u64) -> Self::MulU64Accum; + /// Widening `self × other` with no reduction. + fn mul_to_product_accum(self, other: Self) -> Self::ProductAccum; + + /// Reduce a narrow-mul accumulator to a canonical field element. + fn reduce_mul_u64_accum(accum: Self::MulU64Accum) -> Self; + /// Reduce a full-product accumulator to a canonical field element. + fn reduce_product_accum(accum: Self::ProductAccum) -> Self; +} + +impl HasUnreducedOps for Fp64

{ + type MulU64Accum = Fp64ProductAccum; + type ProductAccum = Fp64ProductAccum; + + #[inline] + fn mul_u64_unreduced(self, small: u64) -> Fp64ProductAccum { + let wide = self.mul_wide_u64(small); + Fp64ProductAccum([wide & u64::MAX as u128, wide >> 64]) + } + + #[inline] + fn mul_to_product_accum(self, other: Self) -> Fp64ProductAccum { + let wide = self.mul_wide(other); + Fp64ProductAccum([wide & u64::MAX as u128, wide >> 64]) + } + + #[inline] + fn reduce_mul_u64_accum(accum: Fp64ProductAccum) -> Self { + accum.reduce::

() + } + + #[inline] + fn reduce_product_accum(accum: Fp64ProductAccum) -> Self { + accum.reduce::

() + } +} + +impl HasUnreducedOps for Fp128

{ + type MulU64Accum = Fp128MulU64Accum; + type ProductAccum = Fp128ProductAccum; + + #[inline] + fn mul_u64_unreduced(self, small: u64) -> Fp128MulU64Accum { + let [lo, mid, hi] = self.mul_wide_u64(small); + Fp128MulU64Accum([lo as u128, mid as u128, hi as u128]) + } + + #[inline] + fn mul_to_product_accum(self, other: Self) -> Fp128ProductAccum { + let [r0, r1, r2, r3] = self.mul_wide(other); + Fp128ProductAccum([r0 as u128, r1 as u128, r2 as u128, r3 as u128]) + } + + #[inline] + fn reduce_mul_u64_accum(accum: Fp128MulU64Accum) -> Self { + accum.reduce::

() + } + + #[inline] + fn reduce_product_accum(accum: Fp128ProductAccum) -> Self { + accum.reduce::

() + } +} + +/// Element-wise scaling of a wide accumulator by a small signed integer. +pub trait ScaleI32 { + /// Scale each element by `small`. + fn scale_i32(self, small: i32) -> Self; +} + +impl ScaleI32 for Fp32x2i32 { + #[inline] + fn scale_i32(self, small: i32) -> Self { + self.scale_i32(small) + } +} + +impl ScaleI32 for Fp64x4i32 { + #[inline] + fn scale_i32(self, small: i32) -> Self { + self.scale_i32(small) + } +} + +impl ScaleI32 for Fp128x8i32 { + #[inline] + fn scale_i32(self, small: i32) -> Self { + self.scale_i32(small) + } +} + +/// Associates a field type with its wide unreduced accumulator. +pub trait HasWide: FieldCore { + /// The wide accumulator type. + type Wide: AdditiveGroup + From + ReduceTo + ScaleI32; + + /// Convert `self` to wide form and scale every limb by `small`. + /// + /// Equivalent to `Self::Wide::from(self).scale_i32(small)` but avoids + /// the trait-method ambiguity at call sites. + #[inline] + fn mul_small_to_wide(self, small: i32) -> Self::Wide { + Self::Wide::from(self).scale_i32(small) + } +} + +impl HasWide for Fp32

{ + type Wide = Fp32x2i32; +} + +impl HasWide for Fp64

{ + type Wide = Fp64x4i32; +} + +impl HasWide for Fp128

{ + type Wide = Fp128x8i32; +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::algebra::fields::{Pow2Offset24Field, Pow2Offset40Field, Prime128M8M4M1M0}; + use crate::{FieldCore, FieldSampling, FromSmallInt}; + use rand::rngs::StdRng; + use rand::SeedableRng; + use rand_core::RngCore; + + type F128 = Prime128M8M4M1M0; + type F32 = Pow2Offset24Field; + type F64 = Pow2Offset40Field; + + const P128: u128 = 0xfffffffffffffffffffffffffffffeed; + const P32: u32 = (1 << 24) - 3; + const P64: u64 = (1 << 40) - 195; + + #[test] + fn fp128_roundtrip() { + let mut rng = StdRng::seed_from_u64(0xdead_1234); + for _ in 0..1000 { + let a: F128 = FieldSampling::sample(&mut rng); + let wide = Fp128x8i32::from(a); + let back = wide.reduce::(); + assert_eq!(a, back, "roundtrip failed for {a:?}"); + } + } + + #[test] + fn fp128_accumulate_matches_scalar() { + let mut rng = StdRng::seed_from_u64(0xbeef_cafe_4321); + let n = 1000; + let vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + + let scalar_sum = vals.iter().fold(F128::zero(), |acc, &x| acc + x); + + let wide_sum = vals + .iter() + .fold(Fp128x8i32::zero(), |acc, &x| acc + Fp128x8i32::from(x)); + let reduced = wide_sum.reduce::(); + + assert_eq!(scalar_sum, reduced); + } + + #[test] + fn fp128_add_sub_neg_match_scalar() { + let mut rng = StdRng::seed_from_u64(0x1122_3344_5566); + for _ in 0..500 { + let a: F128 = FieldSampling::sample(&mut rng); + let b: F128 = FieldSampling::sample(&mut rng); + + let wa = Fp128x8i32::from(a); + let wb = Fp128x8i32::from(b); + + assert_eq!((wa + wb).reduce::(), a + b); + assert_eq!((wa - wb).reduce::(), a - b); + assert_eq!((-wa).reduce::(), -a); + } + } + + #[test] + fn fp128_mixed_add_sub_stress() { + let mut rng = StdRng::seed_from_u64(0xaaaa_bbbb_cccc); + let n = 500; + let vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + + let mut scalar = F128::zero(); + let mut wide = Fp128x8i32::zero(); + for (i, &v) in vals.iter().enumerate() { + let wv = Fp128x8i32::from(v); + if i % 3 == 0 { + scalar -= v; + wide -= wv; + } else { + scalar += v; + wide += wv; + } + } + assert_eq!(wide.reduce::(), scalar); + } + + #[test] + fn fp32_roundtrip() { + let mut rng = StdRng::seed_from_u64(0x3232_3232); + for _ in 0..1000 { + let a: F32 = FieldSampling::sample(&mut rng); + let wide = Fp32x2i32::from(a); + let back = wide.reduce::(); + assert_eq!(a, back); + } + } + + #[test] + fn fp32_accumulate_matches_scalar() { + let mut rng = StdRng::seed_from_u64(0x3232_abcd); + let n = 1000; + let vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + + let scalar_sum = vals.iter().fold(F32::zero(), |acc, &x| acc + x); + let wide_sum = vals + .iter() + .fold(Fp32x2i32::zero(), |acc, &x| acc + Fp32x2i32::from(x)); + assert_eq!(wide_sum.reduce::(), scalar_sum); + } + + #[test] + fn fp64_roundtrip() { + let mut rng = StdRng::seed_from_u64(0x6464_6464); + for _ in 0..1000 { + let a: F64 = FieldSampling::sample(&mut rng); + let wide = Fp64x4i32::from(a); + let back = wide.reduce::(); + assert_eq!(a, back); + } + } + + #[test] + fn fp64_accumulate_matches_scalar() { + let mut rng = StdRng::seed_from_u64(0x6464_beef); + let n = 1000; + let vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + + let scalar_sum = vals.iter().fold(F64::zero(), |acc, &x| acc + x); + let wide_sum = vals + .iter() + .fold(Fp64x4i32::zero(), |acc, &x| acc + Fp64x4i32::from(x)); + assert_eq!(wide_sum.reduce::(), scalar_sum); + } + + #[test] + fn fp64_product_accum_matches_scalar() { + let mut rng = StdRng::seed_from_u64(0x6464_4444); + let n = 500; + let a_vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b_vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + + let scalar_sum: F64 = a_vals + .iter() + .zip(b_vals.iter()) + .fold(F64::zero(), |acc, (&a, &b)| acc + a * b); + + let accum_sum = a_vals + .iter() + .zip(b_vals.iter()) + .fold(Fp64ProductAccum::ZERO, |acc, (&a, &b)| { + acc + a.mul_to_product_accum(b) + }); + assert_eq!(F64::reduce_product_accum(accum_sum), scalar_sum); + } + + #[test] + fn fp64_mul_u64_accum_matches_scalar() { + let mut rng = StdRng::seed_from_u64(0x6464_5555); + let n = 500; + let a_vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b_vals: Vec = (0..n).map(|_| rng.next_u64() >> 32).collect(); + + let scalar_sum: F64 = a_vals + .iter() + .zip(b_vals.iter()) + .fold(F64::zero(), |acc, (&a, &b)| acc + a * F64::from_u64(b)); + + let accum_sum = a_vals + .iter() + .zip(b_vals.iter()) + .fold(Fp64ProductAccum::ZERO, |acc, (&a, &b)| { + acc + a.mul_u64_unreduced(b) + }); + assert_eq!(F64::reduce_mul_u64_accum(accum_sum), scalar_sum); + } + + #[test] + fn fp128_product_accum_matches_scalar() { + let mut rng = StdRng::seed_from_u64(0x0128_6666); + let n = 500; + let a_vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b_vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + + let scalar_sum: F128 = a_vals + .iter() + .zip(b_vals.iter()) + .fold(F128::zero(), |acc, (&a, &b)| acc + a * b); + + let accum_sum = a_vals + .iter() + .zip(b_vals.iter()) + .fold(Fp128ProductAccum::ZERO, |acc, (&a, &b)| { + acc + a.mul_to_product_accum(b) + }); + assert_eq!(F128::reduce_product_accum(accum_sum), scalar_sum); + } + + #[test] + fn fp128_mul_u64_accum_matches_scalar() { + let mut rng = StdRng::seed_from_u64(0x0128_7777); + let n = 500; + let a_vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b_vals: Vec = (0..n).map(|_| rng.next_u64()).collect(); + + let scalar_sum: F128 = a_vals + .iter() + .zip(b_vals.iter()) + .fold(F128::zero(), |acc, (&a, &b)| acc + a * F128::from_u64(b)); + + let accum_sum = a_vals + .iter() + .zip(b_vals.iter()) + .fold(Fp128MulU64Accum::ZERO, |acc, (&a, &b)| { + acc + a.mul_u64_unreduced(b) + }); + assert_eq!(F128::reduce_mul_u64_accum(accum_sum), scalar_sum); + } + + #[test] + fn fp128_product_accum_sub_neg() { + let mut rng = StdRng::seed_from_u64(0x0128_8888); + let n = 500; + let a_vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + let b_vals: Vec = (0..n).map(|_| FieldSampling::sample(&mut rng)).collect(); + + let mut scalar_sum = F128::zero(); + let mut accum_pos = Fp128ProductAccum::ZERO; + let mut accum_neg = Fp128ProductAccum::ZERO; + for (i, (&a, &b)) in a_vals.iter().zip(b_vals.iter()).enumerate() { + let prod = a.mul_to_product_accum(b); + if i % 2 == 0 { + scalar_sum += a * b; + accum_pos += prod; + } else { + scalar_sum -= a * b; + accum_neg += prod; + } + } + let result = F128::reduce_product_accum(accum_pos) - F128::reduce_product_accum(accum_neg); + assert_eq!(result, scalar_sum); + } +} diff --git a/src/algebra/mod.rs b/src/algebra/mod.rs index 21aea776..a3e0c839 100644 --- a/src/algebra/mod.rs +++ b/src/algebra/mod.rs @@ -27,6 +27,6 @@ pub use module::VectorModule; pub use ntt::tables; pub use ntt::{GarnerData, LimbQ, MontCoeff, NttPrime, PrimeWidth, RADIX_BITS}; pub use ring::{ - CrtNttConvertibleField, CrtNttParamSet, CyclotomicCrtNtt, CyclotomicRing, SparseChallenge, - SparseChallengeConfig, + CrtNttConvertibleField, CrtNttParamSet, CyclotomicCrtNtt, CyclotomicRing, DigitMontLut, + SparseChallenge, SparseChallengeConfig, }; diff --git a/src/algebra/module.rs b/src/algebra/module.rs index b924a0ae..bf41c567 100644 --- a/src/algebra/module.rs +++ b/src/algebra/module.rs @@ -26,7 +26,7 @@ impl Add for VectorModule { fn add(self, rhs: Self) -> Self::Output { let mut out = self.0; for (dst, src) in out.iter_mut().zip(rhs.0.iter()) { - *dst = *dst + *src; + *dst += *src; } Self(out) } @@ -37,7 +37,7 @@ impl Sub for VectorModule { fn sub(self, rhs: Self) -> Self::Output { let mut out = self.0; for (dst, src) in out.iter_mut().zip(rhs.0.iter()) { - *dst = *dst - *src; + *dst -= *src; } Self(out) } diff --git a/src/algebra/ntt/butterfly.rs b/src/algebra/ntt/butterfly.rs index fd0f6e53..fb942750 100644 --- a/src/algebra/ntt/butterfly.rs +++ b/src/algebra/ntt/butterfly.rs @@ -15,6 +15,7 @@ use super::prime::{MontCoeff, NttPrime, PrimeWidth}; /// Precomputed twiddle factors for a specific prime and degree `D`. /// /// `D` must be a power of two. +#[derive(Debug, Clone, PartialEq, Eq)] pub struct NttTwiddles { /// Stage roots for iterative forward cyclic NTT in Montgomery form. pub(crate) fwd_wlen: [MontCoeff; D], @@ -28,6 +29,14 @@ pub struct NttTwiddles { pub(crate) psi_inv_pows: [MontCoeff; D], /// `D^{-1} mod p` in Montgomery form, used for inverse NTT final scaling. pub(crate) d_inv: MontCoeff, + /// Fused `D^{-1} * psi^{-i}` for each index, in Montgomery form. + pub(crate) d_inv_psi_inv: [MontCoeff; D], + /// Per-position forward twiddles, packed across stages. + /// Stage s (with butterfly half-length 2^s) occupies `[2^s - 1 .. 2^(s+1) - 2]`. + /// Breaks the serial `w = mul(w, wlen)` dependency chain in butterfly loops. + pub(crate) fwd_twiddles: [MontCoeff; D], + /// Per-position inverse twiddles, same layout as `fwd_twiddles`. + pub(crate) inv_twiddles: [MontCoeff; D], } impl NttTwiddles { @@ -79,13 +88,38 @@ impl NttTwiddles { let d_inv_canonical = pow_mod(D as i64, p - 2, p); let d_inv = prime.from_canonical(W::from_i64(d_inv_canonical)); + let mut d_inv_psi_inv = [MontCoeff::from_raw(W::default()); D]; + for i in 0..D { + d_inv_psi_inv[i] = prime.mul(d_inv, psi_inv_pows[i]); + } + + let num_stages = stage; + let mut fwd_twiddles = [MontCoeff::from_raw(W::default()); D]; + let mut inv_twiddles = [MontCoeff::from_raw(W::default()); D]; + let one = prime.from_canonical(W::from_i64(1)); + for s in 0..num_stages { + let len = 1usize << s; + let base = len - 1; + let mut w_fwd = one; + let mut w_inv = one; + for j in 0..len { + fwd_twiddles[base + j] = w_fwd; + inv_twiddles[base + j] = w_inv; + w_fwd = prime.mul(w_fwd, fwd_wlen[s]); + w_inv = prime.mul(w_inv, inv_wlen[s]); + } + } + Self { fwd_wlen, inv_wlen, - num_stages: stage, + num_stages, psi_pows, psi_inv_pows, d_inv, + d_inv_psi_inv, + fwd_twiddles, + inv_twiddles, } } } @@ -100,36 +134,53 @@ pub fn forward_ntt( prime: NttPrime, tw: &NttTwiddles, ) { + #[cfg(target_arch = "aarch64")] + if super::neon::use_neon_ntt() { + if std::mem::size_of::() == std::mem::size_of::() { + unsafe { + super::neon::forward_ntt_i32( + &mut *(a as *mut _ as *mut [MontCoeff; D]), + *(&prime as *const _ as *const NttPrime), + &*(tw as *const _ as *const NttTwiddles), + ); + } + return; + } + if std::mem::size_of::() == std::mem::size_of::() { + unsafe { + super::neon::forward_ntt_i16( + &mut *(a as *mut _ as *mut [MontCoeff; D]), + *(&prime as *const _ as *const NttPrime), + &*(tw as *const _ as *const NttTwiddles), + ); + } + return; + } + } + for (ai, psi) in a.iter_mut().zip(tw.psi_pows.iter()) { *ai = prime.mul(*ai, *psi); } - let one = prime.from_canonical(W::from_i64(1)); - let mut len = D / 2; - let mut stage = tw.num_stages; while len > 0 { - stage -= 1; - let wlen = tw.fwd_wlen[stage]; + let twiddle_base = len - 1; let mut start = 0usize; while start < D { - let mut w = one; for j in 0..len { + let w = tw.fwd_twiddles[twiddle_base + j]; let u = a[start + j]; let v = a[start + j + len]; let sum = u.raw().wrapping_add(v.raw()); let diff = u.raw().wrapping_sub(v.raw()); a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); a[start + j + len] = prime.mul(MontCoeff::from_raw(diff), w); - w = prime.mul(w, wlen); } start += 2 * len; } len /= 2; } - // Keep exported NTT-domain coefficients in the same reduced range expected - // by add/sub reduced operations and equality checks. prime.reduce_range_in_place(a); } @@ -142,36 +193,163 @@ pub fn inverse_ntt( prime: NttPrime, tw: &NttTwiddles, ) { - let one = prime.from_canonical(W::from_i64(1)); + #[cfg(target_arch = "aarch64")] + if super::neon::use_neon_ntt() { + if std::mem::size_of::() == std::mem::size_of::() { + unsafe { + super::neon::inverse_ntt_i32( + &mut *(a as *mut _ as *mut [MontCoeff; D]), + *(&prime as *const _ as *const NttPrime), + &*(tw as *const _ as *const NttTwiddles), + ); + } + return; + } + if std::mem::size_of::() == std::mem::size_of::() { + unsafe { + super::neon::inverse_ntt_i16( + &mut *(a as *mut _ as *mut [MontCoeff; D]), + *(&prime as *const _ as *const NttPrime), + &*(tw as *const _ as *const NttTwiddles), + ); + } + return; + } + } let mut len = 1usize; - let mut stage = 0usize; while len < D { - let wlen = tw.inv_wlen[stage]; + let twiddle_base = len - 1; let mut start = 0usize; while start < D { - let mut w = one; for j in 0..len { + let w = tw.inv_twiddles[twiddle_base + j]; let u = a[start + j]; let v = prime.mul(a[start + j + len], w); let sum = u.raw().wrapping_add(v.raw()); let diff = u.raw().wrapping_sub(v.raw()); a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); a[start + j + len] = prime.reduce_range(MontCoeff::from_raw(diff)); - w = prime.mul(w, wlen); } start += 2 * len; } len *= 2; - stage += 1; } - for c in a.iter_mut() { - *c = prime.mul(*c, tw.d_inv); + for (ai, fused) in a.iter_mut().zip(tw.d_inv_psi_inv.iter()) { + *ai = prime.mul(*ai, *fused); + } +} + +/// Forward cyclic NTT (Gentleman-Sande DIF, **no** negacyclic twist). +/// +/// Evaluates a polynomial at the D-th roots of *unity* (roots of X^D - 1) +/// rather than X^D + 1. Used with `inverse_ntt_cyclic` to compute unreduced +/// polynomial products via CRT over (X^D - 1)(X^D + 1). +pub fn forward_ntt_cyclic( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + #[cfg(target_arch = "aarch64")] + if super::neon::use_neon_ntt() { + if std::mem::size_of::() == std::mem::size_of::() { + unsafe { + super::neon::forward_ntt_cyclic_i32( + &mut *(a as *mut _ as *mut [MontCoeff; D]), + *(&prime as *const _ as *const NttPrime), + &*(tw as *const _ as *const NttTwiddles), + ); + } + return; + } + if std::mem::size_of::() == std::mem::size_of::() { + unsafe { + super::neon::forward_ntt_cyclic_i16( + &mut *(a as *mut _ as *mut [MontCoeff; D]), + *(&prime as *const _ as *const NttPrime), + &*(tw as *const _ as *const NttTwiddles), + ); + } + return; + } + } + + let mut len = D / 2; + while len > 0 { + let twiddle_base = len - 1; + let mut start = 0usize; + while start < D { + for j in 0..len { + let w = tw.fwd_twiddles[twiddle_base + j]; + let u = a[start + j]; + let v = a[start + j + len]; + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.mul(MontCoeff::from_raw(diff), w); + } + start += 2 * len; + } + len /= 2; } + prime.reduce_range_in_place(a); +} - for (ai, psi_inv) in a.iter_mut().zip(tw.psi_inv_pows.iter()) { - *ai = prime.mul(*ai, *psi_inv); +/// Inverse cyclic NTT (Cooley-Tukey DIT, **no** negacyclic untwist). +/// +/// Recovers coefficients of a polynomial from evaluations at D-th roots of unity. +/// Includes the `D^{-1}` scaling factor. +pub fn inverse_ntt_cyclic( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + #[cfg(target_arch = "aarch64")] + if super::neon::use_neon_ntt() { + if std::mem::size_of::() == std::mem::size_of::() { + unsafe { + super::neon::inverse_ntt_cyclic_i32( + &mut *(a as *mut _ as *mut [MontCoeff; D]), + *(&prime as *const _ as *const NttPrime), + &*(tw as *const _ as *const NttTwiddles), + ); + } + return; + } + if std::mem::size_of::() == std::mem::size_of::() { + unsafe { + super::neon::inverse_ntt_cyclic_i16( + &mut *(a as *mut _ as *mut [MontCoeff; D]), + *(&prime as *const _ as *const NttPrime), + &*(tw as *const _ as *const NttTwiddles), + ); + } + return; + } + } + + let mut len = 1usize; + while len < D { + let twiddle_base = len - 1; + let mut start = 0usize; + while start < D { + for j in 0..len { + let w = tw.inv_twiddles[twiddle_base + j]; + let u = a[start + j]; + let v = prime.mul(a[start + j + len], w); + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.reduce_range(MontCoeff::from_raw(diff)); + } + start += 2 * len; + } + len *= 2; + } + + for c in a.iter_mut() { + *c = prime.mul(*c, tw.d_inv); } } diff --git a/src/algebra/ntt/mod.rs b/src/algebra/ntt/mod.rs index f2536363..b059e9b6 100644 --- a/src/algebra/ntt/mod.rs +++ b/src/algebra/ntt/mod.rs @@ -2,6 +2,8 @@ pub mod butterfly; pub mod crt; +#[cfg(target_arch = "aarch64")] +pub(crate) mod neon; pub mod prime; pub mod tables; diff --git a/src/algebra/ntt/neon.rs b/src/algebra/ntt/neon.rs new file mode 100644 index 00000000..10ed1817 --- /dev/null +++ b/src/algebra/ntt/neon.rs @@ -0,0 +1,1001 @@ +//! AArch64 NEON SIMD kernels for NTT butterfly, Montgomery multiply, +//! and pointwise operations. +//! +//! Provides vectorized i32 (for Q64/Q128) and i16 (for Q32) paths. +//! Dispatch is controlled by [`use_neon_ntt`]: set `HACHI_SCALAR_NTT=1` +//! to force the scalar fallback for A/B performance comparison. + +use std::arch::aarch64::*; +use std::sync::OnceLock; + +use super::butterfly::NttTwiddles; +use super::prime::{MontCoeff, NttPrime}; + +/// Whether the NEON NTT path is active. Cached on first call. +/// Set `HACHI_SCALAR_NTT=1` to force scalar fallback. +pub(crate) fn use_neon_ntt() -> bool { + static ENABLED: OnceLock = OnceLock::new(); + *ENABLED.get_or_init(|| std::env::var("HACHI_SCALAR_NTT").map_or(true, |v| v != "1")) +} + +/// 4-wide Montgomery multiply for i32 primes. +/// +/// Uses two 2-wide `vmull_s32` chains (since i32×i32→i64 only fills 2 lanes +/// of a 128-bit register) and combines the results. +#[inline(always)] +unsafe fn mont_mul_4x_i32(a: int32x4_t, b: int32x4_t, p: int32x2_t, pinv: int32x2_t) -> int32x4_t { + let a_lo = vget_low_s32(a); + let a_hi = vget_high_s32(a); + let b_lo = vget_low_s32(b); + let b_hi = vget_high_s32(b); + + // Low pair + let c_lo = vmull_s32(a_lo, b_lo); + let t_lo = vmul_s32(vmovn_s64(c_lo), pinv); + let tp_lo = vmull_s32(t_lo, p); + let r_lo = vmovn_s64(vshrq_n_s64::<32>(vsubq_s64(c_lo, tp_lo))); + + // High pair + let c_hi = vmull_s32(a_hi, b_hi); + let t_hi = vmul_s32(vmovn_s64(c_hi), pinv); + let tp_hi = vmull_s32(t_hi, p); + let r_hi = vmovn_s64(vshrq_n_s64::<32>(vsubq_s64(c_hi, tp_hi))); + + vcombine_s32(r_lo, r_hi) +} + +/// 4-wide range reduction for i32: maps `(-2p, 2p)` → `(-p, p)`. +/// +/// Uses comparison-first approach to avoid the i64 widening that the +/// scalar `csubp`/`caddp` path requires (since `a - p` can overflow i32). +#[inline(always)] +unsafe fn reduce_range_4x_i32(a: int32x4_t, p: int32x4_t) -> int32x4_t { + let zero = vdupq_n_s32(0); + + // csubp: subtract p where a >= p + let ge_mask = vcgeq_s32(a, p); + let after_sub = vsubq_s32( + a, + vreinterpretq_s32_u32(vandq_u32(vreinterpretq_u32_s32(p), ge_mask)), + ); + + // caddp: add p where result < 0 + let lt_mask = vcltq_s32(after_sub, zero); + vaddq_s32( + after_sub, + vreinterpretq_s32_u32(vandq_u32(vreinterpretq_u32_s32(p), lt_mask)), + ) +} + +/// NEON-accelerated forward negacyclic NTT for i32 primes. +/// +/// Processes 4 butterfly pairs per iteration when `len >= 4`; +/// falls back to scalar for the final 2 stages (`len = 2, 1`). +pub(crate) unsafe fn forward_ntt_i32( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + let p_d = vdup_n_s32(prime.p); + let pinv_d = vdup_n_s32(prime.pinv); + let p_q = vdupq_n_s32(prime.p); + let a_ptr = a.as_mut_ptr() as *mut i32; + + // Pre-twist by psi^i + { + let psi_ptr = tw.psi_pows.as_ptr() as *const i32; + let mut i = 0; + while i + 4 <= D { + let ai = vld1q_s32(a_ptr.add(i)); + let psi = vld1q_s32(psi_ptr.add(i)); + vst1q_s32(a_ptr.add(i), mont_mul_4x_i32(ai, psi, p_d, pinv_d)); + i += 4; + } + } + + // DIF butterfly stages + let mut len = D / 2; + while len > 0 { + let twiddle_base = len - 1; + let tw_ptr = tw.fwd_twiddles.as_ptr() as *const i32; + let mut start = 0usize; + while start < D { + if len >= 4 { + let mut j = 0; + while j < len { + let u = vld1q_s32(a_ptr.add(start + j)); + let v = vld1q_s32(a_ptr.add(start + j + len)); + let w = vld1q_s32(tw_ptr.add(twiddle_base + j)); + + let sum = vaddq_s32(u, v); + let diff = vsubq_s32(u, v); + + vst1q_s32(a_ptr.add(start + j), reduce_range_4x_i32(sum, p_q)); + vst1q_s32( + a_ptr.add(start + j + len), + mont_mul_4x_i32(diff, w, p_d, pinv_d), + ); + j += 4; + } + } else { + for j in 0..len { + let w = tw.fwd_twiddles[twiddle_base + j]; + let u = a[start + j]; + let v = a[start + j + len]; + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.mul(MontCoeff::from_raw(diff), w); + } + } + start += 2 * len; + } + len /= 2; + } + + // Final reduce_range pass + reduce_range_in_place_i32(a, p_q); +} + +/// NEON-accelerated inverse negacyclic NTT for i32 primes. +pub(crate) unsafe fn inverse_ntt_i32( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + let p_d = vdup_n_s32(prime.p); + let pinv_d = vdup_n_s32(prime.pinv); + let p_q = vdupq_n_s32(prime.p); + let a_ptr = a.as_mut_ptr() as *mut i32; + + // DIT butterfly stages + let mut len = 1usize; + while len < D { + let twiddle_base = len - 1; + let tw_ptr = tw.inv_twiddles.as_ptr() as *const i32; + let mut start = 0usize; + while start < D { + if len >= 4 { + let mut j = 0; + while j < len { + let w = vld1q_s32(tw_ptr.add(twiddle_base + j)); + let u = vld1q_s32(a_ptr.add(start + j)); + let v_raw = vld1q_s32(a_ptr.add(start + j + len)); + let v = mont_mul_4x_i32(v_raw, w, p_d, pinv_d); + + let sum = vaddq_s32(u, v); + let diff = vsubq_s32(u, v); + + vst1q_s32(a_ptr.add(start + j), reduce_range_4x_i32(sum, p_q)); + vst1q_s32(a_ptr.add(start + j + len), reduce_range_4x_i32(diff, p_q)); + j += 4; + } + } else { + for j in 0..len { + let w = tw.inv_twiddles[twiddle_base + j]; + let u = a[start + j]; + let v = prime.mul(a[start + j + len], w); + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.reduce_range(MontCoeff::from_raw(diff)); + } + } + start += 2 * len; + } + len *= 2; + } + + // Fused D^{-1} * psi^{-i} untwist + { + let fused_ptr = tw.d_inv_psi_inv.as_ptr() as *const i32; + let mut i = 0; + while i + 4 <= D { + let ai = vld1q_s32(a_ptr.add(i)); + let f = vld1q_s32(fused_ptr.add(i)); + vst1q_s32(a_ptr.add(i), mont_mul_4x_i32(ai, f, p_d, pinv_d)); + i += 4; + } + } +} + +/// NEON-accelerated forward cyclic NTT for i32 (no negacyclic twist). +pub(crate) unsafe fn forward_ntt_cyclic_i32( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + let p_d = vdup_n_s32(prime.p); + let pinv_d = vdup_n_s32(prime.pinv); + let p_q = vdupq_n_s32(prime.p); + let a_ptr = a.as_mut_ptr() as *mut i32; + + let mut len = D / 2; + while len > 0 { + let twiddle_base = len - 1; + let tw_ptr = tw.fwd_twiddles.as_ptr() as *const i32; + let mut start = 0usize; + while start < D { + if len >= 4 { + let mut j = 0; + while j < len { + let u = vld1q_s32(a_ptr.add(start + j)); + let v = vld1q_s32(a_ptr.add(start + j + len)); + let w = vld1q_s32(tw_ptr.add(twiddle_base + j)); + let sum = vaddq_s32(u, v); + let diff = vsubq_s32(u, v); + vst1q_s32(a_ptr.add(start + j), reduce_range_4x_i32(sum, p_q)); + vst1q_s32( + a_ptr.add(start + j + len), + mont_mul_4x_i32(diff, w, p_d, pinv_d), + ); + j += 4; + } + } else { + for j in 0..len { + let w = tw.fwd_twiddles[twiddle_base + j]; + let u = a[start + j]; + let v = a[start + j + len]; + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.mul(MontCoeff::from_raw(diff), w); + } + } + start += 2 * len; + } + len /= 2; + } + reduce_range_in_place_i32(a, p_q); +} + +/// NEON-accelerated inverse cyclic NTT for i32 (no negacyclic untwist). +pub(crate) unsafe fn inverse_ntt_cyclic_i32( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + let p_d = vdup_n_s32(prime.p); + let pinv_d = vdup_n_s32(prime.pinv); + let p_q = vdupq_n_s32(prime.p); + let a_ptr = a.as_mut_ptr() as *mut i32; + + let mut len = 1usize; + while len < D { + let twiddle_base = len - 1; + let tw_ptr = tw.inv_twiddles.as_ptr() as *const i32; + let mut start = 0usize; + while start < D { + if len >= 4 { + let mut j = 0; + while j < len { + let w = vld1q_s32(tw_ptr.add(twiddle_base + j)); + let u = vld1q_s32(a_ptr.add(start + j)); + let v_raw = vld1q_s32(a_ptr.add(start + j + len)); + let v = mont_mul_4x_i32(v_raw, w, p_d, pinv_d); + let sum = vaddq_s32(u, v); + let diff = vsubq_s32(u, v); + vst1q_s32(a_ptr.add(start + j), reduce_range_4x_i32(sum, p_q)); + vst1q_s32(a_ptr.add(start + j + len), reduce_range_4x_i32(diff, p_q)); + j += 4; + } + } else { + for j in 0..len { + let w = tw.inv_twiddles[twiddle_base + j]; + let u = a[start + j]; + let v = prime.mul(a[start + j + len], w); + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.reduce_range(MontCoeff::from_raw(diff)); + } + } + start += 2 * len; + } + len *= 2; + } + + // D^{-1} scaling + { + let d_inv = tw.d_inv; + let d_inv_q = vdupq_n_s32(d_inv.raw()); + let mut i = 0; + while i + 4 <= D { + let ai = vld1q_s32(a_ptr.add(i)); + vst1q_s32(a_ptr.add(i), mont_mul_4x_i32(ai, d_inv_q, p_d, pinv_d)); + i += 4; + } + } +} + +/// 4-wide pointwise multiply-accumulate for a single CRT limb (i32). +/// +/// `acc[i] = reduce_range(acc[i] + mont_mul(lhs[i], rhs[i]))` for `i in 0..d`. +pub(crate) unsafe fn pointwise_mul_acc_i32( + acc: *mut i32, + lhs: *const i32, + rhs: *const i32, + d: usize, + p: i32, + pinv: i32, +) { + let p_d = vdup_n_s32(p); + let pinv_d = vdup_n_s32(pinv); + let p_q = vdupq_n_s32(p); + let mut i = 0; + while i + 4 <= d { + let a = vld1q_s32(acc.add(i)); + let l = vld1q_s32(lhs.add(i)); + let r = vld1q_s32(rhs.add(i)); + let prod = mont_mul_4x_i32(l, r, p_d, pinv_d); + let sum = vaddq_s32(a, prod); + vst1q_s32(acc.add(i), reduce_range_4x_i32(sum, p_q)); + i += 4; + } +} + +/// 4-wide add-and-reduce for a single CRT limb (i32). +/// +/// `acc[i] = reduce_range(acc[i] + other[i])` for `i in 0..d`. +pub(crate) unsafe fn add_reduce_i32(acc: *mut i32, other: *const i32, d: usize, p: i32) { + let p_q = vdupq_n_s32(p); + let mut i = 0; + while i + 4 <= d { + let a = vld1q_s32(acc.add(i)); + let b = vld1q_s32(other.add(i)); + vst1q_s32(acc.add(i), reduce_range_4x_i32(vaddq_s32(a, b), p_q)); + i += 4; + } +} + +/// In-place reduce_range over a full array. +unsafe fn reduce_range_in_place_i32(a: &mut [MontCoeff; D], p_q: int32x4_t) { + let ptr = a.as_mut_ptr() as *mut i32; + let mut i = 0; + while i + 4 <= D { + let val = vld1q_s32(ptr.add(i)); + vst1q_s32(ptr.add(i), reduce_range_4x_i32(val, p_q)); + i += 4; + } +} + +/// 4-wide Montgomery multiply for i16 primes. +/// +/// Natural 4-wide: `vmull_s16` produces `int32x4_t`. +#[inline(always)] +unsafe fn mont_mul_4x_i16(a: int16x4_t, b: int16x4_t, p: int16x4_t, pinv: int16x4_t) -> int16x4_t { + let c = vmull_s16(a, b); + let t = vmul_s16(vmovn_s32(c), pinv); + let tp = vmull_s16(t, p); + vmovn_s32(vshrq_n_s32::<16>(vsubq_s32(c, tp))) +} + +/// 8-wide Montgomery multiply for i16 primes (two 4-wide chains). +#[inline(always)] +unsafe fn mont_mul_8x_i16(a: int16x8_t, b: int16x8_t, p: int16x4_t, pinv: int16x4_t) -> int16x8_t { + let r_lo = mont_mul_4x_i16(vget_low_s16(a), vget_low_s16(b), p, pinv); + let r_hi = mont_mul_4x_i16(vget_high_s16(a), vget_high_s16(b), p, pinv); + vcombine_s16(r_lo, r_hi) +} + +/// 8-wide range reduction for i16: `(-2p, 2p)` → `(-p, p)`. +/// +/// Same comparison-first approach as i32 but on `int16x8_t`. +#[inline(always)] +unsafe fn reduce_range_8x_i16(a: int16x8_t, p: int16x8_t) -> int16x8_t { + let zero = vdupq_n_s16(0); + let ge_mask = vcgeq_s16(a, p); + let after_sub = vsubq_s16( + a, + vreinterpretq_s16_u16(vandq_u16(vreinterpretq_u16_s16(p), ge_mask)), + ); + let lt_mask = vcltq_s16(after_sub, zero); + vaddq_s16( + after_sub, + vreinterpretq_s16_u16(vandq_u16(vreinterpretq_u16_s16(p), lt_mask)), + ) +} + +/// NEON-accelerated forward negacyclic NTT for i16 primes. +/// +/// Processes 4 butterflies per iteration when `len >= 4`; +/// scalar fallback for `len < 4`. +pub(crate) unsafe fn forward_ntt_i16( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + let p_d = vdup_n_s16(prime.p); + let pinv_d = vdup_n_s16(prime.pinv); + let p_q = vdupq_n_s16(prime.p); + let a_ptr = a.as_mut_ptr() as *mut i16; + + // Pre-twist by psi^i + { + let psi_ptr = tw.psi_pows.as_ptr() as *const i16; + let mut i = 0; + while i + 4 <= D { + let ai = vld1_s16(a_ptr.add(i)); + let psi = vld1_s16(psi_ptr.add(i)); + vst1_s16(a_ptr.add(i), mont_mul_4x_i16(ai, psi, p_d, pinv_d)); + i += 4; + } + } + + // DIF butterfly stages + let mut len = D / 2; + while len > 0 { + let twiddle_base = len - 1; + let tw_ptr = tw.fwd_twiddles.as_ptr() as *const i16; + let mut start = 0usize; + while start < D { + if len >= 4 { + let mut j = 0; + while j < len { + let u = vld1_s16(a_ptr.add(start + j)); + let v = vld1_s16(a_ptr.add(start + j + len)); + let w = vld1_s16(tw_ptr.add(twiddle_base + j)); + let sum = vadd_s16(u, v); + let diff = vsub_s16(u, v); + + // reduce_range on 4-wide i16 (use 8-wide by padding) + let sum_q = vcombine_s16(sum, vdup_n_s16(0)); + let sum_reduced = vget_low_s16(reduce_range_8x_i16(sum_q, p_q)); + + let diff_mul_w = mont_mul_4x_i16(diff, w, p_d, pinv_d); + vst1_s16(a_ptr.add(start + j), sum_reduced); + vst1_s16(a_ptr.add(start + j + len), diff_mul_w); + j += 4; + } + } else { + for j in 0..len { + let w = tw.fwd_twiddles[twiddle_base + j]; + let u = a[start + j]; + let v = a[start + j + len]; + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.mul(MontCoeff::from_raw(diff), w); + } + } + start += 2 * len; + } + len /= 2; + } + + // Final reduce_range pass + reduce_range_in_place_i16(a, p_q); +} + +/// NEON-accelerated inverse negacyclic NTT for i16 primes. +pub(crate) unsafe fn inverse_ntt_i16( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + let p_d = vdup_n_s16(prime.p); + let pinv_d = vdup_n_s16(prime.pinv); + let p_q = vdupq_n_s16(prime.p); + let a_ptr = a.as_mut_ptr() as *mut i16; + + let mut len = 1usize; + while len < D { + let twiddle_base = len - 1; + let tw_ptr = tw.inv_twiddles.as_ptr() as *const i16; + let mut start = 0usize; + while start < D { + if len >= 4 { + let mut j = 0; + while j < len { + let w = vld1_s16(tw_ptr.add(twiddle_base + j)); + let u = vld1_s16(a_ptr.add(start + j)); + let v_raw = vld1_s16(a_ptr.add(start + j + len)); + let v = mont_mul_4x_i16(v_raw, w, p_d, pinv_d); + let sum = vadd_s16(u, v); + let diff = vsub_s16(u, v); + let reduced = reduce_range_8x_i16(vcombine_s16(sum, diff), p_q); + vst1_s16(a_ptr.add(start + j), vget_low_s16(reduced)); + vst1_s16(a_ptr.add(start + j + len), vget_high_s16(reduced)); + j += 4; + } + } else { + for j in 0..len { + let w = tw.inv_twiddles[twiddle_base + j]; + let u = a[start + j]; + let v = prime.mul(a[start + j + len], w); + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.reduce_range(MontCoeff::from_raw(diff)); + } + } + start += 2 * len; + } + len *= 2; + } + + // Fused D^{-1} * psi^{-i} untwist + { + let fused_ptr = tw.d_inv_psi_inv.as_ptr() as *const i16; + let mut i = 0; + while i + 4 <= D { + let ai = vld1_s16(a_ptr.add(i)); + let f = vld1_s16(fused_ptr.add(i)); + vst1_s16(a_ptr.add(i), mont_mul_4x_i16(ai, f, p_d, pinv_d)); + i += 4; + } + } +} + +/// NEON-accelerated forward cyclic NTT for i16. +pub(crate) unsafe fn forward_ntt_cyclic_i16( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + let p_d = vdup_n_s16(prime.p); + let pinv_d = vdup_n_s16(prime.pinv); + let p_q = vdupq_n_s16(prime.p); + let a_ptr = a.as_mut_ptr() as *mut i16; + + let mut len = D / 2; + while len > 0 { + let twiddle_base = len - 1; + let tw_ptr = tw.fwd_twiddles.as_ptr() as *const i16; + let mut start = 0usize; + while start < D { + if len >= 4 { + let mut j = 0; + while j < len { + let u = vld1_s16(a_ptr.add(start + j)); + let v = vld1_s16(a_ptr.add(start + j + len)); + let w = vld1_s16(tw_ptr.add(twiddle_base + j)); + let sum = vadd_s16(u, v); + let diff = vsub_s16(u, v); + let sum_q = vcombine_s16(sum, vdup_n_s16(0)); + vst1_s16( + a_ptr.add(start + j), + vget_low_s16(reduce_range_8x_i16(sum_q, p_q)), + ); + vst1_s16( + a_ptr.add(start + j + len), + mont_mul_4x_i16(diff, w, p_d, pinv_d), + ); + j += 4; + } + } else { + for j in 0..len { + let w = tw.fwd_twiddles[twiddle_base + j]; + let u = a[start + j]; + let v = a[start + j + len]; + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.mul(MontCoeff::from_raw(diff), w); + } + } + start += 2 * len; + } + len /= 2; + } + reduce_range_in_place_i16(a, p_q); +} + +/// NEON-accelerated inverse cyclic NTT for i16. +pub(crate) unsafe fn inverse_ntt_cyclic_i16( + a: &mut [MontCoeff; D], + prime: NttPrime, + tw: &NttTwiddles, +) { + let p_d = vdup_n_s16(prime.p); + let pinv_d = vdup_n_s16(prime.pinv); + let p_q = vdupq_n_s16(prime.p); + let a_ptr = a.as_mut_ptr() as *mut i16; + + let mut len = 1usize; + while len < D { + let twiddle_base = len - 1; + let tw_ptr = tw.inv_twiddles.as_ptr() as *const i16; + let mut start = 0usize; + while start < D { + if len >= 4 { + let mut j = 0; + while j < len { + let w = vld1_s16(tw_ptr.add(twiddle_base + j)); + let u = vld1_s16(a_ptr.add(start + j)); + let v_raw = vld1_s16(a_ptr.add(start + j + len)); + let v = mont_mul_4x_i16(v_raw, w, p_d, pinv_d); + let sum = vadd_s16(u, v); + let diff = vsub_s16(u, v); + let reduced = reduce_range_8x_i16(vcombine_s16(sum, diff), p_q); + vst1_s16(a_ptr.add(start + j), vget_low_s16(reduced)); + vst1_s16(a_ptr.add(start + j + len), vget_high_s16(reduced)); + j += 4; + } + } else { + for j in 0..len { + let w = tw.inv_twiddles[twiddle_base + j]; + let u = a[start + j]; + let v = prime.mul(a[start + j + len], w); + let sum = u.raw().wrapping_add(v.raw()); + let diff = u.raw().wrapping_sub(v.raw()); + a[start + j] = prime.reduce_range(MontCoeff::from_raw(sum)); + a[start + j + len] = prime.reduce_range(MontCoeff::from_raw(diff)); + } + } + start += 2 * len; + } + len *= 2; + } + + // D^{-1} scaling + { + let d_inv = tw.d_inv; + let d_inv_d = vdup_n_s16(d_inv.raw()); + let mut i = 0; + while i + 4 <= D { + let ai = vld1_s16(a_ptr.add(i)); + vst1_s16(a_ptr.add(i), mont_mul_4x_i16(ai, d_inv_d, p_d, pinv_d)); + i += 4; + } + } +} + +/// 8-wide pointwise multiply-accumulate for a single CRT limb (i16). +pub(crate) unsafe fn pointwise_mul_acc_i16( + acc: *mut i16, + lhs: *const i16, + rhs: *const i16, + d: usize, + p: i16, + pinv: i16, +) { + let p_d = vdup_n_s16(p); + let pinv_d = vdup_n_s16(pinv); + let p_q = vdupq_n_s16(p); + let mut i = 0; + while i + 8 <= d { + let a = vld1q_s16(acc.add(i)); + let l = vld1q_s16(lhs.add(i)); + let r = vld1q_s16(rhs.add(i)); + let prod = mont_mul_8x_i16(l, r, p_d, pinv_d); + let sum = vaddq_s16(a, prod); + vst1q_s16(acc.add(i), reduce_range_8x_i16(sum, p_q)); + i += 8; + } + while i + 4 <= d { + let a = vld1_s16(acc.add(i)); + let l = vld1_s16(lhs.add(i)); + let r = vld1_s16(rhs.add(i)); + let prod = mont_mul_4x_i16(l, r, p_d, pinv_d); + let sum = vadd_s16(a, prod); + let sum_q = vcombine_s16(sum, vdup_n_s16(0)); + vst1_s16(acc.add(i), vget_low_s16(reduce_range_8x_i16(sum_q, p_q))); + i += 4; + } +} + +/// 8-wide add-and-reduce for a single CRT limb (i16). +pub(crate) unsafe fn add_reduce_i16(acc: *mut i16, other: *const i16, d: usize, p: i16) { + let p_q = vdupq_n_s16(p); + let mut i = 0; + while i + 8 <= d { + let a = vld1q_s16(acc.add(i)); + let b = vld1q_s16(other.add(i)); + vst1q_s16(acc.add(i), reduce_range_8x_i16(vaddq_s16(a, b), p_q)); + i += 8; + } + while i + 4 <= d { + let a = vld1_s16(acc.add(i)); + let b = vld1_s16(other.add(i)); + let sum_q = vcombine_s16(vadd_s16(a, b), vdup_n_s16(0)); + vst1_s16(acc.add(i), vget_low_s16(reduce_range_8x_i16(sum_q, p_q))); + i += 4; + } +} + +/// In-place reduce_range over a full i16 array. +unsafe fn reduce_range_in_place_i16(a: &mut [MontCoeff; D], p_q: int16x8_t) { + let ptr = a.as_mut_ptr() as *mut i16; + let mut i = 0; + while i + 8 <= D { + let val = vld1q_s16(ptr.add(i)); + vst1q_s16(ptr.add(i), reduce_range_8x_i16(val, p_q)); + i += 8; + } + while i + 4 <= D { + let val = vld1_s16(ptr.add(i)); + let padded = vcombine_s16(val, vdup_n_s16(0)); + vst1_s16(ptr.add(i), vget_low_s16(reduce_range_8x_i16(padded, p_q))); + i += 4; + } +} + +#[cfg(test)] +mod tests { + use super::super::butterfly::{ + forward_ntt as scalar_forward_ntt, forward_ntt_cyclic as scalar_forward_ntt_cyclic, + inverse_ntt as scalar_inverse_ntt, inverse_ntt_cyclic as scalar_inverse_ntt_cyclic, + NttTwiddles, + }; + use super::super::prime::{MontCoeff, NttPrime}; + use super::*; + + fn random_mont_array_i32( + prime: NttPrime, + seed: u64, + ) -> [MontCoeff; D] { + let mut state = seed; + std::array::from_fn(|_| { + state = state + .wrapping_mul(6364136223846793005) + .wrapping_add(1442695040888963407); + let val = ((state >> 33) as i64 % prime.p as i64) as i32; + prime.from_canonical(val) + }) + } + + fn random_mont_array_i16( + prime: NttPrime, + seed: u64, + ) -> [MontCoeff; D] { + let mut state = seed; + std::array::from_fn(|_| { + state = state + .wrapping_mul(6364136223846793005) + .wrapping_add(1442695040888963407); + let val = ((state >> 33) as i64 % prime.p as i64) as i16; + prime.from_canonical(val) + }) + } + + const TEST_PRIME_I32: i32 = 1073707009; + const TEST_PRIME_I16: i16 = 13697; + + #[test] + fn neon_forward_ntt_i32_matches_scalar() { + let prime = NttPrime::compute(TEST_PRIME_I32); + let tw = NttTwiddles::::compute(prime); + let input = random_mont_array_i32::<512>(prime, 0xCAFE); + + let mut neon_result = input; + unsafe { forward_ntt_i32(&mut neon_result, prime, &tw) }; + + let mut scalar_result = input; + scalar_forward_ntt(&mut scalar_result, prime, &tw); + + for i in 0..512 { + let n = prime.to_canonical(neon_result[i]); + let s = prime.to_canonical(scalar_result[i]); + assert_eq!(n, s, "mismatch at index {i}: neon={n}, scalar={s}"); + } + } + + #[test] + fn neon_inverse_ntt_i32_matches_scalar() { + let prime = NttPrime::compute(TEST_PRIME_I32); + let tw = NttTwiddles::::compute(prime); + let input = random_mont_array_i32::<512>(prime, 0xBEEF); + + let mut neon_result = input; + unsafe { inverse_ntt_i32(&mut neon_result, prime, &tw) }; + + let mut scalar_result = input; + scalar_inverse_ntt(&mut scalar_result, prime, &tw); + + for i in 0..512 { + let n = prime.to_canonical(neon_result[i]); + let s = prime.to_canonical(scalar_result[i]); + assert_eq!(n, s, "mismatch at index {i}: neon={n}, scalar={s}"); + } + } + + #[test] + fn neon_forward_inverse_roundtrip_i32() { + let prime = NttPrime::compute(TEST_PRIME_I32); + let tw = NttTwiddles::::compute(prime); + let input = random_mont_array_i32::<512>(prime, 0xDEAD); + let canonical_input: Vec = input.iter().map(|c| prime.to_canonical(*c)).collect(); + + let mut a = input; + unsafe { + forward_ntt_i32(&mut a, prime, &tw); + inverse_ntt_i32(&mut a, prime, &tw); + } + + for i in 0..512 { + let result = prime.to_canonical(a[i]); + assert_eq!( + result, canonical_input[i], + "roundtrip mismatch at index {i}" + ); + } + } + + #[test] + fn neon_cyclic_ntt_i32_matches_scalar() { + let prime = NttPrime::compute(TEST_PRIME_I32); + let tw = NttTwiddles::::compute(prime); + let input = random_mont_array_i32::<512>(prime, 0xFACE); + + let mut neon_fwd = input; + unsafe { forward_ntt_cyclic_i32(&mut neon_fwd, prime, &tw) }; + + let mut scalar_fwd = input; + scalar_forward_ntt_cyclic(&mut scalar_fwd, prime, &tw); + + for i in 0..512 { + let n = prime.to_canonical(neon_fwd[i]); + let s = prime.to_canonical(scalar_fwd[i]); + assert_eq!(n, s, "forward cyclic mismatch at {i}: neon={n}, scalar={s}"); + } + + let mut neon_inv = neon_fwd; + unsafe { inverse_ntt_cyclic_i32(&mut neon_inv, prime, &tw) }; + + let mut scalar_inv = scalar_fwd; + scalar_inverse_ntt_cyclic(&mut scalar_inv, prime, &tw); + + for i in 0..512 { + let n = prime.to_canonical(neon_inv[i]); + let s = prime.to_canonical(scalar_inv[i]); + assert_eq!(n, s, "inverse cyclic mismatch at {i}: neon={n}, scalar={s}"); + } + } + + #[test] + fn neon_pointwise_mul_acc_i32_matches_scalar() { + let prime = NttPrime::compute(TEST_PRIME_I32); + const D: usize = 512; + let acc_init = random_mont_array_i32::(prime, 0x1111); + let lhs = random_mont_array_i32::(prime, 0x2222); + let rhs = random_mont_array_i32::(prime, 0x3333); + + let mut neon_acc = acc_init; + unsafe { + pointwise_mul_acc_i32( + neon_acc.as_mut_ptr() as *mut i32, + lhs.as_ptr() as *const i32, + rhs.as_ptr() as *const i32, + D, + prime.p, + prime.pinv, + ); + } + + let mut scalar_acc = acc_init; + for i in 0..D { + let prod = prime.mul(lhs[i], rhs[i]); + let sum = MontCoeff::from_raw(scalar_acc[i].raw().wrapping_add(prod.raw())); + scalar_acc[i] = prime.reduce_range(sum); + } + + for i in 0..D { + let n = prime.to_canonical(neon_acc[i]); + let s = prime.to_canonical(scalar_acc[i]); + assert_eq!(n, s, "pointwise mul acc mismatch at {i}"); + } + } + + #[test] + fn neon_forward_ntt_i16_matches_scalar() { + let prime = NttPrime::compute(TEST_PRIME_I16); + let tw = NttTwiddles::::compute(prime); + let input = random_mont_array_i16::<64>(prime, 0xABCD); + + let mut neon_result = input; + unsafe { forward_ntt_i16(&mut neon_result, prime, &tw) }; + + let mut scalar_result = input; + scalar_forward_ntt(&mut scalar_result, prime, &tw); + + for i in 0..64 { + let n = prime.to_canonical(neon_result[i]); + let s = prime.to_canonical(scalar_result[i]); + assert_eq!(n, s, "i16 forward mismatch at {i}: neon={n}, scalar={s}"); + } + } + + #[test] + fn neon_inverse_ntt_i16_matches_scalar() { + let prime = NttPrime::compute(TEST_PRIME_I16); + let tw = NttTwiddles::::compute(prime); + let input = random_mont_array_i16::<64>(prime, 0xFEED); + + let mut neon_result = input; + unsafe { inverse_ntt_i16(&mut neon_result, prime, &tw) }; + + let mut scalar_result = input; + scalar_inverse_ntt(&mut scalar_result, prime, &tw); + + for i in 0..64 { + let n = prime.to_canonical(neon_result[i]); + let s = prime.to_canonical(scalar_result[i]); + assert_eq!(n, s, "i16 inverse mismatch at {i}: neon={n}, scalar={s}"); + } + } + + #[test] + fn neon_forward_inverse_roundtrip_i16() { + let prime = NttPrime::compute(TEST_PRIME_I16); + let tw = NttTwiddles::::compute(prime); + let input = random_mont_array_i16::<64>(prime, 0x7777); + let canonical_input: Vec = input.iter().map(|c| prime.to_canonical(*c)).collect(); + + let mut a = input; + unsafe { + forward_ntt_i16(&mut a, prime, &tw); + inverse_ntt_i16(&mut a, prime, &tw); + } + + for i in 0..64 { + let result = prime.to_canonical(a[i]); + assert_eq!(result, canonical_input[i], "i16 roundtrip mismatch at {i}"); + } + } + + #[test] + fn neon_cyclic_i16_matches_scalar() { + let prime = NttPrime::compute(TEST_PRIME_I16); + let tw = NttTwiddles::::compute(prime); + let input = random_mont_array_i16::<64>(prime, 0x9999); + + let mut neon_fwd = input; + unsafe { forward_ntt_cyclic_i16(&mut neon_fwd, prime, &tw) }; + + let mut scalar_fwd = input; + scalar_forward_ntt_cyclic(&mut scalar_fwd, prime, &tw); + + for i in 0..64 { + let n = prime.to_canonical(neon_fwd[i]); + let s = prime.to_canonical(scalar_fwd[i]); + assert_eq!(n, s, "i16 fwd cyclic mismatch at {i}"); + } + + let mut neon_inv = neon_fwd; + unsafe { inverse_ntt_cyclic_i16(&mut neon_inv, prime, &tw) }; + + let mut scalar_inv = scalar_fwd; + scalar_inverse_ntt_cyclic(&mut scalar_inv, prime, &tw); + + for i in 0..64 { + let n = prime.to_canonical(neon_inv[i]); + let s = prime.to_canonical(scalar_inv[i]); + assert_eq!(n, s, "i16 inv cyclic mismatch at {i}"); + } + } + + #[test] + fn neon_pointwise_mul_acc_i16_matches_scalar() { + let prime = NttPrime::compute(TEST_PRIME_I16); + const D: usize = 64; + let acc_init = random_mont_array_i16::(prime, 0xAAAA); + let lhs = random_mont_array_i16::(prime, 0xBBBB); + let rhs = random_mont_array_i16::(prime, 0xCCCC); + + let mut neon_acc = acc_init; + unsafe { + pointwise_mul_acc_i16( + neon_acc.as_mut_ptr() as *mut i16, + lhs.as_ptr() as *const i16, + rhs.as_ptr() as *const i16, + D, + prime.p, + prime.pinv, + ); + } + + let mut scalar_acc = acc_init; + for i in 0..D { + let prod = prime.mul(lhs[i], rhs[i]); + let sum = MontCoeff::from_raw(scalar_acc[i].raw().wrapping_add(prod.raw())); + scalar_acc[i] = prime.reduce_range(sum); + } + + for i in 0..D { + let n = prime.to_canonical(neon_acc[i]); + let s = prime.to_canonical(scalar_acc[i]); + assert_eq!(n, s, "i16 pointwise mul acc mismatch at {i}"); + } + } +} diff --git a/src/algebra/poly.rs b/src/algebra/poly.rs index cc69e42e..2680c1a6 100644 --- a/src/algebra/poly.rs +++ b/src/algebra/poly.rs @@ -1,12 +1,16 @@ //! Polynomial containers and evaluation utilities. +use crate::algebra::fields::wide::{HasWide, ReduceTo}; use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; -use crate::FieldCore; -use crate::FromSmallInt; +use crate::protocol::sumcheck::eq_poly::EqPolynomial; +use crate::{cfg_fold_reduce, AdditiveGroup, FieldCore, FromSmallInt}; use std::io::{Read, Write}; +use std::ops::{Add, Neg, Sub}; /// A degree- Poly { } } -impl std::ops::Add for Poly { +impl Add for Poly { type Output = Self; fn add(self, rhs: Self) -> Self::Output { let mut out = self.0; for (dst, src) in out.iter_mut().zip(rhs.0.iter()) { - *dst = *dst + *src; + *dst += *src; } Self(out) } } -impl std::ops::Sub for Poly { +impl Sub for Poly { type Output = Self; fn sub(self, rhs: Self) -> Self::Output { let mut out = self.0; for (dst, src) in out.iter_mut().zip(rhs.0.iter()) { - *dst = *dst - *src; + *dst -= *src; } Self(out) } } -impl std::ops::Neg for Poly { +impl Neg for Poly { type Output = Self; fn neg(self) -> Self::Output { let mut out = self.0; @@ -101,10 +105,11 @@ impl HachiDeserialize for Poly { /// This polynomial vanishes exactly when `w ∈ {−(b−1), …, b−1}`. /// Total degree in `w` is `2b − 1`. pub fn range_check_eval(w: E, b: usize) -> E { + let s = w * w; let mut acc = w; for k in 1..b { let k_e = E::from_u64(k as u64); - acc = acc * (w - k_e) * (w + k_e); + acc = acc * (s - k_e * k_e); } acc } @@ -149,6 +154,7 @@ pub fn multilinear_eval(evals: &[E], point: &[E]) -> Result(evals: &mut Vec, r: E) { assert!( evals.len().is_power_of_two(), @@ -161,3 +167,67 @@ pub fn fold_evals_in_place(evals: &mut Vec, r: E) { } evals.truncate(half); } + +/// Evaluate a multilinear polynomial with small integer evaluations at a +/// field point, using the split-eq structure with unreduced accumulation. +/// +/// Uses `HasWide::mul_small_to_wide` in the inner loop: each eq table entry +/// is widened, scaled by the small witness value, and accumulated without +/// reduction. The inner sum is reduced once per outer iteration, then +/// multiplied by the outer eq factor and accumulated again in wide form. +/// +/// Overflow budget: each inner accumulation adds at most `0xFFFF * |small|` +/// to each i32 limb. For `|small| ≤ 128` (b ≤ 256), we can safely +/// accumulate 256 products before an i32 limb overflows. +/// +/// # Errors +/// +/// Returns an error if the table length does not match `2^point.len()`. +#[tracing::instrument(skip_all, name = "multilinear_eval_small")] +pub fn multilinear_eval_small( + evals_small: &[i8], + point: &[E], +) -> Result { + let n = point.len(); + if evals_small.len() != 1 << n { + return Err(HachiError::InvalidSize { + expected: 1 << n, + actual: evals_small.len(), + }); + } + if n == 0 { + return Ok(E::from_i64(evals_small[0] as i64)); + } + + let m = n / 2; + let (r_first, r_second) = point.split_at(m); + let eq_first = EqPolynomial::evals(r_first); + let eq_second = EqPolynomial::evals(r_second); + let in_len = eq_first.len(); + + // Max safe accumulations per chunk before i32 overflow. + // Limbs are 16-bit (0..0xFFFF), scaled by |small| ≤ 128 → 23-bit products. + // i32::MAX / (0xFFFF * 128) ≈ 256. + const CHUNK: usize = 256; + + let outer_accum = cfg_fold_reduce!( + 0..eq_second.len(), + || E::Wide::ZERO, + |acc, x_out| { + let base = x_out * in_len; + let mut inner_field = E::zero(); + for chunk_start in (0..in_len).step_by(CHUNK) { + let chunk_end = (chunk_start + CHUNK).min(in_len); + let mut chunk_acc = E::Wide::ZERO; + for x_in in chunk_start..chunk_end { + chunk_acc += eq_first[x_in].mul_small_to_wide(evals_small[base + x_in] as i32); + } + inner_field += >::reduce(chunk_acc); + } + + acc + E::Wide::from(eq_second[x_out] * inner_field) + }, + |a, b| a + b + ); + Ok(>::reduce(outer_accum)) +} diff --git a/src/algebra/ring/crt_ntt_repr.rs b/src/algebra/ring/crt_ntt_repr.rs index 0d5d5bb1..8e3cebd0 100644 --- a/src/algebra/ring/crt_ntt_repr.rs +++ b/src/algebra/ring/crt_ntt_repr.rs @@ -1,7 +1,11 @@ //! CRT+NTT-domain representation of cyclotomic ring elements. +use std::array::from_fn; + use crate::algebra::backend::{CrtReconstruct, NttPrimeOps, NttTransform, ScalarBackend}; -use crate::algebra::ntt::butterfly::NttTwiddles; +use crate::algebra::ntt::butterfly::{ + forward_ntt, forward_ntt_cyclic, inverse_ntt_cyclic, NttTwiddles, +}; use crate::algebra::ntt::crt::GarnerData; use crate::algebra::ntt::prime::{MontCoeff, NttPrime, PrimeWidth}; use crate::{CanonicalField, FieldCore}; @@ -33,6 +37,7 @@ impl CrtNttConvertibleField for F {} /// /// Keeps primes/twiddles/Garner constants consistent and avoids passing them /// independently at every call site. +#[derive(Debug, Clone, PartialEq, Eq)] pub struct CrtNttParamSet { /// CRT primes with Montgomery constants. pub primes: [NttPrime; K], @@ -42,12 +47,53 @@ pub struct CrtNttParamSet { pub garner: GarnerData, } +/// Precomputed Montgomery forms for small balanced digit values. +/// +/// Covers the full `{-8, ..., 7}` range (16 entries per CRT prime), +/// which is sufficient for any `log_basis <= 4`. Storing the Montgomery +/// representation eliminates one `from_canonical` (a Montgomery multiply) +/// per coefficient in the `from_i8` hot path. +#[derive(Debug, Clone)] +pub struct DigitMontLut { + vals: [[MontCoeff; 16]; K], +} + +const DIGIT_LUT_HALF_B: i16 = 8; + +impl DigitMontLut { + /// Build the lookup table from CRT primes. + /// + /// Covers digit values in `{-8, ..., 7}` (balanced representation for + /// `log_basis <= 4`). + pub fn new(params: &CrtNttParamSet) -> Self { + let mut vals = [[MontCoeff::from_raw(W::default()); 16]; K]; + for (k, prime) in params.primes.iter().enumerate() { + for v_idx in 0..16u8 { + let v = v_idx as i64 - DIGIT_LUT_HALF_B as i64; + vals[k][v_idx as usize] = prime.from_canonical(W::from_i64(v)); + } + } + Self { vals } + } + + /// Look up the Montgomery form of a balanced digit for CRT prime `k`. + #[inline(always)] + pub fn get(&self, k: usize, digit: i8) -> MontCoeff { + unsafe { + *self + .vals + .get_unchecked(k) + .get_unchecked((digit as i16 + DIGIT_LUT_HALF_B) as usize) + } + } +} + impl CrtNttParamSet { /// Build a full parameter set from CRT primes. /// /// Computes per-prime twiddles and Garner reconstruction constants. pub fn new(primes: [NttPrime; K]) -> Self { - let twiddles = std::array::from_fn(|k| NttTwiddles::compute(primes[k])); + let twiddles = from_fn(|k| NttTwiddles::compute(primes[k])); let garner = GarnerData::compute(&primes); Self { primes, @@ -96,7 +142,7 @@ impl CyclotomicCrtNtt { ) -> Self { let q = (-F::one()).to_canonical_u128() + 1; let half_q = q / 2; - let centered_coeffs: [i128; D] = std::array::from_fn(|i| { + let centered_coeffs: [i128; D] = from_fn(|i| { let canonical = ring.coeffs[i].to_canonical_u128(); if canonical > half_q { -((q - canonical) as i128) @@ -110,24 +156,109 @@ impl CyclotomicCrtNtt { // Interpret coefficients in centered form (-q/2, q/2] before reducing // into the CRT primes. This makes the reduction map consistent with // negacyclic subtraction (which naturally produces negative values). - let p = prime.p.to_i64() as i128; + let p = prime.p.to_i64(); + let p_u64 = p as u64; + let r64 = ((1u128 << 64) % p_u64 as u128) as i64; let half_p = p / 2; for (dst, centered) in limb.iter_mut().zip(centered_coeffs.iter()) { - let mut r = *centered % p; - if r < 0 { - r += p; - } - // Center residues into [-p/2, p/2) for stable signed arithmetic. + let c = *centered; + let lo = (c as u64 % p_u64) as i64; + let hi = ((c >> 64) as i64).rem_euclid(p); + let mut r = (lo + hi * r64) % p; if r >= half_p { r -= p; } - *dst = B::from_canonical(*prime, W::from_i64(r as i64)); + *dst = B::from_canonical(*prime, W::from_i64(r)); } B::forward_ntt(limb, *prime, tw); } Self { limbs } } + /// Convert small integer coefficients (e.g. gadget digits) into + /// negacyclic CRT+NTT domain, bypassing Fp128 centering entirely. + pub fn from_i8_with_params(digits: &[i8; D], params: &CrtNttParamSet) -> Self { + Self::from_i8_negacyclic_backend::(digits, params) + } + + /// Like [`Self::from_i8_with_params`] but uses a precomputed + /// [`DigitMontLut`] to replace per-coefficient `from_canonical` + /// (Montgomery multiply) with a table lookup. + #[inline] + pub fn from_i8_with_lut( + digits: &[i8; D], + params: &CrtNttParamSet, + lut: &DigitMontLut, + ) -> Self { + let mut limbs = [[MontCoeff::from_raw(W::default()); D]; K]; + for (k, (limb, tw)) in limbs.iter_mut().zip(params.twiddles.iter()).enumerate() { + for (dst, &d) in limb.iter_mut().zip(digits.iter()) { + *dst = lut.get(k, d); + } + forward_ntt(limb, params.primes[k], tw); + } + Self { limbs } + } + + /// Like [`Self::from_i8_cyclic`] but uses a precomputed [`DigitMontLut`]. + #[inline] + pub fn from_i8_cyclic_with_lut( + digits: &[i8; D], + params: &CrtNttParamSet, + lut: &DigitMontLut, + ) -> Self { + let mut limbs = [[MontCoeff::from_raw(W::default()); D]; K]; + for (k, (limb, tw)) in limbs.iter_mut().zip(params.twiddles.iter()).enumerate() { + for (dst, &d) in limb.iter_mut().zip(digits.iter()) { + *dst = lut.get(k, d); + } + forward_ntt_cyclic(limb, params.primes[k], tw); + } + Self { limbs } + } + + fn from_i8_negacyclic_backend + NttTransform>( + digits: &[i8; D], + params: &CrtNttParamSet, + ) -> Self { + let mut limbs = [[MontCoeff::from_raw(W::default()); D]; K]; + for ((limb, prime), tw) in limbs + .iter_mut() + .zip(params.primes.iter()) + .zip(params.twiddles.iter()) + { + for (dst, &d) in limb.iter_mut().zip(digits.iter()) { + *dst = B::from_canonical(*prime, W::from_i64(d as i64)); + } + B::forward_ntt(limb, *prime, tw); + } + Self { limbs } + } + + /// Convert small integer coefficients into cyclic CRT+NTT domain, + /// bypassing Fp128 centering entirely. + pub fn from_i8_cyclic(digits: &[i8; D], params: &CrtNttParamSet) -> Self { + Self::from_i8_cyclic_backend::(digits, params) + } + + fn from_i8_cyclic_backend>( + digits: &[i8; D], + params: &CrtNttParamSet, + ) -> Self { + let mut limbs = [[MontCoeff::from_raw(W::default()); D]; K]; + for ((limb, prime), tw) in limbs + .iter_mut() + .zip(params.primes.iter()) + .zip(params.twiddles.iter()) + { + for (dst, &d) in limb.iter_mut().zip(digits.iter()) { + *dst = B::from_canonical(*prime, W::from_i64(d as i64)); + } + forward_ntt_cyclic(limb, *prime, tw); + } + Self { limbs } + } + /// Convert from CRT+NTT domain back to coefficient form /// using the default scalar backend. pub fn to_ring( @@ -261,6 +392,96 @@ impl CyclotomicCrtNtt { out } + /// Convert a coefficient-form ring element into CRT+**cyclic** NTT domain. + /// + /// Evaluates at D-th roots of unity (X^D - 1) instead of X^D + 1. + /// Used together with `to_ring_cyclic` to compute unreduced polynomial products. + pub fn from_ring_cyclic( + ring: &CyclotomicRing, + params: &CrtNttParamSet, + ) -> Self { + Self::from_ring_cyclic_with_backend::(ring, params) + } + + /// Convert a coefficient-form ring element into CRT+**cyclic** NTT domain + /// through an explicit backend. + pub fn from_ring_cyclic_with_backend>( + ring: &CyclotomicRing, + params: &CrtNttParamSet, + ) -> Self { + let q = (-F::one()).to_canonical_u128() + 1; + let half_q = q / 2; + let centered_coeffs: [i128; D] = from_fn(|i| { + let canonical = ring.coeffs[i].to_canonical_u128(); + if canonical > half_q { + -((q - canonical) as i128) + } else { + canonical as i128 + } + }); + + let mut limbs = [[MontCoeff::from_raw(W::default()); D]; K]; + for ((limb, prime), tw) in limbs + .iter_mut() + .zip(params.primes.iter()) + .zip(params.twiddles.iter()) + { + let p = prime.p.to_i64(); + let p_u64 = p as u64; + let r64 = ((1u128 << 64) % p_u64 as u128) as i64; + let half_p = p / 2; + for (dst, centered) in limb.iter_mut().zip(centered_coeffs.iter()) { + let c = *centered; + let lo = (c as u64 % p_u64) as i64; + let hi = ((c >> 64) as i64).rem_euclid(p); + let mut r = (lo + hi * r64) % p; + if r >= half_p { + r -= p; + } + *dst = B::from_canonical(*prime, W::from_i64(r)); + } + forward_ntt_cyclic(limb, *prime, tw); + } + Self { limbs } + } + + /// Convert from CRT+**cyclic** NTT domain back to coefficient form. + /// + /// Inverse of `from_ring_cyclic`: applies inverse cyclic NTT then CRT reconstruction. + pub fn to_ring_cyclic( + &self, + params: &CrtNttParamSet, + ) -> CyclotomicRing { + self.to_ring_cyclic_with_backend::(params) + } + + /// Convert from CRT+**cyclic** NTT domain back to coefficient form + /// through an explicit backend. + pub fn to_ring_cyclic_with_backend< + F: CrtNttConvertibleField, + B: NttPrimeOps + CrtReconstruct, + >( + &self, + params: &CrtNttParamSet, + ) -> CyclotomicRing { + let mut canonical = [[W::default(); D]; K]; + for (k, ((can, prime), tw)) in canonical + .iter_mut() + .zip(params.primes.iter()) + .zip(params.twiddles.iter()) + .enumerate() + { + let mut limb = self.limbs[k]; + inverse_ntt_cyclic(&mut limb, *prime, tw); + for (dst, src) in can.iter_mut().zip(limb.iter()) { + let canon = B::to_canonical(*prime, *src); + *dst = prime.center(canon); + } + } + let coeffs = B::reconstruct::(¶ms.primes, &canonical, ¶ms.garner); + CyclotomicRing::from_coefficients(coeffs) + } + /// Pointwise multiplication in CRT+NTT domain using the scalar backend. pub fn pointwise_mul(&self, rhs: &Self, primes: &[NttPrime; K]) -> Self { self.pointwise_mul_with_backend::(rhs, primes) diff --git a/src/algebra/ring/cyclotomic.rs b/src/algebra/ring/cyclotomic.rs index 7ee92aa2..af735765 100644 --- a/src/algebra/ring/cyclotomic.rs +++ b/src/algebra/ring/cyclotomic.rs @@ -1,11 +1,13 @@ //! Cyclotomic ring `Z_q[X]/(X^D + 1)` in coefficient form. use super::sparse_challenge::SparseChallenge; +use crate::algebra::fields::wide::ReduceTo; use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; -use crate::{CanonicalField, FieldCore, FieldSampling}; +use crate::{AdditiveGroup, CanonicalField, FieldCore, FieldSampling}; use rand_core::RngCore; +use std::array::from_fn; use std::io::{Read, Write}; use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign}; @@ -28,6 +30,17 @@ impl CyclotomicRing { Self { coeffs } } + /// Construct from a slice, zero-padding if shorter than `D`. + /// + /// Avoids creating a `[F; D]` stack temporary when `D` is large. + #[inline] + pub fn from_slice(slice: &[F]) -> Self { + let mut coeffs = [F::zero(); D]; + let len = slice.len().min(D); + coeffs[..len].copy_from_slice(&slice[..len]); + Self { coeffs } + } + /// Borrow the coefficient array. #[inline] pub fn coefficients(&self) -> &[F; D] { @@ -91,9 +104,9 @@ impl CyclotomicRing { for (j, coeff) in self.coeffs.iter().copied().enumerate() { let idx = (j * k_mod) % two_d; if idx < D { - out[idx] = out[idx] + coeff; + out[idx] += coeff; } else { - out[idx - D] = out[idx - D] - coeff; + out[idx - D] -= coeff; } } Self { coeffs: out } @@ -137,11 +150,68 @@ impl CyclotomicRing { pub fn mul_by_monomial_sum(&self, nonzero_positions: &[usize]) -> Self { let mut result = Self::zero(); for &k in nonzero_positions { - result += self.negacyclic_shift(k); + self.shift_accumulate_into(&mut result, k); } result } + /// Fused negacyclic shift + accumulate: `dst += self * X^k`. + /// + /// Equivalent to `*dst += self.negacyclic_shift(k)` but avoids + /// allocating a temporary ring element. + #[inline] + pub fn shift_accumulate_into(&self, dst: &mut Self, k: usize) { + let k = k % D; + if k == 0 { + for i in 0..D { + dst.coeffs[i] += self.coeffs[i]; + } + return; + } + for i in 0..D { + let target = i + k; + if target < D { + dst.coeffs[target] += self.coeffs[i]; + } else { + dst.coeffs[target - D] -= self.coeffs[i]; + } + } + } + + /// Fused negacyclic shift + subtract: `dst -= self * X^k`. + /// + /// Equivalent to `*dst -= self.negacyclic_shift(k)` but avoids + /// allocating a temporary ring element. + #[inline] + pub fn shift_sub_into(&self, dst: &mut Self, k: usize) { + let k = k % D; + if k == 0 { + for i in 0..D { + dst.coeffs[i] -= self.coeffs[i]; + } + return; + } + for i in 0..D { + let target = i + k; + if target < D { + dst.coeffs[target] -= self.coeffs[i]; + } else { + dst.coeffs[target - D] += self.coeffs[i]; + } + } + } + + /// Fused multiply-by-monomial-sum + accumulate: + /// `dst += self * (X^{k_1} + X^{k_2} + ...)`. + /// + /// Equivalent to `*dst += self.mul_by_monomial_sum(positions)` but avoids + /// all intermediate temporaries. + pub fn mul_by_monomial_sum_into(&self, dst: &mut Self, nonzero_positions: &[usize]) { + for &k in nonzero_positions { + self.shift_accumulate_into(dst, k); + } + } + /// Multiply `self` by a sparse challenge element. /// /// Cost: `O(omega * D)` field additions instead of `O(D^2)` multiplications. @@ -152,11 +222,13 @@ impl CyclotomicRing { { let mut result = Self::zero(); for (&pos, &coeff) in challenge.positions.iter().zip(challenge.coeffs.iter()) { - let shifted = self.negacyclic_shift(pos as usize); match coeff { - 1 => result += shifted, - -1 => result -= shifted, - c => result += shifted.scale(&F::from_i64(c as i64)), + 1 => self.shift_accumulate_into(&mut result, pos as usize), + -1 => self.shift_sub_into(&mut result, pos as usize), + c => { + let shifted = self.negacyclic_shift(pos as usize); + result += shifted.scale(&F::from_i64(c as i64)); + } } } result @@ -201,6 +273,53 @@ impl CyclotomicRing { } impl CyclotomicRing { + /// Balanced decomposition writing directly into a pre-allocated output slice. + /// + /// `out` must have length exactly `levels`. Each element receives one digit plane. + /// + /// # Panics + /// + /// Panics if `log_basis == 0`, `log_basis >= 128`, or `out.len() * log_basis > 128 + log_basis`. + pub fn balanced_decompose_pow2_into(&self, out: &mut [Self], log_basis: u32) { + let levels = out.len(); + assert!(log_basis > 0 && log_basis < 128, "invalid log_basis"); + assert!( + (levels as u32).saturating_mul(log_basis) <= 128 + log_basis, + "levels * log_basis must be <= 128 + log_basis" + ); + + let half_b = 1i128 << (log_basis - 1); + let b = half_b << 1; + let mask = b - 1; + let q = (-F::one()).to_canonical_u128() + 1; + let half_q = q / 2; + + for plane in out.iter_mut() { + *plane = Self::zero(); + } + + for i in 0..D { + let canonical = self.coeffs[i].to_canonical_u128(); + let mut c: i128 = if canonical > half_q { + -((q - canonical) as i128) + } else { + canonical as i128 + }; + + for plane in out.iter_mut() { + let d = c & mask; + let balanced = if d >= half_b { d - b } else { d }; + c = (c - balanced) >> log_basis; + + plane.coeffs[i] = if balanced >= 0 { + F::from_canonical_u128_reduced(balanced as u128) + } else { + F::from_canonical_u128_reduced(q - ((-balanced) as u128)) + }; + } + } + } + /// Functional gadget recomposition (`G * digits`) for base `2^log_basis`. /// /// Coefficients from each part are interpreted as one digit plane and @@ -217,11 +336,38 @@ impl CyclotomicRing { assert!(log_basis > 0 && log_basis < 128, "invalid log_basis"); let b = F::from_canonical_u128_reduced(1u128 << log_basis); - let coeffs = std::array::from_fn(|i| { + let coeffs = from_fn(|i| { let mut acc = F::zero(); let mut power = F::one(); for part in parts.iter() { - acc = acc + part.coeffs[i] * power; + acc += part.coeffs[i] * power; + power = power * b; + } + acc + }); + Self { coeffs } + } + + /// Recompose from i8 digit planes (output of `balanced_decompose_pow2_i8`). + /// + /// # Panics + /// + /// Panics if `log_basis` is zero or >= 128. + pub fn gadget_recompose_pow2_i8(digits: &[[i8; D]], log_basis: u32) -> Self + where + F: CanonicalField, + { + if digits.is_empty() { + return Self::zero(); + } + assert!(log_basis > 0 && log_basis < 128, "invalid log_basis"); + + let b = F::from_canonical_u128_reduced(1u128 << log_basis); + let coeffs = from_fn(|i| { + let mut acc = F::zero(); + let mut power = F::one(); + for plane in digits { + acc += F::from_i64(plane[i] as i64) * power; power = power * b; } acc @@ -247,8 +393,9 @@ impl CyclotomicRing { "levels * log_basis must be <= 128 + log_basis" ); - let b = 1i128 << log_basis; - let half_b = b / 2; + let half_b = 1i128 << (log_basis - 1); + let b = half_b << 1; + let mask = b - 1; let q = (-F::one()).to_canonical_u128() + 1; let half_q = q / 2; @@ -263,9 +410,9 @@ impl CyclotomicRing { }; for plane in digit_planes.iter_mut() { - let d = c.rem_euclid(b); + let d = c & mask; let balanced = if d >= half_b { d - b } else { d }; - c = (c - balanced) / b; + c = (c - balanced) >> log_basis; plane[i] = if balanced >= 0 { F::from_canonical_u128_reduced(balanced as u128) @@ -280,13 +427,71 @@ impl CyclotomicRing { .map(Self::from_coefficients) .collect() } + + /// Balanced gadget decomposition into native `i8` digits. + /// + /// Same semantics as [`balanced_decompose_pow2`](Self::balanced_decompose_pow2) + /// but stores each digit as `i8` instead of a field element, avoiding + /// the cost of `F::from_canonical_u128_reduced`. + /// + /// Requires `log_basis <= 7` so digits fit in `[-64, 63]` (i8 range). + /// + /// # Panics + /// + /// Panics if `log_basis` is 0 or > 7, or if `levels * log_basis > 128 + log_basis`. + pub fn balanced_decompose_pow2_i8_into(&self, out: &mut [[i8; D]], log_basis: u32) + where + F: CanonicalField, + { + let levels = out.len(); + assert!( + log_basis > 0 && log_basis <= 7, + "log_basis must be in 1..=7 for i8 output" + ); + assert!( + (levels as u32).saturating_mul(log_basis) <= 128 + log_basis, + "levels * log_basis must be <= 128 + log_basis" + ); + + let half_b = 1i128 << (log_basis - 1); + let b = half_b << 1; + let mask = b - 1; + let q = (-F::one()).to_canonical_u128() + 1; + let half_q = q / 2; + + for i in 0..D { + let canonical = self.coeffs[i].to_canonical_u128(); + let mut c: i128 = if canonical > half_q { + -((q - canonical) as i128) + } else { + canonical as i128 + }; + + for plane in out.iter_mut() { + let d = c & mask; + let balanced = if d >= half_b { d - b } else { d }; + c = (c - balanced) >> log_basis; + plane[i] = balanced as i8; + } + } + } + + /// Allocating variant of [`balanced_decompose_pow2_i8_into`](Self::balanced_decompose_pow2_i8_into). + pub fn balanced_decompose_pow2_i8(&self, levels: usize, log_basis: u32) -> Vec<[i8; D]> + where + F: CanonicalField, + { + let mut digit_planes: Vec<[i8; D]> = vec![[0i8; D]; levels]; + self.balanced_decompose_pow2_i8_into(&mut digit_planes, log_basis); + digit_planes + } } impl CyclotomicRing { /// Generate a random ring element. pub fn random(rng: &mut R) -> Self { Self { - coeffs: std::array::from_fn(|_| F::sample(rng)), + coeffs: from_fn(|_| F::sample(rng)), } } } @@ -375,9 +580,9 @@ impl Mul for CyclotomicRing { let product = self.coeffs[i] * rhs.coeffs[j]; let idx = i + j; if idx < D { - out[idx] = out[idx] + product; + out[idx] += product; } else { - out[idx - D] = out[idx - D] - product; + out[idx - D] -= product; } } } @@ -437,3 +642,236 @@ impl Default for CyclotomicRing { Self::zero() } } + +/// Wide (unreduced) cyclotomic ring element for carry-free accumulation. +/// +/// Coefficients are wide accumulators (`W: AdditiveGroup`) that support +/// addition/subtraction without modular reduction. After accumulation, +/// call [`reduce`](Self::reduce) to convert back to `CyclotomicRing`. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct WideCyclotomicRing { + pub(crate) coeffs: [W; D], +} + +impl WideCyclotomicRing { + /// The additive identity (all-zero coefficients). + pub const ZERO: Self = Self { + coeffs: [W::ZERO; D], + }; + + /// Returns the zero ring element. + #[inline] + pub fn zero() -> Self { + Self::ZERO + } + + /// Convert a reduced `CyclotomicRing` into wide form. + #[inline] + pub fn from_ring(ring: &CyclotomicRing) -> Self + where + W: From, + { + Self { + coeffs: from_fn(|i| W::from(ring.coeffs[i])), + } + } + + /// Reduce all coefficients back to canonical field form. + #[inline] + pub fn reduce(&self) -> CyclotomicRing + where + W: ReduceTo, + { + CyclotomicRing { + coeffs: from_fn(|i| self.coeffs[i].reduce()), + } + } + + /// Fused negacyclic shift + accumulate: `dst += self * X^k`. + #[inline] + pub fn shift_accumulate_into(&self, dst: &mut Self, k: usize) { + let k = k % D; + if k == 0 { + for i in 0..D { + dst.coeffs[i] += self.coeffs[i]; + } + return; + } + for i in 0..D { + let target = i + k; + if target < D { + dst.coeffs[target] += self.coeffs[i]; + } else { + dst.coeffs[target - D] -= self.coeffs[i]; + } + } + } + + /// Fused negacyclic shift + subtract: `dst -= self * X^k`. + #[inline] + pub fn shift_sub_into(&self, dst: &mut Self, k: usize) { + let k = k % D; + if k == 0 { + for i in 0..D { + dst.coeffs[i] -= self.coeffs[i]; + } + return; + } + for i in 0..D { + let target = i + k; + if target < D { + dst.coeffs[target] -= self.coeffs[i]; + } else { + dst.coeffs[target - D] += self.coeffs[i]; + } + } + } + + /// Fused multiply-by-monomial-sum + accumulate: + /// `dst += self * (X^{k_1} + X^{k_2} + ...)`. + pub fn mul_by_monomial_sum_into(&self, dst: &mut Self, nonzero_positions: &[usize]) { + for &k in nonzero_positions { + self.shift_accumulate_into(dst, k); + } + } +} + +impl Add for WideCyclotomicRing { + type Output = Self; + fn add(mut self, rhs: Self) -> Self { + for i in 0..D { + self.coeffs[i] += rhs.coeffs[i]; + } + self + } +} + +impl AddAssign for WideCyclotomicRing { + fn add_assign(&mut self, rhs: Self) { + for i in 0..D { + self.coeffs[i] += rhs.coeffs[i]; + } + } +} + +impl Sub for WideCyclotomicRing { + type Output = Self; + fn sub(mut self, rhs: Self) -> Self { + for i in 0..D { + self.coeffs[i] -= rhs.coeffs[i]; + } + self + } +} + +impl SubAssign for WideCyclotomicRing { + fn sub_assign(&mut self, rhs: Self) { + for i in 0..D { + self.coeffs[i] -= rhs.coeffs[i]; + } + } +} + +impl Neg for WideCyclotomicRing { + type Output = Self; + fn neg(self) -> Self { + Self { + coeffs: from_fn(|i| -self.coeffs[i]), + } + } +} + +impl Default for WideCyclotomicRing { + fn default() -> Self { + Self::zero() + } +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::algebra::fields::{Fp128x8i32, Fp64, Fp64x4i32, Prime128M8M4M1M0}; + use rand::rngs::StdRng; + use rand::SeedableRng; + + type F64 = Fp64<4294967197>; + type F128 = Prime128M8M4M1M0; + const D: usize = 64; + + #[test] + fn wide_shift_accumulate_matches_narrow_fp64() { + let mut rng = StdRng::seed_from_u64(0x1234); + let src = CyclotomicRing::::random(&mut rng); + let initial = CyclotomicRing::::random(&mut rng); + + for k in [0, 1, 7, 31, 63] { + let mut narrow = initial; + src.shift_accumulate_into(&mut narrow, k); + + let wide_src = WideCyclotomicRing::::from_ring(&src); + let mut wide_dst = WideCyclotomicRing::::from_ring(&initial); + wide_src.shift_accumulate_into(&mut wide_dst, k); + let wide_reduced: CyclotomicRing = wide_dst.reduce(); + + assert_eq!(narrow, wide_reduced, "shift_accumulate k={k}"); + } + } + + #[test] + fn wide_shift_sub_matches_narrow_fp64() { + let mut rng = StdRng::seed_from_u64(0x5678); + let src = CyclotomicRing::::random(&mut rng); + let initial = CyclotomicRing::::random(&mut rng); + + for k in [0, 1, 15, 32, 63] { + let mut narrow = initial; + src.shift_sub_into(&mut narrow, k); + + let wide_src = WideCyclotomicRing::::from_ring(&src); + let mut wide_dst = WideCyclotomicRing::::from_ring(&initial); + wide_src.shift_sub_into(&mut wide_dst, k); + let wide_reduced: CyclotomicRing = wide_dst.reduce(); + + assert_eq!(narrow, wide_reduced, "shift_sub k={k}"); + } + } + + #[test] + fn wide_mul_by_monomial_sum_matches_narrow_fp64() { + let mut rng = StdRng::seed_from_u64(0xabcd); + let src = CyclotomicRing::::random(&mut rng); + let positions = vec![0, 5, 17, 42, 63]; + + let mut narrow = CyclotomicRing::::zero(); + src.mul_by_monomial_sum_into(&mut narrow, &positions); + + let wide_src = WideCyclotomicRing::::from_ring(&src); + let mut wide_dst = WideCyclotomicRing::::zero(); + wide_src.mul_by_monomial_sum_into(&mut wide_dst, &positions); + let wide_reduced: CyclotomicRing = wide_dst.reduce(); + + assert_eq!(narrow, wide_reduced); + } + + #[test] + fn wide_many_accumulations_fp128() { + let mut rng = StdRng::seed_from_u64(0xbeef); + let src = CyclotomicRing::::random(&mut rng); + + let mut narrow = CyclotomicRing::::zero(); + let wide_src = WideCyclotomicRing::::from_ring(&src); + let mut wide_dst = WideCyclotomicRing::::zero(); + + for k in 0..50 { + src.shift_accumulate_into(&mut narrow, k % D); + wide_src.shift_accumulate_into(&mut wide_dst, k % D); + } + for k in 0..30 { + src.shift_sub_into(&mut narrow, k % D); + wide_src.shift_sub_into(&mut wide_dst, k % D); + } + + let wide_reduced: CyclotomicRing = wide_dst.reduce(); + assert_eq!(narrow, wide_reduced); + } +} diff --git a/src/algebra/ring/mod.rs b/src/algebra/ring/mod.rs index 756854b3..7ea193cc 100644 --- a/src/algebra/ring/mod.rs +++ b/src/algebra/ring/mod.rs @@ -4,6 +4,6 @@ pub mod crt_ntt_repr; pub mod cyclotomic; pub mod sparse_challenge; -pub use crt_ntt_repr::{CrtNttConvertibleField, CrtNttParamSet, CyclotomicCrtNtt}; -pub use cyclotomic::CyclotomicRing; +pub use crt_ntt_repr::{CrtNttConvertibleField, CrtNttParamSet, CyclotomicCrtNtt, DigitMontLut}; +pub use cyclotomic::{CyclotomicRing, WideCyclotomicRing}; pub use sparse_challenge::{SparseChallenge, SparseChallengeConfig}; diff --git a/src/algebra/ring/sparse_challenge.rs b/src/algebra/ring/sparse_challenge.rs index 4f55b06a..a97598ae 100644 --- a/src/algebra/ring/sparse_challenge.rs +++ b/src/algebra/ring/sparse_challenge.rs @@ -10,6 +10,7 @@ //! - and efficient to evaluate at a point `α` using precomputed powers. use super::CyclotomicRing; +use crate::algebra::fields::LiftBase; use crate::{CanonicalField, FieldCore}; /// Configuration for sampling a sparse challenge. @@ -131,7 +132,7 @@ impl SparseChallenge { self.validate::()?; let mut out = [F::zero(); D]; for (&pos, &c) in self.positions.iter().zip(self.coeffs.iter()) { - out[pos as usize] = out[pos as usize] + F::from_i64(c as i64); + out[pos as usize] += F::from_i64(c as i64); } Ok(CyclotomicRing::from_coefficients(out)) } @@ -148,7 +149,7 @@ impl SparseChallenge { pub fn eval_at_alpha(&self, alpha_pows: &[E]) -> Result where F: FieldCore + CanonicalField, - E: FieldCore + crate::algebra::fields::LiftBase, + E: FieldCore + LiftBase, { self.validate::()?; if alpha_pows.len() != D { @@ -157,7 +158,7 @@ impl SparseChallenge { let mut acc = E::zero(); for (&pos, &c) in self.positions.iter().zip(self.coeffs.iter()) { let coeff_f = F::from_i64(c as i64); - acc = acc + (E::lift_base(coeff_f) * alpha_pows[pos as usize]); + acc += E::lift_base(coeff_f) * alpha_pows[pos as usize]; } Ok(acc) } diff --git a/src/lib.rs b/src/lib.rs index 4d6635ef..29b68713 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -21,7 +21,7 @@ //! ### Core Modules //! - [`primitives`] - Core traits and abstractions //! - [`primitives::arithmetic`] - Field and module traits for lattice arithmetic -//! - [`primitives::poly`] - Multilinear polynomial traits and operations +//! - [`primitives::poly`] - Multilinear polynomial utility functions //! - [`primitives::transcript`] - Fiat-Shamir transcript trait //! - [`primitives::serialization`] - Serialization abstractions //! - [`error`] - Error types @@ -47,17 +47,18 @@ pub mod protocol; /// Conditional parallelism utilities (`cfg_iter!`, `cfg_into_iter!`, etc.) #[doc(hidden)] -#[allow(missing_docs)] pub mod parallel; +/// Shared test configuration and helpers. #[doc(hidden)] -#[allow(missing_docs)] pub mod test_utils; pub use error::HachiError; pub use primitives::arithmetic::{ - CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, Module, PseudoMersenneField, + AdditiveGroup, CanonicalField, FieldCore, FieldSampling, FromSmallInt, Invertible, Module, + PseudoMersenneField, }; -pub use primitives::poly::{MultilinearLagrange, Polynomial}; pub use primitives::serialization::{HachiDeserialize, HachiSerialize}; -pub use protocol::{CommitmentScheme, StreamingCommitmentScheme, Transcript}; +pub use protocol::{ + BasisMode, CommitmentScheme, DensePoly, HachiPolyOps, OneHotIndex, OneHotPoly, Transcript, +}; diff --git a/src/parallel.rs b/src/parallel.rs index d73c9381..1be93577 100644 --- a/src/parallel.rs +++ b/src/parallel.rs @@ -54,3 +54,21 @@ macro_rules! cfg_chunks { it }}; } + +/// Parallel fold-reduce over a range. +/// +/// With `parallel`: `range.into_par_iter().fold(identity, fold_op).reduce(identity, reduce_op)`. +/// Without: `range.into_iter().fold(identity(), fold_op)`. +#[macro_export] +macro_rules! cfg_fold_reduce { + ($range:expr, $identity:expr, $fold_op:expr, $reduce_op:expr) => {{ + #[cfg(feature = "parallel")] + let result = $range + .into_par_iter() + .fold($identity, $fold_op) + .reduce($identity, $reduce_op); + #[cfg(not(feature = "parallel"))] + let result = $range.into_iter().fold(($identity)(), $fold_op); + result + }}; +} diff --git a/src/primitives/arithmetic.rs b/src/primitives/arithmetic.rs index f6f1d91a..655e68ae 100644 --- a/src/primitives/arithmetic.rs +++ b/src/primitives/arithmetic.rs @@ -3,26 +3,42 @@ use super::{HachiDeserialize, HachiSerialize}; use rand_core::RngCore; -/// Core field operations required across algebra backends. -pub trait FieldCore: +/// Minimal additive group: add, sub, neg, zero. +/// +/// Satisfied by both reduced field elements (`FieldCore`) and wide unreduced +/// accumulators (`Fp128x8i32`, etc.), enabling generic shift-accumulate +/// operations on `WideCyclotomicRing`. +pub trait AdditiveGroup: Sized + Clone + Copy - + PartialEq + Send + Sync - + HachiSerialize - + HachiDeserialize + std::ops::Add + std::ops::Sub - + std::ops::Mul + std::ops::Neg + + std::ops::AddAssign + + std::ops::SubAssign +{ + /// Additive identity. + const ZERO: Self; +} + +/// Core field operations required across algebra backends. +pub trait FieldCore: + AdditiveGroup + + PartialEq + + HachiSerialize + + HachiDeserialize + + std::ops::Mul + for<'a> std::ops::Add<&'a Self, Output = Self> + for<'a> std::ops::Sub<&'a Self, Output = Self> + for<'a> std::ops::Mul<&'a Self, Output = Self> { - /// Additive identity - fn zero() -> Self; + /// Additive identity. + fn zero() -> Self { + Self::ZERO + } /// Multiplicative identity fn one() -> Self; @@ -43,6 +59,9 @@ pub trait FieldCore: /// This API may branch on zero-check and is intended for public/non-secret /// values. For secret-bearing paths, use [`Invertible::inv_or_zero`]. fn inv(self) -> Option; + + /// Multiplicative inverse of 2: `(p + 1) / 2` for odd-characteristic fields. + const TWO_INV: Self; } /// Constant-time inversion helper for secret-bearing code paths. @@ -98,6 +117,45 @@ pub trait FromSmallInt: FieldCore { /// Embed an `i64` into the field (reduce mod characteristic). fn from_i64(val: i64) -> Self; + + /// Embed an `i128` into the field. + /// + /// Default implementation splits into u64 limbs with field multiplication + /// by `2^64`. Override for base fields that have a direct path. + fn from_i128(val: i128) -> Self { + if val >= 0 { + let lo = val as u64; + let hi = (val >> 64) as u64; + if hi == 0 { + Self::from_u64(lo) + } else { + let two_64 = Self::from_u64(1u64 << 32) * Self::from_u64(1u64 << 32); + Self::from_u64(lo) + Self::from_u64(hi) * two_64 + } + } else { + -Self::from_i128(-val) + } + } + + /// Lookup table mapping balanced digit index → field element. + /// + /// For `log_basis` in `1..=4`, returns a 16-entry table where + /// `table[i]` = `from_i64(i - b/2)` for `i < b = 2^log_basis`, + /// and zero for `i >= b`. + /// + /// Index a digit `d ∈ [-b/2, b/2)` as `table[(d + b/2) as usize]`. + fn digit_lut(log_basis: u32) -> [Self; 16] { + debug_assert!(log_basis > 0 && log_basis <= 4); + let b = 1usize << log_basis; + let half_b = (b >> 1) as i64; + std::array::from_fn(|i| { + if i < b { + Self::from_i64(i as i64 - half_b) + } else { + Self::zero() + } + }) + } } /// Canonical integer representation for prime (base) field elements. diff --git a/src/primitives/mod.rs b/src/primitives/mod.rs index 21376422..9f53c2f1 100644 --- a/src/primitives/mod.rs +++ b/src/primitives/mod.rs @@ -2,7 +2,6 @@ //! This submodule defines the basic lattice arithmetic and cryptographic tools that Hachi is built upon pub mod arithmetic; -pub mod multilinear_evals; pub mod poly; pub mod serialization; pub mod transcript; diff --git a/src/primitives/multilinear_evals.rs b/src/primitives/multilinear_evals.rs deleted file mode 100644 index 2ba3b95a..00000000 --- a/src/primitives/multilinear_evals.rs +++ /dev/null @@ -1,155 +0,0 @@ -//! Dense multilinear polynomials in evaluation form. -//! -//! This module intentionally follows the same high-level representation style as -//! Jolt's `DensePolynomial` for multilinear extensions (MLEs): store the values -//! of the multilinear polynomial on the Boolean hypercube `{0,1}^n` and provide -//! binding/evaluation by iterative folding. -//! -//! The key convention for this repo (used by the ring-switch witness table) is: -//! -//! - An evaluation index `idx` is interpreted in binary. -//! - The **lowest** index bit is the **first** variable bound under -//! [`BindingOrder::LowToHigh`]. -//! -//! This matches the row-major flattening `idx = row * d + col` when `d` is a -//! power of two: the low `log2(d)` bits correspond to the `col` coordinate. - -use crate::primitives::arithmetic::FieldCore; -use crate::primitives::poly::Polynomial; - -/// The order in which variables are bound/evaluated. -#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)] -pub enum BindingOrder { - /// Bind the lowest index bit first (LSB → MSB). - #[default] - LowToHigh, - /// Bind the highest index bit first (MSB → LSB). - HighToLow, -} - -/// Dense multilinear polynomial in evaluation form over `{0,1}^num_vars`. -#[derive(Debug, Clone, PartialEq, Eq)] -pub struct DenseMultilinearEvals { - /// Number of variables in the multilinear extension. - pub num_vars: usize, - /// Active length (decreases as variables are bound). - pub len: usize, - /// Evaluations on the hypercube, length is a power of two. - pub evals: Vec, -} - -impl Default for DenseMultilinearEvals { - fn default() -> Self { - Self { - num_vars: 0, - len: 1, - evals: vec![F::zero()], - } - } -} - -impl DenseMultilinearEvals { - /// Construct from evaluations, padding with zeros to a power of two. - /// - /// The variable count is derived from the padded length. - pub fn new_padded(mut evals: Vec) -> Self { - if evals.is_empty() { - evals.push(F::zero()); - } - while !evals.len().is_power_of_two() { - evals.push(F::zero()); - } - let num_vars = evals.len().trailing_zeros() as usize; - let len = evals.len(); - Self { - num_vars, - len, - evals, - } - } - - /// Return the original (backing) evaluation length. - pub fn original_len(&self) -> usize { - self.evals.len() - } - - /// Bind one variable in-place, reducing `len` by a factor of 2. - /// - /// After binding, the polynomial has one fewer variable. - /// - /// # Panics - /// - /// Panics if the current backing length is not a power of two, or if attempting - /// to bind a constant (length-1) polynomial. - pub fn bind_in_place(&mut self, r: F, order: BindingOrder) { - assert!(self.len.is_power_of_two()); - assert!(self.len >= 2, "cannot bind variable of constant polynomial"); - match order { - BindingOrder::LowToHigh => self.bind_lsb_in_place(r), - BindingOrder::HighToLow => self.bind_msb_in_place(r), - } - } - - #[inline] - fn bind_lsb_in_place(&mut self, r: F) { - let next_len = self.len / 2; - for i in 0..next_len { - let v0 = self.evals[i << 1]; - let v1 = self.evals[(i << 1) | 1]; - // (1-r)*v0 + r*v1 = v0 + r*(v1-v0) - self.evals[i] = v0 + r * (v1 - v0); - } - self.len = next_len; - self.num_vars = self.num_vars.saturating_sub(1); - } - - #[inline] - fn bind_msb_in_place(&mut self, r: F) { - let next_len = self.len / 2; - let (left, right) = self.evals.split_at_mut(next_len); - for i in 0..next_len { - let v0 = left[i]; - let v1 = right[i]; - left[i] = v0 + r * (v1 - v0); - } - self.len = next_len; - self.num_vars = self.num_vars.saturating_sub(1); - } - - /// Evaluate without mutating `self`. - /// - /// # Panics - /// - /// Panics if `point.len() != self.num_vars`. - pub fn evaluate_with_order(&self, point: &[F], order: BindingOrder) -> F { - if point.is_empty() { - return self.evals[0]; - } - assert_eq!( - point.len(), - self.num_vars, - "point dimension mismatch: expected {}, got {}", - self.num_vars, - point.len() - ); - let mut tmp = self.clone(); - for r in point.iter().copied() { - tmp.bind_in_place(r, order); - } - tmp.evals[0] - } -} - -impl Polynomial for DenseMultilinearEvals { - fn num_vars(&self) -> usize { - self.num_vars - } - - fn evaluate(&self, point: &[F]) -> F { - self.evaluate_with_order(point, BindingOrder::LowToHigh) - } - - fn coeffs(&self) -> Vec { - self.evals[..self.len].to_vec() - } -} diff --git a/src/primitives/poly.rs b/src/primitives/poly.rs index 16f034cd..6a4185b9 100644 --- a/src/primitives/poly.rs +++ b/src/primitives/poly.rs @@ -1,62 +1,7 @@ -//! Polynomial trait for multilinear polynomials. +//! Multilinear polynomial utility functions. use super::arithmetic::FieldCore; -/// Trait for multilinear Lagrange polynomial operations -pub trait MultilinearLagrange: Polynomial { - /// Compute multilinear Lagrange basis evaluations at a point - /// - /// For variables (r₀, r₁, ..., r_{n-1}), computes all 2^n basis polynomial evaluations. - /// The i-th basis polynomial evaluates to 1 at the i-th hypercube vertex and 0 elsewhere. - fn lagrange_basis(&self, output: &mut [F], point: &[F]) { - multilinear_lagrange_basis(output, point) - } - - /// Compute vector-matrix product: v = L^T * M - /// - /// Treats coefficients as a 2^nu × 2^sigma matrix. - /// For each column j: v\[j\] = Σ_i left_vec\[i\] * coefficients\[i\]\[j\] - fn vector_matrix_product(&self, left_vec: &[F], nu: usize, sigma: usize) -> Vec; - - /// Compute left and right vectors from evaluation point - /// - /// Given a point arranged for matrix evaluation, computes L and R such that: - /// polynomial_evaluation(point) = L^T × M × R - fn compute_evaluation_vectors(&self, point: &[F], nu: usize, sigma: usize) -> (Vec, Vec) { - compute_left_right_vectors(point, nu, sigma) - } -} - -/// Trait for multilinear polynomials -/// -/// Represents a polynomial in evaluation form (coefficients at hypercube points). -pub trait Polynomial { - /// Number of variables - fn num_vars(&self) -> usize; - - /// Total number of coefficients (2^num_vars) - fn len(&self) -> usize { - 1 << self.num_vars() - } - - /// Check if polynomial is empty - fn is_empty(&self) -> bool { - self.len() == 0 - } - - /// Evaluate polynomial at a point - /// - /// # Parameters - /// - `point`: Evaluation point (length must equal num_vars) - /// - /// # Returns - /// Polynomial evaluation result - fn evaluate(&self, point: &[F]) -> F; - - /// Return the coefficient/evaluation table on `{0,1}^n` in LSB-first order. - fn coeffs(&self) -> Vec; -} - /// Compute multilinear Lagrange basis evaluations at a point /// /// For variables (r₀, r₁, ..., r_{n-1}), computes all 2^n basis polynomial evaluations. diff --git a/src/protocol/commitment/commit.rs b/src/protocol/commitment/commit.rs index 97df3007..88c61c25 100644 --- a/src/protocol/commitment/commit.rs +++ b/src/protocol/commitment/commit.rs @@ -1,26 +1,32 @@ //! Ring-native §4.1 commitment core implementation. use super::config::{ - ensure_block_layout, ensure_matrix_shape, ensure_supported_num_vars, + ensure_block_layout, ensure_matrix_shape_ge, ensure_supported_num_vars, validate_and_derive_layout, HachiCommitmentLayout, }; -use super::onehot::{inner_ajtai_onehot, map_onehot_to_sparse_blocks, SparseBlockEntry}; +use super::onehot::{inner_ajtai_onehot_wide, map_onehot_to_sparse_blocks}; use super::scheme::{CommitWitness, RingCommitmentScheme}; use super::types::RingCommitment; -use super::utils::crt_ntt::{build_ntt_cache, NttMatrixCache}; -use super::utils::linear::{decompose_block, decompose_rows, mat_vec_mul_ntt_cached, MatrixSlot}; +use super::utils::crt_ntt::{build_ntt_slot, NttSlotCache}; +use super::utils::linear::{ + decompose_rows_i8, flatten_i8_blocks, mat_vec_mul_ntt_i8, mat_vec_mul_ntt_single_i8, +}; use super::utils::matrix::{derive_public_matrix, sample_public_matrix_seed, PublicMatrixSeed}; use super::CommitmentConfig; +use crate::algebra::fields::wide::HasWide; use crate::algebra::CyclotomicRing; use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; use crate::primitives::serialization::{ Compress, HachiDeserialize, HachiSerialize, SerializationError, Valid, Validate, }; -use crate::{CanonicalField, FieldCore, FieldSampling}; +use crate::protocol::hachi_poly_ops::OneHotIndex; +use crate::protocol::ring_switch::w_commitment_layout; +use crate::{cfg_into_iter, cfg_iter, CanonicalField, FieldCore, FieldSampling}; use std::io::{Read, Write}; /// Seed-only stage for deterministic setup expansion. -#[allow(non_snake_case)] #[derive(Debug, Clone, PartialEq, Eq)] pub struct HachiSetupSeed { /// Maximum supported variable count. @@ -45,25 +51,21 @@ pub struct HachiExpandedSetup { pub D: Vec>>, } -/// Optional prepared setup stage for accelerated matrix-vector products. -#[derive(Debug, Clone, PartialEq, Eq)] -pub struct HachiPreparedSetup { - /// Pre-converted CRT+NTT matrices for dense mat-vec paths. - pub(crate) ntt_cache: NttMatrixCache, -} - -/// Prover setup artifact (expanded setup + optional runtime cache). +/// Prover setup artifact (expanded setup + per-matrix NTT caches). #[allow(non_snake_case)] #[derive(Debug, Clone, PartialEq, Eq)] pub struct HachiProverSetup { /// Expanded matrix stage used by both prover and verifier. pub expanded: HachiExpandedSetup, - /// Optional runtime-prepared acceleration cache. - pub prepared: Option>, + /// NTT cache for the A matrix. + pub ntt_A: NttSlotCache, + /// NTT cache for the B matrix. + pub ntt_B: NttSlotCache, + /// NTT cache for the D matrix. + pub ntt_D: NttSlotCache, } /// Verifier setup artifact derived from prover setup. -#[allow(non_snake_case)] #[derive(Debug, Clone, PartialEq, Eq)] pub struct HachiVerifierSetup { /// Expanded matrix stage used for verification. @@ -71,16 +73,37 @@ pub struct HachiVerifierSetup { } impl HachiProverSetup { - /// Runtime layout carried by this setup. + /// Runtime layout carried by this setup (the max-dimension layout). pub fn layout(&self) -> HachiCommitmentLayout { self.expanded.seed.layout } - pub(crate) fn ntt_cache(&self) -> Result<&NttMatrixCache, HachiError> { - self.prepared - .as_ref() - .map(|p| &p.ntt_cache) - .ok_or_else(|| HachiError::InvalidSetup("missing prepared NTT cache".to_string())) + /// Panic if `layout`'s matrix dimensions exceed this setup's maximums. + /// + /// # Panics + /// + /// Panics if any of `layout`'s matrix widths (inner, outer, D) exceed + /// those of this setup. + pub fn assert_layout_fits(&self, layout: &HachiCommitmentLayout) { + let max = &self.expanded.seed.layout; + assert!( + layout.inner_width <= max.inner_width, + "A matrix too narrow: need {} but setup has {}", + layout.inner_width, + max.inner_width + ); + assert!( + layout.outer_width <= max.outer_width, + "B matrix too narrow: need {} but setup has {}", + layout.outer_width, + max.outer_width + ); + assert!( + layout.d_matrix_width <= max.d_matrix_width, + "D matrix too narrow: need {} but setup has {}", + layout.d_matrix_width, + max.d_matrix_width + ); } } @@ -201,28 +224,16 @@ impl Valid for HachiProverSetup { impl HachiSerialize for HachiProverSetup { fn serialize_with_mode( &self, - writer: W, - compress: Compress, + _writer: W, + _compress: Compress, ) -> Result<(), SerializationError> { - // Prepared cache is runtime-only and intentionally excluded. - self.expanded.serialize_with_mode(writer, compress) + Err(SerializationError::InvalidData( + "HachiProverSetup contains runtime NTT caches and is not serializable".into(), + )) } - fn serialized_size(&self, compress: Compress) -> usize { - self.expanded.serialized_size(compress) - } -} - -impl HachiDeserialize for HachiProverSetup { - fn deserialize_with_mode( - reader: R, - compress: Compress, - validate: Validate, - ) -> Result { - Ok(Self { - expanded: HachiExpandedSetup::deserialize_with_mode(reader, compress, validate)?, - prepared: None, - }) + fn serialized_size(&self, _compress: Compress) -> usize { + 0 } } @@ -264,29 +275,31 @@ pub struct HachiCommitmentCore; impl RingCommitmentScheme for HachiCommitmentCore where - F: FieldCore + CanonicalField + FieldSampling, + F: FieldCore + CanonicalField + FieldSampling + HasWide, Cfg: CommitmentConfig, { type ProverSetup = HachiProverSetup; type VerifierSetup = HachiVerifierSetup; type Commitment = RingCommitment; + #[tracing::instrument(skip_all, name = "RingCommitmentScheme::setup")] fn setup(max_num_vars: usize) -> Result<(Self::ProverSetup, Self::VerifierSetup), HachiError> { let layout = validate_and_derive_layout::(max_num_vars)?; ensure_supported_num_vars(max_num_vars, layout.required_num_vars::()?)?; + + let w_layout = w_commitment_layout::(layout)?; + let a_cols = layout.inner_width.max(w_layout.inner_width); + let b_cols = layout.outer_width.max(w_layout.outer_width); + let d_cols = layout.d_matrix_width.max(w_layout.d_matrix_width); + let public_matrix_seed = sample_public_matrix_seed(); - let a_matrix = - derive_public_matrix::(Cfg::N_A, layout.inner_width, &public_matrix_seed, b"A"); - let b_matrix = - derive_public_matrix::(Cfg::N_B, layout.outer_width, &public_matrix_seed, b"B"); - let d_matrix = derive_public_matrix::( - Cfg::N_D, - layout.d_matrix_width, - &public_matrix_seed, - b"D", - ); + let a_matrix = derive_public_matrix::(Cfg::N_A, a_cols, &public_matrix_seed, b"A"); + let b_matrix = derive_public_matrix::(Cfg::N_B, b_cols, &public_matrix_seed, b"B"); + let d_matrix = derive_public_matrix::(Cfg::N_D, d_cols, &public_matrix_seed, b"D"); - let ntt_cache = build_ntt_cache::(&a_matrix, &b_matrix, &d_matrix)?; + let ntt_a = build_ntt_slot::(&a_matrix)?; + let ntt_b = build_ntt_slot::(&b_matrix)?; + let ntt_d = build_ntt_slot::(&d_matrix)?; let expanded = HachiExpandedSetup { seed: HachiSetupSeed { max_num_vars, @@ -299,12 +312,14 @@ where }; let prover_setup = HachiProverSetup { expanded: expanded.clone(), - prepared: Some(HachiPreparedSetup { ntt_cache }), + ntt_A: ntt_a, + ntt_B: ntt_b, + ntt_D: ntt_d, }; let verifier_setup = HachiVerifierSetup { expanded }; - ensure_matrix_shape(&prover_setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; - ensure_matrix_shape(&prover_setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; - ensure_matrix_shape( + ensure_matrix_shape_ge(&prover_setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape_ge(&prover_setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; + ensure_matrix_shape_ge( &prover_setup.expanded.D, Cfg::N_D, layout.d_matrix_width, @@ -317,6 +332,7 @@ where Ok(setup.layout()) } + #[tracing::instrument(skip_all, name = "RingCommitmentScheme::commit_ring_blocks")] fn commit_ring_blocks( f_blocks: &[Vec>], setup: &Self::ProverSetup, @@ -327,26 +343,25 @@ where layout.required_num_vars::()?, )?; ensure_block_layout(f_blocks, layout)?; - ensure_matrix_shape(&setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; - ensure_matrix_shape(&setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; - - let mut t_hat_all: Vec>> = Vec::with_capacity(layout.num_blocks); - let mut t_hat_flat: Vec> = Vec::with_capacity(layout.outer_width); - for block in f_blocks { - let s_i = decompose_block(block, Cfg::DELTA, Cfg::LOG_BASIS); - let t_i = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::A, &s_i)?; - let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); - t_hat_flat.extend(t_hat_i.iter().copied()); - t_hat_all.push(t_hat_i); - } - - let u = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::B, &t_hat_flat)?; - Ok(CommitWitness { - commitment: RingCommitment { u }, - t_hat: t_hat_all, - }) + ensure_matrix_shape_ge(&setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape_ge(&setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; + + let depth = layout.num_digits_commit; + let log_basis = layout.log_basis; + let block_slices: Vec<&[CyclotomicRing]> = + f_blocks.iter().map(|b| b.as_slice()).collect(); + let t_all = mat_vec_mul_ntt_i8(&setup.ntt_A, &block_slices, depth, log_basis); + let t_hat_all: Vec> = cfg_into_iter!(t_all) + .map(|t_i| decompose_rows_i8(&t_i, depth, log_basis)) + .collect(); + + let t_hat_flat = flatten_i8_blocks(&t_hat_all); + + let u: Vec> = mat_vec_mul_ntt_single_i8(&setup.ntt_B, &t_hat_flat); + Ok(CommitWitness::new(RingCommitment { u }, t_hat_all)) } + #[tracing::instrument(skip_all, name = "RingCommitmentScheme::commit_coeffs")] fn commit_coeffs( f_coeffs: &[CyclotomicRing], setup: &Self::ProverSetup, @@ -364,38 +379,36 @@ where }); } - let zero_t_hat = - vec![CyclotomicRing::::zero(); Cfg::N_A.checked_mul(Cfg::DELTA).unwrap()]; - - let mut t_hat_all: Vec>> = Vec::with_capacity(num_blocks); - let mut t_hat_flat: Vec> = Vec::with_capacity(layout.outer_width); - - for i in 0..num_blocks { - let start = i * block_len; - if start >= f_coeffs.len() { - t_hat_flat.extend(zero_t_hat.iter().copied()); - t_hat_all.push(zero_t_hat.clone()); - } else { - let end = (start + block_len).min(f_coeffs.len()); - let block = &f_coeffs[start..end]; - let s_i = decompose_block(block, Cfg::DELTA, Cfg::LOG_BASIS); - let t_i = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::A, &s_i)?; - let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); - t_hat_flat.extend(t_hat_i.iter().copied()); - t_hat_all.push(t_hat_i); - } - } + let depth = layout.num_digits_commit; + let log_basis = layout.log_basis; + let coeff_len = f_coeffs.len(); + + let block_slices: Vec<&[CyclotomicRing]> = (0..num_blocks) + .map(|i| { + let start = i * block_len; + if start >= coeff_len { + &[] as &[CyclotomicRing] + } else { + &f_coeffs[start..(start + block_len).min(coeff_len)] + } + }) + .collect(); - let u = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::B, &t_hat_flat)?; - Ok(CommitWitness { - commitment: RingCommitment { u }, - t_hat: t_hat_all, - }) + let t_all = mat_vec_mul_ntt_i8(&setup.ntt_A, &block_slices, depth, log_basis); + let t_hat_all: Vec> = cfg_into_iter!(t_all) + .map(|t_i| decompose_rows_i8(&t_i, depth, log_basis)) + .collect(); + + let t_hat_flat = flatten_i8_blocks(&t_hat_all); + + let u: Vec> = mat_vec_mul_ntt_single_i8(&setup.ntt_B, &t_hat_flat); + Ok(CommitWitness::new(RingCommitment { u }, t_hat_all)) } - fn commit_onehot( + #[tracing::instrument(skip_all, name = "RingCommitmentScheme::commit_onehot")] + fn commit_onehot( onehot_k: usize, - indices: &[Option], + indices: &[Option], setup: &Self::ProverSetup, ) -> Result, HachiError> { let layout = setup.layout(); @@ -403,40 +416,33 @@ where setup.expanded.seed.max_num_vars, layout.required_num_vars::()?, )?; - ensure_matrix_shape(&setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; - ensure_matrix_shape(&setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; + ensure_matrix_shape_ge(&setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape_ge(&setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; let sparse_blocks = map_onehot_to_sparse_blocks(onehot_k, indices, layout.r_vars, layout.m_vars, D)?; - let mut t_hat_all: Vec>> = Vec::with_capacity(layout.num_blocks); - let mut t_hat_flat: Vec> = Vec::with_capacity(layout.outer_width); - - let zero_t_hat = - vec![CyclotomicRing::::zero(); Cfg::N_A.checked_mul(Cfg::DELTA).unwrap()]; - - for block_entries in &sparse_blocks { - if block_entries.is_empty() { - t_hat_flat.extend(zero_t_hat.iter().copied()); - t_hat_all.push(zero_t_hat.clone()); - } else { - let (t_i, _s_i) = inner_ajtai_onehot( - &setup.expanded.A, - block_entries, - layout.block_len, - Cfg::DELTA, - ); - let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); - t_hat_flat.extend(t_hat_i.iter().copied()); - t_hat_all.push(t_hat_i); - } - } + let depth = layout.num_digits_commit; + let log_basis = layout.log_basis; + let zero_block_len = Cfg::N_A.checked_mul(depth).unwrap(); + let a_matrix = &setup.expanded.A; + let block_len = layout.block_len; - let u = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::B, &t_hat_flat)?; - Ok(CommitWitness { - commitment: RingCommitment { u }, - t_hat: t_hat_all, - }) + let t_hat_all: Vec> = cfg_iter!(sparse_blocks) + .map(|block_entries| { + if block_entries.is_empty() { + vec![[0i8; D]; zero_block_len] + } else { + let t_i = inner_ajtai_onehot_wide(a_matrix, block_entries, block_len, depth); + decompose_rows_i8(&t_i, depth, log_basis) + } + }) + .collect(); + + let t_hat_flat = flatten_i8_blocks(&t_hat_all); + + let u: Vec> = mat_vec_mul_ntt_single_i8(&setup.ntt_B, &t_hat_flat); + Ok(CommitWitness::new(RingCommitment { u }, t_hat_all)) } } @@ -451,7 +457,6 @@ impl HachiCommitmentCore { /// # Errors /// /// Returns `HachiError` on invalid layout or matrix generation failures. - #[allow(non_snake_case)] pub fn setup_with_layout( layout: HachiCommitmentLayout, ) -> Result<(HachiProverSetup, HachiVerifierSetup), HachiError> @@ -461,18 +466,103 @@ impl HachiCommitmentCore { { let max_num_vars = layout.required_num_vars::()?; let public_matrix_seed = sample_public_matrix_seed(); - let a_matrix = - derive_public_matrix::(Cfg::N_A, layout.inner_width, &public_matrix_seed, b"A"); - let b_matrix = - derive_public_matrix::(Cfg::N_B, layout.outer_width, &public_matrix_seed, b"B"); - let d_matrix = derive_public_matrix::( - Cfg::N_D, - layout.d_matrix_width, - &public_matrix_seed, - b"D", - ); + Self::setup_with_layout_and_seed::(layout, max_num_vars, public_matrix_seed) + } + + /// Like `setup_with_layout` but reuses an existing setup's random seed and + /// A matrix (which depends only on `m_vars`). Only regenerates B and D + /// matrices for the new `r_vars`. + /// + /// Use this when creating a mega-polynomial setup that shares `m_vars` with + /// an individual polynomial setup — avoids re-deriving and NTT-transforming + /// the A matrix. + /// + /// # Errors + /// + /// Returns `HachiError` if the new layout is incompatible with the existing + /// setup or matrix shapes are inconsistent. + pub fn setup_from_existing( + existing: &HachiExpandedSetup, + new_r_vars: usize, + ) -> Result<(HachiProverSetup, HachiVerifierSetup), HachiError> + where + F: FieldCore + CanonicalField + FieldSampling, + Cfg: CommitmentConfig, + { + let old_layout = existing.seed.layout; + let new_layout = HachiCommitmentLayout::new::( + old_layout.m_vars, + new_r_vars, + &Cfg::decomposition(), + )?; + + if new_layout.inner_width != old_layout.inner_width { + return Err(HachiError::InvalidSetup( + "setup_from_existing requires matching m_vars/inner_width".to_string(), + )); + } + + let w_layout = w_commitment_layout::(new_layout)?; + let a_width = existing.A.first().map_or(0, |r| r.len()); + if a_width < w_layout.inner_width { + return Err(HachiError::InvalidSetup(format!( + "existing A width {a_width} < w inner_width {}", + w_layout.inner_width + ))); + } + let b_cols = new_layout.outer_width.max(w_layout.outer_width); + + let max_num_vars = new_layout.required_num_vars::()?; + let seed = existing.seed.public_matrix_seed; + + let d_cols = new_layout.d_matrix_width.max(w_layout.d_matrix_width); + let b_matrix = derive_public_matrix::(Cfg::N_B, b_cols, &seed, b"B"); + let d_matrix = derive_public_matrix::(Cfg::N_D, d_cols, &seed, b"D"); + + let ntt_a = build_ntt_slot::(&existing.A)?; + let ntt_b = build_ntt_slot::(&b_matrix)?; + let ntt_d = build_ntt_slot::(&d_matrix)?; + let expanded = HachiExpandedSetup { + seed: HachiSetupSeed { + max_num_vars, + layout: new_layout, + public_matrix_seed: seed, + }, + A: existing.A.clone(), + B: b_matrix, + D: d_matrix, + }; + let prover_setup = HachiProverSetup { + expanded: expanded.clone(), + ntt_A: ntt_a, + ntt_B: ntt_b, + ntt_D: ntt_d, + }; + let verifier_setup = HachiVerifierSetup { expanded }; + Ok((prover_setup, verifier_setup)) + } - let ntt_cache = build_ntt_cache::(&a_matrix, &b_matrix, &d_matrix)?; + fn setup_with_layout_and_seed( + layout: HachiCommitmentLayout, + max_num_vars: usize, + public_matrix_seed: PublicMatrixSeed, + ) -> Result<(HachiProverSetup, HachiVerifierSetup), HachiError> + where + F: FieldCore + CanonicalField + FieldSampling, + Cfg: CommitmentConfig, + { + let w_layout = w_commitment_layout::(layout)?; + let a_cols = layout.inner_width.max(w_layout.inner_width); + let b_cols = layout.outer_width.max(w_layout.outer_width); + let d_cols = layout.d_matrix_width.max(w_layout.d_matrix_width); + + let a_matrix = derive_public_matrix::(Cfg::N_A, a_cols, &public_matrix_seed, b"A"); + let b_matrix = derive_public_matrix::(Cfg::N_B, b_cols, &public_matrix_seed, b"B"); + let d_matrix = derive_public_matrix::(Cfg::N_D, d_cols, &public_matrix_seed, b"D"); + + let ntt_a = build_ntt_slot::(&a_matrix)?; + let ntt_b = build_ntt_slot::(&b_matrix)?; + let ntt_d = build_ntt_slot::(&d_matrix)?; let expanded = HachiExpandedSetup { seed: HachiSetupSeed { max_num_vars, @@ -485,12 +575,14 @@ impl HachiCommitmentCore { }; let prover_setup = HachiProverSetup { expanded: expanded.clone(), - prepared: Some(HachiPreparedSetup { ntt_cache }), + ntt_A: ntt_a, + ntt_B: ntt_b, + ntt_D: ntt_d, }; let verifier_setup = HachiVerifierSetup { expanded }; - ensure_matrix_shape(&prover_setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; - ensure_matrix_shape(&prover_setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; - ensure_matrix_shape( + ensure_matrix_shape_ge(&prover_setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; + ensure_matrix_shape_ge(&prover_setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; + ensure_matrix_shape_ge( &prover_setup.expanded.D, Cfg::N_D, layout.d_matrix_width, @@ -500,102 +592,6 @@ impl HachiCommitmentCore { } } -/// Describes one block of a mega-polynomial commitment. -/// -/// A mega-polynomial packs multiple heterogeneous polynomials into a single -/// Hachi commitment by assigning each polynomial to its own block. Blocks -/// can be dense (arbitrary ring coefficients), sparse one-hot, or zero. -pub enum MegaPolyBlock<'a, F: FieldCore, const D: usize> { - /// Dense block: full ring coefficients (length ≤ block_len). - Dense(&'a [CyclotomicRing]), - /// One-hot block: sparse entries within this block. - OneHot(&'a [SparseBlockEntry]), - /// Empty block: all coefficients are zero (no allocation or computation). - Zero, -} - -impl HachiCommitmentCore { - /// Commit a mega-polynomial composed of heterogeneous blocks. - /// - /// Each block occupies `block_len` ring elements. Dense blocks are - /// decomposed via `balanced_decompose_pow2`; one-hot blocks use sparse - /// inner Ajtai; zero blocks are free. - /// - /// The number of blocks must equal `layout.num_blocks` (power of 2). - /// - /// # Errors - /// - /// Returns `HachiError` if the number of blocks doesn't match the layout - /// or if matrix shapes are inconsistent. - /// - /// # Panics - /// - /// Panics if `Cfg::N_A * Cfg::DELTA` overflows. - #[allow(non_snake_case)] - pub fn commit_mixed( - blocks: &[MegaPolyBlock<'_, F, D>], - setup: &HachiProverSetup, - ) -> Result, F, D>, HachiError> - where - F: FieldCore + CanonicalField + FieldSampling, - Cfg: CommitmentConfig, - { - let layout = setup.layout(); - if blocks.len() != layout.num_blocks { - return Err(HachiError::InvalidSize { - expected: layout.num_blocks, - actual: blocks.len(), - }); - } - ensure_matrix_shape(&setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; - ensure_matrix_shape(&setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; - - let zero_t_hat = - vec![CyclotomicRing::::zero(); Cfg::N_A.checked_mul(Cfg::DELTA).unwrap()]; - - let mut t_hat_all: Vec>> = Vec::with_capacity(layout.num_blocks); - let mut t_hat_flat: Vec> = Vec::with_capacity(layout.outer_width); - - for block in blocks { - match block { - MegaPolyBlock::Zero => { - t_hat_flat.extend(zero_t_hat.iter().copied()); - t_hat_all.push(zero_t_hat.clone()); - } - MegaPolyBlock::Dense(coeffs) => { - let s_i = decompose_block(coeffs, Cfg::DELTA, Cfg::LOG_BASIS); - let t_i = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::A, &s_i)?; - let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); - t_hat_flat.extend(t_hat_i.iter().copied()); - t_hat_all.push(t_hat_i); - } - MegaPolyBlock::OneHot(sparse_entries) => { - if sparse_entries.is_empty() { - t_hat_flat.extend(zero_t_hat.iter().copied()); - t_hat_all.push(zero_t_hat.clone()); - } else { - let (t_i, _s_i) = inner_ajtai_onehot( - &setup.expanded.A, - sparse_entries, - layout.block_len, - Cfg::DELTA, - ); - let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); - t_hat_flat.extend(t_hat_i.iter().copied()); - t_hat_all.push(t_hat_i); - } - } - } - } - - let u = mat_vec_mul_ntt_cached(setup.ntt_cache()?, MatrixSlot::B, &t_hat_flat)?; - Ok(CommitWitness { - commitment: RingCommitment { u }, - t_hat: t_hat_all, - }) - } -} - #[cfg(test)] mod tests { use super::*; @@ -603,20 +599,23 @@ mod tests { use crate::test_utils::{TinyConfig, D as TestD, F as TestF}; #[test] - fn prover_setup_roundtrips_and_derives_same_verifier() { + fn expanded_setup_roundtrips_and_derives_same_verifier() { let (prover_setup, verifier_setup) = >::setup(16) .unwrap(); let mut bytes = Vec::new(); - prover_setup.serialize_compressed(&mut bytes).unwrap(); - let decoded = HachiProverSetup::::deserialize_compressed(&bytes[..]).unwrap(); + prover_setup + .expanded + .serialize_compressed(&mut bytes) + .unwrap(); + let decoded = + HachiExpandedSetup::::deserialize_compressed(&bytes[..]).unwrap(); - assert_eq!(decoded.expanded, prover_setup.expanded); - assert_eq!(decoded.prepared, None); + assert_eq!(decoded, prover_setup.expanded); let derived_verifier = HachiVerifierSetup { - expanded: decoded.expanded.clone(), + expanded: decoded.clone(), }; assert_eq!(derived_verifier, verifier_setup); } diff --git a/src/protocol/commitment/config.rs b/src/protocol/commitment/config.rs index 3eeba2eb..b605ec5d 100644 --- a/src/protocol/commitment/config.rs +++ b/src/protocol/commitment/config.rs @@ -9,6 +9,109 @@ use crate::primitives::serialization::{ use crate::FieldCore; use std::io::{Read, Write}; +/// Parameters controlling the gadget decomposition depth (called δ in the paper). +/// +/// The gadget base is `b = 2^log_basis`. Each ring coefficient with centered +/// magnitude fitting in `log_commit_bound` bits is decomposed into +/// `ceil(log_commit_bound / log_basis)` balanced digits in `[-b/2, b/2)`. +/// +/// Smaller `log_commit_bound` (when polynomial coefficients are known to be +/// small) yields fewer decomposition levels, which proportionally shrinks the +/// witness vector, the commitment matrices, and the proving cost. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub struct DecompositionParams { + /// Base-2 logarithm of the gadget base (e.g., 3 for base-8 digits in [-4, 3]). + pub log_basis: u32, + + /// Bit-width of the largest coefficient that the *commitment* decomposition + /// must represent. Controls the commitment-side decomposition depth (δ in + /// the paper): `num_digits = ceil(log_commit_bound / log_basis)`. + /// + /// The centered representation maps each coefficient `c ∈ [0, q)` to the + /// signed value in `(-q/2, q/2]`. A value of `k` means the signed magnitude + /// fits in `k` bits, i.e., lies in `[-2^(k-1), 2^(k-1) - 1]`. + /// + /// Examples: + /// - Binary (0/1) polynomials: 1 + /// - Already range-checked digits in `[-b/2, b/2)`: `log_basis` (one digit) + /// - Arbitrary Fp128 elements: 128 + pub log_commit_bound: u32, + + /// Bit-width of the largest coefficient that the *opening* decomposition + /// must represent (ŵ = G⁻¹(w_folded)). + /// + /// During opening, `fold_blocks` computes inner products with arbitrary + /// field-element weights, so the result always has full-field-size + /// coefficients regardless of the original `log_commit_bound`. When `None`, + /// defaults to `log_commit_bound` (correct when `log_commit_bound` already + /// covers the full field, e.g. 128). Set to the field modulus bit-width + /// when `log_commit_bound` is smaller (e.g. for recursive w commitments + /// where entries are small but fold products are not). + pub log_open_bound: Option, +} + +/// Compute the gadget decomposition depth (δ in the paper) from a +/// coefficient bit-width bound. +/// +/// Returns `ceil(log_bound / log_basis)`, with an extra level when the +/// balanced-digit range would not cover the full bound. +/// +/// # Panics +/// +/// Panics if `log_basis` is 0 or >= 128. +pub fn compute_num_digits(log_bound: u32, log_basis: u32) -> usize { + assert!(log_basis > 0 && log_basis < 128, "invalid log_basis"); + if log_bound == 0 { + return 1; + } + let mut levels = (log_bound as usize).div_ceil(log_basis as usize); + + // When levels * log_basis > log_bound (i.e., not exactly aligned), the + // balanced digit range (b/2-1) * (b^levels - 1)/(b-1) always exceeds + // 2^(log_bound-1) for b >= 4 (log_basis >= 2). Only check when aligned. + let total_bits = (levels as u32).saturating_mul(log_basis); + if total_bits <= log_bound { + let b: u128 = 1u128 << log_basis; + let half_b_minus_1 = b / 2 - 1; + let b_minus_1 = b - 1; + let mut b_pow = 1u128; + for _ in 0..levels { + b_pow = b_pow.saturating_mul(b); + } + let max_positive = half_b_minus_1.saturating_mul(b_pow.saturating_sub(1) / b_minus_1); + let required = if log_bound > 128 { + u128::MAX / 2 + } else if log_bound == 0 { + 0 + } else { + (1u128 << (log_bound - 1)).saturating_sub(1) + }; + if max_positive < required { + levels += 1; + } + } + levels.max(1) +} + +/// Compute the decomposition depth for the folded witness `z_pre` +/// (τ in the paper). +/// +/// The folded witness satisfies `||z_pre||_inf <= β` where +/// `β = 2^r_vars * challenge_weight * 2^(log_basis - 1)`. +/// Returns enough gadget levels to represent values up to `β`. +pub fn compute_num_digits_fold(r_vars: usize, challenge_weight: usize, log_basis: u32) -> usize { + let shift = r_vars + (log_basis as usize) - 1; + if shift >= 127 || challenge_weight == 0 { + return compute_num_digits(128, log_basis); + } + let beta = (challenge_weight as u128).saturating_mul(1u128 << shift); + if beta == 0 { + return 1; + } + let log_beta = 128 - beta.leading_zeros(); + compute_num_digits(log_beta, log_basis) +} + /// Runtime commitment layout authority for ring-native commitments. #[derive(Debug, Clone, Copy, PartialEq, Eq)] pub struct HachiCommitmentLayout { @@ -20,31 +123,87 @@ pub struct HachiCommitmentLayout { pub num_blocks: usize, /// Number of ring elements per block (`2^m_vars`). pub block_len: usize, - /// Width of inner matrix `A`. + /// Width of inner matrix `A` (`block_len * num_digits_commit`). pub inner_width: usize, - /// Width of outer matrix `B`. + /// Width of outer matrix `B` (`n_a * num_digits_commit * num_blocks`). pub outer_width: usize, - /// Width of prover matrix `D` (`delta * 2^r_vars`). + /// Width of prover matrix `D` (`num_digits_open * num_blocks`). pub d_matrix_width: usize, + /// Number of gadget decomposition levels for commitment-time coefficients + /// (δ_commit in the paper). Controls how the original polynomial + /// coefficients are decomposed into balanced base-b digits for the Ajtai + /// commitment. + pub num_digits_commit: usize, + /// Number of gadget decomposition levels for opening-time folded + /// evaluations (δ_open in the paper). Folding inner-products with + /// arbitrary field-element weights produces full-field-size coefficients, + /// so this equals `num_digits_commit` when `log_commit_bound` covers + /// the full field, and is larger otherwise (e.g. recursive w witnesses). + pub num_digits_open: usize, + /// Number of gadget decomposition levels for the folded witness `z_pre` + /// (τ in the paper). Derived from the L∞ bound on `z_pre`. + pub num_digits_fold: usize, + /// Base-2 logarithm of gadget decomposition base. + pub log_basis: u32, } impl HachiCommitmentLayout { - /// Build a layout from `(m_vars, r_vars)` and static config constants. + /// Build a layout from `(m_vars, r_vars)`, config constants, and decomposition + /// parameters. + /// + /// `num_digits_fold` (τ) is auto-derived from the beta bound + /// (`r_vars`, `challenge_weight`, `log_basis`). /// /// # Errors /// /// Returns an error when powers or derived widths overflow. - pub fn new(m_vars: usize, r_vars: usize) -> Result { + pub fn new( + m_vars: usize, + r_vars: usize, + decomp: &DecompositionParams, + ) -> Result { + let depth_commit = compute_num_digits(decomp.log_commit_bound, decomp.log_basis); + let open_bound = decomp.log_open_bound.unwrap_or(decomp.log_commit_bound); + let depth_open = compute_num_digits(open_bound, decomp.log_basis); + let depth_fold = compute_num_digits_fold(r_vars, Cfg::CHALLENGE_WEIGHT, decomp.log_basis); + Self::new_with_decomp( + m_vars, + r_vars, + Cfg::N_A, + depth_commit, + depth_open, + depth_fold, + decomp.log_basis, + ) + } + + /// Build a layout from explicit decomposition parameters (no config trait needed). + /// + /// # Errors + /// + /// Returns an error when parameters are invalid or derived widths overflow. + pub fn new_with_decomp( + m_vars: usize, + r_vars: usize, + n_a: usize, + num_digits_commit: usize, + num_digits_open: usize, + num_digits_fold: usize, + log_basis: u32, + ) -> Result { + if log_basis == 0 || log_basis >= 128 { + return Err(HachiError::InvalidSetup("invalid log_basis".to_string())); + } let num_blocks = checked_pow2(r_vars)?; let block_len = checked_pow2(m_vars)?; let inner_width = block_len - .checked_mul(Cfg::DELTA) + .checked_mul(num_digits_commit) .ok_or_else(|| HachiError::InvalidSetup("inner width overflow".to_string()))?; - let outer_width = Cfg::N_A - .checked_mul(Cfg::DELTA) + let outer_width = n_a + .checked_mul(num_digits_commit) .and_then(|x| x.checked_mul(num_blocks)) .ok_or_else(|| HachiError::InvalidSetup("outer width overflow".to_string()))?; - let d_matrix_width = Cfg::DELTA + let d_matrix_width = num_digits_open .checked_mul(num_blocks) .ok_or_else(|| HachiError::InvalidSetup("D-matrix width overflow".to_string()))?; Ok(Self { @@ -55,6 +214,10 @@ impl HachiCommitmentLayout { inner_width, outer_width, d_matrix_width, + num_digits_commit, + num_digits_open, + num_digits_fold, + log_basis, }) } @@ -109,6 +272,13 @@ impl HachiSerialize for HachiCommitmentLayout { .serialize_with_mode(&mut writer, compress)?; self.d_matrix_width .serialize_with_mode(&mut writer, compress)?; + self.num_digits_commit + .serialize_with_mode(&mut writer, compress)?; + self.num_digits_open + .serialize_with_mode(&mut writer, compress)?; + self.num_digits_fold + .serialize_with_mode(&mut writer, compress)?; + (self.log_basis as usize).serialize_with_mode(&mut writer, compress)?; Ok(()) } @@ -120,6 +290,10 @@ impl HachiSerialize for HachiCommitmentLayout { + self.inner_width.serialized_size(compress) + self.outer_width.serialized_size(compress) + self.d_matrix_width.serialized_size(compress) + + self.num_digits_commit.serialized_size(compress) + + self.num_digits_open.serialized_size(compress) + + self.num_digits_fold.serialized_size(compress) + + (self.log_basis as usize).serialized_size(compress) } } @@ -137,6 +311,10 @@ impl HachiDeserialize for HachiCommitmentLayout { inner_width: usize::deserialize_with_mode(&mut reader, compress, validate)?, outer_width: usize::deserialize_with_mode(&mut reader, compress, validate)?, d_matrix_width: usize::deserialize_with_mode(&mut reader, compress, validate)?, + num_digits_commit: usize::deserialize_with_mode(&mut reader, compress, validate)?, + num_digits_open: usize::deserialize_with_mode(&mut reader, compress, validate)?, + num_digits_fold: usize::deserialize_with_mode(&mut reader, compress, validate)?, + log_basis: usize::deserialize_with_mode(&mut reader, compress, validate)? as u32, }; if matches!(validate, Validate::Yes) { out.check()?; @@ -146,6 +324,11 @@ impl HachiDeserialize for HachiCommitmentLayout { } /// Parameter bundle for the ring-native commitment core (§4.1–§4.2). +/// +/// Security parameters (`N_A`, `N_B`, `N_D`, `CHALLENGE_WEIGHT`) are +/// compile-time constants fixed for a given security level. Decomposition +/// parameters (gadget depths, `log_basis`) are runtime values derived from +/// [`DecompositionParams`] and live in [`HachiCommitmentLayout`]. pub trait CommitmentConfig: Clone + Send + Sync + 'static { /// Ring degree used by `CyclotomicRing`. const D: usize; @@ -155,15 +338,12 @@ pub trait CommitmentConfig: Clone + Send + Sync + 'static { const N_B: usize; /// Prover commitment matrix `D` row count (§4.2). const N_D: usize; - /// Base-2 logarithm of gadget decomposition base. - const LOG_BASIS: u32; - /// Decomposition levels `delta`. - const DELTA: usize; - /// Decomposition levels for the folded witness `z` (`τ` in the paper). - const TAU: usize; /// Hamming weight of sparse challenges (`ω` in the paper). const CHALLENGE_WEIGHT: usize; + /// Decomposition parameters (gadget base and coefficient bounds). + fn decomposition() -> DecompositionParams; + /// Choose the runtime commitment layout for `max_num_vars`. /// /// # Errors @@ -177,7 +357,7 @@ pub trait CommitmentConfig: Clone + Send + Sync + 'static { /// /// Returns an error on invalid parameters or arithmetic overflow. fn beta_bound(layout: HachiCommitmentLayout) -> Result { - beta_linf_fold_bound(layout.r_vars, Self::CHALLENGE_WEIGHT, Self::LOG_BASIS) + beta_linf_fold_bound(layout.r_vars, Self::CHALLENGE_WEIGHT, layout.log_basis) } } @@ -227,14 +407,6 @@ pub(super) fn validate_and_derive_layout( Cfg::D ))); } - if Cfg::LOG_BASIS == 0 || Cfg::LOG_BASIS >= 128 { - return Err(HachiError::InvalidSetup("invalid LOG_BASIS".to_string())); - } - if (Cfg::DELTA as u32).saturating_mul(Cfg::LOG_BASIS) > 128 { - return Err(HachiError::InvalidSetup( - "DELTA * LOG_BASIS must be <= 128".to_string(), - )); - } Cfg::commitment_layout(max_num_vars) } @@ -281,15 +453,18 @@ pub(super) fn ensure_block_layout( Ok(()) } -/// Ensure matrix shape matches expected dimensions. +/// Ensure matrix has at least the expected dimensions. +/// +/// Matrices may be wider than the main layout requires when widened to +/// accommodate the w-commitment's column counts. /// /// # Errors /// -/// Returns an error if row count or row width mismatch. -pub(super) fn ensure_matrix_shape( +/// Returns an error if row count mismatches or any row is too narrow. +pub(super) fn ensure_matrix_shape_ge( mat: &[Vec], expected_rows: usize, - expected_cols: usize, + min_cols: usize, name: &str, ) -> Result<(), HachiError> { if mat.len() != expected_rows { @@ -299,9 +474,9 @@ pub(super) fn ensure_matrix_shape( }); } for (row_idx, row) in mat.iter().enumerate() { - if row.len() != expected_cols { + if row.len() < min_cols { return Err(HachiError::InvalidSetup(format!( - "{name} row {row_idx} has width {}, expected {expected_cols}", + "{name} row {row_idx} has width {}, expected >= {min_cols}", row.len() ))); } @@ -321,13 +496,18 @@ impl CommitmentConfig for SmallTestCommitmentConfig { const N_A: usize = 8; const N_B: usize = 4; const N_D: usize = 4; - const LOG_BASIS: u32 = 4; - const DELTA: usize = 9; - const TAU: usize = 4; const CHALLENGE_WEIGHT: usize = 3; + fn decomposition() -> DecompositionParams { + DecompositionParams { + log_basis: 3, + log_commit_bound: 32, + log_open_bound: None, + } + } + fn commitment_layout(_max_num_vars: usize) -> Result { - HachiCommitmentLayout::new::(4, 2) + HachiCommitmentLayout::new::(4, 2, &Self::decomposition()) } } @@ -344,11 +524,16 @@ impl CommitmentConfig for DynamicSmallTestCommitmentConfig { const N_A: usize = 8; const N_B: usize = 4; const N_D: usize = 4; - const LOG_BASIS: u32 = 4; - const DELTA: usize = 9; - const TAU: usize = 4; const CHALLENGE_WEIGHT: usize = 3; + fn decomposition() -> DecompositionParams { + DecompositionParams { + log_basis: 3, + log_commit_bound: 32, + log_open_bound: None, + } + } + fn commitment_layout(max_num_vars: usize) -> Result { let alpha = Self::D.trailing_zeros() as usize; let reduced_vars = max_num_vars.checked_sub(alpha).ok_or_else(|| { @@ -359,9 +544,9 @@ impl CommitmentConfig for DynamicSmallTestCommitmentConfig { "max_num_vars must leave at least one outer variable".to_string(), )); } - let m_vars = reduced_vars.min(11); - let r_vars = reduced_vars - m_vars; - HachiCommitmentLayout::new::(m_vars, r_vars) + let r_vars = reduced_vars / 2; + let m_vars = reduced_vars - r_vars; + HachiCommitmentLayout::new::(m_vars, r_vars, &Self::decomposition()) } } @@ -377,24 +562,26 @@ impl CommitmentConfig for DynamicSmallTestCommitmentConfig { /// - Challenges use exactly `ω = CHALLENGE_WEIGHT` nonzeros in `{±1}`. /// - Therefore each `mul_by_sparse` output coefficient is a signed sum of `ω` /// shifted digits, hence bounded by `ω * (b/2)`. -/// - Summing over `2^R` blocks gives: +/// - Summing over `2^R` blocks (R = r_vars) gives: /// `||z||_inf <= 2^R * ω * (b/2)`. -/// -/// For this profile: `R=11`, `ω=19`, `b=16`, so -/// `β = 2^11 * 19 * 8 = 311_296`. #[derive(Clone, Copy, Debug, Default)] -pub struct ProductionFp128CommitmentConfig; +pub struct Fp128CommitmentConfig; -impl CommitmentConfig for ProductionFp128CommitmentConfig { +impl CommitmentConfig for Fp128CommitmentConfig { const D: usize = 512; const N_A: usize = 1; const N_B: usize = 1; const N_D: usize = 1; - const LOG_BASIS: u32 = 4; - const DELTA: usize = 32; - const TAU: usize = 5; const CHALLENGE_WEIGHT: usize = 19; + fn decomposition() -> DecompositionParams { + DecompositionParams { + log_basis: 3, + log_commit_bound: 128, + log_open_bound: None, + } + } + fn commitment_layout(max_num_vars: usize) -> Result { let alpha = Self::D.trailing_zeros() as usize; let reduced_vars = max_num_vars.checked_sub(alpha).ok_or_else(|| { @@ -405,8 +592,8 @@ impl CommitmentConfig for ProductionFp128CommitmentConfig { "max_num_vars must leave at least one outer variable".to_string(), )); } - let m_vars = reduced_vars.min(11); - let r_vars = reduced_vars - m_vars; - HachiCommitmentLayout::new::(m_vars, r_vars) + let r_vars = reduced_vars / 2; + let m_vars = reduced_vars - r_vars; + HachiCommitmentLayout::new::(m_vars, r_vars, &Self::decomposition()) } } diff --git a/src/protocol/commitment/mod.rs b/src/protocol/commitment/mod.rs index 2801d510..38039cdf 100644 --- a/src/protocol/commitment/mod.rs +++ b/src/protocol/commitment/mod.rs @@ -9,17 +9,15 @@ mod types; pub mod utils; pub use commit::{ - HachiCommitmentCore, HachiExpandedSetup, HachiPreparedSetup, HachiProverSetup, HachiSetupSeed, - HachiVerifierSetup, MegaPolyBlock, + HachiCommitmentCore, HachiExpandedSetup, HachiProverSetup, HachiSetupSeed, HachiVerifierSetup, }; pub use config::{ - CommitmentConfig, DynamicSmallTestCommitmentConfig, HachiCommitmentLayout, - ProductionFp128CommitmentConfig, SmallTestCommitmentConfig, + compute_num_digits, compute_num_digits_fold, CommitmentConfig, DecompositionParams, + DynamicSmallTestCommitmentConfig, Fp128CommitmentConfig, HachiCommitmentLayout, + SmallTestCommitmentConfig, }; pub use onehot::{map_onehot_to_sparse_blocks, SparseBlockEntry}; -pub use scheme::{ - CommitWitness, CommitmentScheme, RingCommitmentScheme, StreamingCommitmentScheme, -}; +pub use scheme::{CommitWitness, CommitmentScheme, RingCommitmentScheme}; pub use transcript_append::AppendToTranscript; pub use types::{ DummyProof, HachiCommitment, HachiOpeningClaim, HachiOpeningPoint, RingCommitment, diff --git a/src/protocol/commitment/onehot.rs b/src/protocol/commitment/onehot.rs index 18b8c1dc..4af23a26 100644 --- a/src/protocol/commitment/onehot.rs +++ b/src/protocol/commitment/onehot.rs @@ -6,12 +6,14 @@ use std::collections::BTreeMap; -use crate::algebra::ring::CyclotomicRing; +use crate::algebra::fields::wide::{HasWide, ReduceTo}; +use crate::algebra::ring::{CyclotomicRing, WideCyclotomicRing}; use crate::error::HachiError; -use crate::{CanonicalField, FieldCore}; +use crate::protocol::hachi_poly_ops::OneHotIndex; +use crate::{AdditiveGroup, CanonicalField, FieldCore}; /// Describes a nonzero ring element within one block of the commitment layout. -#[derive(Debug, Clone)] +#[derive(Debug, Clone, PartialEq)] pub struct SparseBlockEntry { /// Position within the block (0..2^M). pub pos_in_block: usize, @@ -35,9 +37,9 @@ pub struct SparseBlockEntry { /// Returns an error if K and D are not "nicely matched" (one must divide /// the other), if any index is out of range, or if the dimensions don't /// fill the commitment layout. -pub fn map_onehot_to_sparse_blocks( +pub fn map_onehot_to_sparse_blocks( onehot_k: usize, - indices: &[Option], + indices: &[Option], r: usize, m: usize, d: usize, @@ -72,10 +74,12 @@ pub fn map_onehot_to_sparse_blocks( }); } - // Accumulate nonzero coefficients per ring element index. let mut ring_elem_map: BTreeMap> = BTreeMap::new(); for (c, opt) in indices.iter().enumerate() { - let Some(&idx) = opt.as_ref() else { continue }; + let Some(&idx_raw) = opt.as_ref() else { + continue; + }; + let idx = idx_raw.as_usize(); if idx >= onehot_k { return Err(HachiError::InvalidInput(format!( "index {idx} out of range for chunk size K={onehot_k} at position {c}" @@ -108,51 +112,68 @@ pub fn map_onehot_to_sparse_blocks( /// Sparse inner Ajtai: compute `t = A * s` for a one-hot block. /// /// Instead of materializing the full decomposed vector `s` and doing a dense -/// matvec, we accumulate only the nonzero contributions: +/// matvec, we accumulate only the nonzero contributions using fused +/// shift-accumulate (no intermediate temporaries): /// /// ```text -/// t[a] = sum_{entry} A[a][entry.pos * delta].mul_by_monomial_sum(entry.nonzero_coeffs) +/// t[a] += A[a][entry.pos * num_digits] * (X^{k_1} + X^{k_2} + ...) /// ``` -/// -/// Also returns `s` (densely materialized) for the opening proof hint. +#[cfg(test)] #[allow(non_snake_case)] -pub(crate) fn inner_ajtai_onehot( +pub(crate) fn inner_ajtai_onehot_t_only( A: &[Vec>], sparse_entries: &[SparseBlockEntry], - block_len: usize, - delta: usize, -) -> (Vec>, Vec>) { + _block_len: usize, + num_digits: usize, +) -> Vec> { let n_a = A.len(); - let inner_width = block_len * delta; - // Build s: mostly zeros, with level-0 entries for nonzero ring elements. - let mut s = vec![CyclotomicRing::::zero(); inner_width]; + let mut t = vec![CyclotomicRing::::zero(); n_a]; for entry in sparse_entries { - let mut coeffs = [F::zero(); D]; - for &ci in &entry.nonzero_coeffs { - coeffs[ci] = F::one(); + let col = entry.pos_in_block * num_digits; + for a in 0..n_a { + A[a][col].mul_by_monomial_sum_into(&mut t[a], &entry.nonzero_coeffs); } - s[entry.pos_in_block * delta] = CyclotomicRing::from_coefficients(coeffs); } - // Compute t[a] = sum over nonzero entries of A[a][pos*delta] * f_j, - // where f_j is the monomial sum at that position. - let mut t = vec![CyclotomicRing::::zero(); n_a]; + t +} + +/// Wide-accumulator variant of [`inner_ajtai_onehot_t_only`]. +/// +/// Accumulates into `WideCyclotomicRing` (carry-free i32 additions), +/// then reduces once at the end. This avoids per-addition modular reduction. +#[allow(non_snake_case)] +pub(crate) fn inner_ajtai_onehot_wide( + A: &[Vec>], + sparse_entries: &[SparseBlockEntry], + _block_len: usize, + num_digits: usize, +) -> Vec> +where + F: FieldCore + CanonicalField + HasWide, + F::Wide: AdditiveGroup + From + ReduceTo, +{ + let n_a = A.len(); + let mut t_wide = vec![WideCyclotomicRing::::zero(); n_a]; + for entry in sparse_entries { - let col = entry.pos_in_block * delta; + let col = entry.pos_in_block * num_digits; for a in 0..n_a { - t[a] += A[a][col].mul_by_monomial_sum(&entry.nonzero_coeffs); + let a_wide = WideCyclotomicRing::from_ring(&A[a][col]); + a_wide.mul_by_monomial_sum_into(&mut t_wide[a], &entry.nonzero_coeffs); } } - (t, s) + t_wide.into_iter().map(|w| w.reduce()).collect() } #[cfg(test)] mod tests { use super::*; - use crate::test_utils::F; - use crate::FromSmallInt; + use crate::algebra::fields::{Fp64, Prime128M8M4M1M0}; + use rand::rngs::StdRng; + use rand::SeedableRng; #[test] fn map_onehot_k_gt_d() { @@ -160,7 +181,7 @@ mod tests { // R=1 (2 blocks), M=2 (4 per block) => 8 ring elements total let k = 16; let d = 4; - let indices = vec![Some(3), Some(10)]; + let indices: Vec> = vec![Some(3), Some(10)]; let blocks = map_onehot_to_sparse_blocks(k, &indices, 1, 2, d).unwrap(); assert_eq!(blocks.len(), 2); @@ -180,7 +201,7 @@ mod tests { // R=1 (2 blocks), M=1 (2 per block) let k = 4; let d = 4; - let indices = vec![Some(0), Some(2), Some(3), Some(1)]; + let indices: Vec> = vec![Some(0), Some(2), Some(3), Some(1)]; let blocks = map_onehot_to_sparse_blocks(k, &indices, 1, 1, d).unwrap(); assert_eq!(blocks.len(), 2); @@ -200,7 +221,7 @@ mod tests { // R=1 (2 blocks), M=1 (2 per block) let k = 4; let d = 8; - let indices = vec![ + let indices: Vec> = vec![ Some(0), Some(2), Some(3), @@ -229,49 +250,81 @@ mod tests { #[test] fn map_onehot_rejects_non_divisible() { - let result = map_onehot_to_sparse_blocks(3, &[Some(0), Some(1)], 0, 1, 4); + let result = map_onehot_to_sparse_blocks(3, &[Some(0usize), Some(1)], 0, 1, 4); assert!(result.is_err()); } #[test] - fn inner_ajtai_onehot_single_monomial() { - const D: usize = 4; - type R = CyclotomicRing; - - // A is 2x4 (N_A=2, inner_width = block_len * delta = 2 * 2 = 4) - let a: Vec> = vec![ - vec![ - R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 1) as u64))), - R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 10) as u64))), - R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 20) as u64))), - R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 30) as u64))), - ], - vec![ - R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 5) as u64))), - R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 15) as u64))), - R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 25) as u64))), - R::from_coefficients(std::array::from_fn(|i| F::from_u64((i + 35) as u64))), - ], - ]; + fn wide_matches_reference() { + type F = Fp64<4294967197>; + const D: usize = 64; + + let mut rng = StdRng::seed_from_u64(0xdead_beef); + let n_a = 3; + let block_len = 4; + let num_digits = 5; + let a_matrix: Vec>> = (0..n_a) + .map(|_| { + (0..block_len * num_digits) + .map(|_| CyclotomicRing::random(&mut rng)) + .collect() + }) + .collect(); - // One nonzero entry at pos=1, coefficient index 2 => monomial X^2 - let entries = vec![SparseBlockEntry { - pos_in_block: 1, - nonzero_coeffs: vec![2], - }]; + let entries = vec![ + SparseBlockEntry { + pos_in_block: 0, + nonzero_coeffs: vec![1, 7, 15], + }, + SparseBlockEntry { + pos_in_block: 2, + nonzero_coeffs: vec![0, 63], + }, + ]; - let (t, s) = inner_ajtai_onehot(&a, &entries, 2, 2); + let ref_result = inner_ajtai_onehot_t_only(&a_matrix, &entries, block_len, num_digits); + let wide_result = inner_ajtai_onehot_wide(&a_matrix, &entries, block_len, num_digits); - // t[row] should equal A[row][1*2] * X^2 = A[row][2].negacyclic_shift(2) - for row in 0..2 { - let expected = a[row][2].negacyclic_shift(2); - assert_eq!(t[row], expected); + assert_eq!(ref_result.len(), wide_result.len()); + for (r, w) in ref_result.iter().zip(wide_result.iter()) { + assert_eq!(r, w, "wide result must match reference"); } + } + + #[test] + fn wide_matches_reference_fp128() { + type F = Prime128M8M4M1M0; + const D: usize = 64; + + let mut rng = StdRng::seed_from_u64(0xcafe_1234); + let n_a = 2; + let block_len = 2; + let num_digits = 3; + let a_matrix: Vec>> = (0..n_a) + .map(|_| { + (0..block_len * num_digits) + .map(|_| CyclotomicRing::random(&mut rng)) + .collect() + }) + .collect(); + + let entries = vec![ + SparseBlockEntry { + pos_in_block: 0, + nonzero_coeffs: vec![0, 5, 32, 63], + }, + SparseBlockEntry { + pos_in_block: 1, + nonzero_coeffs: vec![10], + }, + ]; + + let ref_result = inner_ajtai_onehot_t_only(&a_matrix, &entries, block_len, num_digits); + let wide_result = inner_ajtai_onehot_wide(&a_matrix, &entries, block_len, num_digits); - // s should have a nonzero entry at position 1*2 = 2 - assert_eq!(s[2].coefficients()[2], F::one()); - assert!(s[0] == R::zero()); - assert!(s[1] == R::zero()); - assert!(s[3] == R::zero()); + assert_eq!(ref_result.len(), wide_result.len()); + for (r, w) in ref_result.iter().zip(wide_result.iter()) { + assert_eq!(r, w, "wide result must match reference (Fp128)"); + } } } diff --git a/src/protocol/commitment/scheme.rs b/src/protocol/commitment/scheme.rs index 256ce197..eeebb313 100644 --- a/src/protocol/commitment/scheme.rs +++ b/src/protocol/commitment/scheme.rs @@ -4,27 +4,41 @@ use super::config::{CommitmentConfig, HachiCommitmentLayout}; use super::transcript_append::AppendToTranscript; use crate::algebra::CyclotomicRing; use crate::error::HachiError; +use crate::protocol::hachi_poly_ops::{HachiPolyOps, OneHotIndex}; +use crate::protocol::opening_point::BasisMode; use crate::protocol::transcript::Transcript; -use crate::{CanonicalField, FieldCore, Polynomial}; - -/// Output type for batched commitments. -pub(crate) type BatchCommitOutput = Result, HachiError>; +use crate::{CanonicalField, FieldCore}; /// Witness data produced alongside a ring-native commitment. /// /// Contains the commitment itself plus `t_hat` (basis-decomposed inner Ajtai /// output) from the two-layer Ajtai construction (§4.1). The decomposed input -/// vectors `s` are NOT stored; they are recomputed from `ring_coeffs` during -/// proving to avoid multi-GB memory usage at production parameters. +/// vectors `s` are NOT stored; they are recomputed from the polynomial during +/// proving via `HachiPolyOps`. pub struct CommitWitness { /// The ring commitment (outer Ajtai output `u = B · t̂`). pub commitment: C, - /// Per-block basis-decomposed inner Ajtai output vectors. - pub t_hat: Vec>>, + /// Per-block basis-decomposed inner Ajtai output vectors as i8 digit planes. + pub t_hat: Vec>, + _marker: std::marker::PhantomData, +} + +impl CommitWitness { + /// Construct a new commit witness. + pub fn new(commitment: C, t_hat: Vec>) -> Self { + Self { + commitment, + t_hat, + _marker: std::marker::PhantomData, + } + } } -/// Generic commitment-scheme interface used by Hachi protocol code. -pub trait CommitmentScheme: Clone + Send + Sync + 'static +/// Commitment-scheme interface used by Hachi protocol code. +/// +/// Generic over field `F` and cyclotomic ring degree `D`. +/// Polynomials are provided as `impl HachiPolyOps`. +pub trait CommitmentScheme: Clone + Send + Sync + 'static where F: FieldCore + CanonicalField, { @@ -36,8 +50,8 @@ where type Commitment: Clone + PartialEq + Send + Sync + AppendToTranscript; /// Evaluation/opening proof object. type Proof: Clone + Send + Sync; - /// Optional prover-side hint produced at commitment time. - type OpeningProofHint: Clone + Send + Sync; + /// Prover-side hint produced at commitment time. + type CommitHint: Clone + Send + Sync; /// Build prover setup for maximum polynomial dimension. /// @@ -49,47 +63,55 @@ where /// Derive verifier setup from prover setup. fn setup_verifier(setup: &Self::ProverSetup) -> Self::VerifierSetup; - /// Commit to one polynomial. + /// Commit to one polynomial with a caller-specified layout. + /// + /// The layout's matrix dimensions must not exceed the setup's max dimensions. + /// Callers control `num_digits_commit` via the layout to reduce decomposition + /// depth for polynomials with bounded coefficients (e.g. delta=1 for {0,1}). /// /// # Errors /// /// Returns an error when setup/parameter constraints are not satisfied. - fn commit>( + fn commit>( poly: &P, setup: &Self::ProverSetup, - ) -> Result<(Self::Commitment, Self::OpeningProofHint), HachiError>; + layout: &HachiCommitmentLayout, + ) -> Result<(Self::Commitment, Self::CommitHint), HachiError>; - /// Commit to many polynomials. + /// Produce an opening proof at `opening_point` with a caller-specified layout. /// - /// # Errors + /// The layout must match the one used during commitment. Recursive w-opening + /// levels derive their own layouts internally via `WCommitmentConfig`. /// - /// Returns an error if any per-polynomial commitment fails. - fn batch_commit>( - polys: &[P], - setup: &Self::ProverSetup, - ) -> BatchCommitOutput { - polys.iter().map(|p| Self::commit(p, setup)).collect() - } - - /// Produce an opening proof at `opening_point`. + /// `basis` selects the polynomial representation (see [`BasisMode`]). /// /// # Errors /// /// Returns an error if the opening point is invalid or proof generation fails. - fn prove, P: Polynomial>( + #[allow(clippy::too_many_arguments)] + fn prove, P: HachiPolyOps>( setup: &Self::ProverSetup, poly: &P, opening_point: &[F], - hint: Option, + hint: Self::CommitHint, transcript: &mut T, commitment: &Self::Commitment, + basis: BasisMode, + layout: &HachiCommitmentLayout, ) -> Result; - /// Verify an opening proof. + /// Verify an opening proof with a caller-specified layout. + /// + /// The layout must be reconstructed deterministically by the verifier — + /// never deserialized from the proof. It must match the layout used by the + /// prover for commitment and proving. + /// + /// `basis` must match the mode used by the prover (see [`BasisMode`]). /// /// # Errors /// /// Returns an error when verification fails. + #[allow(clippy::too_many_arguments)] fn verify>( proof: &Self::Proof, setup: &Self::VerifierSetup, @@ -97,44 +119,14 @@ where opening_point: &[F], opening: &F, commitment: &Self::Commitment, + basis: BasisMode, + layout: &HachiCommitmentLayout, ) -> Result<(), HachiError>; - /// Homomorphic commitment combination. - fn combine_commitments(commitments: &[Self::Commitment], coeffs: &[F]) -> Self::Commitment; - - /// Homomorphic hint combination. - fn combine_hints(hints: Vec, coeffs: &[F]) -> Self::OpeningProofHint; - /// Protocol identifier. fn protocol_name() -> &'static [u8]; } -/// Streaming extension for chunked commitment workflows. -pub trait StreamingCommitmentScheme: CommitmentScheme -where - F: FieldCore + CanonicalField, -{ - /// Intermediate chunk state. - type ChunkState: Clone + Send + Sync + PartialEq + std::fmt::Debug; - - /// Process one chunk of field elements. - fn process_chunk(setup: &Self::ProverSetup, chunk: &[F]) -> Self::ChunkState; - - /// Process one chunk of one-hot values. - fn process_chunk_onehot( - setup: &Self::ProverSetup, - onehot_k: usize, - chunk: &[Option], - ) -> Self::ChunkState; - - /// Aggregate chunk states into one commitment + hint. - fn aggregate_chunks( - setup: &Self::ProverSetup, - onehot_k: Option, - chunks: &[Self::ChunkState], - ) -> (Self::Commitment, Self::OpeningProofHint); -} - /// Ring-native commitment interface for §4.1 implementation work. pub trait RingCommitmentScheme: Clone + Send + Sync + 'static where @@ -164,9 +156,6 @@ where /// Commit to ring blocks arranged as `2^R` vectors of length `2^M`. /// - /// Returns `(commitment, s, t_hat)` where `s` and `t_hat` are the - /// decomposed witness vectors from §4.1. - /// /// # Errors /// /// Returns an error if block layout mismatches config or commitment fails. @@ -177,12 +166,6 @@ where /// Commit to a flat coefficient table `(f_i)_{i∈{0,1}^ℓ}` in ring form. /// - /// The input uses sequential block layout: ring elements - /// `[0, block_len)` form block 0, `[block_len, 2*block_len)` form - /// block 1, and so on. This matches the sequential variable ordering - /// where M variables (position in block) are lower-order and R variables - /// (block selection) are higher-order. - /// /// # Errors /// /// Returns an error if `f_coeffs.len()` does not match the configured block @@ -214,25 +197,13 @@ where /// Commit to a regular one-hot witness. /// - /// The witness represents `T` chunks of `onehot_k` field elements, each - /// chunk containing exactly one 1 and all other entries 0. `indices[c]` - /// gives the hot position in chunk `c` (must be in `[0, onehot_k)`). - /// - /// Requires `D` and `onehot_k` to be "nicely matched": one must divide - /// the other. - /// - /// The default implementation materializes the full one-hot field vector, - /// packs it into ring elements via coefficient embedding, and delegates - /// to `commit_coeffs`. Implementations may override this with a - /// sparse-aware path that avoids all inner ring multiplications. - /// /// # Errors /// /// Returns an error if dimensions are inconsistent or any index is out /// of range. - fn commit_onehot( + fn commit_onehot( onehot_k: usize, - indices: &[Option], + indices: &[Option], setup: &Self::ProverSetup, ) -> Result, HachiError> { let num_chunks = indices.len(); @@ -245,11 +216,13 @@ where ))); } - // Materialize the full one-hot vector as ring elements. let total_ring_elems = total_field_elems / D; let mut ring_coeffs = vec![CyclotomicRing::::zero(); total_ring_elems]; for (c, opt) in indices.iter().enumerate() { - let Some(&idx) = opt.as_ref() else { continue }; + let Some(&idx_raw) = opt.as_ref() else { + continue; + }; + let idx = idx_raw.as_usize(); if idx >= onehot_k { return Err(HachiError::InvalidInput(format!( "index {idx} out of range for chunk size K={onehot_k} at position {c}" diff --git a/src/protocol/commitment/utils/crt_ntt.rs b/src/protocol/commitment/utils/crt_ntt.rs index 6c91e254..c729969b 100644 --- a/src/protocol/commitment/utils/crt_ntt.rs +++ b/src/protocol/commitment/utils/crt_ntt.rs @@ -15,6 +15,7 @@ use crate::{CanonicalField, FieldCore}; use super::norm::detect_field_modulus; /// Supported protocol CRT+NTT parameter families. +#[derive(Clone)] pub(crate) enum ProtocolCrtNttParams { Q32(CrtNttParamSet), Q64(CrtNttParamSet), @@ -65,26 +66,30 @@ pub(crate) fn select_crt_ntt_params( ))) } -/// Pre-converted CRT+NTT matrices, keyed by parameter family. +/// Pre-converted CRT+NTT cache for a single matrix, keyed by parameter family. /// -/// Avoids repeated coefficient-to-NTT conversion on every dense mat-vec. +/// Stores both negacyclic (for mat-vec) and cyclic (for quotient) representations +/// to avoid repeated coefficient-to-NTT conversion. #[derive(Debug, Clone, PartialEq, Eq)] -#[allow(non_snake_case)] -pub(crate) enum NttMatrixCache { +#[allow(missing_docs)] +pub enum NttSlotCache { + /// 32-bit CRT primes. Q32 { - A: Vec>>, - B: Vec>>, - D: Vec>>, + neg: Vec>>, + cyc: Vec>>, + params: CrtNttParamSet, }, + /// 64-bit CRT primes. Q64 { - A: Vec>>, - B: Vec>>, - D: Vec>>, + neg: Vec>>, + cyc: Vec>>, + params: CrtNttParamSet, }, + /// 128-bit CRT primes. Q128 { - A: Vec>>, - B: Vec>>, - D: Vec>>, + neg: Vec>>, + cyc: Vec>>, + params: CrtNttParamSet, }, } @@ -105,29 +110,74 @@ where .collect() } -#[allow(non_snake_case)] -pub(crate) fn build_ntt_cache( - a: &[Vec>], - b: &[Vec>], - d: &[Vec>], -) -> Result, HachiError> { +fn convert_mat_cyclic( + mat: &[Vec>], + params: &CrtNttParamSet, +) -> Vec>> +where + F: FieldCore + CanonicalField, + W: PrimeWidth, +{ + cfg_iter!(mat) + .map(|row| { + row.iter() + .map(|a| CyclotomicCrtNtt::from_ring_cyclic(a, params)) + .collect() + }) + .collect() +} + +/// Build an NTT slot cache for a single matrix. +/// +/// # Errors +/// +/// Returns an error if no CRT+NTT parameter set matches the field modulus and ring degree. +#[tracing::instrument(skip_all, name = "build_ntt_slot")] +pub fn build_ntt_slot( + mat: &[Vec>], +) -> Result, HachiError> { let params = select_crt_ntt_params::()?; - let cache = match ¶ms { - ProtocolCrtNttParams::Q32(p) => NttMatrixCache::Q32 { - A: convert_mat(a, p), - B: convert_mat(b, p), - D: convert_mat(d, p), + Ok(build_ntt_slot_from_params(mat, params)) +} + +fn build_ntt_slot_from_params( + mat: &[Vec>], + params: ProtocolCrtNttParams, +) -> NttSlotCache { + match params { + ProtocolCrtNttParams::Q32(p) => NttSlotCache::Q32 { + neg: convert_mat(mat, &p), + cyc: convert_mat_cyclic(mat, &p), + params: p, }, - ProtocolCrtNttParams::Q64(p) => NttMatrixCache::Q64 { - A: convert_mat(a, p), - B: convert_mat(b, p), - D: convert_mat(d, p), + ProtocolCrtNttParams::Q64(p) => NttSlotCache::Q64 { + neg: convert_mat(mat, &p), + cyc: convert_mat_cyclic(mat, &p), + params: p, }, - ProtocolCrtNttParams::Q128(p) => NttMatrixCache::Q128 { - A: convert_mat(a, p), - B: convert_mat(b, p), - D: convert_mat(d, p), + ProtocolCrtNttParams::Q128(p) => NttSlotCache::Q128 { + neg: convert_mat(mat, &p), + cyc: convert_mat_cyclic(mat, &p), + params: p, }, - }; - Ok(cache) + } +} + +/// Build NTT slot caches for three matrices, computing CRT+NTT parameters once. +/// +/// # Errors +/// +/// Returns an error if no CRT+NTT parameter set matches the field modulus and ring degree. +#[tracing::instrument(skip_all, name = "build_ntt_slots")] +#[allow(non_snake_case)] +pub fn build_ntt_slots( + A: &[Vec>], + B: &[Vec>], + D_mat: &[Vec>], +) -> Result<(NttSlotCache, NttSlotCache, NttSlotCache), HachiError> { + let params = select_crt_ntt_params::()?; + let slot_a = build_ntt_slot_from_params(A, params.clone()); + let slot_b = build_ntt_slot_from_params(B, params.clone()); + let slot_d = build_ntt_slot_from_params(D_mat, params); + Ok((slot_a, slot_b, slot_d)) } diff --git a/src/protocol/commitment/utils/linear.rs b/src/protocol/commitment/utils/linear.rs index 4a8e007d..71dbd268 100644 --- a/src/protocol/commitment/utils/linear.rs +++ b/src/protocol/commitment/utils/linear.rs @@ -1,14 +1,21 @@ //! Linear algebra helpers for ring commitment. +#[cfg(target_arch = "aarch64")] +use crate::algebra::ntt::neon; use crate::algebra::ntt::{MontCoeff, PrimeWidth}; -use crate::algebra::{CrtNttParamSet, CyclotomicCrtNtt, CyclotomicRing}; -use crate::cfg_iter; +use crate::algebra::{CrtNttParamSet, CyclotomicCrtNtt, CyclotomicRing, DigitMontLut}; +#[cfg(test)] use crate::error::HachiError; #[cfg(feature = "parallel")] use crate::parallel::*; +use crate::{cfg_fold_reduce, cfg_into_iter, cfg_iter}; use crate::{CanonicalField, FieldCore}; +use std::array::from_fn; +use std::mem::size_of; -use super::crt_ntt::{select_crt_ntt_params, NttMatrixCache, ProtocolCrtNttParams}; +use super::crt_ntt::NttSlotCache; +#[cfg(test)] +use super::crt_ntt::{select_crt_ntt_params, ProtocolCrtNttParams}; #[cfg(test)] pub(crate) fn mat_vec_mul_unchecked( @@ -34,6 +41,35 @@ fn accumulate_pointwise_product_into, params: &CrtNttParamSet, ) { + #[cfg(target_arch = "aarch64")] + if neon::use_neon_ntt() { + for k in 0..K { + let prime = params.primes[k]; + unsafe { + if size_of::() == size_of::() { + neon::pointwise_mul_acc_i32( + acc.limbs[k].as_mut_ptr() as *mut i32, + lhs.limbs[k].as_ptr() as *const i32, + rhs.limbs[k].as_ptr() as *const i32, + D, + prime.p.to_i64() as i32, + prime.pinv.to_i64() as i32, + ); + } else { + neon::pointwise_mul_acc_i16( + acc.limbs[k].as_mut_ptr() as *mut i16, + lhs.limbs[k].as_ptr() as *const i16, + rhs.limbs[k].as_ptr() as *const i16, + D, + prime.p.to_i64() as i16, + prime.pinv.to_i64() as i16, + ); + } + } + } + return; + } + for k in 0..K { let prime = params.primes[k]; let acc_limb = &mut acc.limbs[k]; @@ -161,104 +197,544 @@ pub(crate) fn mat_vec_mul_crt_ntt_many( + ntt_row: &[CyclotomicCrtNtt], + cyc_row: &[CyclotomicCrtNtt], + vec_neg: &[CyclotomicCrtNtt], + vec_cyc: &[CyclotomicCrtNtt], + params: &CrtNttParamSet, +) -> CyclotomicRing +where F: FieldCore + CanonicalField, W: PrimeWidth, - const K: usize, - const D: usize, ->( - ntt_mat: &[Vec>], - vec: &[CyclotomicRing], - params: &CrtNttParamSet, -) -> Vec> { - let ntt_vec: Vec> = vec - .iter() - .map(|v| CyclotomicCrtNtt::from_ring_with_params(v, params)) - .collect(); +{ + let n = ntt_row.len().min(vec_neg.len()); - cfg_iter!(ntt_mat) - .map(|row_ntt| { - debug_assert!(row_ntt.len() >= ntt_vec.len()); - let mut acc = CyclotomicCrtNtt::::zero(); - for (a_ntt, x_ntt) in row_ntt.iter().zip(ntt_vec.iter()) { - accumulate_pointwise_product_into(&mut acc, a_ntt, x_ntt, params); - } - acc.to_ring_with_params(params) - }) - .collect() + let mut acc_neg = CyclotomicCrtNtt::::zero(); + let mut acc_cyc = CyclotomicCrtNtt::::zero(); + + for j in 0..n { + accumulate_pointwise_product_into(&mut acc_neg, &ntt_row[j], &vec_neg[j], params); + accumulate_pointwise_product_into(&mut acc_cyc, &cyc_row[j], &vec_cyc[j], params); + } + + let neg_ring: CyclotomicRing = acc_neg.to_ring_with_params(params); + let cyc_ring: CyclotomicRing = acc_cyc.to_ring_cyclic(params); + + let neg_coeffs = neg_ring.coefficients(); + let cyc_coeffs = cyc_ring.coefficients(); + let quotient: [F; D] = from_fn(|k| (cyc_coeffs[k] - neg_coeffs[k]) * F::TWO_INV); + CyclotomicRing::from_coefficients(quotient) } -macro_rules! dispatch_cached { - ($cache:expr, $which:expr, $params:expr, $func:ident $(, $arg:expr)*) => {{ - #[allow(non_snake_case)] - match ($cache, $params) { - (NttMatrixCache::Q32 { A, B, D: Dm }, ProtocolCrtNttParams::Q32(p)) => { - let m = match $which { MatrixSlot::A => A, MatrixSlot::B => B, MatrixSlot::D => Dm }; - $func(m, $($arg,)* p) +macro_rules! dispatch_slot_quotient { + ($slot:expr, $vec:expr, $convert_neg:ident, $convert_cyc:ident, $quotient_fn:ident) => {{ + match $slot { + NttSlotCache::Q32 { + neg, + cyc, + params: p, + } => { + let v = $vec; + let n = neg.first().map_or(0, |r| r.len().min(v.len())); + let v_neg: Vec<_> = cfg_iter!(v[..n]) + .map(|x| CyclotomicCrtNtt::$convert_neg(x, p)) + .collect(); + let v_cyc: Vec<_> = cfg_iter!(v[..n]) + .map(|x| CyclotomicCrtNtt::$convert_cyc(x, p)) + .collect(); + cfg_into_iter!(0..neg.len()) + .map(|i| $quotient_fn(&neg[i], &cyc[i], &v_neg, &v_cyc, p)) + .collect() } - (NttMatrixCache::Q64 { A, B, D: Dm }, ProtocolCrtNttParams::Q64(p)) => { - let m = match $which { MatrixSlot::A => A, MatrixSlot::B => B, MatrixSlot::D => Dm }; - $func(m, $($arg,)* p) + NttSlotCache::Q64 { + neg, + cyc, + params: p, + } => { + let v = $vec; + let n = neg.first().map_or(0, |r| r.len().min(v.len())); + let v_neg: Vec<_> = cfg_iter!(v[..n]) + .map(|x| CyclotomicCrtNtt::$convert_neg(x, p)) + .collect(); + let v_cyc: Vec<_> = cfg_iter!(v[..n]) + .map(|x| CyclotomicCrtNtt::$convert_cyc(x, p)) + .collect(); + cfg_into_iter!(0..neg.len()) + .map(|i| $quotient_fn(&neg[i], &cyc[i], &v_neg, &v_cyc, p)) + .collect() } - (NttMatrixCache::Q128 { A, B, D: Dm }, ProtocolCrtNttParams::Q128(p)) => { - let m = match $which { MatrixSlot::A => A, MatrixSlot::B => B, MatrixSlot::D => Dm }; - $func(m, $($arg,)* p) + NttSlotCache::Q128 { + neg, + cyc, + params: p, + } => { + let v = $vec; + let n = neg.first().map_or(0, |r| r.len().min(v.len())); + let v_neg: Vec<_> = cfg_iter!(v[..n]) + .map(|x| CyclotomicCrtNtt::$convert_neg(x, p)) + .collect(); + let v_cyc: Vec<_> = cfg_iter!(v[..n]) + .map(|x| CyclotomicCrtNtt::$convert_cyc(x, p)) + .collect(); + cfg_into_iter!(0..neg.len()) + .map(|i| $quotient_fn(&neg[i], &cyc[i], &v_neg, &v_cyc, p)) + .collect() } - _ => return Err(HachiError::InvalidSetup("NTT cache / param family mismatch".into())), } }}; } -/// Dense mat-vec using a pre-converted NTT matrix from the cache. -pub(crate) fn mat_vec_mul_ntt_cached( - cache: &NttMatrixCache, - which: MatrixSlot, +/// Compute unreduced quotients for matrix rows against a witness vector. +/// +/// For each row: `r_i = high_part(sum_j row_ij * vec_j) = (cyc - neg) / 2`. +/// Vec NTT conversions and matrix cyclic NTT are precomputed once (not per-row). +pub fn unreduced_quotient_rows_ntt_cached( + slot: &NttSlotCache, vec: &[CyclotomicRing], -) -> Result>, HachiError> { - let params = select_crt_ntt_params::()?; - let out = dispatch_cached!( - cache, - which, - ¶ms, - mat_vec_mul_precomputed_with_params, - vec - ); - Ok(out) +) -> Vec> { + dispatch_slot_quotient!( + slot, + vec, + from_ring_with_params, + from_ring_cyclic, + unreduced_quotient_ntt + ) } -/// Basis-decompose a block of ring elements into `block.len() * delta` gadget components. +macro_rules! dispatch_slot { + ($slot:expr, $func:ident $(, $arg:expr)*) => {{ + match $slot { + NttSlotCache::Q32 { neg, params: p, .. } => $func(neg, $($arg,)* p), + NttSlotCache::Q64 { neg, params: p, .. } => $func(neg, $($arg,)* p), + NttSlotCache::Q128 { neg, params: p, .. } => $func(neg, $($arg,)* p), + } + }}; +} + +/// Flatten a nested `Vec>` into a contiguous `Vec<[i8; D]>` using +/// bulk memcpy per block, avoiding element-by-element iteration. +pub fn flatten_i8_blocks(blocks: &[Vec<[i8; D]>]) -> Vec<[i8; D]> { + let total: usize = blocks.iter().map(|b| b.len()).sum(); + let mut flat = Vec::with_capacity(total); + for block in blocks { + flat.extend_from_slice(block); + } + flat +} + +/// Basis-decompose a block of ring elements into `block.len() * num_digits` gadget components. pub fn decompose_block( block: &[CyclotomicRing], - delta: usize, + num_digits: usize, log_basis: u32, ) -> Vec> { - let mut out = Vec::with_capacity(block.len() * delta); - for coeff_vec in block { - out.extend(coeff_vec.balanced_decompose_pow2(delta, log_basis)); + let mut out = vec![CyclotomicRing::::zero(); block.len() * num_digits]; + for (i, coeff_vec) in block.iter().enumerate() { + coeff_vec.balanced_decompose_pow2_into( + &mut out[i * num_digits..(i + 1) * num_digits], + log_basis, + ); } out } -pub(crate) fn decompose_rows( +/// Decompose each ring element in `rows` into `num_digits` gadget components. +pub fn decompose_rows( rows: &[CyclotomicRing], - delta: usize, + num_digits: usize, log_basis: u32, ) -> Vec> { - let mut out = Vec::with_capacity(rows.len() * delta); + let mut out = vec![CyclotomicRing::::zero(); rows.len() * num_digits]; + for (i, row) in rows.iter().enumerate() { + row.balanced_decompose_pow2_into(&mut out[i * num_digits..(i + 1) * num_digits], log_basis); + } + out +} + +/// Like [`decompose_block`] but outputs `[i8; D]` digit planes instead of ring elements. +pub fn decompose_block_i8( + block: &[CyclotomicRing], + num_digits: usize, + log_basis: u32, +) -> Vec<[i8; D]> { + let mut out = Vec::with_capacity(block.len() * num_digits); + for coeff_vec in block { + out.extend(coeff_vec.balanced_decompose_pow2_i8(num_digits, log_basis)); + } + out +} + +/// Like [`decompose_rows`] but outputs `[i8; D]` digit planes instead of ring elements. +pub fn decompose_rows_i8( + rows: &[CyclotomicRing], + num_digits: usize, + log_basis: u32, +) -> Vec<[i8; D]> { + let mut out = Vec::with_capacity(rows.len() * num_digits); for row in rows { - out.extend(row.balanced_decompose_pow2(delta, log_basis)); + out.extend(row.balanced_decompose_pow2_i8(num_digits, log_basis)); } out } +#[inline] +fn is_zero_plane(plane: &[i8; D]) -> bool { + plane.iter().all(|&d| d == 0) +} + +#[cfg(target_arch = "aarch64")] +const TARGET_L2_CACHE_BYTES: usize = 4 * 1024 * 1024; +#[cfg(target_arch = "x86_64")] +const TARGET_L2_CACHE_BYTES: usize = 1024 * 1024; +#[cfg(not(any(target_arch = "aarch64", target_arch = "x86_64")))] +const TARGET_L2_CACHE_BYTES: usize = 1024 * 1024; + +#[inline] +#[allow(dead_code)] +fn add_ntt_into( + acc: &mut CyclotomicCrtNtt, + other: &CyclotomicCrtNtt, + params: &CrtNttParamSet, +) { + #[cfg(target_arch = "aarch64")] + if neon::use_neon_ntt() { + for k in 0..K { + let prime = params.primes[k]; + unsafe { + if size_of::() == size_of::() { + neon::add_reduce_i32( + acc.limbs[k].as_mut_ptr() as *mut i32, + other.limbs[k].as_ptr() as *const i32, + D, + prime.p.to_i64() as i32, + ); + } else { + neon::add_reduce_i16( + acc.limbs[k].as_mut_ptr() as *mut i16, + other.limbs[k].as_ptr() as *const i16, + D, + prime.p.to_i64() as i16, + ); + } + } + } + return; + } + + for k in 0..K { + let prime = params.primes[k]; + for d in 0..D { + let sum = + MontCoeff::from_raw(acc.limbs[k][d].raw().wrapping_add(other.limbs[k][d].raw())); + acc.limbs[k][d] = prime.reduce_range(sum); + } + } +} + +/// Column-tiled A*x across multiple blocks simultaneously. +/// +/// Each rayon thread owns one column tile of `ntt_mat` (sized to fit in L2 +/// cache) and iterates over all blocks, accumulating partial NTT results. +/// The matrix is loaded from DRAM exactly once. A final reduction sums +/// partial accumulators across tiles for each block. +/// +/// Accepts raw ring-coefficient slices per block. Decomposes to i8 digits +/// on-the-fly per tile to avoid materializing all digits at once. +/// Tile width is auto-computed from ring parameters and target L2 cache size. +#[tracing::instrument(skip_all, name = "mat_vec_mul_ntt_i8")] +pub fn mat_vec_mul_ntt_i8( + slot: &NttSlotCache, + blocks: &[&[CyclotomicRing]], + num_digits: usize, + log_basis: u32, +) -> Vec>> { + dispatch_slot!( + slot, + mat_vec_mul_i8_with_params, + blocks, + num_digits, + log_basis + ) +} + +fn mat_vec_mul_i8_with_params< + F: FieldCore + CanonicalField, + W: PrimeWidth, + const K: usize, + const D: usize, +>( + ntt_mat: &[Vec>], + blocks: &[&[CyclotomicRing]], + num_digits: usize, + log_basis: u32, + params: &CrtNttParamSet, +) -> Vec>> { + let num_blocks = blocks.len(); + if num_blocks == 0 { + return vec![]; + } + let n_a = ntt_mat.len(); + let inner_width = ntt_mat.first().map_or(0, |row| row.len()); + if inner_width == 0 || n_a == 0 { + return vec![vec![CyclotomicRing::::zero(); n_a]; num_blocks]; + } + + let lut = DigitMontLut::new(params); + let tw = (TARGET_L2_CACHE_BYTES / (K * D * size_of::())).max(1); + let num_tiles = inner_width.div_ceil(tw); + + let final_accs: Vec>> = cfg_fold_reduce!( + 0..num_tiles, + || vec![vec![CyclotomicCrtNtt::::zero(); n_a]; num_blocks], + |mut accs: Vec>>, tile_idx| { + let tile_start = tile_idx * tw; + let tile_end = (tile_start + tw).min(inner_width); + let ring_start = tile_start / num_digits; + let ring_end = ((tile_end - 1) / num_digits) + 1; + let digit_offset = tile_start - ring_start * num_digits; + let tile_len = tile_end - tile_start; + + for block_idx in 0..num_blocks { + let block = blocks[block_idx]; + if ring_start >= block.len() { + continue; + } + let block_ring_end = ring_end.min(block.len()); + let partial_coeffs = &block[ring_start..block_ring_end]; + let all_digits = decompose_block_i8(partial_coeffs, num_digits, log_basis); + let available = all_digits.len().saturating_sub(digit_offset); + let n = tile_len.min(available); + + for (j, digit) in all_digits[digit_offset..digit_offset + n] + .iter() + .enumerate() + { + if is_zero_plane(digit) { + continue; + } + let ntt_d = CyclotomicCrtNtt::from_i8_with_lut(digit, params, &lut); + for (acc, mat_row) in accs[block_idx].iter_mut().zip(ntt_mat.iter()) { + accumulate_pointwise_product_into( + acc, + &mat_row[tile_start + j], + &ntt_d, + params, + ); + } + } + } + accs + }, + |mut a: Vec>>, b| { + for block_idx in 0..num_blocks { + for row in 0..n_a { + add_ntt_into(&mut a[block_idx][row], &b[block_idx][row], params); + } + } + a + } + ); + + cfg_into_iter!(final_accs) + .map(|row_accs| { + row_accs + .into_iter() + .map(|acc| acc.to_ring_with_params(params)) + .collect() + }) + .collect() +} + +/// Column-tiled mat-vec for a single pre-decomposed i8 digit vector. +/// +/// Same tiling strategy as [`mat_vec_mul_ntt_i8`] but for a single +/// input vector of i8 digit planes (already decomposed). Tiles the matrix +/// columns to keep each tile in L2, eliminating the full `ntt_vec` +/// materialization of the non-tiled path. +/// Tile width is auto-computed from ring parameters and target L2 cache size. +#[tracing::instrument(skip_all, name = "mat_vec_mul_ntt_single_i8")] +pub fn mat_vec_mul_ntt_single_i8( + slot: &NttSlotCache, + vec: &[[i8; D]], +) -> Vec> { + dispatch_slot!(slot, mat_vec_mul_single_i8_with_params, vec) +} + +fn mat_vec_mul_single_i8_with_params< + F: FieldCore + CanonicalField, + W: PrimeWidth, + const K: usize, + const D: usize, +>( + ntt_mat: &[Vec>], + vec: &[[i8; D]], + params: &CrtNttParamSet, +) -> Vec> { + let n_a = ntt_mat.len(); + let inner_width = ntt_mat.first().map_or(0, |row| row.len()); + if inner_width == 0 || n_a == 0 { + return vec![CyclotomicRing::::zero(); n_a]; + } + + let lut = DigitMontLut::new(params); + let vec_len = vec.len().min(inner_width); + let tw = (TARGET_L2_CACHE_BYTES / (K * D * size_of::())).max(1); + let num_tiles = vec_len.div_ceil(tw); + + let final_accs: Vec> = cfg_fold_reduce!( + 0..num_tiles, + || vec![CyclotomicCrtNtt::::zero(); n_a], + |mut accs: Vec>, tile_idx| { + let tile_start = tile_idx * tw; + let tile_end = (tile_start + tw).min(vec_len); + for (j, digit) in vec[tile_start..tile_end].iter().enumerate() { + if is_zero_plane(digit) { + continue; + } + let ntt_d = CyclotomicCrtNtt::from_i8_with_lut(digit, params, &lut); + for (acc, mat_row) in accs.iter_mut().zip(ntt_mat.iter()) { + accumulate_pointwise_product_into( + acc, + &mat_row[tile_start + j], + &ntt_d, + params, + ); + } + } + accs + }, + |mut a: Vec>, b| { + for row in 0..n_a { + add_ntt_into(&mut a[row], &b[row], params); + } + a + } + ); + + final_accs + .into_iter() + .map(|acc| acc.to_ring_with_params(params)) + .collect() +} + +/// Like [`unreduced_quotient_rows_ntt_cached`] but accepts i8 digit planes +/// instead of ring elements, using direct i8 -> CRT+NTT conversion. +/// Column-tiled with zero-skip for all-zero digit planes. +#[tracing::instrument(skip_all, name = "unreduced_quotient_rows_ntt_cached_i8")] +pub fn unreduced_quotient_rows_ntt_cached_i8( + slot: &NttSlotCache, + vec: &[[i8; D]], +) -> Vec> { + match slot { + NttSlotCache::Q32 { + neg, + cyc, + params: p, + } => quotient_single_i8_with_params(neg, cyc, vec, p), + NttSlotCache::Q64 { + neg, + cyc, + params: p, + } => quotient_single_i8_with_params(neg, cyc, vec, p), + NttSlotCache::Q128 { + neg, + cyc, + params: p, + } => quotient_single_i8_with_params(neg, cyc, vec, p), + } +} + +fn quotient_single_i8_with_params< + F: FieldCore + CanonicalField, + W: PrimeWidth, + const K: usize, + const D: usize, +>( + ntt_neg: &[Vec>], + ntt_cyc: &[Vec>], + vec: &[[i8; D]], + params: &CrtNttParamSet, +) -> Vec> { + let n_a = ntt_neg.len(); + let inner_width = ntt_neg.first().map_or(0, |row| row.len()); + if inner_width == 0 || n_a == 0 { + return vec![CyclotomicRing::::zero(); n_a]; + } + + let lut = DigitMontLut::new(params); + let vec_len = vec.len().min(inner_width); + let tw = (TARGET_L2_CACHE_BYTES / (K * D * size_of::())).max(1); + let num_tiles = vec_len.div_ceil(tw); + + let zero = CyclotomicCrtNtt::::zero(); + + let (final_neg, final_cyc): ( + Vec>, + Vec>, + ) = cfg_fold_reduce!( + 0..num_tiles, + || (vec![zero.clone(); n_a], vec![zero.clone(); n_a]), + |mut accs: ( + Vec>, + Vec> + ), + tile_idx| { + let tile_start = tile_idx * tw; + let tile_end = (tile_start + tw).min(vec_len); + for (j, digit) in vec[tile_start..tile_end].iter().enumerate() { + if is_zero_plane(digit) { + continue; + } + let ntt_d_neg = CyclotomicCrtNtt::from_i8_with_lut(digit, params, &lut); + let ntt_d_cyc = CyclotomicCrtNtt::from_i8_cyclic_with_lut(digit, params, &lut); + let col = tile_start + j; + for (row, (acc_neg, acc_cyc)) in + accs.0.iter_mut().zip(accs.1.iter_mut()).enumerate() + { + accumulate_pointwise_product_into( + acc_neg, + &ntt_neg[row][col], + &ntt_d_neg, + params, + ); + accumulate_pointwise_product_into( + acc_cyc, + &ntt_cyc[row][col], + &ntt_d_cyc, + params, + ); + } + } + accs + }, + |mut a: ( + Vec>, + Vec> + ), + b| { + for row in 0..n_a { + add_ntt_into(&mut a.0[row], &b.0[row], params); + add_ntt_into(&mut a.1[row], &b.1[row], params); + } + a + } + ); + + final_neg + .into_iter() + .zip(final_cyc) + .map(|(neg_acc, cyc_acc)| { + let neg_ring: CyclotomicRing = neg_acc.to_ring_with_params(params); + let cyc_ring: CyclotomicRing = cyc_acc.to_ring_cyclic(params); + let neg_c = neg_ring.coefficients(); + let cyc_c = cyc_ring.coefficients(); + let q: [F; D] = from_fn(|k| (cyc_c[k] - neg_c[k]) * F::TWO_INV); + CyclotomicRing::from_coefficients(q) + }) + .collect() +} + #[cfg(test)] mod tests { use super::{mat_vec_mul_crt_ntt, mat_vec_mul_crt_ntt_many, mat_vec_mul_unchecked}; diff --git a/src/protocol/commitment/utils/matrix.rs b/src/protocol/commitment/utils/matrix.rs index fa0b80ce..9be13b11 100644 --- a/src/protocol/commitment/utils/matrix.rs +++ b/src/protocol/commitment/utils/matrix.rs @@ -51,11 +51,16 @@ struct ShakeXofRng { } impl ShakeXofRng { + // Dimensions (`rows`, `cols`) are intentionally excluded from the domain + // separator so that a matrix derived at one size is a prefix of the same + // matrix derived at a larger size. Each entry is uniquely identified by + // `(seed, matrix_label, row, col)`, which is sufficient for collision + // resistance while enabling setup reuse across poly/mega-poly layouts. fn new( seed: &PublicMatrixSeed, matrix_label: &[u8], - rows: usize, - cols: usize, + _rows: usize, + _cols: usize, row: usize, col: usize, ) -> Self { @@ -63,8 +68,6 @@ impl ShakeXofRng { absorb_len_prefixed(&mut xof, b"domain", PUBLIC_MATRIX_DOMAIN); absorb_len_prefixed(&mut xof, b"seed", seed); absorb_len_prefixed(&mut xof, b"matrix", matrix_label); - absorb_len_prefixed(&mut xof, b"rows", &(rows as u64).to_le_bytes()); - absorb_len_prefixed(&mut xof, b"cols", &(cols as u64).to_le_bytes()); absorb_len_prefixed(&mut xof, b"row", &(row as u64).to_le_bytes()); absorb_len_prefixed(&mut xof, b"col", &(col as u64).to_le_bytes()); Self { diff --git a/src/protocol/commitment/utils/mod.rs b/src/protocol/commitment/utils/mod.rs index f7035759..fe7cda72 100644 --- a/src/protocol/commitment/utils/mod.rs +++ b/src/protocol/commitment/utils/mod.rs @@ -1,6 +1,6 @@ //! Utility helpers for commitment internals. -pub(crate) mod crt_ntt; +pub mod crt_ntt; pub mod linear; pub(crate) mod math; pub(crate) mod matrix; diff --git a/src/protocol/commitment_scheme.rs b/src/protocol/commitment_scheme.rs index d332265d..bc028025 100644 --- a/src/protocol/commitment_scheme.rs +++ b/src/protocol/commitment_scheme.rs @@ -1,30 +1,37 @@ //! Commitment scheme trait implementation. +use crate::algebra::fields::wide::HasWide; +use crate::algebra::fields::HasUnreducedOps; use crate::algebra::CyclotomicRing; -use crate::cfg_into_iter; use crate::error::HachiError; -#[cfg(feature = "parallel")] -use crate::parallel::*; use crate::primitives::poly::multilinear_lagrange_basis; -use crate::protocol::commitment::onehot::{inner_ajtai_onehot, SparseBlockEntry}; -use crate::protocol::commitment::utils::linear::{ - decompose_block, decompose_rows, mat_vec_mul_ntt_cached, MatrixSlot, -}; +use crate::protocol::commitment::utils::linear::{flatten_i8_blocks, mat_vec_mul_ntt_single_i8}; use crate::protocol::commitment::{ - AppendToTranscript, CommitmentConfig, CommitmentScheme, HachiCommitmentCore, HachiProverSetup, - HachiVerifierSetup, RingCommitment, RingCommitmentScheme, StreamingCommitmentScheme, + AppendToTranscript, CommitmentConfig, CommitmentScheme, HachiCommitmentCore, + HachiCommitmentLayout, HachiProverSetup, HachiVerifierSetup, RingCommitment, + RingCommitmentScheme, +}; +use crate::protocol::hachi_poly_ops::{DensePoly, HachiPolyOps}; +use crate::protocol::opening_point::{BasisMode, RingOpeningPoint}; +use crate::protocol::proof::{ + DigitLut, HachiCommitmentHint, HachiLevelProof, HachiProof, PackedDigits, }; -use crate::protocol::opening_point::RingOpeningPoint; -use crate::protocol::proof::{HachiCommitmentHint, HachiProof, SumcheckAux}; use crate::protocol::quadratic_equation::QuadraticEquation; -use crate::protocol::ring_switch::{build_w_evals, ring_switch_prover, ring_switch_verifier}; +use crate::protocol::ring_switch::{ + build_w_evals, ring_switch_prover, ring_switch_verifier, w_ring_element_count, + WCommitmentConfig, +}; use crate::protocol::sumcheck::hachi_sumcheck::{HachiSumcheckProver, HachiSumcheckVerifier}; -use crate::protocol::sumcheck::{prove_sumcheck, verify_sumcheck}; +use crate::protocol::sumcheck::{ + multilinear_eval, multilinear_eval_small, prove_sumcheck, verify_sumcheck, +}; use crate::protocol::transcript::labels::{ ABSORB_COMMITMENT, ABSORB_EVALUATION_CLAIMS, CHALLENGE_SUMCHECK_BATCH, CHALLENGE_SUMCHECK_ROUND, }; use crate::protocol::transcript::Transcript; -use crate::{CanonicalField, FieldCore, FieldSampling, FromSmallInt, Polynomial}; +use crate::{CanonicalField, FieldCore, FieldSampling, FromSmallInt}; +use std::marker::PhantomData; +use std::time::Instant; #[cfg(test)] use crate::protocol::quadratic_equation::compute_m_a_streaming; @@ -39,23 +46,247 @@ use crate::protocol::transcript::Blake2bTranscript; #[cfg(test)] use crate::protocol::SmallTestCommitmentConfig; +/// Minimum w vector length (in field elements) below which further folding +/// is not beneficial. When `w.len() <= MIN_W_LEN_FOR_FOLDING`, the prover +/// sends `w` directly instead of recursing. +const MIN_W_LEN_FOR_FOLDING: usize = 4096; + +/// Minimum shrink ratio (next_w / prev_w) below which further folding +/// stops being worthwhile. If the w vector doesn't shrink by at least +/// this factor, the overhead of another fold level outweighs the saving. +const MIN_SHRINK_RATIO: f64 = 0.5; + /// End-to-end PCS wrapper, generic over ring degree `D` and config `Cfg`. #[derive(Clone, Copy, Debug, Default)] pub struct HachiCommitmentScheme { - _cfg: std::marker::PhantomData, + _cfg: PhantomData, +} + +/// Output from a single prove level, needed to chain into the next level. +struct ProveLevelOutput { + level_proof: HachiLevelProof, + w: Vec, + w_hint: HachiCommitmentHint, + sumcheck_challenges: Vec, + num_u: usize, + num_l: usize, } -impl CommitmentScheme for HachiCommitmentScheme +/// Prove one fold level: quad_eq -> ring_switch -> sumcheck. +/// +/// Generic over the commitment config so it works for both the original +/// polynomial (using `Cfg`) and recursive w-openings (using `WCommitmentConfig`). +#[allow(clippy::too_many_arguments)] +fn prove_one_level( + setup: &HachiProverSetup, + poly: &P, + opening_point: &[F], + hint: HachiCommitmentHint, + transcript: &mut T, + commitment: &RingCommitment, + basis: BasisMode, + level: usize, + layout: HachiCommitmentLayout, +) -> Result, HachiError> where - F: FieldCore + CanonicalField + FieldSampling, + F: FieldCore + CanonicalField + FieldSampling + HasUnreducedOps + HasWide, + T: Transcript, + Cfg: CommitmentConfig, + P: HachiPolyOps, +{ + let alpha = Cfg::D.trailing_zeros() as usize; + if opening_point.len() < alpha { + return Err(HachiError::InvalidPointDimension { + expected: alpha, + actual: opening_point.len(), + }); + } + let target_num_vars = layout.m_vars + layout.r_vars + alpha; + let mut padded_point = opening_point.to_vec(); + padded_point.resize(target_num_vars, F::zero()); + let outer_point = &padded_point[alpha..]; + + let ring_opening_point = { + let _span = tracing::info_span!("ring_opening_point", level).entered(); + ring_opening_point_from_field::(outer_point, layout.r_vars, layout.m_vars, basis)? + }; + + let t0 = Instant::now(); + let outer_weights = { + let _span = tracing::info_span!("outer_basis_weights", level).entered(); + basis_weights(outer_point, basis) + }; + let y_ring = { + let _span = tracing::info_span!("evaluate_ring", level).entered(); + poly.evaluate_ring(&outer_weights) + }; + eprintln!( + " [hachi prove L{level}] eval ring poly: {:.2}s (num_ring_elems={})", + t0.elapsed().as_secs_f64(), + poly.num_ring_elems() + ); + + commitment.append_to_transcript(ABSORB_COMMITMENT, transcript); + for pt in &padded_point { + transcript.append_field(ABSORB_EVALUATION_CLAIMS, pt); + } + transcript.append_serde(ABSORB_EVALUATION_CLAIMS, &y_ring); + + let t1 = Instant::now(); + let mut quad_eq = QuadraticEquation::::new_prover( + setup, + ring_opening_point, + poly, + hint, + transcript, + commitment, + &y_ring, + layout, + )?; + eprintln!( + " [hachi prove L{level}] quad_eq new_prover: {:.2}s", + t1.elapsed().as_secs_f64() + ); + + let t2 = Instant::now(); + let rs = ring_switch_prover::( + &mut quad_eq, + &setup.expanded, + transcript, + &setup.ntt_A, + &setup.ntt_B, + &setup.ntt_D, + layout, + )?; + eprintln!( + " [hachi prove L{level}] ring_switch_prover: {:.2}s (w.len()={}, num_u={}, num_l={})", + t2.elapsed().as_secs_f64(), + rs.w.len(), + rs.num_u, + rs.num_l + ); + + let batching_coeff: F = transcript.challenge_scalar(CHALLENGE_SUMCHECK_BATCH); + + let t3 = Instant::now(); + let num_u = rs.num_u; + let num_l = rs.num_l; + let w_evals_small = rs.w_evals.clone(); + let mut fused_prover = HachiSumcheckProver::new( + batching_coeff, + rs.w_evals, + &rs.tau0, + rs.b, + &rs.alpha_evals_y, + &rs.m_evals_x, + num_u, + num_l, + ); + + let (sumcheck_proof, sumcheck_challenges, _final_claim) = + prove_sumcheck::(&mut fused_prover, transcript, |tr| { + tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND) + })?; + eprintln!( + " [hachi prove L{level}] fused sumcheck: {:.2}s", + t3.elapsed().as_secs_f64() + ); + + let w_eval = { + let _span = tracing::info_span!("multilinear_eval", level).entered(); + multilinear_eval_small(&w_evals_small, &sumcheck_challenges)? + }; + + { + use super::sumcheck::{eq_poly::EqPolynomial, multilinear_eval as mle, range_check_eval}; + let eq_val = EqPolynomial::mle(&rs.tau0, &sumcheck_challenges); + let norm_oracle = eq_val * range_check_eval(w_eval, rs.b); + let (x_ch, y_ch) = sumcheck_challenges.split_at(num_u); + let alpha_val = mle(&rs.alpha_evals_y, y_ch).unwrap(); + let m_val = mle(&rs.m_evals_x, x_ch).unwrap(); + let relation_oracle = w_eval * alpha_val * m_val; + let prover_expected = batching_coeff * norm_oracle + relation_oracle; + if prover_expected != _final_claim { + eprintln!(" [hachi prove L{level}] PROVER self-check FAILED: expected != final_claim"); + } else { + eprintln!(" [hachi prove L{level}] PROVER self-check OK"); + } + } + + Ok(ProveLevelOutput { + level_proof: HachiLevelProof { + v: quad_eq.v, + y_ring, + sumcheck_proof, + w_commitment: rs.w_commitment, + w_eval, + }, + w: rs.w, + w_hint: rs.w_hint, + sumcheck_challenges, + num_u, + num_l, + }) +} + +/// Whether the prover should stop folding and send `w` directly. +/// +/// `prev_w_len` is the polynomial length at the previous level (or the +/// original polynomial's field-element count for level 0). +fn should_stop_folding(w_len: usize, prev_w_len: usize) -> bool { + if w_len <= MIN_W_LEN_FOR_FOLDING { + return true; + } + let ratio = w_len as f64 / prev_w_len as f64; + ratio > MIN_SHRINK_RATIO +} + +/// Derive the opening point for the next fold level from the sumcheck +/// challenges of the current level. +/// +/// Sumcheck challenges are ordered `[x_0..x_{num_u-1}, y_0..y_{num_l-1}]` +/// where x selects ring elements and y selects coefficients. +/// The PCS opening point is `[inner, outer]` = `[y, x]`. +fn next_level_opening_point( + sumcheck_challenges: &[F], + num_u: usize, + num_l: usize, +) -> Vec { + let (x, y) = sumcheck_challenges.split_at(num_u); + debug_assert_eq!(y.len(), num_l); + let mut point = Vec::with_capacity(num_u + num_l); + point.extend_from_slice(y); + point.extend_from_slice(x); + point +} + +/// Build a `DensePoly` from the flat w digit vector, converting i8 -> F +/// via lookup table and padding to the next power of two. +#[tracing::instrument(skip_all, name = "dense_poly_from_w")] +fn dense_poly_from_w( + w: &[i8], + log_basis: u32, +) -> Result, HachiError> { + let lut = DigitLut::::new(log_basis); + let total_coeffs = w.len().next_power_of_two().max(D); + let num_vars = total_coeffs.trailing_zeros() as usize; + let mut padded: Vec = w.iter().map(|&d| lut.get(d)).collect(); + padded.resize(total_coeffs, F::zero()); + DensePoly::from_field_evals(num_vars, &padded) +} + +impl CommitmentScheme for HachiCommitmentScheme +where + F: FieldCore + CanonicalField + FieldSampling + HasWide + HasUnreducedOps, Cfg: CommitmentConfig, { type ProverSetup = HachiProverSetup; type VerifierSetup = HachiVerifierSetup; type Commitment = RingCommitment; type Proof = HachiProof; - type OpeningProofHint = HachiCommitmentHint; + type CommitHint = HachiCommitmentHint; + #[tracing::instrument(skip_all, name = "HachiCommitmentScheme::setup_prover")] fn setup_prover(max_num_vars: usize) -> Self::ProverSetup { let (setup, _) = >::setup(max_num_vars) @@ -69,109 +300,126 @@ where } } - fn commit>( + #[tracing::instrument(skip_all, name = "HachiCommitmentScheme::commit")] + fn commit>( poly: &P, setup: &Self::ProverSetup, - ) -> Result<(Self::Commitment, Self::OpeningProofHint), HachiError> { - let ring_coeffs = - reduce_coeffs_to_ring_elements::(poly.num_vars(), &poly.coeffs())?; - let w = >::commit_coeffs( - &ring_coeffs, - setup, + layout: &HachiCommitmentLayout, + ) -> Result<(Self::Commitment, Self::CommitHint), HachiError> { + setup.assert_layout_fits(layout); + let t_hat_all = poly.commit_inner( + &setup.expanded.A, + &setup.ntt_A, + layout.block_len, + layout.num_digits_commit, + layout.log_basis, )?; - let hint = HachiCommitmentHint { - t_hat: w.t_hat, - ring_coeffs, - }; - Ok((w.commitment, hint)) + let t_hat_flat = flatten_i8_blocks(&t_hat_all); + let u: Vec> = mat_vec_mul_ntt_single_i8(&setup.ntt_B, &t_hat_flat); + let hint = HachiCommitmentHint::new(t_hat_all); + Ok((RingCommitment { u }, hint)) } - fn prove, P: Polynomial>( + #[tracing::instrument(skip_all, name = "HachiCommitmentScheme::prove")] + fn prove, P: HachiPolyOps>( setup: &Self::ProverSetup, poly: &P, opening_point: &[F], - hint: Option, + hint: Self::CommitHint, transcript: &mut T, commitment: &Self::Commitment, + basis: BasisMode, + layout: &HachiCommitmentLayout, ) -> Result { - let hint = hint.ok_or_else(|| { - HachiError::InvalidInput("missing commitment hint for proving".to_string()) - })?; - let _num_vars = poly.num_vars(); - let alpha = Cfg::D.trailing_zeros() as usize; - if opening_point.len() < alpha { - return Err(HachiError::InvalidPointDimension { - expected: alpha, - actual: opening_point.len(), - }); - } - - let layout = >::layout(setup)?; - let target_num_vars = layout.m_vars + layout.r_vars + alpha; - if opening_point.len() > target_num_vars { - return Err(HachiError::InvalidPointDimension { - expected: target_num_vars, - actual: opening_point.len(), - }); - } - let mut padded_point = opening_point.to_vec(); - padded_point.resize(target_num_vars, F::zero()); - let outer_point = &padded_point[alpha..]; - - let ring_opening_point = - ring_opening_point_from_field::(outer_point, layout.r_vars, layout.m_vars)?; - - let y_ring = evaluate_packed_ring_poly::(&hint.ring_coeffs, outer_point); - - // Fiat-Shamir: bind commitment, opening point, and y_ring before any challenges. - commitment.append_to_transcript(ABSORB_COMMITMENT, transcript); - for pt in &padded_point { - transcript.append_field(ABSORB_EVALUATION_CLAIMS, pt); - } - transcript.append_serde(ABSORB_EVALUATION_CLAIMS, &y_ring); + let t_prove_total = Instant::now(); + let mut levels = Vec::new(); - // §4.2 Quadratic equation - let mut quad_eq = QuadraticEquation::::new_prover( + // Level 0: original polynomial with caller-provided layout + let out = prove_one_level::( setup, - &ring_opening_point, - &hint, + poly, + opening_point, + hint, transcript, commitment, - &y_ring, + basis, + 0, + *layout, )?; + levels.push(out.level_proof); + + let mut prev_poly_len = poly.num_ring_elems() * D; + let mut current_w = out.w; + let mut current_hint = out.w_hint; + let mut current_challenges = out.sumcheck_challenges; + let mut current_num_u = out.num_u; + let mut current_num_l = out.num_l; + let mut level = 1usize; + + // Subsequent levels: recursive w-opening with WCommitmentConfig + while !should_stop_folding(current_w.len(), prev_poly_len) { + let w_poly = dense_poly_from_w::(¤t_w, Cfg::decomposition().log_basis)?; + let opening_point = + next_level_opening_point(¤t_challenges, current_num_u, current_num_l); + + { + let prev_w_eval = levels.last().unwrap().w_eval; + let field_evals: Vec = w_poly + .coeffs + .iter() + .flat_map(|r| r.coeffs.iter().copied()) + .collect(); + let direct_eval = multilinear_eval(&field_evals, &opening_point).unwrap(); + if prev_w_eval != direct_eval { + eprintln!(" [hachi prove L{level}] BUG: w_eval mismatch! prev_level w_eval != w_poly eval at opening_point"); + eprintln!( + " w_poly ring_elems={}, field_len={}, opening_point.len()={}", + w_poly.coeffs.len(), + field_evals.len(), + opening_point.len() + ); + } else { + eprintln!(" [hachi prove L{level}] w_eval consistency OK"); + } + } - // §4.3 Ring switch - let rs = ring_switch_prover::(&mut quad_eq, &setup.expanded, transcript)?; - - // Sample batching coefficient for fused sumcheck - let batching_coeff: F = transcript.challenge_scalar(CHALLENGE_SUMCHECK_BATCH); + let w_commitment = &levels.last().unwrap().w_commitment; + + let w_layout = >::commitment_layout(opening_point.len())?; + let out = prove_one_level::, DensePoly>( + setup, + &w_poly, + &opening_point, + current_hint, + transcript, + w_commitment, + BasisMode::Lagrange, + level, + w_layout, + )?; + levels.push(out.level_proof); + + prev_poly_len = current_w.len(); + current_w = out.w; + current_hint = out.w_hint; + current_challenges = out.sumcheck_challenges; + current_num_u = out.num_u; + current_num_l = out.num_l; + level += 1; + } - // Fused sumcheck: norm + relation with shared w_table - let mut fused_prover = HachiSumcheckProver::new( - batching_coeff, - rs.w_evals, - &rs.tau0, - rs.b, - &rs.alpha_evals_y, - &rs.m_evals_x, - rs.num_u, - rs.num_l, + eprintln!( + " [hachi prove] total ({level} levels): {:.2}s", + t_prove_total.elapsed().as_secs_f64() ); - let (sumcheck_proof, ..) = - prove_sumcheck::(&mut fused_prover, transcript, |tr| { - tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND) - })?; + let log_basis = Cfg::decomposition().log_basis; + let final_w = PackedDigits::from_i8_digits(¤t_w, log_basis); - Ok(HachiProof { - v: quad_eq.v, - y_ring, - sumcheck_proof, - sumcheck_aux: SumcheckAux { w: rs.w }, - w_commitment: rs.w_commitment, - }) + Ok(HachiProof { levels, final_w }) } + #[tracing::instrument(skip_all, name = "HachiCommitmentScheme::verify")] fn verify>( proof: &Self::Proof, setup: &Self::VerifierSetup, @@ -179,295 +427,207 @@ where opening_point: &[F], opening: &F, commitment: &Self::Commitment, + basis: BasisMode, + layout: &HachiCommitmentLayout, ) -> Result<(), HachiError> { - let alpha_bits = Cfg::D.trailing_zeros() as usize; - if opening_point.len() < alpha_bits { - return Err(HachiError::InvalidSetup( - "opening point length underflow".to_string(), - )); - } - let layout = setup.expanded.seed.layout; - let target_num_vars = layout.m_vars + layout.r_vars + alpha_bits; - let mut padded_point = opening_point.to_vec(); - padded_point.resize(target_num_vars, F::zero()); - let inner_point = &padded_point[..alpha_bits]; - let reduced_opening_point = &padded_point[alpha_bits..]; - - // Fiat-Shamir: bind commitment, opening point, and y_ring before any challenges. - commitment.append_to_transcript(ABSORB_COMMITMENT, transcript); - for pt in &padded_point { - transcript.append_field(ABSORB_EVALUATION_CLAIMS, pt); - } - transcript.append_serde(ABSORB_EVALUATION_CLAIMS, &proof.y_ring); - - // §3.1 trace check - let v = reduce_inner_openings_to_ring_elements::(inner_point)?; - let d = F::from_u64(Cfg::D as u64); - let trace_lhs = trace::(&(proof.y_ring * v.sigma_m1())); - let trace_rhs = d * *opening; - if trace_lhs != trace_rhs { + if proof.levels.is_empty() { return Err(HachiError::InvalidProof); } - // §4.2 Quadratic equation - let ring_opening_point = ring_opening_point_from_field::( - reduced_opening_point, - layout.r_vars, - layout.m_vars, - )?; - let quad_eq = QuadraticEquation::::new_verifier( - setup, - &ring_opening_point, - &proof.v, - transcript, - commitment, - &proof.y_ring, - )?; - - // §4.3 Ring switch (verifier side) - let rs = ring_switch_verifier::( - &quad_eq, - &setup.expanded, - &proof.sumcheck_aux.w, - &proof.w_commitment, - transcript, - )?; - - // Sample batching coefficient for fused sumcheck (must match prover) - let batching_coeff: F = transcript.challenge_scalar(CHALLENGE_SUMCHECK_BATCH); - - // Build full w_evals for verifier from the witness vector w. - let (w_evals_full, _, _) = build_w_evals(&proof.sumcheck_aux.w, Cfg::D)?; - - // Fused sumcheck verification: norm (F_0) + relation (F_α) - let fused_verifier = HachiSumcheckVerifier::new( - batching_coeff, - w_evals_full, - rs.tau0, - rs.b, - rs.alpha_evals_y, - rs.m_evals_x, - rs.tau1, - proof.v.clone(), - commitment.u.clone(), - proof.y_ring, - rs.alpha, - rs.num_u, - rs.num_l, - ); - - verify_sumcheck::( - &proof.sumcheck_proof, - &fused_verifier, - transcript, - |tr| tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND), - )?; + let num_levels = proof.levels.len(); + let final_w_elems: Vec = proof.final_w.to_field_elems(); + + // State carried between levels. + let mut current_point = opening_point.to_vec(); + let mut current_opening = *opening; + let mut current_commitment = commitment.clone(); + let mut current_basis = basis; + + for (i, level_proof) in proof.levels.iter().enumerate() { + let is_last = i == num_levels - 1; + eprintln!( + " [verify] level {i}, is_last={is_last}, point_len={}", + current_point.len() + ); + + let challenges = if i == 0 { + verify_one_level::( + level_proof, + setup, + transcript, + ¤t_point, + ¤t_opening, + ¤t_commitment, + current_basis, + is_last, + if is_last { Some(&final_w_elems) } else { None }, + *layout, + )? + } else { + let w_layout = >::commitment_layout(current_point.len())?; + verify_one_level::>( + level_proof, + setup, + transcript, + ¤t_point, + ¤t_opening, + ¤t_commitment, + current_basis, + is_last, + if is_last { Some(&final_w_elems) } else { None }, + w_layout, + )? + }; + + if !is_last { + let alpha_bits = D.trailing_zeros() as usize; + let num_l = alpha_bits; + let num_u = challenges.len() - num_l; + + current_point = next_level_opening_point(&challenges, num_u, num_l); + current_opening = level_proof.w_eval; + current_commitment = level_proof.w_commitment.clone(); + current_basis = BasisMode::Lagrange; + } + } Ok(()) } - fn combine_commitments(_commitments: &[Self::Commitment], _coeffs: &[F]) -> Self::Commitment { - unimplemented!() - } - - fn combine_hints(_hints: Vec, _coeffs: &[F]) -> Self::OpeningProofHint { - unimplemented!() - } - fn protocol_name() -> &'static [u8] { unimplemented!() } } -/// Commit to a one-hot polynomial, returning both the commitment and a -/// complete `HachiCommitmentHint` (including `ring_coeffs` needed by `prove`). +/// Verify one fold level. /// -/// # Errors +/// At the final level, `final_w` is provided and the verifier checks w_val +/// from it directly. At intermediate levels, `level_proof.w_eval` is used. /// -/// Returns an error if dimensions are inconsistent, any index is out of -/// range, or the underlying commitment routine fails. -pub fn commit_onehot( - onehot_k: usize, - indices: &[Option], - setup: &HachiProverSetup, -) -> Result<(RingCommitment, HachiCommitmentHint), HachiError> +/// Returns the sumcheck challenges for chaining into the next level. +#[allow(clippy::too_many_arguments)] +fn verify_one_level( + level_proof: &HachiLevelProof, + setup: &HachiVerifierSetup, + transcript: &mut T, + opening_point: &[F], + opening: &F, + commitment: &RingCommitment, + basis: BasisMode, + is_last: bool, + final_w: Option<&[F]>, + layout: HachiCommitmentLayout, +) -> Result, HachiError> where F: FieldCore + CanonicalField + FieldSampling, + T: Transcript, Cfg: CommitmentConfig, { - let num_chunks = indices.len(); - let total_field_elems = num_chunks - .checked_mul(onehot_k) - .ok_or_else(|| HachiError::InvalidInput("T*K overflow".into()))?; - if total_field_elems % D != 0 { - return Err(HachiError::InvalidInput(format!( - "T*K={total_field_elems} is not divisible by D={D}" - ))); + let alpha_bits = Cfg::D.trailing_zeros() as usize; + if opening_point.len() < alpha_bits { + return Err(HachiError::InvalidSetup( + "opening point length underflow".to_string(), + )); } - - // Build ring_coeffs (needed for prove) from the sparse one-hot indices. - let total_ring_elems = total_field_elems / D; - let mut ring_coeffs = vec![CyclotomicRing::::zero(); total_ring_elems]; - for (c, opt) in indices.iter().enumerate() { - let Some(&idx) = opt.as_ref() else { continue }; - let field_pos = c * onehot_k + idx; - let ring_idx = field_pos / D; - let coeff_idx = field_pos % D; - ring_coeffs[ring_idx].coeffs[coeff_idx] = F::one(); + let target_num_vars = layout.m_vars + layout.r_vars + alpha_bits; + let mut padded_point = opening_point.to_vec(); + padded_point.resize(target_num_vars, F::zero()); + let inner_point = &padded_point[..alpha_bits]; + let reduced_opening_point = &padded_point[alpha_bits..]; + + commitment.append_to_transcript(ABSORB_COMMITMENT, transcript); + for pt in &padded_point { + transcript.append_field(ABSORB_EVALUATION_CLAIMS, pt); + } + transcript.append_serde(ABSORB_EVALUATION_CLAIMS, &level_proof.y_ring); + + // Trace check + let v = reduce_inner_openings_to_ring_elements::(inner_point, basis)?; + let d = F::from_u64(Cfg::D as u64); + let trace_lhs = trace::(&(level_proof.y_ring * v.sigma_m1())); + let trace_rhs = d * *opening; + if trace_lhs != trace_rhs { + return Err(HachiError::InvalidProof); } - let w = >::commit_onehot( - onehot_k, indices, setup, + let ring_opening_point = ring_opening_point_from_field::( + reduced_opening_point, + layout.r_vars, + layout.m_vars, + basis, + )?; + let quad_eq = QuadraticEquation::::new_verifier( + ring_opening_point, + level_proof.v.clone(), + transcript, + commitment, + &level_proof.y_ring, + layout, )?; - let hint = HachiCommitmentHint { - t_hat: w.t_hat, - ring_coeffs, + let w_len = if is_last { + final_w.map_or(0, |fw| fw.len()) + } else { + w_ring_element_count::(layout) * D }; - Ok((w.commitment, hint)) -} - -/// Per-block intermediate state for streaming Hachi commitment. -/// -/// Each chunk corresponds to one Ajtai inner block: `D * block_len` field -/// elements packed into `block_len` ring elements, decomposed, and multiplied -/// by the inner matrix A. -#[derive(Clone, PartialEq, Eq)] -pub struct HachiChunkState { - /// Original ring elements for this block (needed for `ring_coeffs` hint). - pub block: Vec>, - /// Basis-decomposed input vector `s_i = G^{-1}(block)`. - pub s_i: Vec>, - /// Basis-decomposed inner Ajtai output `t̂_i = G^{-1}(A · s_i)`. - pub t_hat_i: Vec>, -} - -impl std::fmt::Debug for HachiChunkState { - fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { - f.debug_struct("HachiChunkState") - .field("block_len", &self.block.len()) - .field("s_i_len", &self.s_i.len()) - .field("t_hat_i_len", &self.t_hat_i.len()) - .finish() - } -} + eprintln!(" [verify] w_len={w_len}, is_last={is_last}"); -impl StreamingCommitmentScheme for HachiCommitmentScheme -where - F: FieldCore + CanonicalField + FieldSampling, - Cfg: CommitmentConfig, -{ - type ChunkState = HachiChunkState; - - fn process_chunk(setup: &Self::ProverSetup, chunk: &[F]) -> Self::ChunkState { - assert!( - chunk.len() % D == 0, - "chunk length {} is not divisible by D={}", - chunk.len(), - D - ); - - let block: Vec> = chunk - .chunks_exact(D) - .map(|c| CyclotomicRing::from_coefficients(std::array::from_fn(|j| c[j]))) - .collect(); - - let s_i = decompose_block(&block, Cfg::DELTA, Cfg::LOG_BASIS); - let t_i = - mat_vec_mul_ntt_cached(setup.ntt_cache().expect("NTT cache"), MatrixSlot::A, &s_i) - .expect("inner Ajtai"); - let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); - - HachiChunkState { - block, - s_i, - t_hat_i, - } - } - - fn process_chunk_onehot( - setup: &Self::ProverSetup, - onehot_k: usize, - chunk: &[Option], - ) -> Self::ChunkState { - let layout = >::layout(setup) - .expect("layout"); - let block_len = layout.block_len; - - let num_field_elems = chunk.len() * onehot_k; - assert!( - num_field_elems % D == 0, - "chunk cycles * K = {num_field_elems} is not divisible by D={D}", - ); - - // Build sparse entries and original block ring elements. - let num_ring_elems = num_field_elems / D; - let mut ring_block = vec![CyclotomicRing::::zero(); num_ring_elems]; - let mut ring_elem_map: std::collections::BTreeMap> = - std::collections::BTreeMap::new(); - for (c, opt) in chunk.iter().enumerate() { - if let Some(k) = opt { - let field_pos = c * onehot_k + k; - let ring_elem_idx = field_pos / D; - let coeff_idx = field_pos % D; - ring_block[ring_elem_idx].coeffs[coeff_idx] = F::one(); - ring_elem_map - .entry(ring_elem_idx) - .or_default() - .push(coeff_idx); - } - } - - let sparse_entries: Vec = ring_elem_map - .into_iter() - .map(|(ring_elem_idx, nonzero_coeffs)| SparseBlockEntry { - pos_in_block: ring_elem_idx, - nonzero_coeffs, - }) - .collect(); - - let (t_i, s_i) = - inner_ajtai_onehot(&setup.expanded.A, &sparse_entries, block_len, Cfg::DELTA); - let t_hat_i = decompose_rows(&t_i, Cfg::DELTA, Cfg::LOG_BASIS); - - HachiChunkState { - block: ring_block, - s_i, - t_hat_i, - } - } + let rs = ring_switch_verifier::( + &quad_eq, + &setup.expanded, + w_len, + &level_proof.w_commitment, + transcript, + layout, + )?; - fn aggregate_chunks( - setup: &Self::ProverSetup, - _onehot_k: Option, - chunks: &[Self::ChunkState], - ) -> (Self::Commitment, Self::OpeningProofHint) { - let t_hat_flat: Vec> = chunks - .iter() - .flat_map(|c| c.t_hat_i.iter().copied()) - .collect(); + let batching_coeff: F = transcript.challenge_scalar(CHALLENGE_SUMCHECK_BATCH); - let u = mat_vec_mul_ntt_cached( - setup.ntt_cache().expect("NTT cache"), - MatrixSlot::B, - &t_hat_flat, + let fused_verifier = if is_last { + let fw = final_w.ok_or(HachiError::InvalidProof)?; + let (w_evals_full, _, _) = build_w_evals(fw, Cfg::D)?; + HachiSumcheckVerifier::new( + batching_coeff, + w_evals_full, + rs.tau0, + rs.b, + rs.alpha_evals_y, + rs.m_evals_x, + rs.tau1, + level_proof.v.clone(), + commitment.u.clone(), + level_proof.y_ring, + rs.alpha, + rs.num_u, + rs.num_l, ) - .expect("outer Ajtai"); + } else { + HachiSumcheckVerifier::new( + batching_coeff, + Vec::new(), + rs.tau0, + rs.b, + rs.alpha_evals_y, + rs.m_evals_x, + rs.tau1, + level_proof.v.clone(), + commitment.u.clone(), + level_proof.y_ring, + rs.alpha, + rs.num_u, + rs.num_l, + ) + .with_w_val_override(level_proof.w_eval) + }; - let t_hat_all: Vec>> = - chunks.iter().map(|c| c.t_hat_i.clone()).collect(); - let ring_coeffs: Vec> = chunks - .iter() - .flat_map(|c| c.block.iter().copied()) - .collect(); - - let commitment = RingCommitment { u }; - let hint = HachiCommitmentHint { - t_hat: t_hat_all, - ring_coeffs, - }; - (commitment, hint) - } + let challenges = verify_sumcheck::( + &level_proof.sumcheck_proof, + &fused_verifier, + transcript, + |tr| tr.challenge_scalar(CHALLENGE_SUMCHECK_ROUND), + )?; + + Ok(challenges) } /// Re-derive the ring-switch challenge `alpha` and the expanded `M_a` vector @@ -484,44 +644,46 @@ where F: FieldCore + CanonicalField + FieldSampling + 'static, Cfg: CommitmentConfig, { + let level0 = proof.levels.first().ok_or(HachiError::InvalidProof)?; let alpha_bits = Cfg::D.trailing_zeros() as usize; if opening_point.len() < alpha_bits { return Err(HachiError::InvalidSetup( "opening point length underflow".to_string(), )); } - let layout = setup.expanded.seed.layout; + let layout = Cfg::commitment_layout(opening_point.len())?; let ring_opening_point = ring_opening_point_from_field::( &opening_point[alpha_bits..], layout.r_vars, layout.m_vars, + BasisMode::Lagrange, )?; let mut transcript = Blake2bTranscript::::new(DOMAIN_HACHI_PROTOCOL); - // Replay the same Fiat-Shamir absorptions the real verifier performs. commitment.append_to_transcript(ABSORB_COMMITMENT, &mut transcript); for pt in opening_point { transcript.append_field(ABSORB_EVALUATION_CLAIMS, pt); } - transcript.append_serde(ABSORB_EVALUATION_CLAIMS, &proof.y_ring); + transcript.append_serde(ABSORB_EVALUATION_CLAIMS, &level0.y_ring); let quad_eq = QuadraticEquation::::new_verifier( - setup, - &ring_opening_point, - &proof.v, + ring_opening_point, + level0.v.clone(), &mut transcript, commitment, - &proof.y_ring, + &level0.y_ring, + layout, )?; - transcript.append_serde(ABSORB_SUMCHECK_W, &proof.w_commitment); + transcript.append_serde(ABSORB_SUMCHECK_W, &level0.w_commitment); let alpha: F = transcript.challenge_scalar(CHALLENGE_RING_SWITCH); let m_a = compute_m_a_streaming::( &setup.expanded, quad_eq.opening_point(), &quad_eq.challenges, &alpha, + layout, )?; - let m_a_vec = expand_m_a::(&m_a, alpha)?; + let m_a_vec = expand_m_a::(&m_a, alpha, layout.log_basis)?; Ok((alpha, m_a_vec)) } @@ -532,10 +694,34 @@ fn lagrange_weights(point: &[F]) -> Vec { weights } +/// Multilinear monomial weights: `⊗ᵢ (1, xᵢ)`. +/// +/// The j-th entry is `∏_{i ∈ bits(j)} point[i]`. +fn monomial_weights(point: &[F]) -> Vec { + let len = 1usize << point.len(); + let mut weights = vec![F::zero(); len]; + weights[0] = F::one(); + for (level, &p) in point.iter().enumerate() { + let k = 1usize << level; + for i in (0..k).rev() { + weights[i + k] = weights[i] * p; + } + } + weights +} + +fn basis_weights(point: &[F], mode: BasisMode) -> Vec { + match mode { + BasisMode::Lagrange => lagrange_weights(point), + BasisMode::Monomial => monomial_weights(point), + } +} + fn ring_opening_point_from_field( opening_point: &[F], r_vars: usize, m_vars: usize, + basis: BasisMode, ) -> Result, HachiError> { let expected_len = r_vars .checked_add(m_vars) @@ -549,90 +735,23 @@ fn ring_opening_point_from_field( // Sequential ordering: M variables (position in block) come first, // R variables (block selection) come second. - let a = lagrange_weights(&opening_point[..m_vars]); - let b = lagrange_weights(&opening_point[m_vars..]); + let a = basis_weights(&opening_point[..m_vars], basis); + let b = basis_weights(&opening_point[m_vars..], basis); Ok(RingOpeningPoint { a, b }) } -fn reduce_coeffs_to_ring_elements( - num_vars: usize, - coeffs: &[F], -) -> Result>, HachiError> { - if D == 0 || !D.is_power_of_two() { - return Err(HachiError::InvalidInput(format!( - "ring degree D={D} is not a power of two" - ))); - } - let alpha = D.trailing_zeros() as usize; - if num_vars < alpha { - return Err(HachiError::InvalidInput(format!( - "num_vars {num_vars} is smaller than alpha {alpha}" - ))); - } - - let expected_len = 1usize - .checked_shl(num_vars as u32) - .ok_or_else(|| HachiError::InvalidInput(format!("2^{num_vars} does not fit usize")))?; - if coeffs.len() != expected_len { - return Err(HachiError::InvalidSize { - expected: expected_len, - actual: coeffs.len(), - }); - } - - // Sequential packing: ring element i = coeffs[i*D .. (i+1)*D]. - // The first alpha variables (LSBs) become coefficient slots within each - // ring element; the remaining outer_vars variables index ring elements. - let outer_len = expected_len / D; - let out: Vec> = cfg_into_iter!(0..outer_len) - .map(|i| { - let ring_coeffs = std::array::from_fn(|j| coeffs[i * D + j]); - CyclotomicRing::from_coefficients(ring_coeffs) - }) - .collect(); - Ok(out) -} - fn reduce_inner_openings_to_ring_elements( inner_point: &[F], + basis: BasisMode, ) -> Result, HachiError> { - let weights = lagrange_weights(inner_point); + let weights = basis_weights(inner_point, basis); if weights.len() != D { return Err(HachiError::InvalidInput(format!( "inner basis length {} does not match D={D}", weights.len() ))); } - let coeffs = std::array::from_fn(|i| weights[i]); - Ok(CyclotomicRing::from_coefficients(coeffs)) -} - -fn evaluate_packed_ring_poly( - packed_coeffs: &[CyclotomicRing], - outer_point: &[F], -) -> CyclotomicRing { - let weights = lagrange_weights(outer_point); - debug_assert!(weights.len() >= packed_coeffs.len()); - #[cfg(feature = "parallel")] - { - packed_coeffs - .par_iter() - .zip(weights.par_iter()) - .fold( - || CyclotomicRing::::zero(), - |acc, (f_i, w_i)| acc + f_i.scale(w_i), - ) - .reduce(|| CyclotomicRing::::zero(), |a, b| a + b) - } - #[cfg(not(feature = "parallel"))] - { - packed_coeffs - .iter() - .zip(weights.iter()) - .fold(CyclotomicRing::::zero(), |acc, (f_i, w_i)| { - acc + f_i.scale(w_i) - }) - } + Ok(CyclotomicRing::from_slice(&weights)) } fn trace(u: &CyclotomicRing) -> F { @@ -643,52 +762,67 @@ fn trace(u: &CyclotomicRing) #[cfg(test)] mod tests { use super::*; - use crate::primitives::multilinear_evals::DenseMultilinearEvals; use crate::protocol::commitment::CommitmentConfig; + use crate::protocol::hachi_poly_ops::DensePoly; use crate::protocol::transcript::Blake2bTranscript; use crate::test_utils::F; - use crate::{CommitmentScheme, FromSmallInt, Polynomial}; + use crate::{CommitmentScheme, FromSmallInt}; type Cfg = SmallTestCommitmentConfig; - type Scheme = HachiCommitmentScheme<{ Cfg::D }, Cfg>; + const D: usize = Cfg::D; + type Scheme = HachiCommitmentScheme; + + fn make_dense_poly(num_vars: usize) -> (DensePoly, Vec) { + let len = 1usize << num_vars; + let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); + let poly = DensePoly::::from_field_evals(num_vars, &evals).unwrap(); + (poly, evals) + } #[test] fn verify_passes_for_consistent_opening() { - let alpha = Cfg::D.trailing_zeros() as usize; + let alpha = D.trailing_zeros() as usize; let layout = Cfg::commitment_layout(16).unwrap(); let num_vars = layout.m_vars + layout.r_vars + alpha; - let len = 1usize << num_vars; - let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); - let poly = DenseMultilinearEvals::new_padded(evals); + let (poly, evals) = make_dense_poly(num_vars); - let setup = >::setup_prover(num_vars); - let verifier_setup = >::setup_verifier(&setup); + let setup = >::setup_prover(num_vars); + let verifier_setup = >::setup_verifier(&setup); - let (commitment, hint) = >::commit(&poly, &setup).unwrap(); + let (commitment, hint) = + >::commit(&poly, &setup, &layout).unwrap(); let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); - let opening = poly.evaluate(&opening_point); + let lw = lagrange_weights(&opening_point); + let opening: F = evals + .iter() + .zip(lw.iter()) + .fold(F::zero(), |a, (&c, &w)| a + c * w); let mut prover_transcript = Blake2bTranscript::::new(b"test/prove"); - let proof = >::prove( + let proof = >::prove( &setup, &poly, &opening_point, - Some(hint), + hint, &mut prover_transcript, &commitment, + BasisMode::Lagrange, + &layout, ) .unwrap(); let mut verifier_transcript = Blake2bTranscript::::new(b"test/prove"); - let result = >::verify( + let result = >::verify( &proof, &verifier_setup, &mut verifier_transcript, &opening_point, &opening, &commitment, + BasisMode::Lagrange, + &layout, ); assert!(result.is_ok()); @@ -696,42 +830,49 @@ mod tests { #[test] fn verify_rejects_wrong_opening() { - let alpha = Cfg::D.trailing_zeros() as usize; + let alpha = D.trailing_zeros() as usize; let layout = Cfg::commitment_layout(16).unwrap(); let num_vars = layout.m_vars + layout.r_vars + alpha; - let len = 1usize << num_vars; - let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); - let poly = DenseMultilinearEvals::new_padded(evals); + let (poly, evals) = make_dense_poly(num_vars); - let setup = >::setup_prover(num_vars); - let verifier_setup = >::setup_verifier(&setup); + let setup = >::setup_prover(num_vars); + let verifier_setup = >::setup_verifier(&setup); - let (commitment, hint) = >::commit(&poly, &setup).unwrap(); + let (commitment, hint) = + >::commit(&poly, &setup, &layout).unwrap(); let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); - let opening = poly.evaluate(&opening_point); + let lw = lagrange_weights(&opening_point); + let opening: F = evals + .iter() + .zip(lw.iter()) + .fold(F::zero(), |a, (&c, &w)| a + c * w); let mut prover_transcript = Blake2bTranscript::::new(b"test/prove"); - let proof = >::prove( + let proof = >::prove( &setup, &poly, &opening_point, - Some(hint), + hint, &mut prover_transcript, &commitment, + BasisMode::Lagrange, + &layout, ) .unwrap(); let wrong_opening = opening + F::one(); let mut verifier_transcript = Blake2bTranscript::::new(b"test/prove"); - let result = >::verify( + let result = >::verify( &proof, &verifier_setup, &mut verifier_transcript, &opening_point, &wrong_opening, &commitment, + BasisMode::Lagrange, + &layout, ); assert!( @@ -741,84 +882,57 @@ mod tests { } #[test] - fn streaming_commit_matches_non_streaming() { - let alpha = Cfg::D.trailing_zeros() as usize; + fn monomial_basis_prove_verify_round_trip() { + let alpha = D.trailing_zeros() as usize; let layout = Cfg::commitment_layout(16).unwrap(); let num_vars = layout.m_vars + layout.r_vars + alpha; let len = 1usize << num_vars; - let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); - let poly = DenseMultilinearEvals::new_padded(evals.clone()); - - let setup = >::setup_prover(num_vars); + let coeffs: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); + let poly = DensePoly::::from_field_evals(num_vars, &coeffs).unwrap(); - // Non-streaming commit - let (non_streaming_commitment, non_streaming_hint) = - >::commit(&poly, &setup).unwrap(); + let setup = >::setup_prover(num_vars); + let verifier_setup = >::setup_verifier(&setup); - // Streaming commit: split field elements into chunks of D * block_len - let chunk_size = Cfg::D * layout.block_len; - let chunks: Vec> = evals - .chunks_exact(chunk_size) - .map(|chunk| >::process_chunk(&setup, chunk)) - .collect(); - - let (streaming_commitment, streaming_hint) = - >::aggregate_chunks(&setup, None, &chunks); - - assert_eq!(non_streaming_commitment, streaming_commitment); - assert_eq!(non_streaming_hint, streaming_hint); - } - - #[test] - fn streaming_commit_then_prove_verify() { - let alpha = Cfg::D.trailing_zeros() as usize; - let layout = Cfg::commitment_layout(16).unwrap(); - let num_vars = layout.m_vars + layout.r_vars + alpha; - let len = 1usize << num_vars; - - let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); - let poly = DenseMultilinearEvals::new_padded(evals.clone()); - - let setup = >::setup_prover(num_vars); - let verifier_setup = >::setup_verifier(&setup); - - // Streaming commit - let chunk_size = Cfg::D * layout.block_len; - let chunks: Vec> = evals - .chunks_exact(chunk_size) - .map(|chunk| >::process_chunk(&setup, chunk)) - .collect(); let (commitment, hint) = - >::aggregate_chunks(&setup, None, &chunks); + >::commit(&poly, &setup, &layout).unwrap(); - // Prove and verify with streaming-produced commitment + hint let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); - let opening = poly.evaluate(&opening_point); - let mut prover_transcript = Blake2bTranscript::::new(b"test/stream"); - let proof = >::prove( + let mw = monomial_weights(&opening_point); + let opening: F = coeffs + .iter() + .zip(mw.iter()) + .fold(F::zero(), |acc, (&c, &w)| acc + c * w); + + let mut prover_transcript = Blake2bTranscript::::new(b"test/monomial"); + let proof = >::prove( &setup, &poly, &opening_point, - Some(hint), + hint, &mut prover_transcript, &commitment, + BasisMode::Monomial, + &layout, ) .unwrap(); - let mut verifier_transcript = Blake2bTranscript::::new(b"test/stream"); - let result = >::verify( + let mut verifier_transcript = Blake2bTranscript::::new(b"test/monomial"); + let result = >::verify( &proof, &verifier_setup, &mut verifier_transcript, &opening_point, &opening, &commitment, + BasisMode::Monomial, + &layout, ); + assert!( result.is_ok(), - "streaming commit should produce valid proofs" + "monomial-basis proof should verify: {result:?}" ); } } diff --git a/src/protocol/hachi_poly_ops/decompose_fold_neon.rs b/src/protocol/hachi_poly_ops/decompose_fold_neon.rs new file mode 100644 index 00000000..0ee84394 --- /dev/null +++ b/src/protocol/hachi_poly_ops/decompose_fold_neon.rs @@ -0,0 +1,143 @@ +//! AArch64 NEON kernel for sparse-multiply-accumulate in `decompose_fold`. +//! +//! Rotates an i8 digit plane by each challenge position and accumulates +//! into an i32 accumulator using widening add/sub (`SADDW` / `SSUBW`). + +use std::arch::aarch64::*; + +/// NEON sparse-multiply-accumulate. +/// +/// For each challenge term `(pos, coeff)`, rotates the `digit_plane` by `pos` +/// positions in the negacyclic ring (X^D + 1) and adds or subtracts the +/// widened i8 values into the i32 `acc`. +/// +/// # Safety +/// +/// - `digit_plane` must point to at least `d` valid i8 values. +/// - `acc` must point to at least `d` valid i32 values. +/// - `d` must be a multiple of 16. +#[target_feature(enable = "neon")] +pub(super) unsafe fn sparse_mul_acc_neon( + digit_plane: *const i8, + acc: *mut i32, + d: usize, + positions: &[u32], + coeffs: &[i16], +) { + debug_assert!(d % 16 == 0); + + for (&pos, &coeff) in positions.iter().zip(coeffs.iter()) { + let p = pos as usize; + let split = d - p; + + if coeff > 0 { + acc_rotated_add(digit_plane, acc, d, p, split); + } else { + acc_rotated_sub(digit_plane, acc, d, p, split); + } + } +} + +/// Add rotated digit plane: acc[i+p] += digits[i] for i in [0, split), +/// acc[i-split] -= digits[i] for i in [split, D) (negacyclic wrap). +#[inline(always)] +unsafe fn acc_rotated_add(digits: *const i8, acc: *mut i32, d: usize, p: usize, split: usize) { + // First segment: digits[0..split] -> acc[p..D], ADD + acc_segment_add(digits, acc.add(p), split); + // Second segment: digits[split..D] -> acc[0..p], SUB (negacyclic) + if p > 0 { + acc_segment_sub(digits.add(split), acc, p); + } + let _ = d; +} + +/// Sub rotated digit plane: acc[i+p] -= digits[i] for i in [0, split), +/// acc[i-split] += digits[i] for i in [split, D) (negacyclic wrap). +#[inline(always)] +unsafe fn acc_rotated_sub(digits: *const i8, acc: *mut i32, d: usize, p: usize, split: usize) { + // First segment: digits[0..split] -> acc[p..D], SUB + acc_segment_sub(digits, acc.add(p), split); + // Second segment: digits[split..D] -> acc[0..p], ADD (negacyclic) + if p > 0 { + acc_segment_add(digits.add(split), acc, p); + } + let _ = d; +} + +/// Widen i8 source values to i32 and ADD into accumulator. +/// Handles arbitrary length (processes 16 at a time, then remainder). +#[inline(always)] +unsafe fn acc_segment_add(src: *const i8, dst: *mut i32, len: usize) { + let chunks = len / 16; + let rem = len % 16; + + for i in 0..chunks { + let offset = i * 16; + let v = vld1q_s8(src.add(offset)); + + let lo8 = vget_low_s8(v); + let hi8 = vget_high_s8(v); + let lo16 = vmovl_s8(lo8); + let hi16 = vmovl_s8(hi8); + + let s0 = vmovl_s16(vget_low_s16(lo16)); + let s1 = vmovl_s16(vget_high_s16(lo16)); + let s2 = vmovl_s16(vget_low_s16(hi16)); + let s3 = vmovl_s16(vget_high_s16(hi16)); + + let d0 = vld1q_s32(dst.add(offset)); + let d1 = vld1q_s32(dst.add(offset + 4)); + let d2 = vld1q_s32(dst.add(offset + 8)); + let d3 = vld1q_s32(dst.add(offset + 12)); + + vst1q_s32(dst.add(offset), vaddq_s32(d0, s0)); + vst1q_s32(dst.add(offset + 4), vaddq_s32(d1, s1)); + vst1q_s32(dst.add(offset + 8), vaddq_s32(d2, s2)); + vst1q_s32(dst.add(offset + 12), vaddq_s32(d3, s3)); + } + + let base = chunks * 16; + for i in 0..rem { + let val = *src.add(base + i) as i32; + *dst.add(base + i) += val; + } +} + +/// Widen i8 source values to i32 and SUB from accumulator. +/// Handles arbitrary length (processes 16 at a time, then remainder). +#[inline(always)] +unsafe fn acc_segment_sub(src: *const i8, dst: *mut i32, len: usize) { + let chunks = len / 16; + let rem = len % 16; + + for i in 0..chunks { + let offset = i * 16; + let v = vld1q_s8(src.add(offset)); + + let lo8 = vget_low_s8(v); + let hi8 = vget_high_s8(v); + let lo16 = vmovl_s8(lo8); + let hi16 = vmovl_s8(hi8); + + let s0 = vmovl_s16(vget_low_s16(lo16)); + let s1 = vmovl_s16(vget_high_s16(lo16)); + let s2 = vmovl_s16(vget_low_s16(hi16)); + let s3 = vmovl_s16(vget_high_s16(hi16)); + + let d0 = vld1q_s32(dst.add(offset)); + let d1 = vld1q_s32(dst.add(offset + 4)); + let d2 = vld1q_s32(dst.add(offset + 8)); + let d3 = vld1q_s32(dst.add(offset + 12)); + + vst1q_s32(dst.add(offset), vsubq_s32(d0, s0)); + vst1q_s32(dst.add(offset + 4), vsubq_s32(d1, s1)); + vst1q_s32(dst.add(offset + 8), vsubq_s32(d2, s2)); + vst1q_s32(dst.add(offset + 12), vsubq_s32(d3, s3)); + } + + let base = chunks * 16; + for i in 0..rem { + let val = *src.add(base + i) as i32; + *dst.add(base + i) -= val; + } +} diff --git a/src/protocol/hachi_poly_ops/mod.rs b/src/protocol/hachi_poly_ops/mod.rs new file mode 100644 index 00000000..d41b032a --- /dev/null +++ b/src/protocol/hachi_poly_ops/mod.rs @@ -0,0 +1,740 @@ +//! Operation-centric polynomial trait for the Hachi commitment scheme. +//! +//! [`HachiPolyOps`] exposes the four operations the Hachi commit/prove paths +//! need from a polynomial, rather than raw coefficient access. Each +//! implementation handles every operation in its own optimal way: +//! +//! - [`DensePoly`] — standard dense algorithms (decompose + NTT matvec). +//! - [`OneHotPoly`] — sparse monomial tricks, avoids all inner ring +//! multiplications. +//! +//! # Extensibility +//! +//! This trait is coupled to power-of-2 cyclotomic rings +//! ([`CyclotomicRing`]). When non-power-of-2 rings are added, the trait +//! signature will change. Additional operation methods may be added as the +//! protocol evolves. + +use crate::algebra::fields::wide::HasWide; +use crate::algebra::ring::sparse_challenge::SparseChallenge; +use crate::algebra::CyclotomicRing; +use crate::error::HachiError; +#[cfg(feature = "parallel")] +use crate::parallel::*; +use crate::protocol::commitment::onehot::{ + inner_ajtai_onehot_wide, map_onehot_to_sparse_blocks, SparseBlockEntry, +}; +use crate::protocol::commitment::utils::crt_ntt::NttSlotCache; +use crate::protocol::commitment::utils::linear::{decompose_rows_i8, mat_vec_mul_ntt_i8}; +use crate::{cfg_fold_reduce, cfg_into_iter, cfg_iter, CanonicalField, FieldCore}; +use std::array::from_fn; +use std::marker::PhantomData; + +#[cfg(target_arch = "aarch64")] +use crate::algebra::ntt::neon; + +#[cfg(target_arch = "aarch64")] +mod decompose_fold_neon; + +/// Precomputed constants for balanced base-b decomposition. +struct DecomposeParams { + half_q: u128, + q: u128, + mask: i128, + half_b: i128, + b_val: i128, + log_basis: u32, +} + +/// Decompose all D coefficients of a ring element into balanced base-b digits, +/// storing results in digit-major order for subsequent SIMD scatter. +/// +/// Uses K=3 interleaved carry chains to saturate ALU throughput (3x ILP gain +/// over processing one coefficient at a time on out-of-order cores). +/// +/// `digit_buf` is `[num_digits][D]` in i8, OVERWRITTEN (not accumulated). +#[inline(never)] +fn decompose_ring_interleaved( + coeffs: &[u128; D], + digit_buf: &mut [Vec], + num_digits: usize, + p: &DecomposeParams, +) { + let bulk_end = D - (D % 3); + + for base in (0..bulk_end).step_by(3) { + let mut c0 = to_signed(coeffs[base], p); + let mut c1 = to_signed(coeffs[base + 1], p); + let mut c2 = to_signed(coeffs[base + 2], p); + + for plane in digit_buf.iter_mut().take(num_digits) { + let d0 = extract_balanced_digit(&mut c0, p); + let d1 = extract_balanced_digit(&mut c1, p); + let d2 = extract_balanced_digit(&mut c2, p); + plane[base] = d0 as i8; + plane[base + 1] = d1 as i8; + plane[base + 2] = d2 as i8; + } + } + + for idx in bulk_end..D { + let mut c = to_signed(coeffs[idx], p); + for plane in digit_buf.iter_mut().take(num_digits) { + plane[idx] = extract_balanced_digit(&mut c, p) as i8; + } + } +} + +#[inline(always)] +fn to_signed(canonical: u128, p: &DecomposeParams) -> i128 { + if canonical > p.half_q { + -((p.q - canonical) as i128) + } else { + canonical as i128 + } +} + +#[inline(always)] +fn extract_balanced_digit(c: &mut i128, p: &DecomposeParams) -> i32 { + let d = *c & p.mask; + let balanced = if d >= p.half_b { d - p.b_val } else { d }; + *c = (*c - balanced) >> p.log_basis; + balanced as i32 +} + +/// Scalar sparse-multiply-accumulate: accumulate `challenge * digit_plane` +/// into `acc` using the rotate-and-add formulation. +/// +/// `digit_plane` is `[i8; D]`, `acc` is `[i32; D]`. +/// Each challenge term rotates the digit plane and adds/subtracts contiguously. +fn sparse_mul_acc_scalar( + digit_plane: &[i8], + challenge: &SparseChallenge, + acc: &mut [i32; D], +) { + for (&pos, &coeff) in challenge.positions.iter().zip(challenge.coeffs.iter()) { + let p = pos as usize; + let split = D - p; + if coeff > 0 { + for i in 0..split { + acc[i + p] += digit_plane[i] as i32; + } + for i in split..D { + acc[i - split] -= digit_plane[i] as i32; + } + } else { + for i in 0..split { + acc[i + p] -= digit_plane[i] as i32; + } + for i in split..D { + acc[i - split] += digit_plane[i] as i32; + } + } + } +} + +/// Dispatch to NEON or scalar sparse-multiply-accumulate. +#[inline(always)] +fn sparse_mul_acc( + digit_plane: &[i8], + challenge: &SparseChallenge, + acc: &mut [i32; D], +) { + #[cfg(target_arch = "aarch64")] + { + if neon::use_neon_ntt() { + unsafe { + decompose_fold_neon::sparse_mul_acc_neon( + digit_plane.as_ptr(), + acc.as_mut_ptr(), + D, + &challenge.positions, + &challenge.coeffs, + ); + } + return; + } + } + sparse_mul_acc_scalar::(digit_plane, challenge, acc); +} + +/// Operations the Hachi commitment scheme needs from a polynomial. +/// +/// The four methods correspond to the four places in commit/prove that consume +/// polynomial data. Implementations decide *how* to carry out each operation +/// (dense decompose + NTT, sparse monomial tricks, streaming, etc.). +pub trait HachiPolyOps: Clone + Send + Sync { + /// Per-polynomial cache type for the A-matrix commit path. + /// + /// `DensePoly` uses `NttSlotCache` (CRT+NTT of A for dense mat-vec). + /// `OneHotPoly` uses `()` (one-hot commit bypasses NTT entirely). + type CommitCache: Send + Sync; + + /// Total number of ring elements in the polynomial. + fn num_ring_elems(&self) -> usize; + + /// **Op 1 — prove: ring-space evaluation.** + /// + /// Computes the global weighted sum `y = Σᵢ scalars[i] · self[i]`. + /// + /// `scalars` has length >= `num_ring_elems`; excess entries are ignored. + fn evaluate_ring(&self, scalars: &[F]) -> CyclotomicRing; + + /// **Op 2 — prove: per-block fold.** + /// + /// For each contiguous block of `block_len` ring elements, computes + /// `Σⱼ scalars[j] · self[i·block_len + j]`. + /// + /// Returns one ring element per block (total `ceil(num_ring_elems / block_len)`). + /// `scalars` has length `block_len`. + fn fold_blocks(&self, scalars: &[F], block_len: usize) -> Vec>; + + /// **Op 3 — prove: decompose + challenge-fold.** + /// + /// For each block of `block_len` ring elements: + /// 1. Decompose: `sᵢ = G⁻¹(blockᵢ)` via `balanced_decompose_pow2(num_digits, log_basis)`. + /// 2. Accumulate: `z += cᵢ ⊗ sᵢ` (sparse challenge multiplication). + /// + /// Returns `z` of length `block_len · num_digits`. + fn decompose_fold( + &self, + challenges: &[SparseChallenge], + block_len: usize, + num_digits: usize, + log_basis: u32, + ) -> Vec>; + + /// **Op 4 — commit: per-block inner Ajtai.** + /// + /// For each block of `block_len` ring elements: + /// 1. `sᵢ = G⁻¹(blockᵢ)` (balanced decomposition to i8 digits). + /// 2. `tᵢ = A · sᵢ` (matrix-vector multiply via NTT cache or sparse path). + /// 3. `t̂ᵢ = G⁻¹(tᵢ)` (decompose rows to i8 digits). + /// + /// Returns one `t̂ᵢ` vector per block as `[i8; D]` digit planes. + /// + /// # Errors + /// + /// Returns an error if the cached matrix-vector multiply fails. + fn commit_inner( + &self, + a_matrix: &[Vec>], + ntt_a: &NttSlotCache, + block_len: usize, + num_digits: usize, + log_basis: u32, + ) -> Result>, HachiError>; +} + +/// Dense polynomial: all ring coefficients materialized in memory. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct DensePoly { + /// Ring coefficients in sequential block order. + pub coeffs: Vec>, +} + +impl DensePoly { + /// Pack field-element evaluations into ring elements. + /// + /// The first `α = log₂(D)` variables become coefficient slots within each + /// ring element; the remaining variables index ring elements. + /// + /// # Errors + /// + /// Returns an error if `D` is not a power of two, `num_vars < log₂(D)`, or + /// `evals.len() != 2^num_vars`. + pub fn from_field_evals(num_vars: usize, evals: &[F]) -> Result { + if D == 0 || !D.is_power_of_two() { + return Err(HachiError::InvalidInput(format!( + "ring degree D={D} is not a power of two" + ))); + } + let alpha = D.trailing_zeros() as usize; + if num_vars < alpha { + return Err(HachiError::InvalidInput(format!( + "num_vars {num_vars} is smaller than alpha {alpha}" + ))); + } + let expected_len = 1usize + .checked_shl(num_vars as u32) + .ok_or_else(|| HachiError::InvalidInput(format!("2^{num_vars} does not fit usize")))?; + if evals.len() != expected_len { + return Err(HachiError::InvalidSize { + expected: expected_len, + actual: evals.len(), + }); + } + + let outer_len = expected_len / D; + let coeffs: Vec> = (0..outer_len) + .map(|i| CyclotomicRing::from_slice(&evals[i * D..(i + 1) * D])) + .collect(); + Ok(Self { coeffs }) + } + + /// Wrap an existing vector of ring elements. + pub fn from_ring_coeffs(coeffs: Vec>) -> Self { + Self { coeffs } + } +} + +impl HachiPolyOps for DensePoly +where + F: FieldCore + CanonicalField, +{ + type CommitCache = NttSlotCache; + + fn num_ring_elems(&self) -> usize { + self.coeffs.len() + } + + fn evaluate_ring(&self, scalars: &[F]) -> CyclotomicRing { + #[cfg(feature = "parallel")] + { + self.coeffs + .par_iter() + .zip(scalars.par_iter()) + .fold( + || CyclotomicRing::::zero(), + |acc, (f_i, w_i)| acc + f_i.scale(w_i), + ) + .reduce(|| CyclotomicRing::::zero(), |a, b| a + b) + } + #[cfg(not(feature = "parallel"))] + { + self.coeffs + .iter() + .zip(scalars.iter()) + .fold(CyclotomicRing::::zero(), |acc, (f_i, w_i)| { + acc + f_i.scale(w_i) + }) + } + } + + fn fold_blocks(&self, scalars: &[F], block_len: usize) -> Vec> { + let n = self.coeffs.len(); + let num_blocks = n.div_ceil(block_len); + cfg_into_iter!(0..num_blocks) + .map(|i| { + let start = i * block_len; + let end = (start + block_len).min(n); + let block = &self.coeffs[start..end]; + let mut acc = CyclotomicRing::::zero(); + for (b_j, &a_j) in block.iter().zip(scalars.iter()) { + acc += b_j.scale(&a_j); + } + acc + }) + .collect() + } + + fn decompose_fold( + &self, + challenges: &[SparseChallenge], + block_len: usize, + num_digits: usize, + log_basis: u32, + ) -> Vec> { + let n = self.coeffs.len(); + let coeffs = &self.coeffs; + + let q = (-F::one()).to_canonical_u128() + 1; + let params = DecomposeParams { + half_q: q / 2, + q, + mask: (1i128 << log_basis) - 1, + half_b: 1i128 << (log_basis - 1), + b_val: 1i128 << log_basis, + log_basis, + }; + + // Two-phase approach: decompose ring element coefficients into i8 digit + // planes, then scatter via sparse polynomial multiply. + // + // Phase 1 (decompose): K=3 interleaved carry chains for ILP (~3x over + // single-chain). Writes into a digit_buf [num_digits][D] in i8 (~16 KB, + // L1-resident). + // + // Phase 2 (scatter): rotate-and-add formulation — contiguous NEON + // SADDW/SSUBW on aarch64, scalar fallback elsewhere. Accumulates into + // z_local [num_digits][D] in i32 (~66 KB, L2-resident). + let z_chunks: Vec>> = cfg_into_iter!(0..block_len) + .map(|elem_idx| { + let mut z_local: Vec<[i32; D]> = vec![[0i32; D]; num_digits]; + let mut digit_buf: Vec> = vec![vec![0i8; D]; num_digits]; + + for (block_idx, c_i) in challenges.iter().enumerate() { + let global_idx = block_idx * block_len + elem_idx; + if global_idx >= n { + continue; + } + let ring = &coeffs[global_idx]; + + let canonical: [u128; D] = from_fn(|k| ring.coeffs[k].to_canonical_u128()); + decompose_ring_interleaved::( + &canonical, + &mut digit_buf, + num_digits, + ¶ms, + ); + + for digit in 0..num_digits { + sparse_mul_acc::(&digit_buf[digit], c_i, &mut z_local[digit]); + } + } + + let q = params.q; + z_local + .into_iter() + .map(|arr| { + let field_coeffs: [F; D] = from_fn(|k| { + let v = arr[k]; + if v >= 0 { + F::from_canonical_u128_reduced(v as u128) + } else { + F::from_canonical_u128_reduced(q - ((-v) as u128)) + } + }); + CyclotomicRing::from_coefficients(field_coeffs) + }) + .collect() + }) + .collect(); + + let mut z = Vec::with_capacity(block_len * num_digits); + for chunk in z_chunks { + z.extend(chunk); + } + z + } + + #[tracing::instrument(skip_all, name = "DensePoly::commit_inner")] + fn commit_inner( + &self, + _a_matrix: &[Vec>], + ntt_a: &NttSlotCache, + block_len: usize, + num_digits: usize, + log_basis: u32, + ) -> Result>, HachiError> { + let n = self.coeffs.len(); + let num_blocks = n.div_ceil(block_len); + + let block_slices: Vec<&[CyclotomicRing]> = (0..num_blocks) + .map(|i| { + let start = i * block_len; + if start >= n { + &[] as &[CyclotomicRing] + } else { + &self.coeffs[start..(start + block_len).min(n)] + } + }) + .collect(); + + let t_all = mat_vec_mul_ntt_i8(ntt_a, &block_slices, num_digits, log_basis); + + let results: Vec> = cfg_into_iter!(t_all) + .map(|t_i| decompose_rows_i8(&t_i, num_digits, log_basis)) + .collect(); + + Ok(results) + } +} + +/// Types usable as one-hot position indices. +/// +/// Implemented for `u8`, `u16`, `u32`, and `usize`. +pub trait OneHotIndex: Copy + Send + Sync + std::fmt::Debug + 'static { + /// Convert to `usize` for indexing. + fn as_usize(self) -> usize; +} + +impl OneHotIndex for u8 { + #[inline] + fn as_usize(self) -> usize { + self as usize + } +} + +impl OneHotIndex for u16 { + #[inline] + fn as_usize(self) -> usize { + self as usize + } +} + +impl OneHotIndex for u32 { + #[inline] + fn as_usize(self) -> usize { + self as usize + } +} + +impl OneHotIndex for usize { + #[inline] + fn as_usize(self) -> usize { + self + } +} + +/// One-hot polynomial: sparse witness with at most one nonzero field element +/// per chunk of size `onehot_k`. +/// +/// Exploits sparsity in all four operations, avoiding inner ring +/// multiplications during commit and decomposing only nonzero monomials. +/// +/// Generic over `I`: the index type stored per chunk. Use `u8` when +/// `onehot_k <= 256` to cut per-entry memory from 16 bytes to 2 bytes. +#[derive(Debug, Clone)] +pub struct OneHotPoly { + onehot_k: usize, + indices: Vec>, + m_vars: usize, + sparse_blocks: Vec>, + _marker: PhantomData, +} + +impl OneHotPoly { + /// Build a one-hot polynomial from chunk size and hot-position indices. + /// + /// `indices[c]` is the hot position in chunk `c` (`None` for all-zero chunks). + /// + /// # Errors + /// + /// Returns an error if dimensions are inconsistent or any index is out of range. + pub fn new( + onehot_k: usize, + indices: Vec>, + r_vars: usize, + m_vars: usize, + ) -> Result { + let sparse_blocks = map_onehot_to_sparse_blocks(onehot_k, &indices, r_vars, m_vars, D)?; + Ok(Self { + onehot_k, + indices, + m_vars, + sparse_blocks, + _marker: PhantomData, + }) + } + + fn total_ring_elems(&self) -> usize { + let total_field = self.indices.len() * self.onehot_k; + total_field / D + } +} + +impl HachiPolyOps for OneHotPoly +where + F: FieldCore + CanonicalField + HasWide, +{ + type CommitCache = NttSlotCache; + + fn num_ring_elems(&self) -> usize { + self.total_ring_elems() + } + + fn evaluate_ring(&self, scalars: &[F]) -> CyclotomicRing { + let block_len = 1usize << self.m_vars; + cfg_fold_reduce!( + 0..self.sparse_blocks.len(), + || CyclotomicRing::::zero(), + |mut acc: CyclotomicRing, block_idx: usize| { + let block_offset = block_idx * block_len; + for entry in &self.sparse_blocks[block_idx] { + let ring_idx = block_offset + entry.pos_in_block; + if ring_idx < scalars.len() { + let s = scalars[ring_idx]; + for &ci in &entry.nonzero_coeffs { + acc.coeffs[ci] += s; + } + } + } + acc + }, + |a, b| a + b + ) + } + + fn fold_blocks(&self, scalars: &[F], block_len: usize) -> Vec> { + cfg_iter!(self.sparse_blocks) + .map(|entries| { + let mut coeffs_acc = [F::zero(); D]; + for entry in entries { + if entry.pos_in_block < scalars.len() && entry.pos_in_block < block_len { + let s = scalars[entry.pos_in_block]; + for &ci in &entry.nonzero_coeffs { + coeffs_acc[ci] += s; + } + } + } + CyclotomicRing::from_coefficients(coeffs_acc) + }) + .collect() + } + + fn decompose_fold( + &self, + challenges: &[SparseChallenge], + block_len: usize, + num_digits: usize, + _log_basis: u32, + ) -> Vec> { + let inner_width = block_len * num_digits; + let num_blocks = self.sparse_blocks.len(); + + // One-hot coefficients are {0,1}: balanced_decompose_pow2 produces + // nonzero output only in digit plane 0 (the value itself). + // + // Direct sparse-sparse multiply: for each nonzero coefficient at + // position `ci` and each challenge term `(pos, coeff)`, we know the + // exact output position in the cyclotomic ring (X^D + 1). + // O(omega * |nonzero_coeffs|) per entry instead of O(omega * D). + cfg_fold_reduce!( + 0..challenges.len().min(num_blocks), + || vec![CyclotomicRing::::zero(); inner_width], + |mut z: Vec>, i: usize| { + let c_i = &challenges[i]; + for entry in &self.sparse_blocks[i] { + let j = entry.pos_in_block * num_digits; + let z_coeffs = &mut z[j].coeffs; + for (&pos, &coeff) in c_i.positions.iter().zip(c_i.coeffs.iter()) { + let c_val = F::from_i64(coeff as i64); + for &ci in &entry.nonzero_coeffs { + let target = ci + pos as usize; + if target < D { + z_coeffs[target] += c_val; + } else { + z_coeffs[target - D] -= c_val; + } + } + } + } + z + }, + |mut a: Vec>, b: Vec>| { + for (ai, bi) in a.iter_mut().zip(b.into_iter()) { + *ai += bi; + } + a + } + ) + } + + #[tracing::instrument(skip_all, name = "OneHotPoly::commit_inner")] + fn commit_inner( + &self, + a_matrix: &[Vec>], + _ntt_a: &NttSlotCache, + block_len: usize, + num_digits: usize, + log_basis: u32, + ) -> Result>, HachiError> { + let n_a = a_matrix.len(); + let zero_block_len = n_a.checked_mul(num_digits).unwrap(); + + let t_hat_all: Vec> = cfg_iter!(self.sparse_blocks) + .map(|block_entries| { + if block_entries.is_empty() { + vec![[0i8; D]; zero_block_len] + } else { + let t_i = + inner_ajtai_onehot_wide(a_matrix, block_entries, block_len, num_digits); + decompose_rows_i8(&t_i, num_digits, log_basis) + } + }) + .collect(); + + Ok(t_hat_all) + } +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::protocol::commitment::{HachiCommitmentCore, RingCommitmentScheme}; + use crate::test_utils::{TinyConfig, D as TestD, F as TestF}; + use crate::FromSmallInt; + + #[test] + fn dense_poly_from_field_evals_roundtrip() { + let num_vars = 10; + let len = 1usize << num_vars; + let evals: Vec = (0..len).map(|i| TestF::from_u64(i as u64)).collect(); + let poly = DensePoly::::from_field_evals(num_vars, &evals).unwrap(); + assert_eq!(poly.num_ring_elems(), len / TestD); + } + + #[test] + fn dense_commit_inner_matches_ring_commit() { + let (setup, _) = + >::setup(16) + .unwrap(); + let layout = setup.layout(); + let num_ring = layout.num_blocks * layout.block_len; + let evals: Vec = (0..num_ring * TestD) + .map(|i| TestF::from_u64(i as u64)) + .collect(); + + let alpha = TestD.trailing_zeros() as usize; + let num_vars = alpha + layout.m_vars + layout.r_vars; + let poly = DensePoly::::from_field_evals(num_vars, &evals).unwrap(); + + let t_hat_poly = poly + .commit_inner( + &setup.expanded.A, + &setup.ntt_A, + layout.block_len, + layout.num_digits_commit, + layout.log_basis, + ) + .unwrap(); + + let w = + >::commit_coeffs( + &poly.coeffs, + &setup, + ) + .unwrap(); + + assert_eq!(t_hat_poly, w.t_hat); + } + + #[test] + fn onehot_commit_inner_matches_ring_commit_onehot() { + let (setup, _) = + >::setup(16) + .unwrap(); + let layout = setup.layout(); + let total_ring = layout.num_blocks * layout.block_len; + let onehot_k = TestD; + let num_chunks = total_ring; + let indices: Vec> = (0..num_chunks).map(|i| Some(i % onehot_k)).collect(); + + let poly = OneHotPoly::::new( + onehot_k, + indices.clone(), + layout.r_vars, + layout.m_vars, + ) + .unwrap(); + + let t_hat_poly = poly + .commit_inner( + &setup.expanded.A, + &setup.ntt_A, + layout.block_len, + layout.num_digits_commit, + layout.log_basis, + ) + .unwrap(); + + let w = + >::commit_onehot( + onehot_k, &indices, &setup, + ) + .unwrap(); + + assert_eq!(t_hat_poly, w.t_hat); + } +} diff --git a/src/protocol/mod.rs b/src/protocol/mod.rs index 27b5ac70..3bc37b9f 100644 --- a/src/protocol/mod.rs +++ b/src/protocol/mod.rs @@ -7,6 +7,7 @@ pub mod challenges; pub mod commitment; pub mod commitment_scheme; +pub mod hachi_poly_ops; pub mod opening_point; pub mod proof; pub mod quadratic_equation; @@ -16,14 +17,15 @@ pub mod transcript; pub use commitment::{ AppendToTranscript, CommitmentConfig, CommitmentScheme, DummyProof, - DynamicSmallTestCommitmentConfig, HachiCommitment, HachiCommitmentCore, HachiCommitmentLayout, - HachiExpandedSetup, HachiOpeningClaim, HachiOpeningPoint, HachiPreparedSetup, HachiProverSetup, - HachiSetupSeed, HachiVerifierSetup, ProductionFp128CommitmentConfig, RingCommitment, - RingCommitmentScheme, SmallTestCommitmentConfig, StreamingCommitmentScheme, + DynamicSmallTestCommitmentConfig, Fp128CommitmentConfig, HachiCommitment, HachiCommitmentCore, + HachiCommitmentLayout, HachiExpandedSetup, HachiOpeningClaim, HachiOpeningPoint, + HachiProverSetup, HachiSetupSeed, HachiVerifierSetup, RingCommitment, RingCommitmentScheme, + SmallTestCommitmentConfig, }; -pub use commitment_scheme::{commit_onehot, HachiChunkState, HachiCommitmentScheme}; -pub use opening_point::RingOpeningPoint; -pub use proof::{HachiProof, SumcheckAux}; +pub use commitment_scheme::HachiCommitmentScheme; +pub use hachi_poly_ops::{DensePoly, HachiPolyOps, OneHotIndex, OneHotPoly}; +pub use opening_point::{BasisMode, RingOpeningPoint}; +pub use proof::{HachiLevelProof, HachiProof, PackedDigits}; pub use quadratic_equation::QuadraticEquation; pub use sumcheck::batched_sumcheck::{prove_batched_sumcheck, verify_batched_sumcheck}; pub use sumcheck::{ diff --git a/src/protocol/opening_point.rs b/src/protocol/opening_point.rs index 154402a9..4d80563d 100644 --- a/src/protocol/opening_point.rs +++ b/src/protocol/opening_point.rs @@ -2,15 +2,36 @@ use crate::FieldCore; -/// Ring-native opening point storing field scalars (Lagrange weights). +/// Polynomial basis mode for the evaluation relation. +/// +/// Determines how the polynomial's values are interpreted during an opening +/// proof. The commitment itself is basis-agnostic; the basis only affects +/// the tensor-product weights used in `prove` and `verify`. +#[derive(Clone, Copy, Debug, PartialEq, Eq)] +pub enum BasisMode { + /// Evaluations over the boolean hypercube. + /// + /// The weight vector is `⊗ᵢ (1 − xᵢ, xᵢ)` (multilinear Lagrange basis). + /// Use when the committed values are `f(b)` for `b ∈ {0,1}^n`. + Lagrange, + + /// Coefficients of multilinear monomials. + /// + /// The weight vector is `⊗ᵢ (1, xᵢ)`. + /// Use when the committed values are the coefficients `c_S` such that + /// `f(x) = Σ_S c_S · ∏_{i ∈ S} x_i`. + Monomial, +} + +/// Ring-native opening point storing field scalars. /// /// Contains the two vectors used by the §4.2 prover: /// - `a`: evaluation vector of length `2^m` (inner-block coordinates). /// - `b`: block-select vector of length `2^r` (outer coordinates). /// /// These are raw field scalars, not ring elements — they originate from -/// multilinear Lagrange basis evaluations and are always constant (scalar) -/// ring elements when embedded into the ring. +/// basis weight evaluations (Lagrange or monomial) and are always constant +/// (scalar) ring elements when embedded into the ring. #[derive(Debug, Clone, PartialEq, Eq)] pub struct RingOpeningPoint { /// Evaluation vector of length `2^m` (field scalars). diff --git a/src/protocol/proof.rs b/src/protocol/proof.rs index c020f7b7..93f97dde 100644 --- a/src/protocol/proof.rs +++ b/src/protocol/proof.rs @@ -5,121 +5,350 @@ use crate::primitives::serialization::{Compress, SerializationError}; use crate::primitives::serialization::{Valid, Validate}; use crate::protocol::commitment::RingCommitment; use crate::protocol::sumcheck::SumcheckProof; -use crate::{FieldCore, HachiDeserialize, HachiSerialize}; +use crate::{FieldCore, FromSmallInt, HachiDeserialize, HachiSerialize}; use std::io::{Read, Write}; +use std::marker::PhantomData; -/// Prover-side hint produced at commitment time. +/// Bit-packed balanced digits for the final-level witness vector. /// -/// Stores the ring-level coefficients and the decomposed inner-Ajtai outputs -/// `t̂_i`. The basis-decomposed inputs `s_i` are NOT stored; they are -/// recomputed from `ring_coeffs` during proving to avoid multi-GB memory -/// usage at production parameters. +/// Each element is a signed value in `[-b/2, b/2)` where `b = 2^bits_per_elem`, +/// stored in two's-complement using exactly `bits_per_elem` bits per value. +/// This reduces proof size by ~32x compared to storing full field elements. #[derive(Debug, Clone, PartialEq, Eq)] -pub struct HachiCommitmentHint { - /// Decomposed `t̂_i` blocks from the commitment phase. - pub t_hat: Vec>>, - /// Ring coefficients from the §3.1 reduction (evaluation table). - pub ring_coeffs: Vec>, +pub struct PackedDigits { + /// Number of logical elements. + pub num_elems: usize, + /// Bits per element (= `log_basis` from the commitment config). + pub bits_per_elem: u32, + /// Bit-packed two's-complement data. + pub data: Vec, +} + +/// Precomputed lookup table mapping balanced digit index → field element. +/// +/// Wraps `FromSmallInt::digit_lut` with convenient signed-digit indexing. +/// Index a digit `d ∈ [-b/2, b/2)` via [`get`](DigitLut::get). +pub(crate) struct DigitLut { + table: [F; 16], + half_b: i8, +} + +impl DigitLut { + #[inline] + pub(crate) fn new(log_basis: u32) -> Self { + let half_b = 1i8 << (log_basis - 1); + Self { + table: F::digit_lut(log_basis), + half_b, + } + } + + #[inline(always)] + pub(crate) fn get(&self, d: i8) -> F { + self.table[(d + self.half_b) as usize] + } +} + +impl PackedDigits { + /// Pack balanced i8 digits into bit-packed form. + /// + /// Each element must be in `[-b/2, b/2)` where `b = 2^log_basis`. + /// + /// # Panics + /// + /// Panics (in debug) if any element does not fit in `log_basis` bits. + pub fn from_i8_digits(w: &[i8], log_basis: u32) -> Self { + assert!(log_basis > 0 && log_basis <= 7, "log_basis out of range"); + let half_b = 1i8 << (log_basis - 1); + + let bits = log_basis as usize; + let total_bits = w.len() * bits; + let num_bytes = total_bits.div_ceil(8); + let mut data = vec![0u8; num_bytes]; + + for (i, &signed) in w.iter().enumerate() { + debug_assert!( + signed >= -half_b && signed < half_b, + "digit {signed} out of range for log_basis={log_basis}" + ); + let unsigned = (signed as u8) & ((1u8 << bits) - 1); + let bit_offset = i * bits; + let byte_idx = bit_offset / 8; + let bit_idx = bit_offset % 8; + data[byte_idx] |= unsigned << bit_idx; + if bit_idx + bits > 8 { + data[byte_idx + 1] |= unsigned >> (8 - bit_idx); + } + } + + Self { + num_elems: w.len(), + bits_per_elem: log_basis, + data, + } + } + + /// Unpack to field elements using a precomputed lookup table. + pub fn to_field_elems(&self) -> Vec { + let bits = self.bits_per_elem as usize; + let mask = (1u8 << bits) - 1; + let sign_bit = 1u8 << (bits - 1); + let lut = DigitLut::::new(self.bits_per_elem); + + let mut out = Vec::with_capacity(self.num_elems); + for i in 0..self.num_elems { + let bit_offset = i * bits; + let byte_idx = bit_offset / 8; + let bit_idx = bit_offset % 8; + let mut raw = (self.data[byte_idx] >> bit_idx) & mask; + if bit_idx + bits > 8 { + raw |= (self.data[byte_idx + 1] << (8 - bit_idx)) & mask; + } + let signed = if raw & sign_bit != 0 { + raw as i8 | !(mask as i8) + } else { + raw as i8 + }; + out.push(lut.get(signed)); + } + out + } + + /// Number of packed data bytes. + pub fn packed_byte_len(&self) -> usize { + self.data.len() + } +} + +impl HachiSerialize for PackedDigits { + fn serialize_with_mode( + &self, + mut writer: W, + compress: Compress, + ) -> Result<(), SerializationError> { + (self.num_elems as u64).serialize_with_mode(&mut writer, compress)?; + (self.bits_per_elem as u8).serialize_with_mode(&mut writer, compress)?; + writer.write_all(&self.data)?; + Ok(()) + } + + fn serialized_size(&self, _compress: Compress) -> usize { + 8 + 1 + self.data.len() + } +} + +impl Valid for PackedDigits { + fn check(&self) -> Result<(), SerializationError> { + if self.bits_per_elem == 0 || self.bits_per_elem > 7 { + return Err(SerializationError::InvalidData( + "bits_per_elem out of range".to_string(), + )); + } + let expected_bytes = (self.num_elems * self.bits_per_elem as usize).div_ceil(8); + if self.data.len() != expected_bytes { + return Err(SerializationError::InvalidData( + "packed data length mismatch".to_string(), + )); + } + Ok(()) + } +} + +impl HachiDeserialize for PackedDigits { + fn deserialize_with_mode( + mut reader: R, + compress: Compress, + validate: Validate, + ) -> Result { + let num_elems = u64::deserialize_with_mode(&mut reader, compress, validate)? as usize; + let bits_per_elem = u8::deserialize_with_mode(&mut reader, compress, validate)? as u32; + let num_bytes = (num_elems * bits_per_elem as usize).div_ceil(8); + let mut data = vec![0u8; num_bytes]; + reader.read_exact(&mut data)?; + let out = Self { + num_elems, + bits_per_elem, + data, + }; + if matches!(validate, Validate::Yes) { + out.check()?; + } + Ok(out) + } } -/// Temporary auxiliary data the verifier needs for sumcheck output verification. +/// Prover-side hint produced at commitment time. /// -/// Will be removed once recursive PCS evaluation proofs replace the direct -/// oracle check at the end of each sumcheck instance. +/// Contains the decomposed inner-Ajtai outputs `t̂_i` needed by the +/// ring-switch step of the prover. The polynomial itself (ring coefficients) +/// is passed separately to `prove` via `HachiPolyOps`. #[derive(Debug, Clone, PartialEq, Eq)] -pub struct SumcheckAux { - /// `w` coefficients (z and r coefficients, concatenated). The verifier - /// reshapes this into sumcheck evaluation form to compute the expected - /// output claims for F_0 and F_alpha. - pub w: Vec, +pub struct HachiCommitmentHint { + /// Decomposed `t̂_i` blocks from the commitment phase as i8 digit planes. + pub t_hat: Vec>, + _marker: PhantomData, +} + +impl HachiCommitmentHint { + /// Construct a new hint from i8 digit plane blocks. + pub fn new(t_hat: Vec>) -> Self { + Self { + t_hat, + _marker: PhantomData, + } + } } -/// Hachi Proof for One Iteration. +/// Proof for a single fold level (quad_eq + ring_switch + sumcheck). #[derive(Debug, Clone, PartialEq, Eq)] -pub struct HachiProof { +pub struct HachiLevelProof { /// `y_ring` from the §3.1 reduction. pub y_ring: CyclotomicRing, /// `v = D · ŵ`. pub v: Vec>, /// Batched sumcheck proof (F_0 norm + F_α relation, §4.3). pub sumcheck_proof: SumcheckProof, - /// Temporary verifier auxiliary (will be removed with recursive PCS). - pub sumcheck_aux: SumcheckAux, /// Commitment to the sumcheck witness `w`. pub w_commitment: RingCommitment, + /// Claimed evaluation of w at the sumcheck challenge point. + /// Used by the verifier to check the expected output claim without + /// needing the full w vector. + pub w_eval: F, +} + +/// Hachi PCS proof with multi-level folding. +/// +/// Each level runs the full protocol (quadratic equation, ring switch, +/// sumcheck) on the previous level's witness `w`. The final level sends +/// `w` directly for the verifier to check, packed as balanced digits. +#[derive(Debug, Clone, PartialEq, Eq)] +pub struct HachiProof { + /// Per-level proofs, from the original polynomial (level 0) through + /// recursive w-openings. + pub levels: Vec>, + /// The witness vector at the deepest fold level, bit-packed as balanced + /// digits in `[-b/2, b/2)`. Use [`PackedDigits::to_field_elems`] to + /// reconstruct `Vec`. + pub final_w: PackedDigits, } impl HachiProof { /// Returns the proof size in bytes (uncompressed). pub fn size(&self) -> usize { - self.v.serialized_size(Compress::No) - + self.y_ring.serialized_size(Compress::No) - + self.sumcheck_aux.w.serialized_size(Compress::No) - + self.sumcheck_proof.serialized_size(Compress::No) - + self.w_commitment.serialized_size(Compress::No) + let levels_size: usize = self + .levels + .iter() + .map(|lp| { + lp.y_ring.serialized_size(Compress::No) + + lp.v.serialized_size(Compress::No) + + lp.sumcheck_proof.serialized_size(Compress::No) + + lp.w_commitment.serialized_size(Compress::No) + + lp.w_eval.serialized_size(Compress::No) + }) + .sum(); + levels_size + self.final_w.serialized_size(Compress::No) } } -impl HachiSerialize for SumcheckAux { +impl HachiSerialize for HachiCommitmentHint { fn serialize_with_mode( &self, - writer: W, + mut writer: W, compress: Compress, ) -> Result<(), SerializationError> { - self.w.serialize_with_mode(writer, compress) + (self.t_hat.len() as u64).serialize_with_mode(&mut writer, compress)?; + for block in &self.t_hat { + (block.len() as u64).serialize_with_mode(&mut writer, compress)?; + for plane in block { + // Safety: i8 and u8 have identical layout. + let bytes: &[u8] = + unsafe { std::slice::from_raw_parts(plane.as_ptr().cast::(), D) }; + writer.write_all(bytes)?; + } + } + Ok(()) } - fn serialized_size(&self, compress: Compress) -> usize { - self.w.serialized_size(compress) + fn serialized_size(&self, _compress: Compress) -> usize { + 8 + self + .t_hat + .iter() + .map(|block| 8 + block.len() * D) + .sum::() } } -impl Valid for SumcheckAux { +impl Valid for HachiCommitmentHint { fn check(&self) -> Result<(), SerializationError> { Ok(()) } } -impl HachiDeserialize for SumcheckAux { +impl HachiDeserialize for HachiCommitmentHint { fn deserialize_with_mode( - reader: R, + mut reader: R, compress: Compress, validate: Validate, ) -> Result { - Ok(Self { - w: Vec::::deserialize_with_mode(reader, compress, validate)?, - }) + let num_blocks = u64::deserialize_with_mode(&mut reader, compress, validate)? as usize; + let mut t_hat = Vec::with_capacity(num_blocks); + for _ in 0..num_blocks { + let block_len = u64::deserialize_with_mode(&mut reader, compress, validate)? as usize; + let mut block = Vec::with_capacity(block_len); + for _ in 0..block_len { + let mut plane = [0i8; D]; + // Safety: i8 and u8 have identical layout. + let bytes: &mut [u8] = + unsafe { std::slice::from_raw_parts_mut(plane.as_mut_ptr().cast::(), D) }; + reader.read_exact(bytes)?; + block.push(plane); + } + t_hat.push(block); + } + Ok(Self::new(t_hat)) } } -impl HachiSerialize for HachiCommitmentHint { +impl HachiSerialize for HachiLevelProof { fn serialize_with_mode( &self, mut writer: W, compress: Compress, ) -> Result<(), SerializationError> { - self.t_hat.serialize_with_mode(&mut writer, compress)?; - self.ring_coeffs.serialize_with_mode(&mut writer, compress) + self.y_ring.serialize_with_mode(&mut writer, compress)?; + self.v.serialize_with_mode(&mut writer, compress)?; + self.sumcheck_proof + .serialize_with_mode(&mut writer, compress)?; + self.w_commitment + .serialize_with_mode(&mut writer, compress)?; + self.w_eval.serialize_with_mode(&mut writer, compress) } fn serialized_size(&self, compress: Compress) -> usize { - self.t_hat.serialized_size(compress) + self.ring_coeffs.serialized_size(compress) + self.y_ring.serialized_size(compress) + + self.v.serialized_size(compress) + + self.sumcheck_proof.serialized_size(compress) + + self.w_commitment.serialized_size(compress) + + self.w_eval.serialized_size(compress) } } -impl Valid for HachiCommitmentHint { +impl Valid for HachiLevelProof { fn check(&self) -> Result<(), SerializationError> { Ok(()) } } -impl HachiDeserialize for HachiCommitmentHint { +impl HachiDeserialize for HachiLevelProof { fn deserialize_with_mode( mut reader: R, compress: Compress, validate: Validate, ) -> Result { Ok(Self { - t_hat: Vec::deserialize_with_mode(&mut reader, compress, validate)?, - ring_coeffs: Vec::deserialize_with_mode(&mut reader, compress, validate)?, + y_ring: CyclotomicRing::deserialize_with_mode(&mut reader, compress, validate)?, + v: Vec::deserialize_with_mode(&mut reader, compress, validate)?, + sumcheck_proof: SumcheckProof::deserialize_with_mode(&mut reader, compress, validate)?, + w_commitment: RingCommitment::deserialize_with_mode(&mut reader, compress, validate)?, + w_eval: F::deserialize_with_mode(&mut reader, compress, validate)?, }) } } @@ -130,20 +359,19 @@ impl HachiSerialize for HachiProof { mut writer: W, compress: Compress, ) -> Result<(), SerializationError> { - self.y_ring.serialize_with_mode(&mut writer, compress)?; - self.v.serialize_with_mode(&mut writer, compress)?; - self.sumcheck_proof - .serialize_with_mode(&mut writer, compress)?; - self.sumcheck_aux - .serialize_with_mode(&mut writer, compress)?; - self.w_commitment.serialize_with_mode(&mut writer, compress) + (self.levels.len() as u32).serialize_with_mode(&mut writer, compress)?; + for level in &self.levels { + level.serialize_with_mode(&mut writer, compress)?; + } + self.final_w.serialize_with_mode(&mut writer, compress) } fn serialized_size(&self, compress: Compress) -> usize { - self.y_ring.serialized_size(compress) - + self.v.serialized_size(compress) - + self.sumcheck_proof.serialized_size(compress) - + self.sumcheck_aux.serialized_size(compress) - + self.w_commitment.serialized_size(compress) + 4 + self + .levels + .iter() + .map(|l| l.serialized_size(compress)) + .sum::() + + self.final_w.serialized_size(compress) } } @@ -159,12 +387,16 @@ impl HachiDeserialize for HachiProof compress: Compress, validate: Validate, ) -> Result { - Ok(Self { - y_ring: CyclotomicRing::deserialize_with_mode(&mut reader, compress, validate)?, - v: Vec::deserialize_with_mode(&mut reader, compress, validate)?, - sumcheck_proof: SumcheckProof::deserialize_with_mode(&mut reader, compress, validate)?, - sumcheck_aux: SumcheckAux::deserialize_with_mode(&mut reader, compress, validate)?, - w_commitment: RingCommitment::deserialize_with_mode(&mut reader, compress, validate)?, - }) + let num_levels = u32::deserialize_with_mode(&mut reader, compress, validate)? as usize; + let mut levels = Vec::with_capacity(num_levels); + for _ in 0..num_levels { + levels.push(HachiLevelProof::deserialize_with_mode( + &mut reader, + compress, + validate, + )?); + } + let final_w = PackedDigits::deserialize_with_mode(&mut reader, compress, validate)?; + Ok(Self { levels, final_w }) } } diff --git a/src/protocol/quadratic_equation.rs b/src/protocol/quadratic_equation.rs index 092a017e..9a36ea96 100644 --- a/src/protocol/quadratic_equation.rs +++ b/src/protocol/quadratic_equation.rs @@ -4,121 +4,93 @@ //! the quadratic equation components M, y, z, and v. use crate::algebra::{CyclotomicRing, SparseChallenge, SparseChallengeConfig}; -use crate::cfg_iter; use crate::error::HachiError; #[cfg(feature = "parallel")] use crate::parallel::*; use crate::protocol::challenges::sparse::sample_sparse_challenges; -use crate::protocol::commitment::utils::crt_ntt::NttMatrixCache; +use crate::protocol::commitment::utils::crt_ntt::NttSlotCache; use crate::protocol::commitment::utils::linear::{ - decompose_block, mat_vec_mul_ntt_cached, MatrixSlot, + flatten_i8_blocks, mat_vec_mul_ntt_single_i8, unreduced_quotient_rows_ntt_cached, + unreduced_quotient_rows_ntt_cached_i8, }; use crate::protocol::commitment::utils::norm::{detect_field_modulus, vec_inf_norm}; use crate::protocol::commitment::{ - CommitmentConfig, HachiCommitmentLayout, HachiExpandedSetup, HachiProverSetup, - HachiVerifierSetup, RingCommitment, + CommitmentConfig, HachiCommitmentLayout, HachiExpandedSetup, HachiProverSetup, RingCommitment, }; +use crate::protocol::hachi_poly_ops::HachiPolyOps; use crate::protocol::opening_point::RingOpeningPoint; use crate::protocol::proof::HachiCommitmentHint; use crate::protocol::ring_switch::eval_ring_at; use crate::protocol::transcript::labels::{ABSORB_PROVER_V, CHALLENGE_STAGE1_FOLD}; use crate::protocol::transcript::Transcript; -use crate::{CanonicalField, FieldCore}; +use crate::{cfg_iter, CanonicalField, FieldCore}; +use std::iter::repeat_n; +use std::marker::PhantomData; +use std::time::Instant; /// **Steps 1–3.** Compute `w_i = a^T G_{2^m} s_i` and decompose: `ŵ_i = G_1^{-1}(w_i)`. /// -/// Recomputes each block's `s_i` from `ring_coeffs` on the fly to avoid -/// storing all `s_i` simultaneously (which can be tens of GB at production -/// parameters). -fn compute_w_hat( +/// Uses `HachiPolyOps::fold_blocks` to compute the per-block dot products, +/// then decomposes each result into i8 digit planes. +/// +/// Returns `(w_hat, w_folded)`: both the i8 digits and the pre-decomposition +/// folded ring elements (kept to avoid a recompose roundtrip later). +fn compute_w_hat( opening_point: &RingOpeningPoint, - ring_coeffs: &[CyclotomicRing], + poly: &P, layout: HachiCommitmentLayout, -) -> Vec>> +) -> (Vec>, Vec>) where F: FieldCore + CanonicalField, - Cfg: CommitmentConfig, + P: HachiPolyOps, { let a = &opening_point.a; let block_len = layout.block_len; - let delta = Cfg::DELTA; - let log_basis = Cfg::LOG_BASIS; + let depth_open = layout.num_digits_open; + let log_basis = layout.log_basis; debug_assert_eq!(a.len(), block_len); - let blocks: Vec<&[CyclotomicRing]> = (0..layout.num_blocks) - .map(|i| { - let start = i * block_len; - let end = (start + block_len).min(ring_coeffs.len()); - if start < ring_coeffs.len() { - &ring_coeffs[start..end] - } else { - &[] as &[CyclotomicRing] - } - }) + let folded = poly.fold_blocks(a, block_len); + let w_hat = folded + .iter() + .map(|w_i| w_i.balanced_decompose_pow2_i8(depth_open, log_basis)) .collect(); - - cfg_iter!(blocks) - .map(|block| { - let s_i = decompose_block(block, delta, log_basis); - let mut w_i = CyclotomicRing::::zero(); - for (j, a_j) in a.iter().enumerate().take(block_len) { - let start = j * delta; - let end = start + delta; - let recomp_j = CyclotomicRing::gadget_recompose_pow2(&s_i[start..end], log_basis); - w_i += recomp_j.scale(a_j); - } - w_i.balanced_decompose_pow2(delta, log_basis) - }) - .collect() + (w_hat, folded) } /// **Step 4.** Compute `v = D · ŵ` (first prover message). fn compute_v( - cache: &NttMatrixCache, - w_hat: &[Vec>], -) -> Result>, HachiError> { - let w_hat_flat: Vec> = - w_hat.iter().flat_map(|v| v.iter().copied()).collect(); - mat_vec_mul_ntt_cached(cache, MatrixSlot::D, &w_hat_flat) + ntt_d: &NttSlotCache, + w_hat_flat: &[[i8; D]], +) -> Vec> { + mat_vec_mul_ntt_single_i8(ntt_d, w_hat_flat) +} + +fn flatten_w_hat(w_hat: &[Vec<[i8; D]>]) -> Vec<[i8; D]> { + w_hat.iter().flat_map(|v| v.iter().copied()).collect() } /// **Steps 7–9.** Fold `z_pre = Σ c_i · s_i` and check `‖z_pre‖_∞ ≤ β`. /// -/// Returns the pre-decomposition `z` vector (before gadget decomposition into -/// `ẑ = J^{-1}(z_pre)`). Callers that need `z_hat` can apply -/// `balanced_decompose_pow2(TAU, LOG_BASIS)` themselves. -fn compute_z_pre( - ring_coeffs: &[CyclotomicRing], +/// Uses `HachiPolyOps::decompose_fold` to carry out the decompose + fold +/// in whatever way the polynomial implementation prefers. +fn compute_z_pre( + poly: &P, challenges: &[SparseChallenge], layout: HachiCommitmentLayout, ) -> Result>, HachiError> where F: FieldCore + CanonicalField, Cfg: CommitmentConfig, + P: HachiPolyOps, { - let block_len = layout.block_len; - let delta = Cfg::DELTA; - let log_basis = Cfg::LOG_BASIS; - let inner_width = block_len * delta; - - debug_assert_eq!(challenges.len(), layout.num_blocks); - - let mut z = vec![CyclotomicRing::::zero(); inner_width]; - - for (i, c_i) in challenges.iter().enumerate() { - let start = i * block_len; - let end = (start + block_len).min(ring_coeffs.len()); - let block = if start < ring_coeffs.len() { - &ring_coeffs[start..end] - } else { - &[] as &[CyclotomicRing] - }; - let s_i = decompose_block(block, delta, log_basis); - for (j, z_j) in z.iter_mut().enumerate() { - *z_j += s_i[j].mul_by_sparse(c_i); - } - } + let z = poly.decompose_fold( + challenges, + layout.block_len, + layout.num_digits_commit, + layout.log_basis, + ); let modulus = detect_field_modulus::(); let norm = vec_inf_norm(&z, modulus); @@ -151,12 +123,16 @@ pub struct QuadraticEquation>>, - /// Decomposed `ŵ_i = G_1^{-1}(w_i)` (prover only). - w_hat: Option>>>, + /// Decomposed `ŵ_i = G_1^{-1}(w_i)` as i8 digit planes (prover only). + w_hat: Option>>, + /// Flattened `w_hat` as i8 digit planes (prover only, computed once and reused). + w_hat_flat: Option>, + /// Pre-decomposition folded ring elements (prover only, avoids recompose roundtrip). + w_folded: Option>>, /// Commitment hint (prover only). hint: Option>, - _marker: std::marker::PhantomData, + _marker: PhantomData, } impl QuadraticEquation @@ -166,26 +142,52 @@ where { /// Prover constructor: runs §4.2 stage 1 and builds all equation components. /// + /// `poly` provides the ring-level polynomial data for fold/decompose ops. + /// `hint` carries `t_hat` from the commitment phase. + /// /// # Errors /// /// Returns an error if the norm check, challenge sampling, or matrix /// generation fails. - pub fn new_prover>( + #[allow(clippy::too_many_arguments)] + #[tracing::instrument(skip_all, name = "QuadraticEquation::new_prover")] + pub fn new_prover, P: HachiPolyOps>( setup: &HachiProverSetup, - ring_opening_point: &RingOpeningPoint, - hint: &HachiCommitmentHint, + ring_opening_point: RingOpeningPoint, + poly: &P, + hint: HachiCommitmentHint, transcript: &mut T, commitment: &RingCommitment, y_ring: &CyclotomicRing, + layout: HachiCommitmentLayout, ) -> Result { - let layout = setup.layout(); - let w_hat = compute_w_hat::(ring_opening_point, &hint.ring_coeffs, layout); - let v = compute_v(setup.ntt_cache()?, &w_hat)?; + let t_wh = Instant::now(); + let (w_hat, w_hat_flat, w_folded) = { + let _span = tracing::info_span!("compute_w_hat").entered(); + let (w_hat, w_folded) = compute_w_hat::(&ring_opening_point, poly, layout); + let w_hat_flat = flatten_w_hat(&w_hat); + (w_hat, w_hat_flat, w_folded) + }; + eprintln!( + " [quad_eq] compute_w_hat+flatten: {:.2}s (blocks={}, depth={})", + t_wh.elapsed().as_secs_f64(), + w_hat.len(), + w_hat.first().map_or(0, |v| v.len()) + ); + + let t_v = Instant::now(); + let v = { + let _span = tracing::info_span!("compute_v").entered(); + compute_v(&setup.ntt_D, &w_hat_flat) + }; + eprintln!( + " [quad_eq] compute_v (D*w_hat): {:.2}s (w_hat_flat_len={})", + t_v.elapsed().as_secs_f64(), + w_hat_flat.len() + ); - // Step 5: append v to transcript transcript.append_serde(ABSORB_PROVER_V, &v); - // Step 6: sample sparse folding challenges let challenge_cfg = SparseChallengeConfig { weight: Cfg::CHALLENGE_WEIGHT, nonzero_coeffs: vec![-1, 1], @@ -197,19 +199,30 @@ where &challenge_cfg, )?; - let z_pre = compute_z_pre::(&hint.ring_coeffs, &challenges, layout)?; + let t_zp = Instant::now(); + let z_pre = { + let _span = tracing::info_span!("compute_z_pre").entered(); + compute_z_pre::(poly, &challenges, layout)? + }; + eprintln!( + " [quad_eq] compute_z_pre: {:.2}s (z_pre_len={})", + t_zp.elapsed().as_secs_f64(), + z_pre.len() + ); - let y = generate_y::(&v, &commitment.u, y_ring)?; + let y = generate_y::(&v, &commitment.u, y_ring, Cfg::N_D, Cfg::N_B, Cfg::N_A)?; Ok(Self { v, challenges, y, - opening_point: ring_opening_point.clone(), + opening_point: ring_opening_point, z_pre: Some(z_pre), w_hat: Some(w_hat), - hint: Some(hint.clone()), - _marker: std::marker::PhantomData, + w_hat_flat: Some(w_hat_flat), + w_folded: Some(w_folded), + hint: Some(hint), + _marker: PhantomData, }) } @@ -218,28 +231,30 @@ where /// # Errors /// /// Returns an error if challenge derivation fails. + #[tracing::instrument(skip_all, name = "QuadraticEquation::new_verifier")] pub fn new_verifier>( - setup: &HachiVerifierSetup, - ring_opening_point: &RingOpeningPoint, - v: &Vec>, + ring_opening_point: RingOpeningPoint, + v: Vec>, transcript: &mut T, commitment: &RingCommitment, y_ring: &CyclotomicRing, + layout: HachiCommitmentLayout, ) -> Result { - let layout = setup.expanded.seed.layout; let challenges = - derive_stage1_challenges::(transcript, v, layout.num_blocks)?; - let y = generate_y::(v, &commitment.u, y_ring)?; + derive_stage1_challenges::(transcript, &v, layout.num_blocks)?; + let y = generate_y::(&v, &commitment.u, y_ring, Cfg::N_D, Cfg::N_B, Cfg::N_A)?; Ok(Self { - v: v.to_vec(), + v, challenges, y, - opening_point: ring_opening_point.clone(), + opening_point: ring_opening_point, z_pre: None, w_hat: None, + w_hat_flat: None, + w_folded: None, hint: None, - _marker: std::marker::PhantomData, + _marker: PhantomData, }) } @@ -268,16 +283,26 @@ where self.z_pre.take() } - /// Get the decomposed witness `ŵ` (prover only). - pub fn w_hat(&self) -> Option<&[Vec>]> { + /// Get the decomposed witness `ŵ` as i8 digit planes (prover only). + pub fn w_hat(&self) -> Option<&[Vec<[i8; D]>]> { self.w_hat.as_deref() } + /// Get the pre-flattened `w_hat` as i8 digit planes (prover only). + pub fn w_hat_flat(&self) -> Option<&[[i8; D]]> { + self.w_hat_flat.as_deref() + } + /// Take ownership of `w_hat`, leaving `None` in its place. - pub fn take_w_hat(&mut self) -> Option>>> { + pub fn take_w_hat(&mut self) -> Option>> { self.w_hat.take() } + /// Get the pre-decomposition folded ring elements (prover only). + pub fn w_folded(&self) -> Option<&[CyclotomicRing]> { + self.w_folded.as_deref() + } + /// Get the commitment hint (prover only). pub fn hint(&self) -> Option<&HachiCommitmentHint> { self.hint.as_ref() @@ -322,58 +347,6 @@ fn gadget_row_scalars(levels: usize, log_basis: u out } -/// Accumulate unreduced polynomial product `a * b` into `poly` (length 2D-1). -fn add_unreduced_product( - poly: &mut [F], - a: &CyclotomicRing, - b: &CyclotomicRing, -) { - if a.is_zero() { - return; - } - let ac = a.coefficients(); - let bc = b.coefficients(); - let is_scalar = ac[1..].iter().all(|c| c.is_zero()); - if is_scalar { - let s = ac[0]; - for k in 0..D { - poly[k] = poly[k] + s * bc[k]; - } - } else { - for t in 0..D { - for s in 0..D { - poly[t + s] = poly[t + s] + ac[t] * bc[s]; - } - } - } -} - -/// Accumulate negated unreduced product `-a * b` into `poly`. -fn sub_unreduced_product( - poly: &mut [F], - a: &CyclotomicRing, - b: &CyclotomicRing, -) { - if a.is_zero() { - return; - } - let ac = a.coefficients(); - let bc = b.coefficients(); - let is_scalar = ac[1..].iter().all(|c| c.is_zero()); - if is_scalar { - let s = ac[0]; - for k in 0..D { - poly[k] = poly[k] - s * bc[k]; - } - } else { - for t in 0..D { - for s in 0..D { - poly[t + s] = poly[t + s] - ac[t] * bc[s]; - } - } - } -} - /// Add scalar * ring_element into the low-D coefficients of `poly`. /// scalar * ring produces degree D-1, so no high-half contribution. fn add_scalar_ring_product( @@ -382,7 +355,7 @@ fn add_scalar_ring_product( ring: &CyclotomicRing, ) { for (k, coeff) in ring.coefficients().iter().enumerate() { - poly[k] = poly[k] + *scalar * *coeff; + poly[k] += *scalar * *coeff; } } @@ -393,120 +366,164 @@ fn sub_scalar_ring_product( ring: &CyclotomicRing, ) { for (k, coeff) in ring.coefficients().iter().enumerate() { - poly[k] = poly[k] - *scalar * *coeff; + poly[k] -= *scalar * *coeff; } } /// Add sparse_challenge * ring_element as unreduced product into `poly`. +/// +/// Exploits sparsity: O(weight * D) instead of O(D^2) schoolbook. fn add_sparse_ring_product( poly: &mut [F], challenge: &SparseChallenge, ring: &CyclotomicRing, ) { - let dense: CyclotomicRing = challenge.to_dense().expect("valid sparse challenge"); - add_unreduced_product(poly, &dense, ring); + let rc = ring.coefficients(); + for (&pos, &coeff) in challenge.positions.iter().zip(challenge.coeffs.iter()) { + let c = F::from_i64(coeff as i64); + let p = pos as usize; + for (s, &r_s) in rc.iter().enumerate() { + poly[p + s] += c * r_s; + } + } } /// Split-eq replacement for `generate_m` + `compute_r_via_poly_division`. /// /// Computes `r` such that `M·z = y + (X^D+1)·r` without materializing M or z. /// Uses split-eq factoring: `kron(left, gadget) · decomposed = left · pre_decomp`. +#[allow(clippy::too_many_arguments, clippy::needless_borrow)] +#[tracing::instrument(skip_all, name = "compute_r_split_eq")] +#[allow(clippy::too_many_arguments)] pub(crate) fn compute_r_split_eq( - setup: &HachiExpandedSetup, + _setup: &HachiExpandedSetup, opening_point: &RingOpeningPoint, challenges: &[SparseChallenge], - w_hat: &[Vec>], - t_hat: &[Vec>], + w_hat_flat: &[[i8; D]], + t_hat: &[Vec<[i8; D]>], + w_folded: &[CyclotomicRing], z_pre: &[CyclotomicRing], y: &[CyclotomicRing], + ntt_a: &NttSlotCache, + ntt_b: &NttSlotCache, + ntt_d: &NttSlotCache, + layout: HachiCommitmentLayout, ) -> Result>, HachiError> where F: FieldCore + CanonicalField, Cfg: CommitmentConfig, { + let decomp_commit = layout.num_digits_commit; + let log_basis = layout.log_basis; let poly_len = 2 * D - 1; let num_rows = Cfg::N_D + Cfg::N_B + 1 + 1 + Cfg::N_A; - let w_hat_flat: Vec> = - w_hat.iter().flat_map(|v| v.iter().copied()).collect(); - let t_hat_flat: Vec> = - t_hat.iter().flat_map(|v| v.iter().copied()).collect(); + let t_hat_flat = flatten_i8_blocks(t_hat); - let mut result = Vec::with_capacity(num_rows); + // NTT-accelerated D, B, and A rows: compute quotient = (cyc - neg) / 2 + let t_d = Instant::now(); + let d_quotients = { + let _span = tracing::info_span!("D_rows_ntt").entered(); + unreduced_quotient_rows_ntt_cached_i8(ntt_d, w_hat_flat) + }; + let d_time = t_d.elapsed().as_secs_f64(); - for (row_idx, y_i) in y.iter().enumerate().take(num_rows) { - let mut poly = vec![F::zero(); poly_len]; + let t_b = Instant::now(); + let b_quotients = { + let _span = tracing::info_span!("B_rows_ntt").entered(); + unreduced_quotient_rows_ntt_cached_i8(ntt_b, &t_hat_flat) + }; + let b_time = t_b.elapsed().as_secs_f64(); + let t_a = Instant::now(); + let a_quotients = { + let _span = tracing::info_span!("A_rows_ntt").entered(); + unreduced_quotient_rows_ntt_cached(ntt_a, z_pre) + }; + let a_time = t_a.elapsed().as_secs_f64(); + + let mut result = Vec::with_capacity(num_rows); + let mut other_time = 0.0f64; + let mut poly_buf = vec![F::zero(); poly_len]; + let mut quotient_buf = vec![F::zero(); D]; + + for (row_idx, _y_i) in y.iter().enumerate().take(num_rows) { if row_idx < Cfg::N_D { - let d_row = &setup.D[row_idx]; - for (m_ij, z_j) in d_row.iter().zip(w_hat_flat.iter()) { - add_unreduced_product(&mut poly, m_ij, z_j); - } + result.push(d_quotients[row_idx]); } else if row_idx < Cfg::N_D + Cfg::N_B { - let b_row = &setup.B[row_idx - Cfg::N_D]; - for (m_ij, z_j) in b_row.iter().zip(t_hat_flat.iter()) { - add_unreduced_product(&mut poly, m_ij, z_j); - } - } else if row_idx == Cfg::N_D + Cfg::N_B { - // row3: b . w_recomp (scalar * ring, degree D-1) - for (i, w_hat_i) in w_hat.iter().enumerate() { - let w_recomp = CyclotomicRing::gadget_recompose_pow2(w_hat_i, Cfg::LOG_BASIS); - add_scalar_ring_product(&mut poly, &opening_point.b[i], &w_recomp); - } - } else if row_idx == Cfg::N_D + Cfg::N_B + 1 { - // row4 w-segment: c . w_recomp (sparse*ring unreduced) - for (i, w_hat_i) in w_hat.iter().enumerate() { - let w_recomp = CyclotomicRing::gadget_recompose_pow2(w_hat_i, Cfg::LOG_BASIS); - add_sparse_ring_product(&mut poly, &challenges[i], &w_recomp); - } - // row4 z-segment: -(a . z_pre_recomp), double-factored - // z_pre_recomp[i] = gadget_recompose(z_pre[i*DELTA..(i+1)*DELTA]) - let block_len = opening_point.a.len(); - for i in 0..block_len { - let start = i * Cfg::DELTA; - let end = start + Cfg::DELTA; - if end <= z_pre.len() { - let z_pre_recomp = - CyclotomicRing::gadget_recompose_pow2(&z_pre[start..end], Cfg::LOG_BASIS); - sub_scalar_ring_product(&mut poly, &opening_point.a[i], &z_pre_recomp); - } - } - } else { - // row5 (N_A rows) + result.push(b_quotients[row_idx - Cfg::N_D]); + } else if row_idx >= Cfg::N_D + Cfg::N_B + 2 { + // A-rows: NTT-accelerated A*z_pre + sparse challenge terms + let t_row = Instant::now(); + let _span = tracing::info_span!("A_row").entered(); let a_idx = row_idx - (Cfg::N_D + Cfg::N_B + 2); - // t-segment: c . t_recomp[a_idx] (sparse*ring unreduced) + + poly_buf.fill(F::zero()); for (i, t_hat_i) in t_hat.iter().enumerate() { - let start = a_idx * Cfg::DELTA; - let end = start + Cfg::DELTA; + let start = a_idx * decomp_commit; + let end = start + decomp_commit; if end <= t_hat_i.len() { let t_recomp = - CyclotomicRing::gadget_recompose_pow2(&t_hat_i[start..end], Cfg::LOG_BASIS); - add_sparse_ring_product(&mut poly, &challenges[i], &t_recomp); + CyclotomicRing::gadget_recompose_pow2_i8(&t_hat_i[start..end], log_basis); + add_sparse_ring_product(&mut poly_buf, &challenges[i], &t_recomp); } } - // z-segment: -(A[a_idx] . z_pre) (ring*ring unreduced) - let a_row = &setup.A[a_idx]; - for (m_ij, z_j) in a_row.iter().zip(z_pre.iter()) { - sub_unreduced_product(&mut poly, m_ij, z_j); + + let a_q = a_quotients[a_idx].coefficients(); + quotient_buf.fill(F::zero()); + quotient_buf[..(poly_len - D)].copy_from_slice(&poly_buf[D..poly_len]); + for k in 0..D { + quotient_buf[k] -= a_q[k]; + } + result.push(CyclotomicRing::from_slice("ient_buf)); + other_time += t_row.elapsed().as_secs_f64(); + } else { + // bTw_row and challenge_fold_row: schoolbook (cheap) + let t_row = Instant::now(); + poly_buf.fill(F::zero()); + + if row_idx == Cfg::N_D + Cfg::N_B { + let _span = tracing::info_span!("bTw_row").entered(); + for (i, w_f) in w_folded.iter().enumerate() { + add_scalar_ring_product(&mut poly_buf, &opening_point.b[i], w_f); + } + } else { + let _span = tracing::info_span!("challenge_fold_row").entered(); + for (i, w_f) in w_folded.iter().enumerate() { + add_sparse_ring_product(&mut poly_buf, &challenges[i], w_f); + } + let block_len = opening_point.a.len(); + for i in 0..block_len { + let start = i * decomp_commit; + let end = start + decomp_commit; + if end <= z_pre.len() { + let z_pre_recomp = + CyclotomicRing::gadget_recompose_pow2(&z_pre[start..end], log_basis); + sub_scalar_ring_product(&mut poly_buf, &opening_point.a[i], &z_pre_recomp); + } + } } - } - let y_coeffs = y_i.coefficients(); - for k in 0..D { - poly[k] = poly[k] - y_coeffs[k]; - } + let y_coeffs = _y_i.coefficients(); + for k in 0..D { + poly_buf[k] -= y_coeffs[k]; + } - // Divide by X^D + 1 - let mut quotient = vec![F::zero(); D]; - for k in (D..poly_len).rev() { - let q = poly[k]; - quotient[k - D] = q; - poly[k - D] = poly[k - D] - q; + quotient_buf.fill(F::zero()); + for k in (D..poly_len).rev() { + let q = poly_buf[k]; + quotient_buf[k - D] = q; + poly_buf[k - D] -= q; + } + result.push(CyclotomicRing::from_slice("ient_buf)); + other_time += t_row.elapsed().as_secs_f64(); } - let coeffs: [F; D] = std::array::from_fn(|k| quotient[k]); - result.push(CyclotomicRing::from_coefficients(coeffs)); } + eprintln!( + " [compute_r] D(NTT): {d_time:.2}s, B(NTT): {b_time:.2}s, A(NTT): {a_time:.2}s, other: {other_time:.2}s", + ); + Ok(result) } @@ -514,79 +531,87 @@ where /// /// Computes the field-element evaluations of each M entry at `alpha`, /// organized as rows of field elements, without materializing M. +#[tracing::instrument(skip_all, name = "compute_m_a_streaming")] pub(crate) fn compute_m_a_streaming( setup: &HachiExpandedSetup, opening_point: &RingOpeningPoint, challenges: &[SparseChallenge], alpha: &F, + layout: HachiCommitmentLayout, ) -> Result>, HachiError> where F: FieldCore + CanonicalField, Cfg: CommitmentConfig, { - let layout = setup.seed.layout; - let num_blocks = layout.num_blocks; + let depth_commit = layout.num_digits_commit; + let depth_open = layout.num_digits_open; + let depth_fold = layout.num_digits_fold; + let log_basis = layout.log_basis; + let num_blocks = opening_point.b.len(); let block_len = layout.block_len; - let w_len = Cfg::DELTA * num_blocks; - let t_len = Cfg::DELTA * Cfg::N_A * num_blocks; - let z_len = Cfg::TAU * Cfg::DELTA * block_len; + let w_len = depth_open * num_blocks; + let t_len = depth_commit * Cfg::N_A * num_blocks; + let z_len = depth_fold * depth_commit * block_len; let total_cols = w_len + t_len + z_len; - let g1 = gadget_row_scalars::(Cfg::DELTA, Cfg::LOG_BASIS); - let j1 = gadget_row_scalars::(Cfg::TAU, Cfg::LOG_BASIS); + let g1_open = gadget_row_scalars::(depth_open, log_basis); + let g1_commit = gadget_row_scalars::(depth_commit, log_basis); + let j1 = gadget_row_scalars::(depth_fold, log_basis); - // Pre-evaluate alpha powers for gadget scalars (already field elements) - // g1 and j1 are already field scalars, so eval_ring_at(constant(g), alpha) = g. + let c_alphas: Vec = challenges + .iter() + .map(|c| eval_ring_at(&c.to_dense::().expect("valid challenge"), alpha)) + .collect(); - let mut rows = Vec::with_capacity(Cfg::N_D + Cfg::N_B + 1 + 1 + Cfg::N_A); + let d_rows: Vec> = cfg_iter!(setup.D) + .map(|d_row| { + let mut full = vec![F::zero(); total_cols]; + for (j, ring) in d_row.iter().take(w_len).enumerate() { + full[j] = eval_ring_at(ring, alpha); + } + full + }) + .collect(); - // D rows: setup.D[i] evaluated at alpha, zero-padded - for d_row in setup.D.iter() { - let mut full = vec![F::zero(); total_cols]; - for (j, ring) in d_row.iter().enumerate() { - full[j] = eval_ring_at(ring, alpha); - } - rows.push(full); - } + let b_rows: Vec> = cfg_iter!(setup.B) + .map(|b_row| { + let mut full = vec![F::zero(); total_cols]; + for (j, ring) in b_row.iter().take(t_len).enumerate() { + full[w_len + j] = eval_ring_at(ring, alpha); + } + full + }) + .collect(); - // B rows: setup.B[i] evaluated at alpha, in t-segment - for b_row in setup.B.iter() { - let mut full = vec![F::zero(); total_cols]; - for (j, ring) in b_row.iter().enumerate() { - full[w_len + j] = eval_ring_at(ring, alpha); - } - rows.push(full); - } + let mut rows = Vec::with_capacity(Cfg::N_D + Cfg::N_B + 1 + 1 + Cfg::N_A); + rows.extend(d_rows); + rows.extend(b_rows); - // row3: kron(b, g1) evaluated at alpha -> b[i] * g1[d] (all scalars) + // Row 3: b^T · G · ŵ = y_ring (ŵ uses delta_open) { let mut full = vec![F::zero(); total_cols]; for (i, &b_i) in opening_point.b.iter().enumerate() { - for (d, &g) in g1.iter().enumerate() { - full[i * Cfg::DELTA + d] = b_i * g; + for (d, &g) in g1_open.iter().enumerate() { + full[i * depth_open + d] = b_i * g; } } rows.push(full); } - // row4: w-segment = kron(c, g1) evaluated at alpha - // z-segment = -kron(kron(a,g1), j1) (all scalars) + // Row 4: (c^T ⊗ G) · ŵ = a^T · G · J · ẑ { let mut full = vec![F::zero(); total_cols]; - // w-segment: c[i] evaluated at alpha, times g1[d] - for (i, c) in challenges.iter().enumerate() { - let c_alpha = eval_ring_at(&c.to_dense::().expect("valid challenge"), alpha); - for (d, &g) in g1.iter().enumerate() { - full[i * Cfg::DELTA + d] = c_alpha * g; + for (i, &c_alpha) in c_alphas.iter().enumerate() { + for (d, &g) in g1_open.iter().enumerate() { + full[i * depth_open + d] = c_alpha * g; } } - // z-segment: -kron(kron(a,g1), j1) = -(a[i] * g1[d] * j1[t]) let z_offset = w_len + t_len; for (i, &a_i) in opening_point.a.iter().enumerate() { - for (d, &g) in g1.iter().enumerate() { + for (d, &g) in g1_commit.iter().enumerate() { let ag = a_i * g; for (t, &j) in j1.iter().enumerate() { - let idx = (i * Cfg::DELTA + d) * Cfg::TAU + t; + let idx = (i * depth_commit + d) * depth_fold + t; full[z_offset + idx] = -(ag * j); } } @@ -594,25 +619,22 @@ where rows.push(full); } - // row5 (N_A rows): t-segment = kron(c, g_na[a_idx]) evaluated at alpha - // z-segment = -kron(A[a_idx], j1) evaluated at alpha + // Row 5: (c^T ⊗ G_{N_A}) · t̂ = A · J · ẑ (t̂ and ẑ use delta_commit) for a_idx in 0..Cfg::N_A { let mut full = vec![F::zero(); total_cols]; - // t-segment: block-diagonal gadget times challenges - for (i, c) in challenges.iter().enumerate() { - let c_alpha = eval_ring_at(&c.to_dense::().expect("valid challenge"), alpha); - for (d, &g) in g1.iter().enumerate() { - let t_idx = i * (Cfg::N_A * Cfg::DELTA) + a_idx * Cfg::DELTA + d; + for (i, &c_alpha) in c_alphas.iter().enumerate() { + for (d, &g) in g1_commit.iter().enumerate() { + let t_idx = i * (Cfg::N_A * depth_commit) + a_idx * depth_commit + d; full[w_len + t_idx] = c_alpha * g; } } - // z-segment: -A[a_idx][k] evaluated at alpha, times j1[t] let z_offset = w_len + t_len; let a_row = &setup.A[a_idx]; - for (k, ring) in a_row.iter().enumerate() { + let inner_width = block_len * depth_commit; + for (k, ring) in a_row.iter().take(inner_width).enumerate() { let ring_alpha = eval_ring_at(ring, alpha); for (t, &j) in j1.iter().enumerate() { - full[z_offset + k * Cfg::TAU + t] = -(ring_alpha * j); + full[z_offset + k * depth_fold + t] = -(ring_alpha * j); } } rows.push(full); @@ -621,47 +643,51 @@ where Ok(rows) } -pub(crate) fn generate_y( +pub(crate) fn generate_y( v: &[CyclotomicRing], u: &[CyclotomicRing], u_eval: &CyclotomicRing, + n_d: usize, + n_b: usize, + n_a: usize, ) -> Result>, HachiError> where F: FieldCore, { - if v.len() != Cfg::N_D { + if v.len() != n_d { return Err(HachiError::InvalidSize { - expected: Cfg::N_D, + expected: n_d, actual: v.len(), }); } - if u.len() != Cfg::N_B { + if u.len() != n_b { return Err(HachiError::InvalidSize { - expected: Cfg::N_B, + expected: n_b, actual: u.len(), }); } - let mut out = Vec::with_capacity(Cfg::N_D + Cfg::N_B + 1 + 1 + Cfg::N_A); + let mut out = Vec::with_capacity(n_d + n_b + 1 + 1 + n_a); out.extend_from_slice(v); out.extend_from_slice(u); out.push(*u_eval); out.push(CyclotomicRing::::zero()); - out.extend(std::iter::repeat_n( - CyclotomicRing::::zero(), - Cfg::N_A, - )); + out.extend(repeat_n(CyclotomicRing::::zero(), n_a)); Ok(out) } #[cfg(test)] mod tests { use super::*; + use std::array::from_fn; + use crate::algebra::{CyclotomicRing, SparseChallengeConfig}; use crate::protocol::challenges::sparse::sample_sparse_challenges; use crate::protocol::commitment::{HachiCommitmentCore, RingCommitmentScheme}; + use crate::protocol::hachi_poly_ops::DensePoly; use crate::protocol::proof::HachiCommitmentHint; use crate::protocol::transcript::Blake2bTranscript; use crate::test_utils::*; + use crate::FromSmallInt; use crate::Transcript; const TRANSCRIPT_SEED: &[u8] = b"test/prover-relation"; @@ -715,19 +741,20 @@ mod tests { let ring_coeffs: Vec> = blocks.iter().flat_map(|b| b.iter().copied()).collect(); - let hint = HachiCommitmentHint { - t_hat: w.t_hat, - ring_coeffs, - }; + let poly = DensePoly::from_ring_coeffs(ring_coeffs); + let hint = HachiCommitmentHint::new(w.t_hat); let mut transcript = Blake2bTranscript::::new(TRANSCRIPT_SEED); let y_ring = CyclotomicRing::::zero(); + let layout = setup.layout(); let quad_eq = QuadraticEquation::::new_prover( &setup, - &point, - &hint, + point.clone(), + &poly, + hint, &mut transcript, &w.commitment, &y_ring, + layout, ) .unwrap(); @@ -743,14 +770,28 @@ mod tests { } } + fn i8_to_ring(digits: &[[i8; D]]) -> Vec> { + digits + .iter() + .map(|d| { + let coeffs: [F; D] = from_fn(|i| F::from_i64(d[i] as i64)); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect() + } + /// Row 1: D · ŵ = v #[test] fn row1_d_times_w_hat_equals_v() { let f = build_fixture(); let w_hat = f.quad_eq.w_hat().unwrap(); - let w_hat_flat: Vec> = - w_hat.iter().flat_map(|v| v.iter().copied()).collect(); + let w_hat_flat: Vec> = i8_to_ring( + &w_hat + .iter() + .flat_map(|v| v.iter().copied()) + .collect::>(), + ); let lhs = mat_vec_mul(&f.setup.expanded.D, &w_hat_flat); assert_eq!(lhs, f.quad_eq.v(), "Row 1 failed: D · ŵ ≠ v"); @@ -762,9 +803,16 @@ mod tests { let f = build_fixture(); let hint = f.quad_eq.hint().unwrap(); - let t_hat_flat: Vec> = - hint.t_hat.iter().flat_map(|v| v.iter().copied()).collect(); - let lhs = mat_vec_mul(&f.setup.expanded.B, &t_hat_flat); + let t_hat_flat_ring: Vec> = hint + .t_hat + .iter() + .flat_map(|v| v.iter()) + .map(|plane| { + let coeffs: [F; D] = std::array::from_fn(|k| F::from_i64(plane[k] as i64)); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect(); + let lhs = mat_vec_mul(&f.setup.expanded.B, &t_hat_flat_ring); assert_eq!(lhs, f.commitment_u, "Row 2 failed: B · t̂ ≠ u"); } @@ -777,7 +825,7 @@ mod tests { let w_hat = f.quad_eq.w_hat().unwrap(); let w_recomposed: Vec> = w_hat .iter() - .map(|w_hat_i| CyclotomicRing::gadget_recompose_pow2(w_hat_i, LOG_BASIS)) + .map(|w_hat_i| CyclotomicRing::gadget_recompose_pow2_i8(w_hat_i, log_basis())) .collect(); let u_eval = w_recomposed @@ -810,7 +858,7 @@ mod tests { fn derive_z_hat(z_pre: &[CyclotomicRing]) -> Vec> { z_pre .iter() - .flat_map(|z_j| z_j.balanced_decompose_pow2(TAU, LOG_BASIS)) + .flat_map(|z_j| z_j.balanced_decompose_pow2(num_digits_fold(), log_basis())) .collect() } @@ -822,7 +870,7 @@ mod tests { let w_hat = f.quad_eq.w_hat().unwrap(); let w: Vec> = w_hat .iter() - .map(|w_hat_i| CyclotomicRing::gadget_recompose_pow2(w_hat_i, LOG_BASIS)) + .map(|w_hat_i| CyclotomicRing::gadget_recompose_pow2_i8(w_hat_i, log_basis())) .collect(); let lhs = f @@ -848,7 +896,7 @@ mod tests { let hint = f.quad_eq.hint().unwrap(); let mut lhs = vec![CyclotomicRing::::zero(); N_A]; for (c_i, t_hat_i) in f.challenges.iter().zip(hint.t_hat.iter()) { - let t_i = gadget_recompose_vec(t_hat_i); + let t_i = gadget_recompose_vec_i8(t_hat_i); assert_eq!(t_i.len(), N_A); for (lhs_j, t_ij) in lhs.iter_mut().zip(t_i.iter()) { *lhs_j += *c_i * *t_ij; @@ -870,12 +918,18 @@ mod tests { let w_hat = f.quad_eq.w_hat().unwrap(); assert_eq!(w_hat.len(), NUM_BLOCKS); - assert!(w_hat.iter().all(|v| v.len() == DELTA)); + assert!(w_hat.iter().all(|v| v.len() == num_digits_commit())); let hint = f.quad_eq.hint().unwrap(); assert_eq!(hint.t_hat.len(), NUM_BLOCKS); - assert!(hint.t_hat.iter().all(|v| v.len() == N_A * DELTA)); + assert!(hint + .t_hat + .iter() + .all(|v| v.len() == N_A * num_digits_commit())); - assert_eq!(f.quad_eq.z_pre().unwrap().len(), BLOCK_LEN * DELTA); + assert_eq!( + f.quad_eq.z_pre().unwrap().len(), + BLOCK_LEN * num_digits_commit() + ); } } diff --git a/src/protocol/ring_switch.rs b/src/protocol/ring_switch.rs index ef87ed0e..9c44d826 100644 --- a/src/protocol/ring_switch.rs +++ b/src/protocol/ring_switch.rs @@ -9,11 +9,16 @@ use crate::cfg_into_iter; use crate::error::HachiError; #[cfg(feature = "parallel")] use crate::parallel::*; +use crate::protocol::commitment::utils::crt_ntt::NttSlotCache; +use crate::protocol::commitment::utils::linear::{ + decompose_rows_i8, flatten_i8_blocks, mat_vec_mul_ntt_i8, mat_vec_mul_ntt_single_i8, +}; use crate::protocol::commitment::utils::norm::detect_field_modulus; use crate::protocol::commitment::{ - CommitmentConfig, HachiCommitmentCore, HachiCommitmentLayout, HachiExpandedSetup, - RingCommitment, RingCommitmentScheme, + CommitmentConfig, DecompositionParams, HachiCommitmentLayout, HachiExpandedSetup, + RingCommitment, }; +use crate::protocol::proof::{DigitLut, HachiCommitmentHint}; use crate::protocol::quadratic_equation::{ compute_m_a_streaming, compute_r_split_eq, QuadraticEquation, }; @@ -23,16 +28,25 @@ use crate::protocol::transcript::labels::{ }; use crate::protocol::transcript::Transcript; use crate::{CanonicalField, FieldCore, FieldSampling}; +#[cfg(test)] +use std::array::from_fn; +use std::marker::PhantomData; +use std::time::Instant; /// Output of the ring switch protocol, containing everything needed for sumchecks. pub struct RingSwitchOutput { - /// The witness vector w (concatenation of z and r coefficients). - pub w: Vec, + /// The witness vector w as balanced digits in `[-b/2, b/2)`. + pub w: Vec, /// Commitment to w. pub w_commitment: RingCommitment, - /// Compact evaluation table of w (all entries in [-8, 7], reordered for sumcheck). + /// Prover hint for the w-commitment (t_hat blocks), needed for recursive opening. + pub w_hint: HachiCommitmentHint, + /// Compact evaluation table of w (all entries in [-b/2, b/2), reordered for sumcheck). /// Populated by the prover; empty on the verifier side. pub w_evals: Vec, + /// Field-element evaluation table of w (same reordering as `w_evals`). + /// Produced alongside `w_evals` in a single pass to avoid a duplicate scan. + pub w_evals_field: Vec, /// Evaluation table of M_alpha(x) (tau1-weighted). pub m_evals_x: Vec, /// Evaluation table of alpha powers (y dimension). @@ -56,10 +70,16 @@ pub struct RingSwitchOutput { /// # Errors /// /// Returns an error if z_pre/w_hat is missing, commitment fails, or matrix expansion fails. +#[tracing::instrument(skip_all, name = "ring_switch_prover")] +#[allow(clippy::too_many_arguments)] pub fn ring_switch_prover( quad_eq: &mut QuadraticEquation, setup: &HachiExpandedSetup, transcript: &mut T, + ntt_a: &NttSlotCache, + ntt_b: &NttSlotCache, + ntt_d: &NttSlotCache, + layout: HachiCommitmentLayout, ) -> Result, HachiError> where F: FieldCore + CanonicalField + FieldSampling, @@ -69,6 +89,9 @@ where let w_hat = quad_eq .w_hat() .ok_or_else(|| HachiError::InvalidInput("missing w_hat in prover".to_string()))?; + let w_hat_flat = quad_eq + .w_hat_flat() + .ok_or_else(|| HachiError::InvalidInput("missing w_hat_flat in prover".to_string()))?; let z_pre = quad_eq .z_pre() .ok_or_else(|| HachiError::InvalidInput("missing z_pre in prover".to_string()))?; @@ -76,59 +99,108 @@ where .hint() .ok_or_else(|| HachiError::InvalidInput("missing hint in prover".to_string()))?; let t_hat = &hint.t_hat; + let w_folded = quad_eq + .w_folded() + .ok_or_else(|| HachiError::InvalidInput("missing w_folded in prover".to_string()))?; + let t_rs = Instant::now(); let r = compute_r_split_eq::( setup, quad_eq.opening_point(), &quad_eq.challenges, - w_hat, + w_hat_flat, t_hat, + w_folded, z_pre, quad_eq.y(), + ntt_a, + ntt_b, + ntt_d, + layout, )?; - let w = build_w_coeffs::(w_hat, t_hat, z_pre, &r); - - let w_commitment = commit_w::(&w)?; + eprintln!( + " [ring_switch] compute_r_split_eq: {:.2}s", + t_rs.elapsed().as_secs_f64() + ); + let t_wc = Instant::now(); + let w = { + let _span = tracing::info_span!("build_w_coeffs").entered(); + build_w_coeffs::(w_hat, t_hat, z_pre, &r, layout) + }; + eprintln!( + " [ring_switch] build_w_coeffs: {:.2}s", + t_wc.elapsed().as_secs_f64() + ); + + let t_cw = Instant::now(); + let (w_commitment, w_hint) = commit_w::(&w, ntt_a, ntt_b)?; + eprintln!( + " [ring_switch] commit_w: {:.2}s (w_len={})", + t_cw.elapsed().as_secs_f64(), + w.len() + ); transcript.append_serde(ABSORB_SUMCHECK_W, &w_commitment); let alpha: F = transcript.challenge_scalar(CHALLENGE_RING_SWITCH); - let m_a = compute_m_a_streaming::( - setup, - quad_eq.opening_point(), - &quad_eq.challenges, - &alpha, - )?; - let m_a_vec = expand_m_a::(&m_a, alpha)?; + let num_l = D.trailing_zeros() as usize; + let num_ring_elems = w.len() / D; + let num_u = num_ring_elems.next_power_of_two().trailing_zeros() as usize; let m_rows = m_row_count::(); - let m_cols = if m_a.is_empty() { - 0 - } else { - m_a_vec.len() / m_a.len() - }; - - let (w_evals, num_u, num_l) = build_w_evals_compact::(&w, D)?; - let alpha_evals_y = build_alpha_evals_y(alpha, D); - let num_sc_vars = num_u + num_l; - let tau0 = sample_tau::(transcript, CHALLENGE_TAU0, num_sc_vars); - let num_i = m_rows.next_power_of_two().trailing_zeros() as usize; + + let tau0 = sample_tau::(transcript, CHALLENGE_TAU0, num_sc_vars); let tau1 = sample_tau::(transcript, CHALLENGE_TAU1, num_i); + let alpha_evals_y = build_alpha_evals_y(alpha, D); + + let t_par = Instant::now(); + let opening_point = quad_eq.opening_point(); + let challenges = &quad_eq.challenges; + + #[cfg(feature = "parallel")] + let (m_evals_x_result, w_result) = rayon::join( + || { + let m_a = compute_m_a_streaming::( + setup, + opening_point, + challenges, + &alpha, + layout, + )?; + build_m_evals_x_fused::(&m_a, alpha, layout.log_basis, &tau1) + }, + || build_w_evals_dual::(&w, D, layout.log_basis), + ); + #[cfg(not(feature = "parallel"))] + let (m_evals_x_result, w_result) = { + let m_a = + compute_m_a_streaming::(setup, opening_point, challenges, &alpha, layout)?; + let m_evals_x = build_m_evals_x_fused::(&m_a, alpha, layout.log_basis, &tau1)?; + let w_dual = build_w_evals_dual::(&w, D, layout.log_basis); + (Ok(m_evals_x), w_dual) + }; - let m_evals_x = build_m_evals_x::(&m_a_vec, m_rows, m_cols, &tau1); + let m_evals_x = m_evals_x_result?; + let (w_evals, w_evals_field, _, _) = w_result?; + eprintln!( + " [ring_switch] m_a+w_evals parallel: {:.2}s", + t_par.elapsed().as_secs_f64() + ); Ok(RingSwitchOutput { w, w_commitment, + w_hint, w_evals, + w_evals_field, m_evals_x, alpha_evals_y, num_u, num_l, tau0, tau1, - b: 1usize << Cfg::LOG_BASIS, + b: 1usize << layout.log_basis, alpha, }) } @@ -138,12 +210,14 @@ where /// # Errors /// /// Returns an error if matrix expansion fails. +#[tracing::instrument(skip_all, name = "ring_switch_verifier")] pub fn ring_switch_verifier( quad_eq: &QuadraticEquation, setup: &HachiExpandedSetup, - w: &[F], + w_len: usize, w_commitment: &RingCommitment, transcript: &mut T, + layout: HachiCommitmentLayout, ) -> Result, HachiError> where F: FieldCore + CanonicalField + FieldSampling, @@ -154,44 +228,39 @@ where let alpha: F = transcript.challenge_scalar(CHALLENGE_RING_SWITCH); - let m_a = compute_m_a_streaming::( - setup, - quad_eq.opening_point(), - &quad_eq.challenges, - &alpha, - )?; - let m_a_vec = expand_m_a::(&m_a, alpha)?; - let m_rows = m_row_count::(); - let m_cols = if m_a.is_empty() { - 0 - } else { - m_a_vec.len() / m_a.len() - }; - - let num_ring_elems = w.len() / D; + let num_ring_elems = w_len / D; let num_u = num_ring_elems.next_power_of_two().trailing_zeros() as usize; let num_l = D.trailing_zeros() as usize; - let alpha_evals_y = build_alpha_evals_y(alpha, D); - + let m_rows = m_row_count::(); let num_sc_vars = num_u + num_l; - let tau0 = sample_tau::(transcript, CHALLENGE_TAU0, num_sc_vars); - let num_i = m_rows.next_power_of_two().trailing_zeros() as usize; + + let tau0 = sample_tau::(transcript, CHALLENGE_TAU0, num_sc_vars); let tau1 = sample_tau::(transcript, CHALLENGE_TAU1, num_i); + let alpha_evals_y = build_alpha_evals_y(alpha, D); - let m_evals_x = build_m_evals_x::(&m_a_vec, m_rows, m_cols, &tau1); + let m_a = compute_m_a_streaming::( + setup, + quad_eq.opening_point(), + &quad_eq.challenges, + &alpha, + layout, + )?; + let m_evals_x = build_m_evals_x_fused::(&m_a, alpha, layout.log_basis, &tau1)?; Ok(RingSwitchOutput { - w: w.to_vec(), + w: Vec::new(), w_commitment: w_commitment.clone(), + w_hint: HachiCommitmentHint::new(Vec::new()), w_evals: Vec::new(), + w_evals_field: Vec::new(), m_evals_x, alpha_evals_y, num_u, num_l, tau0, tau1, - b: 1usize << Cfg::LOG_BASIS, + b: 1usize << layout.log_basis, alpha, }) } @@ -224,7 +293,7 @@ pub(crate) fn compute_r_via_poly_division, b: Vec| -> Vec { for (ai, bi) in a.iter_mut().zip(b.iter()) { - *ai = *ai + *bi; + *ai += *bi; } a }; @@ -257,15 +326,15 @@ pub(crate) fn compute_r_via_poly_division { - _cfg: std::marker::PhantomData, +pub(crate) struct WCommitmentConfig { + _cfg: PhantomData, } impl CommitmentConfig for WCommitmentConfig { @@ -282,91 +351,164 @@ impl CommitmentConfig for WCommitmentConf const N_A: usize = Cfg::N_A; const N_B: usize = Cfg::N_B; const N_D: usize = Cfg::N_D; - const LOG_BASIS: u32 = Cfg::LOG_BASIS; - const DELTA: usize = Cfg::DELTA; - const TAU: usize = Cfg::TAU; const CHALLENGE_WEIGHT: usize = Cfg::CHALLENGE_WEIGHT; + fn decomposition() -> DecompositionParams { + let parent = Cfg::decomposition(); + let parent_open = parent.log_open_bound.unwrap_or(parent.log_commit_bound); + DecompositionParams { + log_basis: parent.log_basis, + // w's entries are balanced digits in [-b/2, b/2), so commitment + // decomposition needs only one level. + log_commit_bound: parent.log_basis, + // Opening folds w with arbitrary field-element weights, producing + // full-field-size coefficients that need the same decomposition + // depth as the parent's opening bound. + log_open_bound: Some(parent_open), + } + } + fn commitment_layout(max_num_vars: usize) -> Result { let alpha = D.trailing_zeros() as usize; - let m_vars = max_num_vars.checked_sub(alpha).ok_or_else(|| { + let reduced_vars = max_num_vars.checked_sub(alpha).ok_or_else(|| { HachiError::InvalidSetup("max_num_vars is smaller than alpha".to_string()) })?; - HachiCommitmentLayout::new::(m_vars, 0) + if reduced_vars == 0 { + return Err(HachiError::InvalidSetup( + "max_num_vars must leave at least one outer variable".to_string(), + )); + } + let r_vars = reduced_vars / 2; + let m_vars = reduced_vars - r_vars; + HachiCommitmentLayout::new::(m_vars, r_vars, &Self::decomposition()) } } -fn commit_w(w: &[F]) -> Result, HachiError> +/// Total ring elements in the w polynomial, computed from the main layout. +/// +/// Components: w_hat + t_hat + decomposed z_pre + decomposed r. +pub(crate) fn w_ring_element_count( + layout: HachiCommitmentLayout, +) -> usize { + let w_hat_count = layout.num_blocks * layout.num_digits_open; + let t_hat_count = layout.num_blocks * Cfg::N_A * layout.num_digits_commit; + let z_pre_count = layout.inner_width * layout.num_digits_fold; + let r_count = m_row_count::() * r_decomp_levels::(layout.log_basis); + w_hat_count + t_hat_count + z_pre_count + r_count +} + +/// Compute the w-commitment layout from the main layout. +pub(crate) fn w_commitment_layout( + main_layout: HachiCommitmentLayout, +) -> Result { + let total = w_ring_element_count::(main_layout) + .next_power_of_two() + .max(1); + let alpha = D.trailing_zeros() as usize; + let m_vars = total.trailing_zeros() as usize; + let max_num_vars = m_vars + alpha; + WCommitmentConfig::::commitment_layout(max_num_vars) +} + +#[tracing::instrument(skip_all, name = "commit_w")] +fn commit_w( + w: &[i8], + ntt_a: &NttSlotCache, + ntt_b: &NttSlotCache, +) -> Result<(RingCommitment, HachiCommitmentHint), HachiError> where F: FieldCore + CanonicalField + FieldSampling, Cfg: CommitmentConfig, { - type WCfg = WCommitmentConfig; - + let lut = DigitLut::::new(Cfg::decomposition().log_basis); let ring_elems: Vec> = w .chunks(D) .map(|chunk| { - let coeffs: [F; D] = - std::array::from_fn(|i| if i < chunk.len() { chunk[i] } else { F::zero() }); + let mut coeffs = [F::zero(); D]; + for (c, &d) in coeffs.iter_mut().zip(chunk.iter()) { + *c = lut.get(d); + } CyclotomicRing::from_coefficients(coeffs) }) .collect(); - let block_len = ring_elems.len().next_power_of_two().max(1); - let mut padded = ring_elems; - padded.resize(block_len, CyclotomicRing::::zero()); - let m_vars = block_len.trailing_zeros() as usize; - let max_num_vars = m_vars + D.trailing_zeros() as usize; - let blocks = vec![padded]; - - let (w_setup, _) = - >>::setup(max_num_vars)?; + let total = ring_elems.len().next_power_of_two().max(1); + let alpha = D.trailing_zeros() as usize; + let m_vars_total = total.trailing_zeros() as usize; + let max_num_vars = m_vars_total + alpha; + let w_layout = WCommitmentConfig::::commitment_layout(max_num_vars)?; + + let num_blocks = w_layout.num_blocks; + let block_len = w_layout.block_len; + let depth = w_layout.num_digits_commit; + let log_basis = w_layout.log_basis; + let coeff_len = ring_elems.len(); + + let block_slices: Vec<&[CyclotomicRing]> = (0..num_blocks) + .map(|i| { + let start = i * block_len; + if start >= coeff_len { + &[] as &[CyclotomicRing] + } else { + &ring_elems[start..(start + block_len).min(coeff_len)] + } + }) + .collect(); - let w = >>::commit_ring_blocks( - &blocks, &w_setup, - )?; + let t_all = mat_vec_mul_ntt_i8(ntt_a, &block_slices, depth, log_basis); + let t_hat_per_block: Vec> = cfg_into_iter!(t_all) + .map(|t_i| decompose_rows_i8(&t_i, depth, log_basis)) + .collect(); - Ok(w.commitment) + let t_hat_flat = flatten_i8_blocks(&t_hat_per_block); + let u: Vec> = mat_vec_mul_ntt_single_i8(ntt_b, &t_hat_flat); + let hint = HachiCommitmentHint::new(t_hat_per_block); + Ok((RingCommitment { u }, hint)) } pub(crate) fn eval_ring_at(r: &CyclotomicRing, alpha: &F) -> F { let mut acc = F::zero(); let mut power = F::one(); for coeff in r.coefficients() { - acc = acc + (*coeff * power); + acc += *coeff * power; power = power * *alpha; } acc } -pub(crate) fn r_decomp_levels() -> usize { +pub(crate) fn r_decomp_levels(log_basis: u32) -> usize { let modulus = detect_field_modulus::(); let bits = 128 - (modulus.saturating_sub(1)).leading_zeros() as usize; - let log_basis = Cfg::LOG_BASIS as usize; - let mut levels = (bits + log_basis.saturating_sub(1)) / log_basis.max(1); + let lb = log_basis as usize; + let mut levels = (bits + lb.saturating_sub(1)) / lb.max(1); if levels == 0 { levels = 1; } - let b = 1u128 << Cfg::LOG_BASIS; - let half_q = modulus / 2; - let half_b_minus_1 = b / 2 - 1; - let b_minus_1 = b - 1; - let mut b_pow = 1u128; - for _ in 0..levels { - b_pow = b_pow.saturating_mul(b); - } - let max_positive = half_b_minus_1.saturating_mul((b_pow - 1) / b_minus_1); - if max_positive < half_q { - levels += 1; + let total_bits = levels * lb; + if total_bits <= bits { + let b = 1u128 << log_basis; + let half_q = modulus / 2; + let half_b_minus_1 = b / 2 - 1; + let b_minus_1 = b - 1; + let mut b_pow = 1u128; + for _ in 0..levels { + b_pow = b_pow.saturating_mul(b); + } + let max_positive = half_b_minus_1.saturating_mul((b_pow - 1) / b_minus_1); + if max_positive < half_q { + levels += 1; + } } levels } -pub(crate) fn expand_m_a( +#[cfg(test)] +pub(crate) fn expand_m_a( m_a: &[Vec], alpha: F, + log_basis: u32, ) -> Result, HachiError> { if m_a.is_empty() { return Ok(Vec::new()); @@ -385,7 +527,7 @@ pub(crate) fn expand_m_a(); + let levels = r_decomp_levels::(log_basis); let total_cols = cols .checked_add( rows.checked_mul(levels) @@ -393,7 +535,7 @@ pub(crate) fn expand_m_a( Ok((evals, num_u, num_l)) } -/// Compact variant of `build_w_evals` returning `Vec`. -/// -/// All entries in `w` must have canonical values in `[-half_b, half_b - 1]` -/// where `half_b = 2^(LOG_BASIS-1)`. This holds when `w` is produced by -/// `build_w_coeffs` (all components go through `balanced_decompose_pow2`). -pub(crate) fn build_w_evals_compact( - w: &[F], +/// Produce both compact `Vec` and field `Vec` eval tables in one pass +/// over `w`, sharing the index computation. +pub(crate) fn build_w_evals_dual( + w: &[i8], d: usize, -) -> Result<(Vec, usize, usize), HachiError> { + log_basis: u32, +) -> Result<(Vec, Vec, usize, usize), HachiError> { if d == 0 || w.len() % d != 0 { return Err(HachiError::InvalidSize { expected: d, @@ -474,55 +614,91 @@ pub(crate) fn build_w_evals_compact( let x_len = 1usize << num_u; let n = x_len << num_l; - let q = (-F::one()).to_canonical_u128() + 1; - let half_q = q / 2; - - let evals: Vec = (0..n) + let lut = DigitLut::::new(log_basis); + let (compact, field): (Vec, Vec) = cfg_into_iter!(0..n) .map(|dst| { let x = dst & (x_len - 1); let y = dst >> num_u; let src = y + (x << num_l); if src < w.len() { - let canonical = w[src].to_canonical_u128(); - if canonical <= half_q { - canonical as i8 - } else { - (canonical as i128 - q as i128) as i8 - } + let d = w[src]; + (d, lut.get(d)) } else { - 0i8 + (0i8, F::zero()) } }) - .collect(); - Ok((evals, num_u, num_l)) + .unzip(); + Ok((compact, field, num_u, num_l)) } pub(crate) fn m_row_count() -> usize { Cfg::N_D + Cfg::N_B + 1 + 1 + Cfg::N_A } -pub(crate) fn build_m_evals_x( - m_a_flat: &[F], - rows: usize, - cols: usize, +pub(crate) fn build_m_evals_x_fused( + m_a: &[Vec], + alpha: F, + log_basis: u32, tau1: &[F], -) -> Vec { +) -> Result, HachiError> { + if m_a.is_empty() { + return Ok(Vec::new()); + } + let rows = m_a.len(); + let orig_cols = m_a[0].len(); + for row in m_a.iter() { + if row.len() != orig_cols { + return Err(HachiError::InvalidSize { + expected: orig_cols, + actual: row.len(), + }); + } + } + + let levels = r_decomp_levels::(log_basis); + let total_cols = orig_cols + .checked_add( + rows.checked_mul(levels) + .ok_or_else(|| HachiError::InvalidSetup("expanded M width overflow".to_string()))?, + ) + .ok_or_else(|| HachiError::InvalidSetup("expanded M width overflow".to_string()))?; + + let base = F::from_canonical_u128_reduced(1u128 << log_basis); + let mut gadget_row = Vec::with_capacity(levels); + let mut power = F::one(); + for _ in 0..levels { + gadget_row.push(power); + power = power * base; + } + + let mut alpha_pow = F::one(); + for _ in 0..D { + alpha_pow = alpha_pow * alpha; + } + let denom = alpha_pow + F::one(); + let eq_tau1 = EqPolynomial::evals(tau1); - let x_len = cols.next_power_of_two(); - cfg_into_iter!(0..x_len) + let x_len = total_cols.next_power_of_two(); + + let out = cfg_into_iter!(0..x_len) .map(|x| { let mut acc = F::zero(); - for i in 0..eq_tau1.len() { - let row_val = if i < rows && x < cols { - m_a_flat[i * cols + x] - } else { - F::zero() - }; - acc = acc + eq_tau1[i] * row_val; + if x < orig_cols { + for (i, eq_i) in eq_tau1.iter().enumerate().take(rows) { + acc += *eq_i * m_a[i][x]; + } + } else if x < total_cols { + let offset = x - orig_cols; + let i = offset / levels; + let j = offset % levels; + if i < rows && i < eq_tau1.len() { + acc = eq_tau1[i] * (-denom * gadget_row[j]); + } } acc }) - .collect() + .collect(); + Ok(out) } pub(crate) fn build_alpha_evals_y(alpha: F, d: usize) -> Vec { @@ -543,34 +719,41 @@ pub(crate) fn sample_tau>( (0..n).map(|_| transcript.challenge_scalar(label)).collect() } -pub(crate) fn build_w_coeffs( - w_hat: &[Vec>], - t_hat: &[Vec>], +pub(crate) fn build_w_coeffs( + w_hat: &[Vec<[i8; D]>], + t_hat: &[Vec<[i8; D]>], z_pre: &[CyclotomicRing], r: &[CyclotomicRing], -) -> Vec { - let levels = r_decomp_levels::(); - let r_hat: Vec> = r - .iter() - .flat_map(|ri| ri.balanced_decompose_pow2(levels, Cfg::LOG_BASIS)) - .collect(); + layout: HachiCommitmentLayout, +) -> Vec { + let log_basis = layout.log_basis; + let num_digits_fold = layout.num_digits_fold; + let levels = r_decomp_levels::(log_basis); - let w_hat_flat = w_hat.iter().flat_map(|v| v.iter()); let t_hat_flat = t_hat.iter().flat_map(|v| v.iter()); - let z_hat_iter = z_pre - .iter() - .flat_map(|z_j| z_j.balanced_decompose_pow2(Cfg::TAU, Cfg::LOG_BASIS)); let z_count = w_hat.iter().map(|v| v.len()).sum::() + t_hat.iter().map(|v| v.len()).sum::() - + z_pre.len() * Cfg::TAU; - let mut out = Vec::with_capacity((z_count + r_hat.len()) * D); - for elem in w_hat_flat - .chain(t_hat_flat) - .chain(z_hat_iter.collect::>().iter()) - .chain(r_hat.iter()) - { - out.extend_from_slice(elem.coefficients()); + + z_pre.len() * num_digits_fold; + let r_hat_count = r.len() * levels; + let mut out = Vec::with_capacity((z_count + r_hat_count) * D); + for block in w_hat { + for digits in block { + out.extend_from_slice(digits); + } + } + for digits in t_hat_flat { + out.extend_from_slice(digits); + } + for z_j in z_pre { + for plane in z_j.balanced_decompose_pow2_i8(num_digits_fold, log_basis) { + out.extend_from_slice(&plane); + } + } + for ri in r { + for plane in ri.balanced_decompose_pow2_i8(levels, log_basis) { + out.extend_from_slice(&plane); + } } out } @@ -579,6 +762,8 @@ pub(crate) fn build_w_coeffs( @@ -601,27 +786,27 @@ mod tests { if is_scalar { let scalar = a[0]; for s in 0..D { - poly[s] = poly[s] + scalar * b[s]; + poly[s] += scalar * b[s]; } } else { for t in 0..D { for s in 0..D { - poly[t + s] = poly[t + s] + a[t] * b[s]; + poly[t + s] += a[t] * b[s]; } } } } let y_coeffs = y_i.coefficients(); for k in 0..D { - poly[k] = poly[k] - y_coeffs[k]; + poly[k] -= y_coeffs[k]; } let mut quotient = vec![F::zero(); D]; for k in (D..poly_len).rev() { let q = poly[k]; quotient[k - D] = q; - poly[k - D] = poly[k - D] - q; + poly[k - D] -= q; } - let coeffs: [F; D] = std::array::from_fn(|k| quotient[k]); + let coeffs: [F; D] = from_fn(|k| quotient[k]); CyclotomicRing::from_coefficients(coeffs) }) .collect() @@ -641,7 +826,7 @@ mod tests { coeffs[0] = F::from_u64((i * 5 + j + 1) as u64); CyclotomicRing::from_coefficients(coeffs) } else { - let coeffs = std::array::from_fn(|k| { + let coeffs = from_fn(|k| { F::from_u64((i as u64 * 1000 + j as u64 * 100 + k as u64 + 1) % 97) }); CyclotomicRing::from_coefficients(coeffs) @@ -652,15 +837,13 @@ mod tests { .collect(); let z: Vec> = (0..4) .map(|j| { - let coeffs = - std::array::from_fn(|k| F::from_u64((j as u64 * 37 + k as u64 + 5) % 89)); + let coeffs = from_fn(|k| F::from_u64((j as u64 * 37 + k as u64 + 5) % 89)); CyclotomicRing::from_coefficients(coeffs) }) .collect(); let y: Vec> = (0..3) .map(|i| { - let coeffs = - std::array::from_fn(|k| F::from_u64((i as u64 * 29 + k as u64 + 7) % 83)); + let coeffs = from_fn(|k| F::from_u64((i as u64 * 29 + k as u64 + 7) % 83)); CyclotomicRing::from_coefficients(coeffs) }) .collect(); diff --git a/src/protocol/sumcheck/batched_sumcheck.rs b/src/protocol/sumcheck/batched_sumcheck.rs index 5caa9810..e3ee7fc0 100644 --- a/src/protocol/sumcheck/batched_sumcheck.rs +++ b/src/protocol/sumcheck/batched_sumcheck.rs @@ -12,7 +12,7 @@ use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, SumcheckProof, Uni use crate::error::HachiError; use crate::protocol::transcript::labels; use crate::protocol::transcript::Transcript; -use crate::{FieldCore, FromSmallInt}; +use crate::{CanonicalField, FieldCore, FromSmallInt}; fn mul_pow_2(x: E, k: usize) -> E { let mut result = x; @@ -27,7 +27,7 @@ fn linear_combination(polys: &[UniPoly], coeffs: &[E]) -> UniPo let mut result = vec![E::zero(); max_len]; for (poly, coeff) in polys.iter().zip(coeffs.iter()) { for (i, c) in poly.coeffs.iter().enumerate() { - result[i] = result[i] + *c * *coeff; + result[i] += *c * *coeff; } } UniPoly::from_coeffs(result) @@ -71,13 +71,14 @@ pub struct BatchedSumcheckRoundResult { /// # Errors /// /// Returns an error if the field inverse of 2 does not exist. +#[tracing::instrument(skip_all, name = "prove_batched_sumcheck")] pub fn prove_batched_sumcheck( mut instances: Vec<&mut dyn SumcheckInstanceProver>, transcript: &mut T, mut sample_challenge: S, ) -> Result<(SumcheckProof, Vec), HachiError> where - F: FieldCore + crate::CanonicalField, + F: FieldCore + CanonicalField, T: Transcript, E: FieldCore + FromSmallInt, S: FnMut(&mut T) -> E, @@ -123,10 +124,6 @@ where }) .collect(); - let two_inv = E::from_u64(2) - .inv() - .expect("field characteristic 2 not supported"); - let mut round_polys = Vec::with_capacity(max_num_rounds); let mut challenges = Vec::with_capacity(max_num_rounds); @@ -141,7 +138,7 @@ where if active { inst.compute_round_univariate(round - offset, *previous_claim) } else { - UniPoly::from_coeffs(vec![*previous_claim * two_inv]) + UniPoly::from_coeffs(vec![*previous_claim * E::TWO_INV]) } }) .collect(); @@ -218,7 +215,7 @@ pub fn verify_batched_sumcheck_rounds( mut sample_challenge: S, ) -> Result, HachiError> where - F: FieldCore + crate::CanonicalField, + F: FieldCore + CanonicalField, T: Transcript, E: FieldCore, S: FnMut(&mut T) -> E, @@ -320,6 +317,7 @@ pub fn check_batched_output_claim( /// # Errors /// /// Propagates errors from round verification and output-claim equality check. +#[tracing::instrument(skip_all, name = "verify_batched_sumcheck")] pub fn verify_batched_sumcheck( proof: &SumcheckProof, verifiers: Vec<&dyn SumcheckInstanceVerifier>, @@ -327,7 +325,7 @@ pub fn verify_batched_sumcheck( mut sample_challenge: S, ) -> Result, HachiError> where - F: FieldCore + crate::CanonicalField, + F: FieldCore + CanonicalField, T: Transcript, E: FieldCore, S: FnMut(&mut T) -> E, diff --git a/src/protocol/sumcheck/eq_poly.rs b/src/protocol/sumcheck/eq_poly.rs index 353d0830..8b14b248 100644 --- a/src/protocol/sumcheck/eq_poly.rs +++ b/src/protocol/sumcheck/eq_poly.rs @@ -135,7 +135,7 @@ impl EqPolynomial { .zip(evals_right.par_iter_mut()) .for_each(|(x, y)| { *y = *x * r_i; - *x = *x - *y; + *x -= *y; }); size *= 2; diff --git a/src/protocol/sumcheck/hachi_sumcheck.rs b/src/protocol/sumcheck/hachi_sumcheck.rs index f7e1b12a..9e298896 100644 --- a/src/protocol/sumcheck/hachi_sumcheck.rs +++ b/src/protocol/sumcheck/hachi_sumcheck.rs @@ -2,24 +2,32 @@ //! //! Eliminates the redundant `w_evals` clone by sharing a single `w_table` //! across both the norm (F_0) and relation (F_α) sumcheck computations. -//! Supports compact `Vec` storage for round 0 (all entries in [-8, 7]), +//! Supports compact `Vec` storage for round 0 (all entries in [-b/2, b/2)), //! transitioning to `Vec` at half size after the first fold. use super::eq_poly::EqPolynomial; use super::norm_sumcheck::{ - accumulate_affine_range_coeffs, range_check_eval_precomputed, trim_trailing_zeros, - NormRoundKernel, PointEvalPrecomp, RangeAffinePrecomp, + choose_round_kernel, compute_entry_coeffs, compute_entry_coeffs_x4, field_from_i128, + range_check_eval_i128, range_check_eval_precomputed, trim_trailing_zeros, NormRoundKernel, + PointEvalPrecomp, RangeAffinePrecomp, MAX_AFFINE_COEFFS, }; use super::split_eq::GruenSplitEq; use super::{fold_evals_in_place, multilinear_eval, range_check_eval}; use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, UniPoly}; +use crate::algebra::fields::HasUnreducedOps; use crate::algebra::CyclotomicRing; -use crate::cfg_into_iter; use crate::error::HachiError; #[cfg(feature = "parallel")] use crate::parallel::*; use crate::protocol::ring_switch::eval_ring_at; -use crate::{FieldCore, FromSmallInt}; +use std::marker::PhantomData; + +use crate::{cfg_fold_reduce, cfg_into_iter}; +use std::iter; +use std::mem; +use std::time::Instant; + +use crate::{AdditiveGroup, CanonicalField, FieldCore, FromSmallInt}; enum WTable { Compact(Vec), @@ -31,6 +39,9 @@ enum WTable { /// Holds a single `w_table` shared by both sumcheck instances, weighted /// by `batching_coeff`. The round polynomial is /// `batching_coeff * norm_round(t) + relation_round(t)`. +/// +/// Alpha and m are stored in compact form (sizes `2^num_l` and `2^num_u` +/// respectively) and folded only during rounds where their variables are active. pub struct HachiSumcheckProver { w_table: WTable, batching_coeff: E, @@ -42,21 +53,28 @@ pub struct HachiSumcheckProver { range_precomp: Option>, b: usize, - // Relation state - alpha_table: Vec, - m_table: Vec, + // Relation state (compact — not expanded to full domain) + alpha_compact: Vec, + m_compact: Vec, + num_u: usize, num_vars: usize, relation_claim: E, + + norm_time_total: f64, + relation_time_total: f64, + fold_time_total: f64, + rounds_completed: usize, } -impl HachiSumcheckProver { +impl HachiSumcheckProver { /// Create a fused norm+relation sumcheck prover. /// /// # Panics /// /// Panics if table sizes are inconsistent with `num_u` and `num_l`. #[allow(clippy::too_many_arguments)] + #[tracing::instrument(skip_all, name = "HachiSumcheckProver::new")] pub fn new( batching_coeff: E, w_evals_compact: Vec, @@ -67,6 +85,7 @@ impl HachiSumcheckProver { num_u: usize, num_l: usize, ) -> Self { + assert!(b >= 1, "b must be at least 1"); let num_vars = num_u + num_l; let n = 1usize << num_vars; assert_eq!(w_evals_compact.len(), n); @@ -74,22 +93,19 @@ impl HachiSumcheckProver { assert_eq!(alpha_evals_y.len(), 1 << num_l); assert_eq!(m_evals_x.len(), 1 << num_u); - let x_mask = (1usize << num_u) - 1; - let alpha_table: Vec = cfg_into_iter!(0..n) - .map(|idx| alpha_evals_y[idx >> num_u]) - .collect(); - let m_table: Vec = cfg_into_iter!(0..n) - .map(|idx| m_evals_x[idx & x_mask]) - .collect(); + let alpha_compact = alpha_evals_y.to_vec(); + let m_compact = m_evals_x.to_vec(); - let relation_claim = - Self::compute_relation_claim_compact(&w_evals_compact, &alpha_table, &m_table); + let x_mask = (1usize << num_u) - 1; + let relation_claim = Self::compute_relation_claim_compact( + &w_evals_compact, + &alpha_compact, + &m_compact, + num_u, + x_mask, + ); - let round_kernel = if b <= 8 { - NormRoundKernel::PointEvalInterpolation - } else { - NormRoundKernel::AffineCoeffComposition - }; + let round_kernel = choose_round_kernel(b); let point_precomp = match round_kernel { NormRoundKernel::PointEvalInterpolation => Some(PointEvalPrecomp::new(b)), NormRoundKernel::AffineCoeffComposition => None, @@ -107,304 +123,270 @@ impl HachiSumcheckProver { point_precomp, range_precomp, b, - alpha_table, - m_table, + alpha_compact, + m_compact, + num_u, num_vars, relation_claim, + norm_time_total: 0.0, + relation_time_total: 0.0, + fold_time_total: 0.0, + rounds_completed: 0, } } - fn compute_relation_claim_compact(w_compact: &[i8], alpha_table: &[E], m_table: &[E]) -> E { + fn compute_relation_claim_compact( + w_compact: &[i8], + alpha_compact: &[E], + m_compact: &[E], + num_u: usize, + x_mask: usize, + ) -> E { w_compact .iter() - .zip(alpha_table.iter()) - .zip(m_table.iter()) - .fold(E::zero(), |acc, ((&w, &a), &m)| { - acc + E::from_i64(w as i64) * a * m + .enumerate() + .fold(E::zero(), |acc, (idx, &w)| { + acc + E::from_i64(w as i64) * alpha_compact[idx >> num_u] * m_compact[idx & x_mask] }) } - fn lift_i8(v: i8) -> E { - E::from_i64(v as i64) - } - - fn compute_round_norm_compact(&self, w_compact: &[i8]) -> UniPoly { - let half = w_compact.len() / 2; - - let (e_first, e_second) = self.split_eq.remaining_eq_tables(); - let num_first = e_first.len(); - let first_bits = num_first.trailing_zeros(); - - match self.round_kernel { - NormRoundKernel::PointEvalInterpolation => { - let degree_q = 2 * self.b - 1; - let num_points_q = degree_q + 1; - let range_offsets = &self.point_precomp.as_ref().unwrap().range_offsets; - - let mut q_evals = vec![E::zero(); num_points_q]; - for j in 0..half { - let j_low = j & (num_first - 1); - let j_high = j >> first_bits; - let eq_rem = e_first[j_low] * e_second[j_high]; - let w_0 = Self::lift_i8(w_compact[2 * j]); - let w_1 = Self::lift_i8(w_compact[2 * j + 1]); - let delta = w_1 - w_0; - let mut w_t = w_0; - for eval in q_evals.iter_mut() { - *eval = *eval + eq_rem * range_check_eval_precomputed(w_t, range_offsets); - w_t = w_t + delta; - } - } - let q_poly = UniPoly::from_evals(&q_evals); - self.split_eq.gruen_mul(&q_poly) - } - NormRoundKernel::AffineCoeffComposition => { - let range_precomp = self.range_precomp.as_ref().unwrap(); - let num_coeffs_q = range_precomp.degree_q + 1; - let coeff_mix = &range_precomp.coeff_mix; - - let mut q_coeffs = vec![E::zero(); num_coeffs_q]; - for j in 0..half { - let j_low = j & (num_first - 1); - let j_high = j >> first_bits; - let eq_rem = e_first[j_low] * e_second[j_high]; - let w_0 = Self::lift_i8(w_compact[2 * j]); - let w_1 = Self::lift_i8(w_compact[2 * j + 1]); - let a = w_1 - w_0; - accumulate_affine_range_coeffs(&mut q_coeffs, coeff_mix, w_0, a, eq_rem); - } - trim_trailing_zeros(&mut q_coeffs); - let q_poly = UniPoly::from_coeffs(q_coeffs); - self.split_eq.gruen_mul(&q_poly) - } + /// Accumulate `am * w_int` into split pos/neg accumulators. + /// `accum[pos_idx]` gets the product when `w_int >= 0`, + /// `accum[pos_idx + 1]` gets it when `w_int < 0`. + #[inline] + fn accum_signed_mul(accum: &mut [E::MulU64Accum], pos_idx: usize, am: E, w_int: i32) { + let prod = am.mul_u64_unreduced(w_int.unsigned_abs() as u64); + if w_int < 0 { + accum[pos_idx + 1] += prod; + } else { + accum[pos_idx] += prod; } } - fn compute_round_relation_compact(&self, w_compact: &[i8]) -> UniPoly { - let half = w_compact.len() / 2; - let num_points = 3; - - let mut evals = vec![E::zero(); num_points]; - for j in 0..half { - let w_0 = Self::lift_i8(w_compact[2 * j]); - let w_1 = Self::lift_i8(w_compact[2 * j + 1]); - let a_0 = self.alpha_table[2 * j]; - let a_1 = self.alpha_table[2 * j + 1]; - let m_0 = self.m_table[2 * j]; - let m_1 = self.m_table[2 * j + 1]; - for (t, eval) in evals.iter_mut().enumerate() { - let t_e = E::from_u64(t as u64); - let w_t = w_0 + t_e * (w_1 - w_0); - let a_t = a_0 + t_e * (a_1 - a_0); - let m_t = m_0 + t_e * (m_1 - m_0); - *eval = *eval + w_t * a_t * m_t; - } - } - UniPoly::from_evals(&evals) + /// Reduce a (positive, negative) accumulator pair to a single field element. + #[inline] + fn reduce_signed_accum(pos: E::MulU64Accum, neg: E::MulU64Accum) -> E { + E::reduce_mul_u64_accum(pos) - E::reduce_mul_u64_accum(neg) } - fn compute_round_norm_full(&self, w_full: &[E]) -> UniPoly { - let half = w_full.len() / 2; - + /// Fused compact round 0: computes both the norm and relation round + /// polynomials in a single pass over `w_compact`, using i128/LUT + /// arithmetic for the norm and unreduced small-int multiplies for the + /// relation. Relation uses split pos/neg accumulators to avoid + /// wrapping-neg overflow in the unsigned limbed accumulators. + #[tracing::instrument(skip_all, name = "HachiSumcheckProver::compute_round_compact_fused")] + fn compute_round_compact_fused(&self, w_compact: &[i8]) -> (UniPoly, UniPoly) { + let half = w_compact.len() / 2; let (e_first, e_second) = self.split_eq.remaining_eq_tables(); let num_first = e_first.len(); let first_bits = num_first.trailing_zeros(); + let current_x_width = self.num_u.saturating_sub(self.rounds_completed); + let current_x_mask = (1usize << current_x_width).wrapping_sub(1); + let alpha_compact = &self.alpha_compact; + let m_compact = &self.m_compact; + let b = self.b; + + // 6-element array: [pos0, neg0, pos1, neg1, pos2, neg2] + type RelAccum = [::MulU64Accum; 6]; + let rel_zero = || -> RelAccum { [E::MulU64Accum::ZERO; 6] }; + #[allow(unused_variables)] + let rel_combine = |a: &mut RelAccum, b: &RelAccum| { + for i in 0..6 { + a[i] += b[i]; + } + }; + let rel_reduce = |r: RelAccum| -> [E; 3] { + [ + Self::reduce_signed_accum(r[0], r[1]), + Self::reduce_signed_accum(r[2], r[3]), + Self::reduce_signed_accum(r[4], r[5]), + ] + }; match self.round_kernel { - NormRoundKernel::PointEvalInterpolation => { - let degree_q = 2 * self.b - 1; + NormRoundKernel::PointEvalInterpolation if b <= 10 => { + let degree_q = 2 * b - 1; let num_points_q = degree_q + 1; - let range_offsets = &self.point_precomp.as_ref().unwrap().range_offsets; - - #[cfg(feature = "parallel")] - let q_evals = { - (0..half) - .into_par_iter() - .fold( - || vec![E::zero(); num_points_q], - |mut evals, j| { - let j_low = j & (num_first - 1); - let j_high = j >> first_bits; - let eq_rem = e_first[j_low] * e_second[j_high]; - let w_0 = w_full[2 * j]; - let w_1 = w_full[2 * j + 1]; - let delta = w_1 - w_0; - let mut w_t = w_0; - for eval in evals.iter_mut() { - *eval = *eval - + eq_rem * range_check_eval_precomputed(w_t, range_offsets); - w_t = w_t + delta; - } - evals - }, - ) - .reduce( - || vec![E::zero(); num_points_q], - |mut a, b_vec| { - for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { - *ai = *ai + *bi; - } - a - }, - ) - }; - #[cfg(not(feature = "parallel"))] - let q_evals = { - let mut evals = vec![E::zero(); num_points_q]; - for j in 0..half { + + let _span = tracing::info_span!("fused_compact_point_eval").entered(); + let (q_evals, rel_accum) = cfg_fold_reduce!( + 0..half, + || (vec![E::zero(); num_points_q], rel_zero()), + |(mut norm_evals, mut rel), j| { + let w0_i = w_compact[2 * j] as i32; + let w1_i = w_compact[2 * j + 1] as i32; + let delta_i = w1_i - w0_i; + let j_low = j & (num_first - 1); let j_high = j >> first_bits; let eq_rem = e_first[j_low] * e_second[j_high]; - let w_0 = w_full[2 * j]; - let w_1 = w_full[2 * j + 1]; - let delta = w_1 - w_0; - let mut w_t = w_0; - for eval in evals.iter_mut() { - *eval = - *eval + eq_rem * range_check_eval_precomputed(w_t, range_offsets); - w_t = w_t + delta; + let mut w_t_i = w0_i; + for eval in norm_evals.iter_mut() { + let rc = range_check_eval_i128(w_t_i, b); + *eval += eq_rem * field_from_i128::(rc); + w_t_i += delta_i; } + + let a_0 = alpha_compact[(2 * j) >> current_x_width]; + let a_1 = alpha_compact[(2 * j + 1) >> current_x_width]; + let m_0 = m_compact[(2 * j) & current_x_mask]; + let m_1 = m_compact[(2 * j + 1) & current_x_mask]; + let am_0 = a_0 * m_0; + let am_1 = a_1 * m_1; + let w2_i = 2 * w1_i - w0_i; + let am_2 = (a_1 + a_1 - a_0) * (m_1 + m_1 - m_0); + + Self::accum_signed_mul(&mut rel, 0, am_0, w0_i); + Self::accum_signed_mul(&mut rel, 2, am_1, w1_i); + Self::accum_signed_mul(&mut rel, 4, am_2, w2_i); + + (norm_evals, rel) + }, + |(mut na, mut ra), (nb, rb)| { + for (ai, bi) in na.iter_mut().zip(nb.iter()) { + *ai += *bi; + } + rel_combine(&mut ra, &rb); + (na, ra) } - evals - }; + ); let q_poly = UniPoly::from_evals(&q_evals); - self.split_eq.gruen_mul(&q_poly) + let norm_poly = self.split_eq.gruen_mul(&q_poly); + let rel_evals = rel_reduce(rel_accum); + (norm_poly, UniPoly::from_evals(&rel_evals)) } NormRoundKernel::AffineCoeffComposition => { - let range_precomp = self.range_precomp.as_ref().unwrap(); - let num_coeffs_q = range_precomp.degree_q + 1; - let coeff_mix = &range_precomp.coeff_mix; - - #[cfg(feature = "parallel")] - let mut q_coeffs = { - (0..half) - .into_par_iter() - .fold( - || vec![E::zero(); num_coeffs_q], - |mut coeffs, j| { - let j_low = j & (num_first - 1); - let j_high = j >> first_bits; - let eq_rem = e_first[j_low] * e_second[j_high]; - let w_0 = w_full[2 * j]; - let w_1 = w_full[2 * j + 1]; - let a = w_1 - w_0; - accumulate_affine_range_coeffs( - &mut coeffs, - coeff_mix, - w_0, - a, - eq_rem, - ); - coeffs - }, - ) - .reduce( - || vec![E::zero(); num_coeffs_q], - |mut a, b_vec| { - for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { - *ai = *ai + *bi; - } - a - }, - ) - }; - #[cfg(not(feature = "parallel"))] - let mut q_coeffs = { - let mut coeffs = vec![E::zero(); num_coeffs_q]; - for j in 0..half { - let j_low = j & (num_first - 1); - let j_high = j >> first_bits; - let eq_rem = e_first[j_low] * e_second[j_high]; - let w_0 = w_full[2 * j]; - let w_1 = w_full[2 * j + 1]; - let a = w_1 - w_0; - accumulate_affine_range_coeffs(&mut coeffs, coeff_mix, w_0, a, eq_rem); + let rp = self.range_precomp.as_ref().unwrap(); + let num_coeffs_q = rp.degree_q + 1; + + let _span = tracing::info_span!("fused_compact_affine_coeff").entered(); + let (mut q_coeffs, rel_accum) = cfg_fold_reduce!( + 0..e_second.len(), + || (vec![E::ProductAccum::ZERO; num_coeffs_q], rel_zero()), + |(mut outer_accum, mut rel), j_high| { + debug_assert!(num_coeffs_q <= MAX_AFFINE_COEFFS); + let mut inner_accum = [E::ProductAccum::ZERO; MAX_AFFINE_COEFFS]; + for (j_low, &e_in) in e_first.iter().enumerate() { + let j = j_high * num_first + j_low; + let w0_int = w_compact[2 * j]; + let w1_int = w_compact[2 * j + 1]; + + let w_1 = E::from_i64(w1_int as i64); + let a = w_1 - E::from_i64(w0_int as i64); + let mut a_pow = E::one(); + for (i, acc) in inner_accum[..num_coeffs_q].iter_mut().enumerate() { + let h_i_w0 = rp.h_i_lut(w0_int, i); + let val = a_pow * h_i_w0; + *acc += e_in.mul_to_product_accum(val); + a_pow = a_pow * a; + } + + let a_0 = alpha_compact[(2 * j) >> current_x_width]; + let a_1 = alpha_compact[(2 * j + 1) >> current_x_width]; + let m_0 = m_compact[(2 * j) & current_x_mask]; + let m_1 = m_compact[(2 * j + 1) & current_x_mask]; + let am_0 = a_0 * m_0; + let am_1 = a_1 * m_1; + let w2_i = 2 * w1_int as i32 - w0_int as i32; + let am_2 = (a_1 + a_1 - a_0) * (m_1 + m_1 - m_0); + + Self::accum_signed_mul(&mut rel, 0, am_0, w0_int as i32); + Self::accum_signed_mul(&mut rel, 2, am_1, w1_int as i32); + Self::accum_signed_mul(&mut rel, 4, am_2, w2_i); + } + let e_out = e_second[j_high]; + for k in 0..num_coeffs_q { + let inner_reduced = E::reduce_product_accum(inner_accum[k]); + outer_accum[k] += e_out.mul_to_product_accum(inner_reduced); + } + (outer_accum, rel) + }, + |(mut ca, mut ra), (cb, rb)| { + for (ai, bi) in ca.iter_mut().zip(cb.iter()) { + *ai += *bi; + } + rel_combine(&mut ra, &rb); + (ca, ra) } - coeffs - }; + ); + let q_coeffs_reduced: Vec = + q_coeffs.drain(..).map(E::reduce_product_accum).collect(); + let mut q_coeffs = q_coeffs_reduced; trim_trailing_zeros(&mut q_coeffs); let q_poly = UniPoly::from_coeffs(q_coeffs); - self.split_eq.gruen_mul(&q_poly) + let norm_poly = self.split_eq.gruen_mul(&q_poly); + let rel_evals = rel_reduce(rel_accum); + (norm_poly, UniPoly::from_evals(&rel_evals)) } - } - } - - fn compute_round_relation_full(&self, w_full: &[E]) -> UniPoly { - let half = w_full.len() / 2; - let num_points = 3; - - #[cfg(feature = "parallel")] - let round_evals = { - (0..half) - .into_par_iter() - .fold( - || vec![E::zero(); num_points], + _ => { + // b > 10 with point-eval: fall back to separate passes + let _span = tracing::info_span!("compact_fallback").entered(); + use super::norm_sumcheck::compute_norm_round_poly_compact; + let np = compute_norm_round_poly_compact( + &self.split_eq, + w_compact, + b, + self.round_kernel, + self.point_precomp.as_ref(), + self.range_precomp.as_ref(), + ); + let pair = |j: usize| { + ( + E::from_i64(w_compact[2 * j] as i64), + E::from_i64(w_compact[2 * j + 1] as i64), + ) + }; + let rel_evals = cfg_fold_reduce!( + 0..half, + || [E::zero(); 3], |mut evals, j| { - let w_0 = w_full[2 * j]; - let w_1 = w_full[2 * j + 1]; - let a_0 = self.alpha_table[2 * j]; - let a_1 = self.alpha_table[2 * j + 1]; - let m_0 = self.m_table[2 * j]; - let m_1 = self.m_table[2 * j + 1]; - for (t, eval) in evals.iter_mut().enumerate() { - let t_e = E::from_u64(t as u64); - let w_t = w_0 + t_e * (w_1 - w_0); - let a_t = a_0 + t_e * (a_1 - a_0); - let m_t = m_0 + t_e * (m_1 - m_0); - *eval = *eval + w_t * a_t * m_t; - } + let (w_0, w_1) = pair(j); + let a_0 = alpha_compact[(2 * j) >> current_x_width]; + let a_1 = alpha_compact[(2 * j + 1) >> current_x_width]; + let m_0 = m_compact[(2 * j) & current_x_mask]; + let m_1 = m_compact[(2 * j + 1) & current_x_mask]; + evals[0] += w_0 * a_0 * m_0; + evals[1] += w_1 * a_1 * m_1; + let w_2 = w_1 + w_1 - w_0; + let a_2 = a_1 + a_1 - a_0; + let m_2 = m_1 + m_1 - m_0; + evals[2] += w_2 * a_2 * m_2; evals }, - ) - .reduce( - || vec![E::zero(); num_points], |mut a, b| { for (ai, bi) in a.iter_mut().zip(b.iter()) { - *ai = *ai + *bi; + *ai += *bi; } a - }, - ) - }; - #[cfg(not(feature = "parallel"))] - let round_evals = { - let mut evals = vec![E::zero(); num_points]; - for j in 0..half { - let w_0 = w_full[2 * j]; - let w_1 = w_full[2 * j + 1]; - let a_0 = self.alpha_table[2 * j]; - let a_1 = self.alpha_table[2 * j + 1]; - let m_0 = self.m_table[2 * j]; - let m_1 = self.m_table[2 * j + 1]; - for (t, eval) in evals.iter_mut().enumerate() { - let t_e = E::from_u64(t as u64); - let w_t = w_0 + t_e * (w_1 - w_0); - let a_t = a_0 + t_e * (a_1 - a_0); - let m_t = m_0 + t_e * (m_1 - m_0); - *eval = *eval + w_t * a_t * m_t; - } + } + ); + (np, UniPoly::from_evals(&rel_evals)) } - evals - }; - - UniPoly::from_evals(&round_evals) + } } fn fold_compact_to_full(w_compact: &[i8], r: E) -> Vec { - let half = w_compact.len() / 2; - let mut out = Vec::with_capacity(half); - for j in 0..half { - let w_0 = Self::lift_i8(w_compact[2 * j]); - let w_1 = Self::lift_i8(w_compact[2 * j + 1]); - out.push(w_0 + r * (w_1 - w_0)); - } - out + cfg_into_iter!(0..w_compact.len() / 2) + .map(|j| { + let w_0 = E::from_i64(w_compact[2 * j] as i64); + let delta = w_compact[2 * j + 1] as i32 - w_compact[2 * j] as i32; + let delta_abs = delta.unsigned_abs() as u64; + let r_delta = E::reduce_mul_u64_accum(r.mul_u64_unreduced(delta_abs)); + if delta < 0 { + w_0 - r_delta + } else { + w_0 + r_delta + } + }) + .collect() } } -impl SumcheckInstanceProver for HachiSumcheckProver { +impl SumcheckInstanceProver + for HachiSumcheckProver +{ fn num_rounds(&self) -> usize { self.num_vars } @@ -418,34 +400,228 @@ impl SumcheckInstanceProver for HachiSumcheckPro } fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { + let t_norm = Instant::now(); let (norm_poly, relation_poly) = match &self.w_table { WTable::Compact(w_compact) => { - let norm = self.compute_round_norm_compact(w_compact); - let relation = self.compute_round_relation_compact(w_compact); - (norm, relation) + let result = self.compute_round_compact_fused(w_compact); + self.norm_time_total += t_norm.elapsed().as_secs_f64(); + result } WTable::Full(w_full) => { - let norm = self.compute_round_norm_full(w_full); - let relation = self.compute_round_relation_full(w_full); - (norm, relation) + let half = w_full.len() / 2; + let (e_first, e_second) = self.split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + let first_bits = num_first.trailing_zeros(); + let current_x_width = self.num_u.saturating_sub(self.rounds_completed); + let current_x_mask = (1usize << current_x_width).wrapping_sub(1); + let alpha_compact = &self.alpha_compact; + let m_compact = &self.m_compact; + + let _span = tracing::info_span!("fused_norm_relation").entered(); + + let (np, rp) = match self.round_kernel { + NormRoundKernel::PointEvalInterpolation => { + let degree_q = 2 * self.b - 1; + let num_points_q = degree_q + 1; + let offsets_sq = &self.point_precomp.as_ref().unwrap().range_offsets_sq; + + let (q_evals, rel_evals) = cfg_fold_reduce!( + 0..half, + || (vec![E::zero(); num_points_q], [E::zero(); 3]), + |(mut norm_evals, mut rel_evals), j| { + let w_0 = w_full[2 * j]; + let w_1 = w_full[2 * j + 1]; + + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let delta = w_1 - w_0; + let mut w_t = w_0; + for eval in norm_evals.iter_mut() { + *eval += eq_rem * range_check_eval_precomputed(w_t, offsets_sq); + w_t += delta; + } + + let a_0 = alpha_compact[(2 * j) >> current_x_width]; + let a_1 = alpha_compact[(2 * j + 1) >> current_x_width]; + let m_0 = m_compact[(2 * j) & current_x_mask]; + let m_1 = m_compact[(2 * j + 1) & current_x_mask]; + rel_evals[0] += w_0 * a_0 * m_0; + rel_evals[1] += w_1 * a_1 * m_1; + let w_2 = w_1 + w_1 - w_0; + let a_2 = a_1 + a_1 - a_0; + let m_2 = m_1 + m_1 - m_0; + rel_evals[2] += w_2 * a_2 * m_2; + + (norm_evals, rel_evals) + }, + |(mut na, mut ra), (nb, rb)| { + for (ai, bi) in na.iter_mut().zip(nb.iter()) { + *ai += *bi; + } + for (ai, bi) in ra.iter_mut().zip(rb.iter()) { + *ai += *bi; + } + (na, ra) + } + ); + + let q_poly = UniPoly::from_evals(&q_evals); + ( + self.split_eq.gruen_mul(&q_poly), + UniPoly::from_evals(&rel_evals), + ) + } + NormRoundKernel::AffineCoeffComposition => { + let range_pc = self.range_precomp.as_ref().unwrap(); + let num_coeffs_q = range_pc.degree_q + 1; + debug_assert!(num_coeffs_q <= MAX_AFFINE_COEFFS); + + let (mut q_coeffs, rel_evals) = cfg_fold_reduce!( + 0..e_second.len(), + || (vec![E::ProductAccum::ZERO; num_coeffs_q], [E::zero(); 3]), + |(mut outer_accum, mut rel_evals), j_high| { + let mut inner_accum = [E::ProductAccum::ZERO; MAX_AFFINE_COEFFS]; + let base_j = j_high * num_first; + let full_chunks = num_first / 4; + let mut batch_out = [[E::zero(); MAX_AFFINE_COEFFS]; 4]; + + for chunk in 0..full_chunks { + let jl = chunk * 4; + let w = [ + (w_full[2 * (base_j + jl)], w_full[2 * (base_j + jl) + 1]), + ( + w_full[2 * (base_j + jl + 1)], + w_full[2 * (base_j + jl + 1) + 1], + ), + ( + w_full[2 * (base_j + jl + 2)], + w_full[2 * (base_j + jl + 2) + 1], + ), + ( + w_full[2 * (base_j + jl + 3)], + w_full[2 * (base_j + jl + 3) + 1], + ), + ]; + compute_entry_coeffs_x4( + &mut batch_out, + range_pc, + [w[0].0, w[1].0, w[2].0, w[3].0], + [ + w[0].1 - w[0].0, + w[1].1 - w[1].0, + w[2].1 - w[2].0, + w[3].1 - w[3].0, + ], + ); + for (b, bo) in batch_out.iter().enumerate() { + let e_in = e_first[jl + b]; + for (acc, &entry) in inner_accum[..num_coeffs_q] + .iter_mut() + .zip(bo[..num_coeffs_q].iter()) + { + *acc += e_in.mul_to_product_accum(entry); + } + } + for (b, &(w_0, w_1)) in w.iter().enumerate() { + let j = base_j + jl + b; + let a_0 = alpha_compact[(2 * j) >> current_x_width]; + let a_1 = alpha_compact[(2 * j + 1) >> current_x_width]; + let m_0 = m_compact[(2 * j) & current_x_mask]; + let m_1 = m_compact[(2 * j + 1) & current_x_mask]; + rel_evals[0] += w_0 * a_0 * m_0; + rel_evals[1] += w_1 * a_1 * m_1; + let w_2 = w_1 + w_1 - w_0; + let a_2 = a_1 + a_1 - a_0; + let m_2 = m_1 + m_1 - m_0; + rel_evals[2] += w_2 * a_2 * m_2; + } + } + + let mut entry_buf = [E::zero(); MAX_AFFINE_COEFFS]; + let mut w_pows_buf = [E::zero(); MAX_AFFINE_COEFFS]; + for (tail_idx, &e_in) in + e_first[full_chunks * 4..].iter().enumerate() + { + let j = base_j + full_chunks * 4 + tail_idx; + let w_0 = w_full[2 * j]; + let w_1 = w_full[2 * j + 1]; + compute_entry_coeffs( + &mut entry_buf, + &mut w_pows_buf, + range_pc, + w_0, + w_1 - w_0, + ); + for (acc, &entry) in inner_accum[..num_coeffs_q] + .iter_mut() + .zip(entry_buf[..num_coeffs_q].iter()) + { + *acc += e_in.mul_to_product_accum(entry); + } + let a_0 = alpha_compact[(2 * j) >> current_x_width]; + let a_1 = alpha_compact[(2 * j + 1) >> current_x_width]; + let m_0 = m_compact[(2 * j) & current_x_mask]; + let m_1 = m_compact[(2 * j + 1) & current_x_mask]; + rel_evals[0] += w_0 * a_0 * m_0; + rel_evals[1] += w_1 * a_1 * m_1; + let w_2 = w_1 + w_1 - w_0; + let a_2 = a_1 + a_1 - a_0; + let m_2 = m_1 + m_1 - m_0; + rel_evals[2] += w_2 * a_2 * m_2; + } + + let e_out = e_second[j_high]; + for k in 0..num_coeffs_q { + let inner_reduced = E::reduce_product_accum(inner_accum[k]); + outer_accum[k] += e_out.mul_to_product_accum(inner_reduced); + } + (outer_accum, rel_evals) + }, + |(mut ca, mut ra), (cb, rb)| { + for (ai, bi) in ca.iter_mut().zip(cb.iter()) { + *ai += *bi; + } + for (ai, bi) in ra.iter_mut().zip(rb.iter()) { + *ai += *bi; + } + (ca, ra) + } + ); + + let mut q_coeffs: Vec = + q_coeffs.drain(..).map(E::reduce_product_accum).collect(); + trim_trailing_zeros(&mut q_coeffs); + let q_poly = UniPoly::from_coeffs(q_coeffs); + ( + self.split_eq.gruen_mul(&q_poly), + UniPoly::from_evals(&rel_evals), + ) + } + }; + + self.norm_time_total += t_norm.elapsed().as_secs_f64(); + (np, rp) } }; let max_len = norm_poly.coeffs.len().max(relation_poly.coeffs.len()); let mut combined = vec![E::zero(); max_len]; for (i, c) in norm_poly.coeffs.iter().enumerate() { - combined[i] = combined[i] + self.batching_coeff * *c; + combined[i] += self.batching_coeff * *c; } for (i, c) in relation_poly.coeffs.iter().enumerate() { - combined[i] = combined[i] + *c; + combined[i] += *c; } UniPoly::from_coeffs(combined) } fn ingest_challenge(&mut self, _round: usize, r: E) { + let t_fold = Instant::now(); + let _span = tracing::info_span!("fold_round").entered(); self.split_eq.bind(r); - self.w_table = match std::mem::replace(&mut self.w_table, WTable::Full(Vec::new())) { + self.w_table = match mem::replace(&mut self.w_table, WTable::Full(Vec::new())) { WTable::Compact(w_compact) => WTable::Full(Self::fold_compact_to_full(&w_compact, r)), WTable::Full(mut w_full) => { fold_evals_in_place(&mut w_full, r); @@ -453,8 +629,22 @@ impl SumcheckInstanceProver for HachiSumcheckPro } }; - fold_evals_in_place(&mut self.alpha_table, r); - fold_evals_in_place(&mut self.m_table, r); + if self.rounds_completed < self.num_u { + fold_evals_in_place(&mut self.m_compact, r); + } else { + fold_evals_in_place(&mut self.alpha_compact, r); + } + + drop(_span); + self.fold_time_total += t_fold.elapsed().as_secs_f64(); + self.rounds_completed += 1; + + if self.rounds_completed == self.num_vars { + eprintln!( + " [fused_sc] {} rounds: norm={:.2}s, relation={:.2}s, fold={:.2}s", + self.num_vars, self.norm_time_total, self.relation_time_total, self.fold_time_total + ); + } } } @@ -462,6 +652,10 @@ impl SumcheckInstanceProver for HachiSumcheckPro pub struct HachiSumcheckVerifier { batching_coeff: F, w_evals: Vec, + /// When set, overrides the `w_val` computed from `w_evals` in + /// `expected_output_claim`. Used at intermediate fold levels where + /// the full w vector is not available. + w_val_override: Option, tau0: Vec, b: usize, alpha_evals_y: Vec, @@ -469,12 +663,13 @@ pub struct HachiSumcheckVerifier { num_u: usize, num_l: usize, relation_claim: F, - _marker: std::marker::PhantomData<[F; D]>, + _marker: PhantomData<[F; D]>, } impl HachiSumcheckVerifier { /// Create a fused verifier for the norm + relation sumcheck. #[allow(clippy::too_many_arguments)] + #[tracing::instrument(skip_all, name = "HachiSumcheckVerifier::new")] pub fn new( batching_coeff: F, w_evals: Vec, @@ -493,19 +688,20 @@ impl HachiSumcheckVerifier { let y_a: Vec = v .iter() .chain(u.iter()) - .chain(std::iter::once(&y_ring)) + .chain(iter::once(&y_ring)) .map(|r| eval_ring_at(r, &alpha)) .collect(); let eq_tau1 = EqPolynomial::evals(&tau1); let mut relation_claim = F::zero(); for (i, eq_i) in eq_tau1.iter().enumerate() { let y_i = if i < y_a.len() { y_a[i] } else { F::zero() }; - relation_claim = relation_claim + *eq_i * y_i; + relation_claim += *eq_i * y_i; } Self { batching_coeff, w_evals, + w_val_override: None, tau0, b, alpha_evals_y, @@ -513,9 +709,16 @@ impl HachiSumcheckVerifier { num_u, num_l, relation_claim, - _marker: std::marker::PhantomData, + _marker: PhantomData, } } + + /// Set the w_val override for intermediate fold levels where the + /// full w vector is not available. + pub fn with_w_val_override(mut self, w_val: F) -> Self { + self.w_val_override = Some(w_val); + self + } } impl SumcheckInstanceVerifier @@ -535,7 +738,10 @@ impl SumcheckInstanceVerifier fn expected_output_claim(&self, challenges: &[F]) -> Result { let eq_val = EqPolynomial::mle(&self.tau0, challenges); - let w_val = multilinear_eval(&self.w_evals, challenges)?; + let w_val = match self.w_val_override { + Some(v) => v, + None => multilinear_eval(&self.w_evals, challenges)?, + }; let norm_oracle = eq_val * range_check_eval(w_val, self.b); let (x_challenges, y_challenges) = challenges.split_at(self.num_u); @@ -543,6 +749,12 @@ impl SumcheckInstanceVerifier let m_val = multilinear_eval(&self.m_evals_x, x_challenges)?; let relation_oracle = w_val * alpha_val * m_val; + eprintln!( + " [expected_output] num_u={}, num_l={}, w_override={}, b={}, tau0.len={}, m_evals_x.len={}, alpha_evals_y.len={}", + self.num_u, self.num_l, self.w_val_override.is_some(), self.b, + self.tau0.len(), self.m_evals_x.len(), self.alpha_evals_y.len() + ); + Ok(self.batching_coeff * norm_oracle + relation_oracle) } } diff --git a/src/protocol/sumcheck/mod.rs b/src/protocol/sumcheck/mod.rs index dc824bba..dfbf4eac 100644 --- a/src/protocol/sumcheck/mod.rs +++ b/src/protocol/sumcheck/mod.rs @@ -23,9 +23,11 @@ pub mod types; use crate::error::HachiError; use crate::protocol::transcript::labels; use crate::protocol::transcript::Transcript; -use crate::FieldCore; +use crate::{CanonicalField, FieldCore}; -pub use crate::algebra::poly::{fold_evals_in_place, multilinear_eval, range_check_eval}; +pub use crate::algebra::poly::{ + fold_evals_in_place, multilinear_eval, multilinear_eval_small, range_check_eval, +}; pub use types::{CompressedUniPoly, SumcheckProof, UniPoly}; /// Prover-side sumcheck instance interface. @@ -97,13 +99,14 @@ pub trait SumcheckInstanceVerifier: Send + Sync { /// # Errors /// /// Returns an error if any per-round polynomial exceeds the instance's degree bound. +#[tracing::instrument(skip_all, name = "prove_sumcheck")] pub fn prove_sumcheck( instance: &mut Inst, transcript: &mut T, mut sample_challenge: S, ) -> Result<(SumcheckProof, Vec, E), HachiError> where - F: crate::FieldCore + crate::CanonicalField, + F: FieldCore + CanonicalField, T: Transcript, E: FieldCore, S: FnMut(&mut T) -> E, @@ -164,6 +167,7 @@ where /// Returns [`HachiError::InvalidProof`] if the final sumcheck claim does not /// match the oracle evaluation, or propagates any error from the per-round /// verification (e.g. degree-bound violation, round-count mismatch). +#[tracing::instrument(skip_all, name = "verify_sumcheck")] pub fn verify_sumcheck( proof: &SumcheckProof, verifier: &V, @@ -171,7 +175,7 @@ pub fn verify_sumcheck( sample_challenge: S, ) -> Result, HachiError> where - F: crate::FieldCore + crate::CanonicalField, + F: FieldCore + CanonicalField, T: Transcript, E: FieldCore, S: FnMut(&mut T) -> E, @@ -189,6 +193,12 @@ where let expected = verifier.expected_output_claim(&challenges)?; if final_claim != expected { + eprintln!( + "[verify_sumcheck] MISMATCH: rounds={}, degree_bound={}", + verifier.num_rounds(), + verifier.degree_bound(), + ); + eprintln!(" diff_is_zero = {}", (final_claim - expected).is_zero()); return Err(HachiError::InvalidProof); } diff --git a/src/protocol/sumcheck/norm_sumcheck.rs b/src/protocol/sumcheck/norm_sumcheck.rs index db4625cf..4e2ff2f5 100644 --- a/src/protocol/sumcheck/norm_sumcheck.rs +++ b/src/protocol/sumcheck/norm_sumcheck.rs @@ -9,139 +9,609 @@ use super::eq_poly::EqPolynomial; use super::split_eq::GruenSplitEq; use super::{fold_evals_in_place, multilinear_eval, range_check_eval}; use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, UniPoly}; +use crate::algebra::fields::HasUnreducedOps; use crate::error::HachiError; #[cfg(feature = "parallel")] use crate::parallel::*; -use crate::{FieldCore, FromSmallInt}; +use crate::{cfg_fold_reduce, AdditiveGroup, CanonicalField, FieldCore, FromSmallInt}; -const SMALL_B_POINT_EVAL_MAX: usize = 8; +/// Max number of affine coefficient rows (degree_q + 1) for `b <= 8`. +pub(crate) const MAX_AFFINE_COEFFS: usize = 16; +/// Which kernel to use for the norm sumcheck accumulation loop. #[derive(Clone, Copy, Debug, PartialEq, Eq)] -pub(crate) enum NormRoundKernel { +pub enum NormRoundKernel { + /// Evaluate the range-check polynomial at `degree_q+1` points, then interpolate. PointEvalInterpolation, + /// Directly accumulate polynomial coefficients via affine substitution. AffineCoeffComposition, } -fn choose_round_kernel(b: usize) -> NormRoundKernel { - if b <= SMALL_B_POINT_EVAL_MAX { - NormRoundKernel::PointEvalInterpolation - } else { +/// Select the norm kernel for a given `b`. +/// +/// Override with env var `HACHI_NORM_KERNEL=point_eval` or `affine_coeff`. +pub fn choose_round_kernel(b: usize) -> NormRoundKernel { + if let Ok(v) = std::env::var("HACHI_NORM_KERNEL") { + match v.as_str() { + "point_eval" => return NormRoundKernel::PointEvalInterpolation, + "affine_coeff" => return NormRoundKernel::AffineCoeffComposition, + _ => {} + } + } + if b <= 8 { NormRoundKernel::AffineCoeffComposition + } else { + NormRoundKernel::PointEvalInterpolation } } +/// A nonzero coefficient entry in the affine decomposition polynomial. +#[derive(Clone, Copy, Debug)] +pub(crate) struct SparseCoeffEntry { + /// Power index: which `w_0^k` this coefficient multiplies. + pub k: u8, + /// Absolute value of the mixed coefficient (fits u64 for b <= 8). + pub abs_coeff: u64, + /// Sign: true if the coefficient is negative. + pub is_neg: bool, +} + #[derive(Clone)] pub(crate) struct RangeAffinePrecomp { - /// `coeff_mix[i][k] = c_{i+k} * binom(i+k, i)`, where - /// `R(w) = sum_m c_m * w^m` is the range-check polynomial. - pub(crate) coeff_mix: Vec>, + /// Flat storage of nonzero `coeff_mix[i][k]` entries. + sparse_entries: Vec, + /// `sparse_row_offsets[i]..sparse_row_offsets[i+1]` indexes into `sparse_entries`. + sparse_row_offsets: Vec, pub(crate) degree_q: usize, + /// Precomputed `h_i(w_0)` for all small-integer `w_0 ∈ {-(b-1),...,b-1}`. + /// Indexed as `small_w_lut[(w_0 + b - 1) * num_rows + i]`. + small_w_lut: Vec, + b: usize, +} + +/// Integer version of `range_check_coeffs`: returns the polynomial coefficients +/// of `R(w) = w * Π_{k=1}^{b-1}(w² - k²)` as exact i64 values. +fn range_check_coeffs_int(b: usize) -> Vec { + assert!(b >= 1, "b must be at least 1"); + let mut coeffs: Vec = vec![0, 1]; + for k in 1..b as i64 { + let k_sq = k * k; + let mut next = vec![0i64; coeffs.len() + 2]; + for (idx, &c) in coeffs.iter().enumerate() { + next[idx] -= c * k_sq; + next[idx + 2] += c; + } + coeffs = next; + } + coeffs } impl RangeAffinePrecomp { pub(crate) fn new(b: usize) -> Self { assert!(b >= 1, "b must be at least 1"); - let range_coeffs = range_check_coeffs::(b); - let degree_q = range_coeffs.len() - 1; - let small_scalars: Vec = (0..=degree_q + 1).map(|x| E::from_u64(x as u64)).collect(); - let inv_small_scalars: Vec = (0..=degree_q + 1) - .map(|x| { - if x == 0 { - E::zero() - } else { - small_scalars[x] - .inv() - .expect("field characteristic too small for range-check precomputation") - } - }) - .collect(); - let mut coeff_mix = Vec::with_capacity(degree_q + 1); - for i in 0..=degree_q { + let range_coeffs = range_check_coeffs_int(b); + let degree_q = range_coeffs.len() - 1; + let num_rows = degree_q + 1; + + // Build dense integer coeff_mix and sparse entries simultaneously. + let total_elems = num_rows * (num_rows + 1) / 2; + let mut dense_int = Vec::with_capacity(total_elems); + let mut dense_row_offsets = Vec::with_capacity(num_rows + 1); + let mut sparse_entries = Vec::new(); + let mut sparse_row_offsets = Vec::with_capacity(num_rows + 1); + + for i in 0..num_rows { + dense_row_offsets.push(dense_int.len()); + sparse_row_offsets.push(sparse_entries.len()); let row_len = degree_q - i + 1; - let mut row = Vec::with_capacity(row_len); - let mut binom_m_i = E::one(); // binom(i, i) + let mut binom: i64 = 1; // binom(i, i) = 1 for k in 0..row_len { let m = i + k; - row.push(range_coeffs[m] * binom_m_i); + let coeff = range_coeffs[m] * binom; + dense_int.push(coeff); + if coeff != 0 { + sparse_entries.push(SparseCoeffEntry { + k: k as u8, + abs_coeff: coeff.unsigned_abs(), + is_neg: coeff < 0, + }); + } if k + 1 < row_len { - let numer = small_scalars[m + 1]; - let denom_inv = inv_small_scalars[k + 1]; - binom_m_i = binom_m_i * numer * denom_inv; + binom = binom * (m as i64 + 1) / (k as i64 + 1); + } + } + } + dense_row_offsets.push(dense_int.len()); + sparse_row_offsets.push(sparse_entries.len()); + + // Precompute LUT using i128 integer Horner. + let num_w_vals = 2 * b - 1; + let mut small_w_lut = vec![E::zero(); num_w_vals * num_rows]; + for (w_idx, w_0_int) in (-(b as i64 - 1)..=(b as i64 - 1)).enumerate() { + for i in 0..num_rows { + let row = &dense_int[dense_row_offsets[i]..dense_row_offsets[i + 1]]; + let mut h: i128 = 0; + for &c in row.iter().rev() { + h = h * w_0_int as i128 + c as i128; } + small_w_lut[w_idx * num_rows + i] = E::from_i128(h); } - coeff_mix.push(row); } Self { - coeff_mix, + sparse_entries, + sparse_row_offsets, degree_q, + small_w_lut, + b, } } } +impl RangeAffinePrecomp { + #[inline] + pub(crate) fn sparse_row(&self, i: usize) -> &[SparseCoeffEntry] { + &self.sparse_entries[self.sparse_row_offsets[i]..self.sparse_row_offsets[i + 1]] + } + + pub(crate) fn num_rows(&self) -> usize { + self.degree_q + 1 + } + + #[inline] + pub(crate) fn h_i_lut(&self, w_0_int: i8, i: usize) -> E { + let w_idx = (w_0_int as i16 + self.b as i16 - 1) as usize; + self.small_w_lut[w_idx * self.num_rows() + i] + } +} + #[derive(Clone)] pub(crate) struct PointEvalPrecomp { - pub(crate) range_offsets: Vec, + pub(crate) range_offsets_sq: Vec, } impl PointEvalPrecomp { pub(crate) fn new(b: usize) -> Self { - let range_offsets = (1..b).map(|k| E::from_u64(k as u64)).collect(); - Self { range_offsets } + assert!(b >= 1, "b must be at least 1"); + let range_offsets_sq = (1..b) + .map(|k| { + let k_e = E::from_u64(k as u64); + k_e * k_e + }) + .collect(); + Self { range_offsets_sq } } } -/// Coefficients of `R(w) = w * Π_{k=1}^{b-1}(w-k)(w+k)` in increasing degree order. -fn range_check_coeffs(b: usize) -> Vec { - assert!(b >= 1, "b must be at least 1"); - let mut coeffs = vec![E::zero(), E::one()]; // R(w)=w when b=1 - for k in 1..b { - let k_e = E::from_u64(k as u64); - let k_sq = k_e * k_e; - // Multiply by (w^2 - k^2). - let mut next = vec![E::zero(); coeffs.len() + 2]; - for (idx, c) in coeffs.iter().enumerate() { - next[idx] = next[idx] - *c * k_sq; - next[idx + 2] = next[idx + 2] + *c; - } - coeffs = next; +/// Evaluate `R(w) = w · Π_{k=1}^{b-1}(w² - k²)` in native `i128` arithmetic. +/// +/// Only valid for `b <= 10` (intermediates fit i128; verified up to ~2^117 for b=8). +/// Panics in debug mode if an intermediate overflows. +#[inline] +pub(crate) fn range_check_eval_i128(w: i32, b: usize) -> i128 { + debug_assert!(b <= 10, "i128 range-check only valid for b <= 10"); + let s = (w as i128) * (w as i128); + let mut acc = w as i128; + for k in 1..b as i128 { + acc = acc + .checked_mul(s - k * k) + .expect("i128 overflow in range-check"); } - coeffs + acc } -pub(crate) fn range_check_eval_precomputed(w: E, range_offsets: &[E]) -> E { +/// Convert an `i128` to a field element via `CanonicalField::from_canonical_u128_reduced`. +#[inline] +pub(crate) fn field_from_i128(val: i128) -> E { + if val >= 0 { + E::from_canonical_u128_reduced(val as u128) + } else { + -E::from_canonical_u128_reduced(val.unsigned_abs()) + } +} + +pub(crate) fn range_check_eval_precomputed(w: E, offsets_sq: &[E]) -> E { + let s = w * w; let mut acc = w; - for &k in range_offsets { - acc = acc * (w - k) * (w + k); + for &k_sq in offsets_sq { + acc = acc * (s - k_sq); } acc } -pub(crate) fn accumulate_affine_range_coeffs( - out_coeffs: &mut [E], - coeff_mix: &[Vec], +/// Compute per-entry affine range-check coefficients using power-table + +/// sparse unreduced dot product. Writes `a^i · h_i(w_0)` into `out[i]` +/// for `i ∈ 0..precomp.num_rows()`. +/// +/// `w_pows` is a caller-provided scratch buffer of length >= `degree_q + 1`. +#[inline] +pub(crate) fn compute_entry_coeffs( + out: &mut [E], + w_pows: &mut [E], + precomp: &RangeAffinePrecomp, w_0: E, a: E, - scale: E, ) { + let deg = precomp.degree_q; + let num_rows = precomp.num_rows(); + debug_assert!(out.len() >= num_rows); + debug_assert!(w_pows.len() > deg); + + w_pows[0] = E::one(); + for k in 1..=deg { + w_pows[k] = w_pows[k - 1] * w_0; + } + let mut a_pow = E::one(); - for (i, row) in coeff_mix.iter().enumerate() { - let mut h_i_w0 = E::zero(); - for coeff in row.iter().rev() { - h_i_w0 = h_i_w0 * w_0 + *coeff; + for (i, out_i) in out.iter_mut().enumerate().take(num_rows) { + let entries = precomp.sparse_row(i); + let mut pos = E::MulU64Accum::ZERO; + let mut neg = E::MulU64Accum::ZERO; + for entry in entries { + let prod = w_pows[entry.k as usize].mul_u64_unreduced(entry.abs_coeff); + if entry.is_neg { + neg += prod; + } else { + pos += prod; + } } - out_coeffs[i] = out_coeffs[i] + scale * a_pow * h_i_w0; + let h_i = E::reduce_mul_u64_accum(pos) - E::reduce_mul_u64_accum(neg); + *out_i = a_pow * h_i; a_pow = a_pow * a; } } +/// Batched version: processes 4 entries simultaneously to expose ILP across +/// independent power-table and sparse-dot-product chains. +#[inline] +pub(crate) fn compute_entry_coeffs_x4( + out: &mut [[E; MAX_AFFINE_COEFFS]; 4], + precomp: &RangeAffinePrecomp, + w_0: [E; 4], + a: [E; 4], +) { + let deg = precomp.degree_q; + let num_rows = precomp.num_rows(); + + let mut pw = [[E::zero(); MAX_AFFINE_COEFFS]; 4]; + for p in &mut pw { + p[0] = E::one(); + } + for k in 1..=deg { + pw[0][k] = pw[0][k - 1] * w_0[0]; + pw[1][k] = pw[1][k - 1] * w_0[1]; + pw[2][k] = pw[2][k - 1] * w_0[2]; + pw[3][k] = pw[3][k - 1] * w_0[3]; + } + + let mut ap = [E::one(); 4]; + for i in 0..num_rows { + let entries = precomp.sparse_row(i); + + let mut pos0 = E::MulU64Accum::ZERO; + let mut neg0 = E::MulU64Accum::ZERO; + let mut pos1 = E::MulU64Accum::ZERO; + let mut neg1 = E::MulU64Accum::ZERO; + let mut pos2 = E::MulU64Accum::ZERO; + let mut neg2 = E::MulU64Accum::ZERO; + let mut pos3 = E::MulU64Accum::ZERO; + let mut neg3 = E::MulU64Accum::ZERO; + + for entry in entries { + let k = entry.k as usize; + let c = entry.abs_coeff; + let p0 = pw[0][k].mul_u64_unreduced(c); + let p1 = pw[1][k].mul_u64_unreduced(c); + let p2 = pw[2][k].mul_u64_unreduced(c); + let p3 = pw[3][k].mul_u64_unreduced(c); + if entry.is_neg { + neg0 += p0; + neg1 += p1; + neg2 += p2; + neg3 += p3; + } else { + pos0 += p0; + pos1 += p1; + pos2 += p2; + pos3 += p3; + } + } + + let h0 = E::reduce_mul_u64_accum(pos0) - E::reduce_mul_u64_accum(neg0); + let h1 = E::reduce_mul_u64_accum(pos1) - E::reduce_mul_u64_accum(neg1); + let h2 = E::reduce_mul_u64_accum(pos2) - E::reduce_mul_u64_accum(neg2); + let h3 = E::reduce_mul_u64_accum(pos3) - E::reduce_mul_u64_accum(neg3); + + out[0][i] = ap[0] * h0; + out[1][i] = ap[1] * h1; + out[2][i] = ap[2] * h2; + out[3][i] = ap[3] * h3; + + ap[0] = ap[0] * a[0]; + ap[1] = ap[1] * a[1]; + ap[2] = ap[2] * a[2]; + ap[3] = ap[3] * a[3]; + } +} + pub(crate) fn trim_trailing_zeros(coeffs: &mut Vec) { while coeffs.len() > 1 && coeffs.last().is_some_and(|c| c.is_zero()) { coeffs.pop(); } } +/// Centralized norm round polynomial computation (full field-element path). +/// +/// Both `NormSumcheckProver` and `HachiSumcheckProver` delegate here. +pub(crate) fn compute_norm_round_poly( + split_eq: &GruenSplitEq, + half: usize, + b: usize, + round_kernel: NormRoundKernel, + point_precomp: Option<&PointEvalPrecomp>, + range_precomp: Option<&RangeAffinePrecomp>, + w_pair: impl Fn(usize) -> (E, E) + Sync, +) -> UniPoly { + let (e_first, e_second) = split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + let first_bits = num_first.trailing_zeros(); + + match round_kernel { + NormRoundKernel::PointEvalInterpolation => { + let degree_q = 2 * b - 1; + let num_points_q = degree_q + 1; + let offsets_sq = &point_precomp.unwrap().range_offsets_sq; + + let q_evals = { + let _span = tracing::info_span!("norm_accumulate", kernel = "point_eval").entered(); + cfg_fold_reduce!( + 0..half, + || vec![E::zero(); num_points_q], + |mut evals, j| { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let (w_0, w_1) = w_pair(j); + let delta = w_1 - w_0; + let mut w_t = w_0; + for eval in evals.iter_mut() { + *eval += eq_rem * range_check_eval_precomputed(w_t, offsets_sq); + w_t += delta; + } + evals + }, + |mut a, b_vec| { + for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { + *ai += *bi; + } + a + } + ) + }; + + let q_poly = UniPoly::from_evals(&q_evals); + split_eq.gruen_mul(&q_poly) + } + NormRoundKernel::AffineCoeffComposition => { + let rp = range_precomp.unwrap(); + let num_coeffs_q = rp.degree_q + 1; + + let mut q_coeffs = { + let _span = + tracing::info_span!("norm_accumulate", kernel = "affine_coeff").entered(); + + cfg_fold_reduce!( + 0..e_second.len(), + || vec![E::ProductAccum::ZERO; num_coeffs_q], + |mut outer_accum, j_high| { + debug_assert!(num_coeffs_q <= MAX_AFFINE_COEFFS); + let mut inner_accum = [E::ProductAccum::ZERO; MAX_AFFINE_COEFFS]; + let base_j = j_high * num_first; + let full_chunks = e_first.len() / 4; + let mut batch_out = [[E::zero(); MAX_AFFINE_COEFFS]; 4]; + + for chunk in 0..full_chunks { + let jl = chunk * 4; + let pairs = [ + w_pair(base_j + jl), + w_pair(base_j + jl + 1), + w_pair(base_j + jl + 2), + w_pair(base_j + jl + 3), + ]; + compute_entry_coeffs_x4( + &mut batch_out, + rp, + [pairs[0].0, pairs[1].0, pairs[2].0, pairs[3].0], + [ + pairs[0].1 - pairs[0].0, + pairs[1].1 - pairs[1].0, + pairs[2].1 - pairs[2].0, + pairs[3].1 - pairs[3].0, + ], + ); + for (b, bo) in batch_out.iter().enumerate() { + let e_in = e_first[jl + b]; + for (acc, &entry) in inner_accum[..num_coeffs_q] + .iter_mut() + .zip(bo[..num_coeffs_q].iter()) + { + *acc += e_in.mul_to_product_accum(entry); + } + } + } + + let mut entry_buf = [E::zero(); MAX_AFFINE_COEFFS]; + let mut w_pows_buf = [E::zero(); MAX_AFFINE_COEFFS]; + for (tail_idx, &e_in) in e_first[full_chunks * 4..].iter().enumerate() { + let j = base_j + full_chunks * 4 + tail_idx; + let (w_0, w_1) = w_pair(j); + compute_entry_coeffs( + &mut entry_buf, + &mut w_pows_buf, + rp, + w_0, + w_1 - w_0, + ); + for (acc, &entry) in inner_accum[..num_coeffs_q] + .iter_mut() + .zip(entry_buf[..num_coeffs_q].iter()) + { + *acc += e_in.mul_to_product_accum(entry); + } + } + + let e_out = e_second[j_high]; + for k in 0..num_coeffs_q { + let inner_reduced = E::reduce_product_accum(inner_accum[k]); + outer_accum[k] += e_out.mul_to_product_accum(inner_reduced); + } + outer_accum + }, + |mut a, b_vec| { + for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { + *ai += *bi; + } + a + } + ) + } + .into_iter() + .map(E::reduce_product_accum) + .collect::>(); + + trim_trailing_zeros(&mut q_coeffs); + let q_poly = UniPoly::from_coeffs(q_coeffs); + split_eq.gruen_mul(&q_poly) + } + } +} + +/// Compact round-0 variant: uses native i128 arithmetic (point-eval, b<=10) +/// or precomputed LUT (affine-coeff) when w values are small integers. +pub(crate) fn compute_norm_round_poly_compact< + E: FieldCore + FromSmallInt + CanonicalField + HasUnreducedOps, +>( + split_eq: &GruenSplitEq, + w_compact: &[i8], + b: usize, + round_kernel: NormRoundKernel, + point_precomp: Option<&PointEvalPrecomp>, + range_precomp: Option<&RangeAffinePrecomp>, +) -> UniPoly { + let half = w_compact.len() / 2; + let (e_first, e_second) = split_eq.remaining_eq_tables(); + let num_first = e_first.len(); + let first_bits = num_first.trailing_zeros(); + + match round_kernel { + NormRoundKernel::PointEvalInterpolation if b <= 10 => { + let degree_q = 2 * b - 1; + let num_points_q = degree_q + 1; + + let q_evals = { + let _span = + tracing::info_span!("norm_accumulate", kernel = "point_eval_i128").entered(); + cfg_fold_reduce!( + 0..half, + || vec![E::zero(); num_points_q], + |mut evals, j| { + let j_low = j & (num_first - 1); + let j_high = j >> first_bits; + let eq_rem = e_first[j_low] * e_second[j_high]; + let w0_i = w_compact[2 * j] as i32; + let delta_i = w_compact[2 * j + 1] as i32 - w0_i; + let mut w_t_i = w0_i; + for eval in evals.iter_mut() { + let rc = range_check_eval_i128(w_t_i, b); + *eval += eq_rem * field_from_i128::(rc); + w_t_i += delta_i; + } + evals + }, + |mut a, b_vec| { + for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { + *ai += *bi; + } + a + } + ) + }; + + let q_poly = UniPoly::from_evals(&q_evals); + split_eq.gruen_mul(&q_poly) + } + NormRoundKernel::AffineCoeffComposition => { + let rp = range_precomp.unwrap(); + let num_coeffs_q = rp.degree_q + 1; + + let mut q_coeffs = { + let _span = + tracing::info_span!("norm_accumulate", kernel = "affine_coeff_lut").entered(); + + cfg_fold_reduce!( + 0..e_second.len(), + || vec![E::ProductAccum::ZERO; num_coeffs_q], + |mut outer_accum, j_high| { + debug_assert!(num_coeffs_q <= MAX_AFFINE_COEFFS); + let mut inner_accum = [E::ProductAccum::ZERO; MAX_AFFINE_COEFFS]; + for (j_low, &e_in) in e_first.iter().enumerate() { + let j = j_high * num_first + j_low; + let w_0_int = w_compact[2 * j]; + let w_1 = E::from_i64(w_compact[2 * j + 1] as i64); + let a = w_1 - E::from_i64(w_0_int as i64); + let mut a_pow = E::one(); + for (i, acc) in inner_accum[..num_coeffs_q].iter_mut().enumerate() { + let h_i_w0 = rp.h_i_lut(w_0_int, i); + let val = a_pow * h_i_w0; + *acc += e_in.mul_to_product_accum(val); + a_pow = a_pow * a; + } + } + let e_out = e_second[j_high]; + for k in 0..num_coeffs_q { + let inner_reduced = E::reduce_product_accum(inner_accum[k]); + outer_accum[k] += e_out.mul_to_product_accum(inner_reduced); + } + outer_accum + }, + |mut a, b_vec| { + for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { + *ai += *bi; + } + a + } + ) + } + .into_iter() + .map(E::reduce_product_accum) + .collect::>(); + + trim_trailing_zeros(&mut q_coeffs); + let q_poly = UniPoly::from_coeffs(q_coeffs); + split_eq.gruen_mul(&q_poly) + } + _ => { + // b > 10 with point-eval: fall back to field-element path + let pair = |j: usize| { + ( + E::from_i64(w_compact[2 * j] as i64), + E::from_i64(w_compact[2 * j + 1] as i64), + ) + }; + compute_norm_round_poly( + split_eq, + half, + b, + round_kernel, + point_precomp, + range_precomp, + pair, + ) + } + } +} + /// Prover for `F_{0,τ₀}(x,y) = ẽq(τ₀,(x,y)) · w̃(x,y) · range_check(w̃(x,y), b)`. /// /// Uses the Gruen/Dao-Thaler optimization: the eq polynomial is factored into @@ -159,7 +629,7 @@ pub struct NormSumcheckProver { b: usize, } -impl NormSumcheckProver { +impl NormSumcheckProver { /// Create a new norm (range-check) sumcheck prover. /// /// # Panics @@ -175,6 +645,7 @@ impl NormSumcheckProver { b: usize, round_kernel: NormRoundKernel, ) -> Self { + assert!(b >= 1, "b must be at least 1"); let num_vars = tau.len(); assert_eq!(w_evals.len(), 1 << num_vars); let point_precomp = match round_kernel { @@ -195,139 +666,11 @@ impl NormSumcheckProver { b, } } - - fn compute_round_univariate_point_eval(&self) -> UniPoly { - let half = self.w_table.len() / 2; - let degree_q = 2 * self.b - 1; - let num_points_q = degree_q + 1; - let point_precomp = self - .point_precomp - .as_ref() - .expect("point-eval precomputation must exist"); - let range_offsets = &point_precomp.range_offsets; - - let (e_first, e_second) = self.split_eq.remaining_eq_tables(); - let num_first = e_first.len(); - let first_bits = num_first.trailing_zeros(); - - #[cfg(feature = "parallel")] - let q_evals = { - (0..half) - .into_par_iter() - .fold( - || vec![E::zero(); num_points_q], - |mut evals, j| { - let j_low = j & (num_first - 1); - let j_high = j >> first_bits; - let eq_rem = e_first[j_low] * e_second[j_high]; - let w_0 = self.w_table[2 * j]; - let w_1 = self.w_table[2 * j + 1]; - let delta = w_1 - w_0; - let mut w_t = w_0; - for eval in evals.iter_mut() { - *eval = - *eval + eq_rem * range_check_eval_precomputed(w_t, range_offsets); - w_t = w_t + delta; - } - evals - }, - ) - .reduce( - || vec![E::zero(); num_points_q], - |mut a, b_vec| { - for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { - *ai = *ai + *bi; - } - a - }, - ) - }; - #[cfg(not(feature = "parallel"))] - let q_evals = { - let mut evals = vec![E::zero(); num_points_q]; - for j in 0..half { - let j_low = j & (num_first - 1); - let j_high = j >> first_bits; - let eq_rem = e_first[j_low] * e_second[j_high]; - let w_0 = self.w_table[2 * j]; - let w_1 = self.w_table[2 * j + 1]; - let delta = w_1 - w_0; - let mut w_t = w_0; - for eval in evals.iter_mut() { - *eval = *eval + eq_rem * range_check_eval_precomputed(w_t, range_offsets); - w_t = w_t + delta; - } - } - evals - }; - - let q_poly = UniPoly::from_evals(&q_evals); - self.split_eq.gruen_mul(&q_poly) - } - - fn compute_round_univariate_affine_coeff(&self) -> UniPoly { - let half = self.w_table.len() / 2; - let range_precomp = self - .range_precomp - .as_ref() - .expect("affine-coeff precomputation must exist"); - let num_coeffs_q = range_precomp.degree_q + 1; - - let (e_first, e_second) = self.split_eq.remaining_eq_tables(); - let num_first = e_first.len(); - let first_bits = num_first.trailing_zeros(); - let coeff_mix = &range_precomp.coeff_mix; - - #[cfg(feature = "parallel")] - let q_coeffs = { - (0..half) - .into_par_iter() - .fold( - || vec![E::zero(); num_coeffs_q], - |mut coeffs, j| { - let j_low = j & (num_first - 1); - let j_high = j >> first_bits; - let eq_rem = e_first[j_low] * e_second[j_high]; - let w_0 = self.w_table[2 * j]; - let w_1 = self.w_table[2 * j + 1]; - let a = w_1 - w_0; - accumulate_affine_range_coeffs(&mut coeffs, coeff_mix, w_0, a, eq_rem); - coeffs - }, - ) - .reduce( - || vec![E::zero(); num_coeffs_q], - |mut a, b_vec| { - for (ai, bi) in a.iter_mut().zip(b_vec.iter()) { - *ai = *ai + *bi; - } - a - }, - ) - }; - #[cfg(not(feature = "parallel"))] - let q_coeffs = { - let mut coeffs = vec![E::zero(); num_coeffs_q]; - for j in 0..half { - let j_low = j & (num_first - 1); - let j_high = j >> first_bits; - let eq_rem = e_first[j_low] * e_second[j_high]; - let w_0 = self.w_table[2 * j]; - let w_1 = self.w_table[2 * j + 1]; - let a = w_1 - w_0; - accumulate_affine_range_coeffs(&mut coeffs, coeff_mix, w_0, a, eq_rem); - } - coeffs - }; - - let mut q_coeffs = q_coeffs; - trim_trailing_zeros(&mut q_coeffs); - let q_poly = UniPoly::from_coeffs(q_coeffs); - self.split_eq.gruen_mul(&q_poly) - } } -impl SumcheckInstanceProver for NormSumcheckProver { +impl SumcheckInstanceProver + for NormSumcheckProver +{ fn num_rounds(&self) -> usize { self.num_vars } @@ -341,10 +684,17 @@ impl SumcheckInstanceProver for NormSumcheckProv } fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { - match self.round_kernel { - NormRoundKernel::PointEvalInterpolation => self.compute_round_univariate_point_eval(), - NormRoundKernel::AffineCoeffComposition => self.compute_round_univariate_affine_coeff(), - } + let half = self.w_table.len() / 2; + let w_table = &self.w_table; + compute_norm_round_poly( + &self.split_eq, + half, + self.b, + self.round_kernel, + self.point_precomp.as_ref(), + self.range_precomp.as_ref(), + |j| (w_table[2 * j], w_table[2 * j + 1]), + ) } fn ingest_challenge(&mut self, _round: usize, r: E) { @@ -402,9 +752,12 @@ impl SumcheckInstanceVerifier for NormSumcheckVe #[cfg(test)] mod tests { use super::*; + use crate::algebra::fields::ext::Ext2; + use crate::algebra::fields::lift::LiftBase; use crate::algebra::ring::CyclotomicRing; use crate::algebra::Fp64; - use crate::primitives::multilinear_evals::DenseMultilinearEvals; + use crate::protocol::hachi_poly_ops::DensePoly; + use crate::protocol::opening_point::BasisMode; use crate::protocol::ring_switch::r_decomp_levels; use crate::protocol::sumcheck::eq_poly::EqPolynomial; use crate::protocol::sumcheck::multilinear_eval; @@ -416,11 +769,12 @@ mod tests { use crate::{FieldCore, FromSmallInt}; use rand::rngs::StdRng; use rand::SeedableRng; + use std::array::from_fn; type F = Fp64<4294967197>; - const D: usize = 8; type Cfg = SmallTestCommitmentConfig; - type Scheme = HachiCommitmentScheme<{ Cfg::D }, Cfg>; + const D: usize = Cfg::D; + type Scheme = HachiCommitmentScheme; struct PointEvalReferenceNormSumcheckProver { split_eq: GruenSplitEq, @@ -477,7 +831,7 @@ mod tests { for (t, eval) in q_evals.iter_mut().enumerate() { let t_e = E::from_u64(t as u64); let w_t = w_0 + t_e * (w_1 - w_0); - *eval = *eval + eq_rem * range_check_eval(w_t, b); + *eval += eq_rem * range_check_eval(w_t, b); } } @@ -492,7 +846,7 @@ mod tests { } fn ring_with_small_coeff(value: u64) -> CyclotomicRing { - let coeffs = std::array::from_fn(|_| F::from_u64(value)); + let coeffs = from_fn(|_| F::from_u64(value)); CyclotomicRing::from_coefficients(coeffs) } @@ -517,12 +871,17 @@ mod tests { b, NormRoundKernel::PointEvalInterpolation, ); - let mut affine_coeff = NormSumcheckProver::new_with_kernel( - &tau, - w_evals.clone(), - b, - NormRoundKernel::AffineCoeffComposition, - ); + let use_affine = b <= 8; + let mut affine_coeff = if use_affine { + Some(NormSumcheckProver::new_with_kernel( + &tau, + w_evals.clone(), + b, + NormRoundKernel::AffineCoeffComposition, + )) + } else { + None + }; let mut reference = PointEvalReferenceNormSumcheckProver::new(&tau, w_evals, b); let mut claim_dispatched = F::zero(); @@ -532,17 +891,21 @@ mod tests { for round in 0..num_vars { let g_dispatch = dispatched.compute_round_univariate(round, claim_dispatched); let g_point = point_eval.compute_round_univariate(round, claim_point); - let g_affine = affine_coeff.compute_round_univariate(round, claim_affine); + let g_affine = affine_coeff + .as_mut() + .map(|p| p.compute_round_univariate(round, claim_affine)); let g_ref = reference.compute_round_univariate(round, claim_reference); assert_eq!( g_point, g_ref, "point-eval mismatch for case {case_idx} round {round}" ); - assert_eq!( - g_affine, g_ref, - "affine-coeff mismatch for case {case_idx} round {round}" - ); + if let Some(ref ga) = g_affine { + assert_eq!( + *ga, g_ref, + "affine-coeff mismatch for case {case_idx} round {round}" + ); + } match choose_round_kernel(b) { NormRoundKernel::PointEvalInterpolation => { assert_eq!( @@ -552,7 +915,8 @@ mod tests { } NormRoundKernel::AffineCoeffComposition => { assert_eq!( - g_dispatch, g_affine, + g_dispatch, + g_affine.as_ref().unwrap().clone(), "dispatch mismatch for case {case_idx} round {round}" ); } @@ -572,11 +936,15 @@ mod tests { let r = F::from_u64(rand::Rng::gen_range(&mut rng, 1u64..=257)); claim_dispatched = g_dispatch.evaluate(&r); claim_point = g_point.evaluate(&r); - claim_affine = g_affine.evaluate(&r); + if let Some(ref ga) = g_affine { + claim_affine = ga.evaluate(&r); + } claim_reference = g_ref.evaluate(&r); dispatched.ingest_challenge(round, r); point_eval.ingest_challenge(round, r); - affine_coeff.ingest_challenge(round, r); + if let Some(ref mut p) = affine_coeff { + p.ingest_challenge(round, r); + } reference.ingest_challenge(round, r); } assert_eq!( @@ -587,10 +955,12 @@ mod tests { claim_point, claim_reference, "final point claim mismatch for case {case_idx}" ); - assert_eq!( - claim_affine, claim_reference, - "final affine claim mismatch for case {case_idx}" - ); + if use_affine { + assert_eq!( + claim_affine, claim_reference, + "final affine claim mismatch for case {case_idx}" + ); + } } } @@ -602,10 +972,11 @@ mod tests { ring_with_small_coeff(3), ]; let r = [ring_with_small_coeff(0), ring_with_small_coeff(1)]; - let levels = r_decomp_levels::(); + let log_basis = SmallTestCommitmentConfig::decomposition().log_basis; + let levels = r_decomp_levels::(log_basis); let r_hat: Vec> = r .iter() - .flat_map(|ri| ri.balanced_decompose_pow2(levels, SmallTestCommitmentConfig::LOG_BASIS)) + .flat_map(|ri| ri.balanced_decompose_pow2(levels, log_basis)) .collect(); let mut w_evals: Vec = z .iter() @@ -617,7 +988,7 @@ mod tests { w_evals.resize(target_len, F::zero()); let num_vars = target_len.trailing_zeros() as usize; let tau: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); - let b = 1usize << SmallTestCommitmentConfig::LOG_BASIS; + let b = 1usize << SmallTestCommitmentConfig::decomposition().log_basis; let eq_table = EqPolynomial::evals(&tau); let _claim: F = (0..w_evals.len()) @@ -654,10 +1025,10 @@ mod tests { let num_vars = layout.m_vars + layout.r_vars + alpha; let len = 1usize << num_vars; let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); - let poly = DenseMultilinearEvals::new_padded(evals); + let poly = DensePoly::::from_field_evals(num_vars, &evals).unwrap(); let setup = Scheme::setup_prover(num_vars); - let (commitment, hint) = Scheme::commit(&poly, &setup).unwrap(); + let (commitment, hint) = Scheme::commit(&poly, &setup, &layout).unwrap(); let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); let mut prover_transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); @@ -665,20 +1036,22 @@ mod tests { &setup, &poly, &opening_point, - Some(hint), + hint, &mut prover_transcript, &commitment, + BasisMode::Lagrange, + &layout, ) .unwrap(); - let mut w_evals = proof.sumcheck_aux.w.clone(); + let mut w_evals: Vec = proof.final_w.to_field_elems(); let target_len = w_evals.len().next_power_of_two(); w_evals.resize(target_len, F::zero()); let num_sumcheck_vars = target_len.trailing_zeros() as usize; let tau: Vec = (0..num_sumcheck_vars) .map(|i| F::from_u64((i + 3) as u64)) .collect(); - let b = 1usize << SmallTestCommitmentConfig::LOG_BASIS; + let b = 1usize << SmallTestCommitmentConfig::decomposition().log_basis; let eq_table = EqPolynomial::evals(&tau); let _claim: F = (0..w_evals.len()) @@ -710,9 +1083,6 @@ mod tests { #[test] fn norm_sumcheck_over_ext2() { - use crate::algebra::fields::ext::Ext2; - use crate::algebra::fields::lift::LiftBase; - type E2 = Ext2; let num_vars = 3; @@ -747,4 +1117,20 @@ mod tests { assert_eq!(prover_challenges, verifier_challenges); } + + #[test] + fn range_check_eval_i128_matches_field() { + for b in [2, 4, 8, 10] { + for w in -(b as i32 - 1)..=(b as i32 - 1) { + let i128_val = range_check_eval_i128(w, b); + let field_val: F = range_check_eval(F::from_i64(w as i64), b); + let field_from_i128_val: F = field_from_i128(i128_val); + assert_eq!( + field_from_i128_val, field_val, + "i128 range-check mismatch for b={b}, w={w}: \ + i128={i128_val}, field_from_i128={field_from_i128_val:?}, field={field_val:?}" + ); + } + } + } } diff --git a/src/protocol/sumcheck/relation_sumcheck.rs b/src/protocol/sumcheck/relation_sumcheck.rs index 1f03a09a..a194bf86 100644 --- a/src/protocol/sumcheck/relation_sumcheck.rs +++ b/src/protocol/sumcheck/relation_sumcheck.rs @@ -9,26 +9,27 @@ use super::eq_poly::EqPolynomial; use super::{fold_evals_in_place, multilinear_eval}; use super::{SumcheckInstanceProver, SumcheckInstanceVerifier, UniPoly}; use crate::algebra::ring::CyclotomicRing; -use crate::cfg_into_iter; use crate::error::HachiError; #[cfg(feature = "parallel")] use crate::parallel::*; use crate::protocol::ring_switch::eval_ring_at; use crate::{FieldCore, FromSmallInt}; +use std::iter; /// Prover for `F_{α,τ₁}(x,y) = w̃(x,y) · α̃(y) · m(x)`. /// -/// All three constituent evaluation tables are stored at full domain size -/// (`2^{num_u + num_l}`). `α̃` is replicated along x dimensions and `m` along -/// y dimensions so that a uniform fold-by-pairs works in every round. +/// Alpha and m are stored in compact form (sizes `2^num_l` and `2^num_u`) +/// and folded only during rounds where their variables are active. /// /// Round polynomial degree is 2 (product of at most two multilinear factors /// depending on any single variable). pub struct RelationSumcheckProver { w_table: Vec, - alpha_table: Vec, - m_table: Vec, + alpha_compact: Vec, + m_compact: Vec, + num_u: usize, num_vars: usize, + rounds_completed: usize, } impl RelationSumcheckProver { @@ -38,8 +39,6 @@ impl RelationSumcheckProver { /// - `alpha_evals_y`: evaluations of `α̃` over `{0,1}^{num_l}` (compact). /// - `m_evals_x`: evaluations of `m` over `{0,1}^{num_u}` (compact). /// - /// The constructor extends the compact tables to the full domain by replication. - /// /// # Panics /// /// Panics if table sizes don't match `2^num_u`, `2^num_l`, or `2^(num_u+num_l)`. @@ -56,19 +55,13 @@ impl RelationSumcheckProver { assert_eq!(alpha_evals_y.len(), 1 << num_l); assert_eq!(m_evals_x.len(), 1 << num_u); - let x_mask = (1usize << num_u) - 1; - let alpha_table: Vec = cfg_into_iter!(0..n) - .map(|idx| alpha_evals_y[idx >> num_u]) - .collect(); - let m_table: Vec = cfg_into_iter!(0..n) - .map(|idx| m_evals_x[idx & x_mask]) - .collect(); - Self { w_table: w_evals, - alpha_table, - m_table, + alpha_compact: alpha_evals_y.to_vec(), + m_compact: m_evals_x.to_vec(), + num_u, num_vars, + rounds_completed: 0, } } } @@ -83,28 +76,42 @@ impl SumcheckInstanceProver for RelationSumcheck } fn input_claim(&self) -> E { + let x_mask = (1usize << self.num_u) - 1; + let alpha_compact = &self.alpha_compact; + let m_compact = &self.m_compact; + let num_u = self.num_u; + #[cfg(feature = "parallel")] { self.w_table .par_iter() - .zip(self.alpha_table.par_iter()) - .zip(self.m_table.par_iter()) - .fold(|| E::zero(), |acc, ((&w, &a), &m)| acc + w * a * m) + .enumerate() + .fold( + || E::zero(), + |acc, (idx, &w)| { + acc + w * alpha_compact[idx >> num_u] * m_compact[idx & x_mask] + }, + ) .reduce(|| E::zero(), |a, b| a + b) } #[cfg(not(feature = "parallel"))] { self.w_table .iter() - .zip(self.alpha_table.iter()) - .zip(self.m_table.iter()) - .fold(E::zero(), |acc, ((&w, &a), &m)| acc + w * a * m) + .enumerate() + .fold(E::zero(), |acc, (idx, &w)| { + acc + w * alpha_compact[idx >> num_u] * m_compact[idx & x_mask] + }) } } fn compute_round_univariate(&mut self, _round: usize, _previous_claim: E) -> UniPoly { let half = self.w_table.len() / 2; - let num_points = 3; // degree 2 → 3 evaluation points + let num_points = 3; + let current_x_width = self.num_u.saturating_sub(self.rounds_completed); + let current_x_mask = (1usize << current_x_width).wrapping_sub(1); + let alpha_compact = &self.alpha_compact; + let m_compact = &self.m_compact; #[cfg(feature = "parallel")] let round_evals = { @@ -115,16 +122,16 @@ impl SumcheckInstanceProver for RelationSumcheck |mut evals, j| { let w_0 = self.w_table[2 * j]; let w_1 = self.w_table[2 * j + 1]; - let a_0 = self.alpha_table[2 * j]; - let a_1 = self.alpha_table[2 * j + 1]; - let m_0 = self.m_table[2 * j]; - let m_1 = self.m_table[2 * j + 1]; + let a_0 = alpha_compact[(2 * j) >> current_x_width]; + let a_1 = alpha_compact[(2 * j + 1) >> current_x_width]; + let m_0 = m_compact[(2 * j) & current_x_mask]; + let m_1 = m_compact[(2 * j + 1) & current_x_mask]; for (t, eval) in evals.iter_mut().enumerate() { let t_e = E::from_u64(t as u64); let w_t = w_0 + t_e * (w_1 - w_0); let a_t = a_0 + t_e * (a_1 - a_0); let m_t = m_0 + t_e * (m_1 - m_0); - *eval = *eval + w_t * a_t * m_t; + *eval += w_t * a_t * m_t; } evals }, @@ -133,7 +140,7 @@ impl SumcheckInstanceProver for RelationSumcheck || vec![E::zero(); num_points], |mut a, b| { for (ai, bi) in a.iter_mut().zip(b.iter()) { - *ai = *ai + *bi; + *ai += *bi; } a }, @@ -145,16 +152,16 @@ impl SumcheckInstanceProver for RelationSumcheck for j in 0..half { let w_0 = self.w_table[2 * j]; let w_1 = self.w_table[2 * j + 1]; - let a_0 = self.alpha_table[2 * j]; - let a_1 = self.alpha_table[2 * j + 1]; - let m_0 = self.m_table[2 * j]; - let m_1 = self.m_table[2 * j + 1]; + let a_0 = alpha_compact[(2 * j) >> current_x_width]; + let a_1 = alpha_compact[(2 * j + 1) >> current_x_width]; + let m_0 = m_compact[(2 * j) & current_x_mask]; + let m_1 = m_compact[(2 * j + 1) & current_x_mask]; for (t, eval) in evals.iter_mut().enumerate() { let t_e = E::from_u64(t as u64); let w_t = w_0 + t_e * (w_1 - w_0); let a_t = a_0 + t_e * (a_1 - a_0); let m_t = m_0 + t_e * (m_1 - m_0); - *eval = *eval + w_t * a_t * m_t; + *eval += w_t * a_t * m_t; } } evals @@ -165,8 +172,12 @@ impl SumcheckInstanceProver for RelationSumcheck fn ingest_challenge(&mut self, _round: usize, r: E) { fold_evals_in_place(&mut self.w_table, r); - fold_evals_in_place(&mut self.alpha_table, r); - fold_evals_in_place(&mut self.m_table, r); + if self.rounds_completed < self.num_u { + fold_evals_in_place(&mut self.m_compact, r); + } else { + fold_evals_in_place(&mut self.alpha_compact, r); + } + self.rounds_completed += 1; } } @@ -235,7 +246,7 @@ impl SumcheckInstanceVerifier for RelationSumch .v .iter() .chain(self.u.iter()) - .chain(std::iter::once(&self.y_ring)) + .chain(iter::once(&self.y_ring)) .map(|r| eval_ring_at(r, &self.alpha)) .collect(); @@ -243,7 +254,7 @@ impl SumcheckInstanceVerifier for RelationSumch let mut acc = F::zero(); for (i, eq_i) in eq_tau.iter().enumerate() { let y_i = if i < y_a.len() { y_a[i] } else { F::zero() }; - acc = acc + *eq_i * y_i; + acc += *eq_i * y_i; } acc } @@ -261,8 +272,9 @@ impl SumcheckInstanceVerifier for RelationSumch mod tests { use super::*; use crate::algebra::Fp64; - use crate::primitives::multilinear_evals::DenseMultilinearEvals; use crate::protocol::commitment_scheme::rederive_alpha_and_m_a; + use crate::protocol::hachi_poly_ops::DensePoly; + use crate::protocol::opening_point::BasisMode; use crate::protocol::sumcheck::eq_poly::EqPolynomial; use crate::protocol::transcript::labels; use crate::protocol::{ @@ -273,19 +285,20 @@ mod tests { type F = Fp64<4294967197>; type Cfg = SmallTestCommitmentConfig; - type Scheme = HachiCommitmentScheme<{ Cfg::D }, Cfg>; + const D: usize = Cfg::D; + type Scheme = HachiCommitmentScheme; #[test] fn relation_sumcheck_uses_prove_w_evals() { - let alpha_bits = SmallTestCommitmentConfig::D.trailing_zeros() as usize; + let alpha_bits = D.trailing_zeros() as usize; let layout = SmallTestCommitmentConfig::commitment_layout(8).unwrap(); let num_vars = layout.m_vars + layout.r_vars + alpha_bits; let len = 1usize << num_vars; let evals: Vec = (0..len).map(|i| F::from_u64(i as u64)).collect(); - let poly = DenseMultilinearEvals::new_padded(evals); + let poly = DensePoly::::from_field_evals(num_vars, &evals).unwrap(); let setup = Scheme::setup_prover(num_vars); - let (commitment, hint) = Scheme::commit(&poly, &setup).unwrap(); + let (commitment, hint) = Scheme::commit(&poly, &setup, &layout).unwrap(); let opening_point: Vec = (0..num_vars).map(|i| F::from_u64((i + 2) as u64)).collect(); let mut prover_transcript = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); @@ -293,9 +306,11 @@ mod tests { &setup, &poly, &opening_point, - Some(hint), + hint, &mut prover_transcript, &commitment, + BasisMode::Lagrange, + &layout, ) .unwrap(); @@ -307,9 +322,10 @@ mod tests { ) .unwrap(); + let final_w: Vec = proof.final_w.to_field_elems(); let d = SmallTestCommitmentConfig::D; - assert_eq!(proof.sumcheck_aux.w.len() % d, 0); - let w_u = proof.sumcheck_aux.w.len() / d; + assert_eq!(final_w.len() % d, 0); + let w_u = final_w.len() / d; let rows = SmallTestCommitmentConfig::N_D + SmallTestCommitmentConfig::N_B + 1 @@ -330,9 +346,9 @@ mod tests { for x in 0..x_len { for y in 0..y_len { let src = y + (x << num_l); - if src < proof.sumcheck_aux.w.len() { + if src < final_w.len() { let dst = x + (y << num_u); - w_evals[dst] = proof.sumcheck_aux.w[src]; + w_evals[dst] = final_w[src]; } } } @@ -350,7 +366,7 @@ mod tests { } else { F::zero() }; - acc = acc + eq_tau1[i] * row_val; + acc += eq_tau1[i] * row_val; } m_evals_x[x] = acc; } @@ -359,7 +375,7 @@ mod tests { let mut power = F::one(); for val in alpha_evals_y.iter_mut() { *val = power; - power = power * alpha; + power *= alpha; } let x_mask = x_len - 1; @@ -389,9 +405,9 @@ mod tests { alpha_evals_y, m_evals_x, tau1, - proof.v.clone(), + proof.levels[0].v.clone(), commitment.u.clone(), - proof.y_ring, + proof.levels[0].y_ring, alpha, num_u, num_l, diff --git a/src/protocol/sumcheck/split_eq.rs b/src/protocol/sumcheck/split_eq.rs index 9ecf7269..254cc67c 100644 --- a/src/protocol/sumcheck/split_eq.rs +++ b/src/protocol/sumcheck/split_eq.rs @@ -140,8 +140,8 @@ impl GruenSplitEq { let slope = l_1 - l_0; let mut coeffs = vec![E::zero(); q_poly.coeffs.len() + 1]; for (i, &c) in q_poly.coeffs.iter().enumerate() { - coeffs[i] = coeffs[i] + c * l_0; - coeffs[i + 1] = coeffs[i + 1] + c * slope; + coeffs[i] += c * l_0; + coeffs[i + 1] += c * slope; } UniPoly::from_coeffs(coeffs) } diff --git a/src/protocol/sumcheck/types.rs b/src/protocol/sumcheck/types.rs index 7fbf4d3b..7b4955a2 100644 --- a/src/protocol/sumcheck/types.rs +++ b/src/protocol/sumcheck/types.rs @@ -115,8 +115,8 @@ impl UniPoly { new_coeffs[0] = divided_diffs[k]; for i in 0..old_len { - new_coeffs[i + 1] = new_coeffs[i + 1] + coeffs[i]; - new_coeffs[i] = new_coeffs[i] - shift * coeffs[i]; + new_coeffs[i + 1] += coeffs[i]; + new_coeffs[i] -= shift * coeffs[i]; } coeffs = new_coeffs; @@ -201,7 +201,7 @@ impl CompressedUniPoly { let c0 = self.coeffs_except_linear_term[0]; let mut linear = *hint - c0 - c0; for c in self.coeffs_except_linear_term.iter().skip(1) { - linear = linear - *c; + linear -= *c; } linear } @@ -232,7 +232,7 @@ impl CompressedUniPoly { let mut pow = *x * *x; for c in self.coeffs_except_linear_term.iter().skip(1) { - acc = acc + (*c * pow); + acc += *c * pow; pow = pow * *x; } acc diff --git a/src/test_utils.rs b/src/test_utils.rs index 5de0450f..b8e6c0f3 100644 --- a/src/test_utils.rs +++ b/src/test_utils.rs @@ -4,13 +4,22 @@ //! building blocks for both unit tests (inside `src/`) and integration //! tests (inside `tests/`). +use std::array::from_fn; + use crate::algebra::{CyclotomicRing, Fp64}; -use crate::protocol::commitment::CommitmentConfig; +use crate::error::HachiError; +use crate::protocol::commitment::{ + compute_num_digits, compute_num_digits_fold, CommitmentConfig, DecompositionParams, + HachiCommitmentLayout, +}; use crate::{FieldCore, FromSmallInt}; +/// Default test field: a 32-bit prime `p = 4294967197`. pub type F = Fp64<4294967197>; +/// Ring degree used in tests. pub const D: usize = 64; +/// Minimal commitment config for fast unit tests. #[derive(Clone)] pub struct TinyConfig; @@ -19,32 +28,55 @@ impl CommitmentConfig for TinyConfig { const N_A: usize = 2; const N_B: usize = 2; const N_D: usize = 2; - const LOG_BASIS: u32 = 4; - const DELTA: usize = 9; - const TAU: usize = 4; const CHALLENGE_WEIGHT: usize = 3; - fn commitment_layout( - _max_num_vars: usize, - ) -> Result { - crate::protocol::commitment::HachiCommitmentLayout::new::(1, 1) + fn decomposition() -> DecompositionParams { + DecompositionParams { + log_basis: 3, + log_commit_bound: 32, + log_open_bound: None, + } + } + + fn commitment_layout(_max_num_vars: usize) -> Result { + HachiCommitmentLayout::new::(1, 1, &Self::decomposition()) } } +/// Number of ring elements per block (`2^m_vars`). pub const BLOCK_LEN: usize = 2; +/// Number of blocks (`2^r_vars`). pub const NUM_BLOCKS: usize = 2; -pub const DELTA: usize = TinyConfig::DELTA; -pub const LOG_BASIS: u32 = TinyConfig::LOG_BASIS; +/// Gadget base exponent (`b = 2^log_basis()`), derived from `TinyConfig`. +pub fn log_basis() -> u32 { + TinyConfig::decomposition().log_basis +} +/// Inner Ajtai row count from `TinyConfig`. pub const N_A: usize = TinyConfig::N_A; -pub const TAU: usize = TinyConfig::TAU; +/// Decomposition depth for original coefficients under `TinyConfig`. +pub fn num_digits_commit() -> usize { + let d = TinyConfig::decomposition(); + compute_num_digits(d.log_commit_bound, d.log_basis) +} + +/// Decomposition depth for the folded witness `z_pre` under `TinyConfig`. +pub fn num_digits_fold() -> usize { + let d = TinyConfig::decomposition(); + compute_num_digits_fold(1, TinyConfig::CHALLENGE_WEIGHT, d.log_basis) +} + +/// Dense matrix-vector multiply over cyclotomic rings. +/// +/// Matrix rows may be wider than `vec` (e.g. when matrices are widened for +/// multi-level folding); extra columns are treated as multiplying zero. pub fn mat_vec_mul( mat: &[Vec>], vec: &[CyclotomicRing], ) -> Vec> { mat.iter() .map(|row| { - assert_eq!(row.len(), vec.len()); + assert!(row.len() >= vec.len()); row.iter() .zip(vec.iter()) .fold(CyclotomicRing::::zero(), |acc, (a, x)| { @@ -54,13 +86,13 @@ pub fn mat_vec_mul( .collect() } +/// Generate deterministic test blocks of ring elements. pub fn sample_blocks() -> Vec>> { (0..NUM_BLOCKS) .map(|bi| { (0..BLOCK_LEN) .map(|bj| { - let coeffs = - std::array::from_fn(|k| F::from_u64((bi * 1_000 + bj * 100 + k) as u64)); + let coeffs = from_fn(|k| F::from_u64((bi * 1_000 + bj * 100 + k) as u64)); CyclotomicRing::from_coefficients(coeffs) }) .collect() @@ -68,18 +100,21 @@ pub fn sample_blocks() -> Vec>> { .collect() } +/// Generate deterministic inner opening-point scalars. pub fn sample_a() -> Vec { (0..BLOCK_LEN) .map(|j| F::from_u64((j * 10 + 1) as u64)) .collect() } +/// Generate deterministic outer opening-point scalars. pub fn sample_b() -> Vec { (0..NUM_BLOCKS) .map(|i| F::from_u64((i * 7 + 3) as u64)) .collect() } +/// Recompose a gadget-decomposed ring element: `sum_i parts[i] * b^i`. pub fn field_gadget_recompose( parts: &[CyclotomicRing], log_basis: u32, @@ -89,31 +124,43 @@ pub fn field_gadget_recompose( let mut b_power = F::one(); for part in parts { result += part.scale(&b_power); - b_power = b_power * b; + b_power *= b; } result } +/// Recompose `z_hat` chunks (num_digits_fold-width) back to `z_pre` elements. pub fn recompose_z_hat(z_hat: &[CyclotomicRing]) -> Vec> { z_hat - .chunks(TAU) - .map(|chunk| field_gadget_recompose(chunk, LOG_BASIS)) + .chunks(num_digits_fold()) + .map(|chunk| field_gadget_recompose(chunk, log_basis())) .collect() } +/// Recompose a vector of gadget-decomposed elements (num_digits_commit-width chunks). pub fn gadget_recompose_vec(x_hat: &[CyclotomicRing]) -> Vec> { x_hat - .chunks(DELTA) - .map(|chunk| field_gadget_recompose(chunk, LOG_BASIS)) + .chunks(num_digits_commit()) + .map(|chunk| field_gadget_recompose(chunk, log_basis())) + .collect() +} + +/// Recompose a vector of i8 gadget-decomposed digit planes (num_digits_commit-width chunks). +pub fn gadget_recompose_vec_i8(x_hat: &[[i8; D]]) -> Vec> { + x_hat + .chunks(num_digits_commit()) + .map(|chunk| CyclotomicRing::gadget_recompose_pow2_i8(chunk, log_basis())) .collect() } +/// Alias for [`gadget_recompose_vec`] (same num_digits_commit-width recomposition). pub fn field_gadget_recompose_vec(v: &[CyclotomicRing]) -> Vec> { - v.chunks(DELTA) - .map(|chunk| field_gadget_recompose(chunk, LOG_BASIS)) + v.chunks(num_digits_commit()) + .map(|chunk| field_gadget_recompose(chunk, log_basis())) .collect() } +/// Compute `a^T * G^{-1}(z)`: recompose `z` then inner-product with `a`. pub fn a_transpose_gadget_times_vec(a: &[F], z: &[CyclotomicRing]) -> CyclotomicRing { let recomposed = field_gadget_recompose_vec(z); assert_eq!(recomposed.len(), a.len()); diff --git a/tests/commitment_contract.rs b/tests/commitment_contract.rs index 4aaf3822..2b8855a8 100644 --- a/tests/commitment_contract.rs +++ b/tests/commitment_contract.rs @@ -1,36 +1,79 @@ #![allow(missing_docs)] +use hachi_pcs::algebra::CyclotomicRing; use hachi_pcs::algebra::Fp64; +use hachi_pcs::algebra::SparseChallenge; +use hachi_pcs::protocol::commitment::utils::crt_ntt::NttSlotCache; use hachi_pcs::protocol::commitment::{DummyProof, HachiCommitment}; +use hachi_pcs::protocol::hachi_poly_ops::HachiPolyOps; use hachi_pcs::protocol::transcript::labels; use hachi_pcs::protocol::{ - AppendToTranscript, Blake2bTranscript, CommitmentScheme, StreamingCommitmentScheme, Transcript, + AppendToTranscript, BasisMode, Blake2bTranscript, CommitmentScheme, HachiCommitmentLayout, + Transcript, }; -use hachi_pcs::{CanonicalField, FieldCore, FromSmallInt, HachiError, Polynomial}; +use hachi_pcs::{CanonicalField, FieldCore, FromSmallInt, HachiError}; type F = Fp64<4294967197>; -#[derive(Clone)] -struct SimplePoly { +/// Trivial polynomial wrapper that implements `HachiPolyOps`. +#[derive(Debug, Clone)] +struct DummyPoly { coeffs: Vec, } -impl Polynomial for SimplePoly { - fn num_vars(&self) -> usize { - self.coeffs.len().saturating_sub(1) - } - +impl DummyPoly { fn evaluate(&self, point: &[F]) -> F { assert_eq!(point.len(), self.num_vars()); let mut acc = self.coeffs[0]; for (i, r_i) in point.iter().enumerate() { - acc = acc + self.coeffs[i + 1] * *r_i; + acc += self.coeffs[i + 1] * *r_i; } acc } - fn coeffs(&self) -> Vec { - self.coeffs.clone() + fn num_vars(&self) -> usize { + self.coeffs.len().saturating_sub(1) + } +} + +impl HachiPolyOps for DummyPoly { + type CommitCache = NttSlotCache<1>; + + fn num_ring_elems(&self) -> usize { + self.coeffs.len() + } + + fn evaluate_ring(&self, scalars: &[F]) -> CyclotomicRing { + let mut acc = F::zero(); + for (c, &s) in self.coeffs.iter().zip(scalars.iter()) { + acc += *c * s; + } + CyclotomicRing::from_coefficients([acc]) + } + + fn fold_blocks(&self, _scalars: &[F], _block_len: usize) -> Vec> { + vec![] + } + + fn decompose_fold( + &self, + _challenges: &[SparseChallenge], + _block_len: usize, + _num_digits: usize, + _log_basis: u32, + ) -> Vec> { + vec![] + } + + fn commit_inner( + &self, + _a_matrix: &[Vec>], + _ntt_a: &NttSlotCache<1>, + _block_len: usize, + _num_digits: usize, + _log_basis: u32, + ) -> Result>, HachiError> { + Ok(vec![]) } } @@ -42,12 +85,12 @@ struct DummySetup { #[derive(Clone)] struct DummyScheme; -impl CommitmentScheme for DummyScheme { +impl CommitmentScheme for DummyScheme { type ProverSetup = DummySetup; type VerifierSetup = DummySetup; type Commitment = HachiCommitment; type Proof = DummyProof; - type OpeningProofHint = HachiCommitment; + type CommitHint = HachiCommitment; fn setup_prover(max_num_vars: usize) -> Self::ProverSetup { DummySetup { @@ -59,42 +102,28 @@ impl CommitmentScheme for DummyScheme { setup.clone() } - fn commit>( - poly: &P, + fn commit>( + _poly: &P, _setup: &Self::ProverSetup, - ) -> Result<(Self::Commitment, Self::OpeningProofHint), HachiError> { - let zero = vec![F::zero(); poly.num_vars()]; - let c = HachiCommitment(poly.evaluate(&zero).to_canonical_u128()); + _layout: &HachiCommitmentLayout, + ) -> Result<(Self::Commitment, Self::CommitHint), HachiError> { + let c = HachiCommitment(0); Ok((c, c)) } - fn prove, P: Polynomial>( - setup: &Self::ProverSetup, - poly: &P, - opening_point: &[F], - hint: Option, + fn prove, P: HachiPolyOps>( + _setup: &Self::ProverSetup, + _poly: &P, + _opening_point: &[F], + _hint: Self::CommitHint, transcript: &mut T, - _commitment: &Self::Commitment, + commitment: &Self::Commitment, + _basis: BasisMode, + _layout: &HachiCommitmentLayout, ) -> Result { - if opening_point.len() != poly.num_vars() { - return Err(HachiError::InvalidPointDimension { - expected: poly.num_vars(), - actual: opening_point.len(), - }); - } - - let absorb_commitment = if let Some(h) = hint { - h - } else { - Self::commit(poly, setup)?.0 - }; - absorb_commitment.append_to_transcript(labels::ABSORB_COMMITMENT, transcript); - + commitment.append_to_transcript(labels::ABSORB_COMMITMENT, transcript); let q = transcript.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); - let opening = poly.evaluate(opening_point); - Ok(DummyProof( - opening.to_canonical_u128() ^ q.to_canonical_u128(), - )) + Ok(DummyProof(q.to_canonical_u128())) } fn verify>( @@ -102,98 +131,61 @@ impl CommitmentScheme for DummyScheme { _setup: &Self::VerifierSetup, transcript: &mut T, _opening_point: &[F], - opening: &F, + _opening: &F, commitment: &Self::Commitment, + _basis: BasisMode, + _layout: &HachiCommitmentLayout, ) -> Result<(), HachiError> { commitment.append_to_transcript(labels::ABSORB_COMMITMENT, transcript); let q = transcript.challenge_scalar(labels::CHALLENGE_LINEAR_RELATION); - let expected = opening.to_canonical_u128() ^ q.to_canonical_u128(); - if proof.0 == expected { + if proof.0 == q.to_canonical_u128() { Ok(()) } else { Err(HachiError::InvalidProof) } } - fn combine_commitments(commitments: &[Self::Commitment], coeffs: &[F]) -> Self::Commitment { - let acc = commitments - .iter() - .zip(coeffs.iter()) - .fold(0u128, |sum, (c, coeff)| { - sum.wrapping_add(c.0.wrapping_mul(coeff.to_canonical_u128())) - }); - HachiCommitment(acc) - } - - fn combine_hints(hints: Vec, coeffs: &[F]) -> Self::OpeningProofHint { - let acc = hints - .iter() - .zip(coeffs.iter()) - .fold(0u128, |sum, (h, coeff)| { - sum.wrapping_add(h.0.wrapping_mul(coeff.to_canonical_u128())) - }); - HachiCommitment(acc) - } - fn protocol_name() -> &'static [u8] { b"HachiDummy" } } -impl StreamingCommitmentScheme for DummyScheme { - type ChunkState = HachiCommitment; - - fn process_chunk(_setup: &Self::ProverSetup, chunk: &[F]) -> Self::ChunkState { - let sum = chunk - .iter() - .fold(0u128, |acc, x| acc.wrapping_add(x.to_canonical_u128())); - HachiCommitment(sum) - } - - fn process_chunk_onehot( - _setup: &Self::ProverSetup, - onehot_k: usize, - chunk: &[Option], - ) -> Self::ChunkState { - let sum = chunk.iter().fold(0u128, |acc, x| { - let v = x.unwrap_or(0) as u128; - acc.wrapping_add(v) - }); - HachiCommitment(sum.wrapping_add(onehot_k as u128)) - } - - fn aggregate_chunks( - _setup: &Self::ProverSetup, - _onehot_k: Option, - chunks: &[Self::ChunkState], - ) -> (Self::Commitment, Self::OpeningProofHint) { - let sum = chunks.iter().fold(0u128, |acc, c| acc.wrapping_add(c.0)); - let c = HachiCommitment(sum); - (c, c) - } -} - #[test] fn commitment_scheme_round_trip() { - let poly = SimplePoly { + let poly = DummyPoly { coeffs: vec![F::from_u64(3), F::from_u64(5), F::from_u64(7)], }; let opening_point = [F::from_u64(11), F::from_u64(13)]; - let opening = poly.evaluate(&opening_point); let psetup = DummyScheme::setup_prover(poly.num_vars()); let vsetup = DummyScheme::setup_verifier(&psetup); - let (commitment, hint) = DummyScheme::commit(&poly, &psetup).unwrap(); + let layout = HachiCommitmentLayout { + m_vars: 0, + r_vars: 0, + block_len: 1, + num_blocks: 1, + num_digits_commit: 1, + num_digits_open: 1, + num_digits_fold: 1, + inner_width: 1, + outer_width: 1, + d_matrix_width: 1, + log_basis: 1, + }; + let (commitment, hint) = DummyScheme::commit(&poly, &psetup, &layout).unwrap(); + let opening = poly.evaluate(&opening_point); let mut prover_t = Blake2bTranscript::::new(labels::DOMAIN_HACHI_PROTOCOL); let proof = DummyScheme::prove( &psetup, &poly, &opening_point, - Some(hint), + hint, &mut prover_t, &commitment, + BasisMode::Lagrange, + &layout, ) .unwrap(); @@ -205,32 +197,8 @@ fn commitment_scheme_round_trip() { &opening_point, &opening, &commitment, + BasisMode::Lagrange, + &layout, ) .unwrap(); } - -#[test] -fn combine_commitments_and_hints_are_consistent() { - let c1 = HachiCommitment(10); - let c2 = HachiCommitment(20); - let coeffs = [F::from_u64(3), F::from_u64(7)]; - - let combined_c = DummyScheme::combine_commitments(&[c1, c2], &coeffs); - let combined_h = DummyScheme::combine_hints(vec![c1, c2], &coeffs); - - let expected = 10u128 - .wrapping_mul(coeffs[0].to_canonical_u128()) - .wrapping_add(20u128.wrapping_mul(coeffs[1].to_canonical_u128())); - assert_eq!(combined_c.0, expected); - assert_eq!(combined_h.0, expected); -} - -#[test] -fn streaming_chunk_path_aggregates() { - let setup = DummyScheme::setup_prover(4); - let c1 = DummyScheme::process_chunk(&setup, &[F::from_u64(1), F::from_u64(2)]); - let c2 = DummyScheme::process_chunk_onehot(&setup, 8, &[Some(3), None, Some(5)]); - - let (commitment, hint) = DummyScheme::aggregate_chunks(&setup, Some(8), &[c1, c2]); - assert_eq!(commitment, hint); -} diff --git a/tests/onehot_commitment.rs b/tests/onehot_commitment.rs index e3f6c109..eb80586f 100644 --- a/tests/onehot_commitment.rs +++ b/tests/onehot_commitment.rs @@ -130,8 +130,11 @@ fn onehot_k_lt_d_ratio_2() { #[test] fn onehot_rejects_non_divisible_k_and_d() { let setup = psetup(); - let result = - >::commit_onehot(17, &[Some(0); 4], &setup); + let result = >::commit_onehot( + 17, + &[Some(0usize); 4], + &setup, + ); assert!(result.is_err()); } @@ -140,7 +143,7 @@ fn onehot_rejects_out_of_range_index() { let setup = psetup(); let result = >::commit_onehot( 64, - &[Some(0), Some(64), Some(0), Some(0)], + &[Some(0usize), Some(64), Some(0), Some(0)], &setup, ); assert!(result.is_err()); @@ -151,7 +154,7 @@ fn onehot_rejects_wrong_total_size() { let setup = psetup(); let result = >::commit_onehot( 64, - &[Some(0), Some(0), Some(0)], + &[Some(0usize), Some(0), Some(0)], &setup, ); assert!(result.is_err()); diff --git a/tests/ring_commitment_core.rs b/tests/ring_commitment_core.rs index 4b09501e..dd9f25d1 100644 --- a/tests/ring_commitment_core.rs +++ b/tests/ring_commitment_core.rs @@ -1,12 +1,12 @@ #![allow(missing_docs)] use hachi_pcs::algebra::CyclotomicRing; -use hachi_pcs::error::HachiError; use hachi_pcs::protocol::commitment::{ - CommitmentConfig, HachiCommitmentCore, HachiCommitmentLayout, RingCommitmentScheme, - SmallTestCommitmentConfig, + utils::linear::decompose_block, CommitmentConfig, DecompositionParams, HachiCommitmentCore, + HachiCommitmentLayout, RingCommitmentScheme, SmallTestCommitmentConfig, }; use hachi_pcs::test_utils::*; +use hachi_pcs::{FromSmallInt, HachiError}; #[derive(Clone)] struct BadDegreeConfig; @@ -16,31 +16,18 @@ impl CommitmentConfig for BadDegreeConfig { const N_A: usize = 8; const N_B: usize = 4; const N_D: usize = 4; - const LOG_BASIS: u32 = 4; - const DELTA: usize = 8; - const TAU: usize = 4; const CHALLENGE_WEIGHT: usize = 3; - fn commitment_layout(_max_num_vars: usize) -> Result { - HachiCommitmentLayout::new::(4, 2) + fn decomposition() -> DecompositionParams { + DecompositionParams { + log_basis: 3, + log_commit_bound: 32, + log_open_bound: None, + } } -} - -#[derive(Clone)] -struct BadDigitBudgetConfig; - -impl CommitmentConfig for BadDigitBudgetConfig { - const D: usize = 64; - const N_A: usize = 8; - const N_B: usize = 4; - const N_D: usize = 4; - const LOG_BASIS: u32 = 32; - const DELTA: usize = 5; // 160 > 128 - const TAU: usize = 4; - const CHALLENGE_WEIGHT: usize = 3; fn commitment_layout(_max_num_vars: usize) -> Result { - HachiCommitmentLayout::new::(4, 2) + HachiCommitmentLayout::new::(4, 2, &Self::decomposition()) } } @@ -55,16 +42,11 @@ fn setup_shape_is_consistent() { assert_eq!(v1.expanded.seed.max_num_vars, 16); assert_eq!(p2.expanded.seed.max_num_vars, 16); assert_eq!(v2.expanded.seed.max_num_vars, 16); + let depth = num_digits_commit(); assert_eq!(p1.expanded.A.len(), TinyConfig::N_A); - assert_eq!( - p1.expanded.A[0].len(), - hachi_pcs::test_utils::BLOCK_LEN * TinyConfig::DELTA - ); + assert_eq!(p1.expanded.A[0].len(), BLOCK_LEN * depth); assert_eq!(p1.expanded.B.len(), TinyConfig::N_B); - assert_eq!( - p1.expanded.B[0].len(), - TinyConfig::N_A * TinyConfig::DELTA * hachi_pcs::test_utils::NUM_BLOCKS - ); + assert_eq!(p1.expanded.B[0].len(), TinyConfig::N_A * depth * NUM_BLOCKS); } #[test] @@ -85,13 +67,11 @@ fn commit_is_deterministic_and_shape_consistent() { assert_eq!(w1.commitment, w2.commitment); assert_eq!(w1.t_hat, w2.t_hat); - let num_blocks = hachi_pcs::test_utils::NUM_BLOCKS; + let num_blocks = NUM_BLOCKS; assert_eq!(w1.commitment.u.len(), TinyConfig::N_B); assert_eq!(w1.t_hat.len(), num_blocks); - assert!(w1 - .t_hat - .iter() - .all(|t| t.len() == TinyConfig::N_A * TinyConfig::DELTA)); + let depth = num_digits_commit(); + assert!(w1.t_hat.iter().all(|t| t.len() == TinyConfig::N_A * depth)); } #[test] @@ -130,29 +110,31 @@ fn opening_satisfies_inner_and_outer_equations() { ) .unwrap(); + let depth = num_digits_commit(); + let log_basis = log_basis(); for (i, block) in blocks.iter().enumerate() { - let s_i = hachi_pcs::protocol::commitment::utils::linear::decompose_block( - block, - TinyConfig::DELTA, - TinyConfig::LOG_BASIS, - ); + let s_i = decompose_block(block, depth, log_basis); let lhs = mat_vec_mul(&psetup.expanded.A, &s_i); let rhs: Vec> = (0..TinyConfig::N_A) .map(|j| { - let start = j * TinyConfig::DELTA; - let end = start + TinyConfig::DELTA; - CyclotomicRing::gadget_recompose_pow2( - &w.t_hat[i][start..end], - TinyConfig::LOG_BASIS, - ) + let start = j * depth; + let end = start + depth; + CyclotomicRing::gadget_recompose_pow2_i8(&w.t_hat[i][start..end], log_basis) }) .collect(); assert_eq!(lhs, rhs); } - let t_hat_flat: Vec> = - w.t_hat.iter().flat_map(|x| x.iter().copied()).collect(); - let outer = mat_vec_mul(&psetup.expanded.B, &t_hat_flat); + let t_hat_flat_ring: Vec> = w + .t_hat + .iter() + .flat_map(|x| x.iter()) + .map(|plane| { + let coeffs: [F; D] = std::array::from_fn(|k| F::from_i64(plane[k] as i64)); + CyclotomicRing::from_coefficients(coeffs) + }) + .collect(); + let outer = mat_vec_mul(&psetup.expanded.B, &t_hat_flat_ring); assert_eq!(outer, w.commitment.u); } @@ -162,8 +144,8 @@ fn small_test_config_has_expected_shape() { let layout = SmallTestCommitmentConfig::commitment_layout(8).unwrap(); assert_eq!(layout.block_len, 16); assert_eq!(layout.num_blocks, 4); - let delta = SmallTestCommitmentConfig::DELTA; - assert!(delta > 0); + let depth = layout.num_digits_commit; + assert!(depth > 0); } #[test] @@ -175,13 +157,3 @@ fn setup_rejects_mismatched_degree() { other => panic!("unexpected error: {other:?}"), } } - -#[test] -fn setup_rejects_invalid_digit_budget() { - let err = >::setup(16) - .unwrap_err(); - match err { - HachiError::InvalidSetup(msg) => assert!(msg.contains("DELTA * LOG_BASIS")), - other => panic!("unexpected error: {other:?}"), - } -} diff --git a/tests/sparse_challenge.rs b/tests/sparse_challenge.rs index baba7bd3..fd64ac3c 100644 --- a/tests/sparse_challenge.rs +++ b/tests/sparse_challenge.rs @@ -16,7 +16,7 @@ fn dense_eval>(alpha: E, x: &CyclotomicRing) -> let mut acc = E::zero(); let mut pow = E::one(); for c in x.coefficients().iter().copied() { - acc = acc + E::lift_base(c) * pow; + acc += E::lift_base(c) * pow; pow = pow * alpha; } acc @@ -53,7 +53,7 @@ fn sparse_eval_at_alpha_matches_dense_eval() { let mut acc = F::one(); for _ in 0..D { out.push(acc); - acc = acc * alpha; + acc *= alpha; } out }; diff --git a/tests/sumcheck_core.rs b/tests/sumcheck_core.rs index dcd6486f..b75f0586 100644 --- a/tests/sumcheck_core.rs +++ b/tests/sumcheck_core.rs @@ -111,8 +111,8 @@ impl SumcheckInstanceProver for DenseSumcheckProver { let mut eval_0 = E::zero(); let mut eval_1 = E::zero(); for i in 0..half { - eval_0 = eval_0 + self.evals[2 * i]; - eval_1 = eval_1 + self.evals[2 * i + 1]; + eval_0 += self.evals[2 * i]; + eval_1 += self.evals[2 * i + 1]; } UniPoly::from_coeffs(vec![eval_0, eval_1 - eval_0]) } diff --git a/tests/sumcheck_prover_driver.rs b/tests/sumcheck_prover_driver.rs index 7ef3ebae..3abcaf53 100644 --- a/tests/sumcheck_prover_driver.rs +++ b/tests/sumcheck_prover_driver.rs @@ -44,8 +44,8 @@ impl SumcheckInstanceProver for DenseTableSumcheck { let mut s0 = F::zero(); let mut s1 = F::zero(); for i in 0..half { - s0 = s0 + self.table[i << 1]; - s1 = s1 + self.table[(i << 1) | 1]; + s0 += self.table[i << 1]; + s1 += self.table[(i << 1) | 1]; } UniPoly::from_coeffs(vec![s0, s1 - s0]) } From b34e5c5b66cac974c017bb6447486fbb3e4437dd Mon Sep 17 00:00:00 2001 From: Quang Dao Date: Tue, 3 Mar 2026 22:28:30 -0800 Subject: [PATCH 5/5] fix: separate delta_commit and delta_open for t_hat decomposition t = A * s produces full-field-size coefficients even when s has small (delta_commit-digit) entries. The code was decomposing t_hat using delta_commit instead of delta_open, causing lossy truncation and breaking verification for onehot/logbasis commitment configs. Split commit_inner's num_digits parameter into num_digits_commit (for s) and num_digits_open (for t_hat), and propagate this distinction through layout, commit, quadratic_equation, and ring_switch. Also: - Add Fp128FullCommitmentConfig, Fp128OneHotCommitmentConfig, Fp128LogBasisCommitmentConfig bounded commitment configs - Add optimal_m_r_split for dynamic m/r layout selection - Refactor profile example to be generic over CommitmentConfig and accept HACHI_NUM_VARS / HACHI_MODE env vars Made-with: Cursor --- examples/profile.rs | 317 +++++++++++++---------------- src/protocol/commitment/commit.rs | 24 ++- src/protocol/commitment/config.rs | 121 +++++++++-- src/protocol/commitment/mod.rs | 6 +- src/protocol/commitment_scheme.rs | 112 +++++++++- src/protocol/hachi_poly_ops/mod.rs | 46 ++++- src/protocol/mod.rs | 11 +- src/protocol/quadratic_equation.rs | 69 +++---- src/protocol/ring_switch.rs | 34 +++- src/protocol/sumcheck/mod.rs | 22 ++ src/test_utils.rs | 7 + tests/commitment_contract.rs | 3 +- tests/ring_commitment_core.rs | 5 +- 13 files changed, 498 insertions(+), 279 deletions(-) diff --git a/examples/profile.rs b/examples/profile.rs index d29c6fe0..4455cd55 100644 --- a/examples/profile.rs +++ b/examples/profile.rs @@ -2,15 +2,14 @@ use hachi_pcs::algebra::poly::multilinear_eval; use hachi_pcs::algebra::Fp128; -use hachi_pcs::error::HachiError; use hachi_pcs::primitives::serialization::Compress; use hachi_pcs::protocol::commitment::{ - DecompositionParams, Fp128CommitmentConfig, HachiCommitmentLayout, + Fp128FullCommitmentConfig, Fp128LogBasisCommitmentConfig, Fp128OneHotCommitmentConfig, + HachiCommitmentLayout, }; use hachi_pcs::protocol::commitment_scheme::HachiCommitmentScheme; use hachi_pcs::protocol::hachi_poly_ops::{DensePoly, OneHotPoly}; use hachi_pcs::protocol::proof::HachiProof; -use hachi_pcs::protocol::sumcheck::norm_sumcheck::choose_round_kernel; use hachi_pcs::protocol::transcript::Blake2bTranscript; use hachi_pcs::protocol::CommitmentConfig; use hachi_pcs::{ @@ -26,52 +25,26 @@ use tracing_subscriber::prelude::*; type F = Fp128<0xfffffffffffffffffffffffffffffeed>; -const D: usize = Fp128CommitmentConfig::D; +const D: usize = Fp128FullCommitmentConfig::D; -#[derive(Clone, Copy, Debug)] -struct ProfileCfg; -impl CommitmentConfig for ProfileCfg { - const D: usize = D; - const N_A: usize = Fp128CommitmentConfig::N_A; - const N_B: usize = Fp128CommitmentConfig::N_B; - const N_D: usize = Fp128CommitmentConfig::N_D; - const CHALLENGE_WEIGHT: usize = Fp128CommitmentConfig::CHALLENGE_WEIGHT; +type Scheme = HachiCommitmentScheme; - fn decomposition() -> DecompositionParams { - Fp128CommitmentConfig::decomposition() - } - - fn commitment_layout(max_num_vars: usize) -> Result { - match (env::var("HACHI_M_VARS"), env::var("HACHI_R_VARS")) { - (Ok(m_str), Ok(r_str)) => { - let m: usize = m_str.parse().expect("HACHI_M_VARS must be a number"); - let r: usize = r_str.parse().expect("HACHI_R_VARS must be a number"); - eprintln!(" [layout] override: m_vars={m}, r_vars={r}"); - HachiCommitmentLayout::new::(m, r, &Self::decomposition()) - } - _ => Fp128CommitmentConfig::commitment_layout(max_num_vars), - } - } -} - -type Scheme = HachiCommitmentScheme; - -fn run_prove( +fn run_prove>( label: &str, - setup: &>::ProverSetup, - poly: &DensePoly, + setup: & as CommitmentScheme>::ProverSetup, + poly: &P, pt: &[F], opening: F, layout: &HachiCommitmentLayout, ) { let t0 = Instant::now(); let (commitment, hint) = - >::commit(poly, setup, layout).unwrap(); + as CommitmentScheme>::commit(poly, setup, layout).unwrap(); eprintln!("[{label}] commit: {:.3}s", t0.elapsed().as_secs_f64()); let t0 = Instant::now(); let mut prover_transcript = Blake2bTranscript::::new(b"profile"); - let proof = >::prove( + let proof = as CommitmentScheme>::prove( setup, poly, pt, @@ -86,9 +59,9 @@ fn run_prove( print_proof_summary(label, &proof); let t0 = Instant::now(); - let verifier_setup = >::setup_verifier(setup); + let verifier_setup = as CommitmentScheme>::setup_verifier(setup); let mut verifier_transcript = Blake2bTranscript::::new(b"profile"); - >::verify( + match as CommitmentScheme>::verify( &proof, &verifier_setup, &mut verifier_transcript, @@ -97,9 +70,13 @@ fn run_prove( &commitment, BasisMode::Lagrange, layout, - ) - .unwrap(); - eprintln!("[{label}] verify: {:.3}s", t0.elapsed().as_secs_f64()); + ) { + Ok(()) => eprintln!("[{label}] verify: {:.3}s OK", t0.elapsed().as_secs_f64()), + Err(e) => eprintln!( + "[{label}] verify: {:.3}s FAILED ({e})", + t0.elapsed().as_secs_f64() + ), + } } fn print_proof_summary(label: &str, proof: &HachiProof) { @@ -126,140 +103,50 @@ fn print_proof_summary(label: &str, proof: &HachiProof) { ); } -fn run_prove_onehot( - label: &str, - setup: &>::ProverSetup, - onehot_poly: &OneHotPoly, - pt: &[F], - opening: F, - layout: &HachiCommitmentLayout, -) { - let t0 = Instant::now(); - let (commitment, hint) = - >::commit(onehot_poly, setup, layout).unwrap(); +fn print_layout(layout: &HachiCommitmentLayout) { eprintln!( - "[{label}] onehot commit: {:.3}s", - t0.elapsed().as_secs_f64() + " layout: m_vars={}, r_vars={}, num_blocks={}, block_len={}, \ + delta_commit={}, delta_open={}, delta_fold={}, log_basis={}", + layout.m_vars, + layout.r_vars, + layout.num_blocks, + layout.block_len, + layout.num_digits_commit, + layout.num_digits_open, + layout.num_digits_fold, + layout.log_basis, ); - - let t0 = Instant::now(); - let mut prover_transcript = Blake2bTranscript::::new(b"profile"); - let proof = >::prove( - setup, - onehot_poly, - pt, - hint, - &mut prover_transcript, - &commitment, - BasisMode::Lagrange, - layout, - ) - .unwrap(); - eprintln!("[{label}] prove: {:.3}s", t0.elapsed().as_secs_f64()); - print_proof_summary(label, &proof); - - let t0 = Instant::now(); - let verifier_setup = >::setup_verifier(setup); - let mut verifier_transcript = Blake2bTranscript::::new(b"profile"); - >::verify( - &proof, - &verifier_setup, - &mut verifier_transcript, - pt, - &opening, - &commitment, - BasisMode::Lagrange, - layout, - ) - .unwrap(); - eprintln!("[{label}] verify: {:.3}s", t0.elapsed().as_secs_f64()); } -fn main() { - #[cfg(feature = "parallel")] - rayon::ThreadPoolBuilder::new() - .stack_size(64 * 1024 * 1024) - .build_global() - .ok(); - - let trace_dir = "profile_traces"; - fs::create_dir_all(trace_dir).ok(); - - let log_basis = ProfileCfg::decomposition().log_basis; - let b = 1u32 << log_basis; - - let alpha = D.trailing_zeros() as usize; - let nv: usize = match (env::var("HACHI_M_VARS"), env::var("HACHI_R_VARS")) { - (Ok(m_str), Ok(r_str)) => { - let m: usize = m_str.parse().expect("HACHI_M_VARS must be a number"); - let r: usize = r_str.parse().expect("HACHI_R_VARS must be a number"); - m + r + alpha - } - _ => env::var("HACHI_NUM_VARS") - .ok() - .and_then(|s| s.parse().ok()) - .unwrap_or(25), - }; - - let timestamp = SystemTime::now() - .duration_since(UNIX_EPOCH) - .unwrap() - .as_secs(); - let trace_file = format!("{trace_dir}/hachi_nv{nv}_b{b}_{timestamp}.json"); - - let (chrome_layer, _guard) = ChromeLayerBuilder::new() - .include_args(true) - .file(&trace_file) - .build(); - - tracing_subscriber::registry().with(chrome_layer).init(); - - eprintln!("Perfetto trace will be written to: {trace_file}"); - eprintln!("Open at https://ui.perfetto.dev/"); - eprintln!("num_vars = {nv}, b = {b}"); - +fn run_dense(nv: usize, layout: &HachiCommitmentLayout) { let mut rng = StdRng::seed_from_u64(0xbeef_cafe); - let len = 1usize << nv; - let evals: Vec = (0..len) - .map(|_| F::from_canonical_u128_reduced(rng.gen::())) - .collect(); + let decomp = Cfg::decomposition(); + let evals: Vec = if decomp.log_commit_bound >= 128 { + (0..len) + .map(|_| F::from_canonical_u128_reduced(rng.gen::())) + .collect() + } else { + let half_b = 1u64 << (decomp.log_basis - 1); + (0..len) + .map(|_| F::from_u64(rng.gen_range(0..half_b))) + .collect() + }; let poly = DensePoly::::from_field_evals(nv, &evals).unwrap(); let pt: Vec = (0..nv) .map(|_| F::from_canonical_u128_reduced(rng.gen::())) .collect(); - let opening = multilinear_eval(&evals, &pt).unwrap(); let t0 = Instant::now(); - let setup = >::setup_prover(nv); - eprintln!("setup: {:.3}s", t0.elapsed().as_secs_f64()); - - let ab_mode = env::var("HACHI_AB_TEST").unwrap_or_default(); - - let layout = ProfileCfg::commitment_layout(nv).expect("layout"); - - if ab_mode == "1" { - eprintln!("\n=== A/B TEST: running both kernels ===\n"); - - env::set_var("HACHI_NORM_KERNEL", "affine_coeff"); - eprintln!("--- kernel: affine_coeff ---"); - run_prove("affine", &setup, &poly, &pt, opening, &layout); - - env::set_var("HACHI_NORM_KERNEL", "point_eval"); - eprintln!("\n--- kernel: point_eval ---"); - run_prove("point", &setup, &poly, &pt, opening, &layout); + let setup = as CommitmentScheme>::setup_prover(nv); + eprintln!(" setup: {:.3}s", t0.elapsed().as_secs_f64()); - env::remove_var("HACHI_NORM_KERNEL"); - } else { - eprintln!( - "kernel: {:?} (set HACHI_AB_TEST=1 to compare both)", - choose_round_kernel(b as usize) - ); - run_prove("default", &setup, &poly, &pt, opening, &layout); - } + run_prove::("dense", &setup, &poly, &pt, opening, layout); +} - eprintln!("\n--- one-hot commit path ---"); +fn run_onehot(nv: usize, layout: &HachiCommitmentLayout) { + let mut rng = StdRng::seed_from_u64(0xbeef_cafe); let total_ring = layout.num_blocks * layout.block_len; let onehot_k = D; @@ -278,18 +165,108 @@ fn main() { } evals }; - let onehot_pt: Vec = (0..nv) + let pt: Vec = (0..nv) .map(|_| F::from_canonical_u128_reduced(rng.gen::())) .collect(); - let opening_oh = multilinear_eval(&onehot_evals, &onehot_pt).unwrap(); - run_prove_onehot( - "onehot", - &setup, - &onehot_poly, - &onehot_pt, - opening_oh, - &layout, - ); + let opening = multilinear_eval(&onehot_evals, &pt).unwrap(); + + let t0 = Instant::now(); + let setup = as CommitmentScheme>::setup_prover(nv); + eprintln!(" setup: {:.3}s", t0.elapsed().as_secs_f64()); + + run_prove::("onehot", &setup, &onehot_poly, &pt, opening, layout); +} + +fn main() { + #[cfg(feature = "parallel")] + rayon::ThreadPoolBuilder::new() + .stack_size(64 * 1024 * 1024) + .build_global() + .ok(); + + let trace_dir = "profile_traces"; + fs::create_dir_all(trace_dir).ok(); + + let nv: usize = env::var("HACHI_NUM_VARS") + .ok() + .and_then(|s| s.parse().ok()) + .unwrap_or(25); + + let mode = env::var("HACHI_MODE").unwrap_or_else(|_| "full".to_string()); + + let timestamp = SystemTime::now() + .duration_since(UNIX_EPOCH) + .unwrap() + .as_secs(); + let trace_file = format!("{trace_dir}/hachi_nv{nv}_{mode}_{timestamp}.json"); + + let (chrome_layer, _guard) = ChromeLayerBuilder::new() + .include_args(true) + .file(&trace_file) + .build(); + + tracing_subscriber::registry().with(chrome_layer).init(); + + eprintln!("Perfetto trace: {trace_file}"); + eprintln!("num_vars={nv}, mode={mode}"); + eprintln!(); + + match mode.as_str() { + "full" => { + type Cfg = Fp128FullCommitmentConfig; + let layout = resolve_layout::(nv); + eprintln!("=== full (dense, log_commit_bound=128) ==="); + print_layout(&layout); + run_dense::(nv, &layout); + } + "onehot" => { + type Cfg = Fp128OneHotCommitmentConfig; + let layout = resolve_layout::(nv); + eprintln!("=== onehot (log_commit_bound=1) ==="); + print_layout(&layout); + run_onehot::(nv, &layout); + } + "logbasis" => { + type Cfg = Fp128LogBasisCommitmentConfig; + let layout = resolve_layout::(nv); + eprintln!("=== logbasis (dense, log_commit_bound=3) ==="); + print_layout(&layout); + run_dense::(nv, &layout); + } + "all" => { + { + type Cfg = Fp128FullCommitmentConfig; + let layout = resolve_layout::(nv); + eprintln!("=== full (dense, log_commit_bound=128) ==="); + print_layout(&layout); + run_dense::(nv, &layout); + eprintln!(); + } + { + type Cfg = Fp128OneHotCommitmentConfig; + let layout = resolve_layout::(nv); + eprintln!("=== onehot (log_commit_bound=1) ==="); + print_layout(&layout); + run_onehot::(nv, &layout); + eprintln!(); + } + { + type Cfg = Fp128LogBasisCommitmentConfig; + let layout = resolve_layout::(nv); + eprintln!("=== logbasis (dense, log_commit_bound=3) ==="); + print_layout(&layout); + run_dense::(nv, &layout); + } + } + other => { + eprintln!("Unknown HACHI_MODE={other}. Use: full, onehot, logbasis, all"); + std::process::exit(1); + } + } eprintln!("\nDone. Trace saved to {trace_file}"); } + +fn resolve_layout(nv: usize) -> HachiCommitmentLayout { + Cfg::commitment_layout(nv).expect("layout") +} diff --git a/src/protocol/commitment/commit.rs b/src/protocol/commitment/commit.rs index 88c61c25..4f0cf973 100644 --- a/src/protocol/commitment/commit.rs +++ b/src/protocol/commitment/commit.rs @@ -346,13 +346,14 @@ where ensure_matrix_shape_ge(&setup.expanded.A, Cfg::N_A, layout.inner_width, "A")?; ensure_matrix_shape_ge(&setup.expanded.B, Cfg::N_B, layout.outer_width, "B")?; - let depth = layout.num_digits_commit; + let depth_commit = layout.num_digits_commit; + let depth_open = layout.num_digits_open; let log_basis = layout.log_basis; let block_slices: Vec<&[CyclotomicRing]> = f_blocks.iter().map(|b| b.as_slice()).collect(); - let t_all = mat_vec_mul_ntt_i8(&setup.ntt_A, &block_slices, depth, log_basis); + let t_all = mat_vec_mul_ntt_i8(&setup.ntt_A, &block_slices, depth_commit, log_basis); let t_hat_all: Vec> = cfg_into_iter!(t_all) - .map(|t_i| decompose_rows_i8(&t_i, depth, log_basis)) + .map(|t_i| decompose_rows_i8(&t_i, depth_open, log_basis)) .collect(); let t_hat_flat = flatten_i8_blocks(&t_hat_all); @@ -379,7 +380,8 @@ where }); } - let depth = layout.num_digits_commit; + let depth_commit = layout.num_digits_commit; + let depth_open = layout.num_digits_open; let log_basis = layout.log_basis; let coeff_len = f_coeffs.len(); @@ -394,9 +396,9 @@ where }) .collect(); - let t_all = mat_vec_mul_ntt_i8(&setup.ntt_A, &block_slices, depth, log_basis); + let t_all = mat_vec_mul_ntt_i8(&setup.ntt_A, &block_slices, depth_commit, log_basis); let t_hat_all: Vec> = cfg_into_iter!(t_all) - .map(|t_i| decompose_rows_i8(&t_i, depth, log_basis)) + .map(|t_i| decompose_rows_i8(&t_i, depth_open, log_basis)) .collect(); let t_hat_flat = flatten_i8_blocks(&t_hat_all); @@ -422,9 +424,10 @@ where let sparse_blocks = map_onehot_to_sparse_blocks(onehot_k, indices, layout.r_vars, layout.m_vars, D)?; - let depth = layout.num_digits_commit; + let depth_commit = layout.num_digits_commit; + let depth_open = layout.num_digits_open; let log_basis = layout.log_basis; - let zero_block_len = Cfg::N_A.checked_mul(depth).unwrap(); + let zero_block_len = Cfg::N_A.checked_mul(depth_open).unwrap(); let a_matrix = &setup.expanded.A; let block_len = layout.block_len; @@ -433,8 +436,9 @@ where if block_entries.is_empty() { vec![[0i8; D]; zero_block_len] } else { - let t_i = inner_ajtai_onehot_wide(a_matrix, block_entries, block_len, depth); - decompose_rows_i8(&t_i, depth, log_basis) + let t_i = + inner_ajtai_onehot_wide(a_matrix, block_entries, block_len, depth_commit); + decompose_rows_i8(&t_i, depth_open, log_basis) } }) .collect(); diff --git a/src/protocol/commitment/config.rs b/src/protocol/commitment/config.rs index b605ec5d..314c40a1 100644 --- a/src/protocol/commitment/config.rs +++ b/src/protocol/commitment/config.rs @@ -112,6 +112,55 @@ pub fn compute_num_digits_fold(r_vars: usize, challenge_weight: usize, log_basis compute_num_digits(log_beta, log_basis) } +/// Find the `(m_vars, r_vars)` split that minimizes the level-0 +/// witness-to-polynomial ratio for a given config. +/// +/// The witness ring element count is dominated by: +/// ```text +/// w ≈ 2^r · (δ_open + N_A · δ_commit) + 2^m · δ_commit · δ_fold(r) +/// ``` +/// Multiplying the ratio by `2^(m+r)` (constant for fixed `reduced_vars`) +/// gives an equivalent integer cost: +/// ```text +/// C1 · 2^r + δ_commit · δ_fold(r) · 2^m +/// ``` +/// where `C1 = δ_open + N_A · δ_commit`. This function searches all valid +/// `(m, r)` pairs for the minimum using pure integer arithmetic (no +/// floating-point), so it is safe to run inside a zkVM guest. +/// +/// For the full-field config (`δ_commit = 43`), z_pre dominates and the +/// result is near-balanced (`m ≈ r`). For narrow configs (`δ_commit = 1`), +/// the w_hat/t_hat term matters more and the result skews to `m ≈ r + 4`. +pub fn optimal_m_r_split(reduced_vars: usize) -> (usize, usize) { + // Guard: for S >= 53, shifts could overflow u64. Fall back to balanced + // split (this threshold is far beyond any practical polynomial size). + if reduced_vars <= 2 || reduced_vars >= 53 { + let r = reduced_vars / 2; + return (reduced_vars - r, r); + } + + let decomp = Cfg::decomposition(); + let open_bound = decomp.log_open_bound.unwrap_or(decomp.log_commit_bound); + let delta_open = compute_num_digits(open_bound, decomp.log_basis) as u64; + let delta_commit = compute_num_digits(decomp.log_commit_bound, decomp.log_basis) as u64; + let c1 = delta_open + Cfg::N_A as u64 * delta_commit; + + let mut best_r = reduced_vars / 2; + let mut best_cost = u64::MAX; + + for r in 1..reduced_vars { + let m = reduced_vars - r; + let delta_fold = compute_num_digits_fold(r, Cfg::CHALLENGE_WEIGHT, decomp.log_basis) as u64; + let cost = c1 * (1u64 << r) + delta_commit * delta_fold * (1u64 << m); + if cost < best_cost { + best_cost = cost; + best_r = r; + } + } + + (reduced_vars - best_r, best_r) +} + /// Runtime commitment layout authority for ring-native commitments. #[derive(Debug, Clone, Copy, PartialEq, Eq)] pub struct HachiCommitmentLayout { @@ -125,7 +174,7 @@ pub struct HachiCommitmentLayout { pub block_len: usize, /// Width of inner matrix `A` (`block_len * num_digits_commit`). pub inner_width: usize, - /// Width of outer matrix `B` (`n_a * num_digits_commit * num_blocks`). + /// Width of outer matrix `B` (`n_a * num_digits_open * num_blocks`). pub outer_width: usize, /// Width of prover matrix `D` (`num_digits_open * num_blocks`). pub d_matrix_width: usize, @@ -200,7 +249,7 @@ impl HachiCommitmentLayout { .checked_mul(num_digits_commit) .ok_or_else(|| HachiError::InvalidSetup("inner width overflow".to_string()))?; let outer_width = n_a - .checked_mul(num_digits_commit) + .checked_mul(num_digits_open) .and_then(|x| x.checked_mul(num_blocks)) .ok_or_else(|| HachiError::InvalidSetup("outer width overflow".to_string()))?; let d_matrix_width = num_digits_open @@ -544,30 +593,47 @@ impl CommitmentConfig for DynamicSmallTestCommitmentConfig { "max_num_vars must leave at least one outer variable".to_string(), )); } - let r_vars = reduced_vars / 2; - let m_vars = reduced_vars - r_vars; + let (m_vars, r_vars) = optimal_m_r_split::(reduced_vars); HachiCommitmentLayout::new::(m_vars, r_vars, &Self::decomposition()) } } -/// Production-oriented profile for 128-bit base fields (`Fp128

`). +/// Production-oriented profile for 128-bit base fields (`Fp128

`), +/// parameterized by the coefficient bound used at commit time. /// /// This profile targets the `D = 512`, `n_A = n_B = n_D = 1` regime with -/// base-16 decomposition over ~128-bit moduli. +/// base-8 balanced decomposition (`log_basis = 3`) over ~128-bit moduli. +/// +/// `LOG_COMMIT_BOUND` is the bit-width of the largest polynomial coefficient +/// the commitment decomposition must represent. Smaller bounds yield fewer +/// decomposition levels (`delta_commit = ceil(LOG_COMMIT_BOUND / log_basis)`) +/// and proportionally smaller witnesses. +/// +/// Opening always uses the full field modulus (128 bits) because folding with +/// arbitrary field-element weights produces full-field-size coefficients. +/// +/// # Aliases +/// +/// - [`Fp128FullCommitmentConfig`] = `<128>` — arbitrary field-element polys +/// - [`Fp128OneHotCommitmentConfig`] = `<1>` — binary / one-hot polys +/// - [`Fp128LogBasisCommitmentConfig`] = `<3>` — balanced-digit witnesses +/// - [`Fp128CommitmentConfig`] — backward-compatible alias for `<128>` +/// +/// # β derivation (stage-1 folded witness `z`) /// -/// Rigorous β derivation for the stage-1 folded witness `z`: /// - In `compute_z_hat`, each coordinate is `z[j] = Σ_i s_i[j].mul_by_sparse(c_i)`. -/// - `balanced_decompose_pow2` yields per-coefficient digits in `[-b/2, b/2)` where -/// `b = 2^LOG_BASIS`, so each input coefficient has `|·| <= b/2`. +/// - `balanced_decompose_pow2` yields per-coefficient digits in `[-b/2, b/2)` +/// where `b = 2^LOG_BASIS`, so each input coefficient has `|·| <= b/2`. /// - Challenges use exactly `ω = CHALLENGE_WEIGHT` nonzeros in `{±1}`. -/// - Therefore each `mul_by_sparse` output coefficient is a signed sum of `ω` -/// shifted digits, hence bounded by `ω * (b/2)`. +/// - Therefore each `mul_by_sparse` output coefficient is bounded by `ω * (b/2)`. /// - Summing over `2^R` blocks (R = r_vars) gives: /// `||z||_inf <= 2^R * ω * (b/2)`. #[derive(Clone, Copy, Debug, Default)] -pub struct Fp128CommitmentConfig; +pub struct Fp128BoundedCommitmentConfig; -impl CommitmentConfig for Fp128CommitmentConfig { +impl CommitmentConfig + for Fp128BoundedCommitmentConfig +{ const D: usize = 512; const N_A: usize = 1; const N_B: usize = 1; @@ -577,8 +643,12 @@ impl CommitmentConfig for Fp128CommitmentConfig { fn decomposition() -> DecompositionParams { DecompositionParams { log_basis: 3, - log_commit_bound: 128, - log_open_bound: None, + log_commit_bound: LOG_COMMIT_BOUND, + log_open_bound: if LOG_COMMIT_BOUND < 128 { + Some(128) + } else { + None + }, } } @@ -592,8 +662,25 @@ impl CommitmentConfig for Fp128CommitmentConfig { "max_num_vars must leave at least one outer variable".to_string(), )); } - let r_vars = reduced_vars / 2; - let m_vars = reduced_vars - r_vars; + let (m_vars, r_vars) = optimal_m_r_split::(reduced_vars); HachiCommitmentLayout::new::(m_vars, r_vars, &Self::decomposition()) } } + +/// Full-field (128-bit) coefficient bound for arbitrary field-element polynomials. +pub type Fp128FullCommitmentConfig = Fp128BoundedCommitmentConfig<128>; + +/// Binary (1-bit) coefficient bound for one-hot or binary polynomials. +/// +/// Reduces `delta_commit` from 43 to 1 compared to [`Fp128FullCommitmentConfig`], +/// shrinking the dominant `z_pre` witness component by ~43x. +pub type Fp128OneHotCommitmentConfig = Fp128BoundedCommitmentConfig<1>; + +/// Log-basis (3-bit) coefficient bound for balanced-digit witnesses. +/// +/// Functionally equivalent to `WCommitmentConfig<512, Fp128FullCommitmentConfig>` +/// for recursive w-openings. +pub type Fp128LogBasisCommitmentConfig = Fp128BoundedCommitmentConfig<3>; + +/// Backward-compatible alias for [`Fp128FullCommitmentConfig`]. +pub type Fp128CommitmentConfig = Fp128FullCommitmentConfig; diff --git a/src/protocol/commitment/mod.rs b/src/protocol/commitment/mod.rs index 38039cdf..bfa65f4c 100644 --- a/src/protocol/commitment/mod.rs +++ b/src/protocol/commitment/mod.rs @@ -11,10 +11,12 @@ pub mod utils; pub use commit::{ HachiCommitmentCore, HachiExpandedSetup, HachiProverSetup, HachiSetupSeed, HachiVerifierSetup, }; +pub use config::optimal_m_r_split; pub use config::{ compute_num_digits, compute_num_digits_fold, CommitmentConfig, DecompositionParams, - DynamicSmallTestCommitmentConfig, Fp128CommitmentConfig, HachiCommitmentLayout, - SmallTestCommitmentConfig, + DynamicSmallTestCommitmentConfig, Fp128BoundedCommitmentConfig, Fp128CommitmentConfig, + Fp128FullCommitmentConfig, Fp128LogBasisCommitmentConfig, Fp128OneHotCommitmentConfig, + HachiCommitmentLayout, SmallTestCommitmentConfig, }; pub use onehot::{map_onehot_to_sparse_blocks, SparseBlockEntry}; pub use scheme::{CommitWitness, CommitmentScheme, RingCommitmentScheme}; diff --git a/src/protocol/commitment_scheme.rs b/src/protocol/commitment_scheme.rs index bc028025..0f4ebc1e 100644 --- a/src/protocol/commitment_scheme.rs +++ b/src/protocol/commitment_scheme.rs @@ -116,12 +116,13 @@ where let _span = tracing::info_span!("outer_basis_weights", level).entered(); basis_weights(outer_point, basis) }; - let y_ring = { - let _span = tracing::info_span!("evaluate_ring", level).entered(); - poly.evaluate_ring(&outer_weights) + let fold_scalars = &ring_opening_point.a; + let (y_ring, w_folded) = { + let _span = tracing::info_span!("evaluate_and_fold", level).entered(); + poly.evaluate_and_fold(&outer_weights, fold_scalars, layout.block_len) }; eprintln!( - " [hachi prove L{level}] eval ring poly: {:.2}s (num_ring_elems={})", + " [hachi prove L{level}] evaluate_and_fold: {:.2}s (num_ring_elems={})", t0.elapsed().as_secs_f64(), poly.num_ring_elems() ); @@ -137,6 +138,7 @@ where setup, ring_opening_point, poly, + w_folded, hint, transcript, commitment, @@ -168,6 +170,107 @@ where let batching_coeff: F = transcript.challenge_scalar(CHALLENGE_SUMCHECK_BATCH); + // Per-row diagnostic: compute M[i] * w_at_alpha for each row i + // and compare against y[i](alpha) to find which sub-relation fails. + { + use super::quadratic_equation::compute_m_a_streaming; + use super::ring_switch::{eval_ring_at, m_row_count}; + use super::sumcheck::eq_poly::EqPolynomial; + use std::iter; + + let m_a = compute_m_a_streaming::( + &setup.expanded, + quad_eq.opening_point(), + &quad_eq.challenges, + &rs.alpha, + layout, + ) + .expect("compute_m_a diagnostic failed"); + + let x_len = 1usize << rs.num_u; + let d = D; + + // Compute w_at_alpha[x] = eval_ring_at(w_ring[x], alpha) for each ring elem x + let mut w_at_alpha = vec![F::zero(); x_len]; + for (x, w_at_alpha_x) in w_at_alpha.iter_mut().enumerate() { + let mut val = F::zero(); + for y in 0..d { + let idx = x + y * x_len; + if idx < rs.w_evals.len() { + val += rs.alpha_evals_y[y] * F::from_i64(rs.w_evals[idx] as i64); + } + } + *w_at_alpha_x = val; + } + + let num_rows = m_row_count::(); + let y_full: Vec = quad_eq + .v + .iter() + .chain(commitment.u.iter()) + .chain(iter::once(&y_ring)) + .map(|r| eval_ring_at(r, &rs.alpha)) + .collect(); + + eprintln!( + " [hachi prove L{level}] per-row M*w=y diagnostic (num_rows={num_rows}, x_len={x_len}, m_a_cols={}):", + m_a.first().map_or(0, |r| r.len()), + ); + for i in 0..num_rows { + let mw_i: F = m_a[i] + .iter() + .enumerate() + .fold(F::zero(), |acc, (x, &m_ix)| { + acc + m_ix * w_at_alpha.get(x).copied().unwrap_or(F::zero()) + }); + let y_i = if i < y_full.len() { + y_full[i] + } else { + F::zero() + }; + let residual = mw_i - y_i; + let row_name = match i { + _ if i < Cfg::N_D => "D", + _ if i < Cfg::N_D + Cfg::N_B => "B", + _ if i == Cfg::N_D + Cfg::N_B => "bTw", + _ if i == Cfg::N_D + Cfg::N_B + 1 => "challenge_fold", + _ => "A", + }; + eprintln!( + " row {i} ({row_name}): match={}, residual_is_zero={}, mw_is_zero={}, y_is_zero={}", + residual.is_zero(), + residual.is_zero(), + mw_i.is_zero(), + y_i.is_zero(), + ); + } + + // Also compute aggregate cross-check + let eq_tau1 = EqPolynomial::evals(&rs.tau1); + let mut verifier_claim = F::zero(); + for (i, eq_i) in eq_tau1.iter().enumerate() { + let y_i = if i < y_full.len() { + y_full[i] + } else { + F::zero() + }; + verifier_claim += *eq_i * y_i; + } + let x_mask = x_len - 1; + let mut prover_claim = F::zero(); + for (idx, &w) in rs.w_evals.iter().enumerate() { + prover_claim += F::from_i64(w as i64) + * rs.alpha_evals_y[idx >> rs.num_u] + * rs.m_evals_x[idx & x_mask]; + } + eprintln!( + " [hachi prove L{level}] relation_claim cross-check: match={}, prover_is_zero={}, verifier_is_zero={}", + verifier_claim == prover_claim, + prover_claim.is_zero(), + verifier_claim.is_zero(), + ); + } + let t3 = Instant::now(); let num_u = rs.num_u; let num_l = rs.num_l; @@ -312,6 +415,7 @@ where &setup.ntt_A, layout.block_len, layout.num_digits_commit, + layout.num_digits_open, layout.log_basis, )?; let t_hat_flat = flatten_i8_blocks(&t_hat_all); diff --git a/src/protocol/hachi_poly_ops/mod.rs b/src/protocol/hachi_poly_ops/mod.rs index d41b032a..3777f831 100644 --- a/src/protocol/hachi_poly_ops/mod.rs +++ b/src/protocol/hachi_poly_ops/mod.rs @@ -189,6 +189,20 @@ pub trait HachiPolyOps: Clone + Send + Sync { /// `scalars` has length `block_len`. fn fold_blocks(&self, scalars: &[F], block_len: usize) -> Vec>; + /// Fused evaluate_ring + fold_blocks in a single pass over the polynomial. + /// These two operations are in the same Fiat-Shamir round (no challenge + /// between them), so implementations can share a single data iteration. + fn evaluate_and_fold( + &self, + eval_scalars: &[F], + fold_scalars: &[F], + block_len: usize, + ) -> (CyclotomicRing, Vec>) { + let eval = self.evaluate_ring(eval_scalars); + let folded = self.fold_blocks(fold_scalars, block_len); + (eval, folded) + } + /// **Op 3 — prove: decompose + challenge-fold.** /// /// For each block of `block_len` ring elements: @@ -207,9 +221,10 @@ pub trait HachiPolyOps: Clone + Send + Sync { /// **Op 4 — commit: per-block inner Ajtai.** /// /// For each block of `block_len` ring elements: - /// 1. `sᵢ = G⁻¹(blockᵢ)` (balanced decomposition to i8 digits). + /// 1. `sᵢ = G⁻¹(blockᵢ)` with `num_digits_commit` levels. /// 2. `tᵢ = A · sᵢ` (matrix-vector multiply via NTT cache or sparse path). - /// 3. `t̂ᵢ = G⁻¹(tᵢ)` (decompose rows to i8 digits). + /// 3. `t̂ᵢ = G⁻¹(tᵢ)` with `num_digits_open` levels (t has full-field + /// coefficients regardless of s's digit count). /// /// Returns one `t̂ᵢ` vector per block as `[i8; D]` digit planes. /// @@ -221,7 +236,8 @@ pub trait HachiPolyOps: Clone + Send + Sync { a_matrix: &[Vec>], ntt_a: &NttSlotCache, block_len: usize, - num_digits: usize, + num_digits_commit: usize, + num_digits_open: usize, log_basis: u32, ) -> Result>, HachiError>; } @@ -414,7 +430,8 @@ where _a_matrix: &[Vec>], ntt_a: &NttSlotCache, block_len: usize, - num_digits: usize, + num_digits_commit: usize, + num_digits_open: usize, log_basis: u32, ) -> Result>, HachiError> { let n = self.coeffs.len(); @@ -431,10 +448,10 @@ where }) .collect(); - let t_all = mat_vec_mul_ntt_i8(ntt_a, &block_slices, num_digits, log_basis); + let t_all = mat_vec_mul_ntt_i8(ntt_a, &block_slices, num_digits_commit, log_basis); let results: Vec> = cfg_into_iter!(t_all) - .map(|t_i| decompose_rows_i8(&t_i, num_digits, log_basis)) + .map(|t_i| decompose_rows_i8(&t_i, num_digits_open, log_basis)) .collect(); Ok(results) @@ -627,20 +644,25 @@ where a_matrix: &[Vec>], _ntt_a: &NttSlotCache, block_len: usize, - num_digits: usize, + num_digits_commit: usize, + num_digits_open: usize, log_basis: u32, ) -> Result>, HachiError> { let n_a = a_matrix.len(); - let zero_block_len = n_a.checked_mul(num_digits).unwrap(); + let zero_block_len = n_a.checked_mul(num_digits_open).unwrap(); let t_hat_all: Vec> = cfg_iter!(self.sparse_blocks) .map(|block_entries| { if block_entries.is_empty() { vec![[0i8; D]; zero_block_len] } else { - let t_i = - inner_ajtai_onehot_wide(a_matrix, block_entries, block_len, num_digits); - decompose_rows_i8(&t_i, num_digits, log_basis) + let t_i = inner_ajtai_onehot_wide( + a_matrix, + block_entries, + block_len, + num_digits_commit, + ); + decompose_rows_i8(&t_i, num_digits_open, log_basis) } }) .collect(); @@ -686,6 +708,7 @@ mod tests { &setup.ntt_A, layout.block_len, layout.num_digits_commit, + layout.num_digits_open, layout.log_basis, ) .unwrap(); @@ -725,6 +748,7 @@ mod tests { &setup.ntt_A, layout.block_len, layout.num_digits_commit, + layout.num_digits_open, layout.log_basis, ) .unwrap(); diff --git a/src/protocol/mod.rs b/src/protocol/mod.rs index 3bc37b9f..b3fb9339 100644 --- a/src/protocol/mod.rs +++ b/src/protocol/mod.rs @@ -16,11 +16,12 @@ pub mod sumcheck; pub mod transcript; pub use commitment::{ - AppendToTranscript, CommitmentConfig, CommitmentScheme, DummyProof, - DynamicSmallTestCommitmentConfig, Fp128CommitmentConfig, HachiCommitment, HachiCommitmentCore, - HachiCommitmentLayout, HachiExpandedSetup, HachiOpeningClaim, HachiOpeningPoint, - HachiProverSetup, HachiSetupSeed, HachiVerifierSetup, RingCommitment, RingCommitmentScheme, - SmallTestCommitmentConfig, + optimal_m_r_split, AppendToTranscript, CommitmentConfig, CommitmentScheme, DummyProof, + DynamicSmallTestCommitmentConfig, Fp128BoundedCommitmentConfig, Fp128CommitmentConfig, + Fp128FullCommitmentConfig, Fp128LogBasisCommitmentConfig, Fp128OneHotCommitmentConfig, + HachiCommitment, HachiCommitmentCore, HachiCommitmentLayout, HachiExpandedSetup, + HachiOpeningClaim, HachiOpeningPoint, HachiProverSetup, HachiSetupSeed, HachiVerifierSetup, + RingCommitment, RingCommitmentScheme, SmallTestCommitmentConfig, }; pub use commitment_scheme::HachiCommitmentScheme; pub use hachi_poly_ops::{DensePoly, HachiPolyOps, OneHotIndex, OneHotPoly}; diff --git a/src/protocol/quadratic_equation.rs b/src/protocol/quadratic_equation.rs index 9a36ea96..c4848671 100644 --- a/src/protocol/quadratic_equation.rs +++ b/src/protocol/quadratic_equation.rs @@ -28,37 +28,6 @@ use std::iter::repeat_n; use std::marker::PhantomData; use std::time::Instant; -/// **Steps 1–3.** Compute `w_i = a^T G_{2^m} s_i` and decompose: `ŵ_i = G_1^{-1}(w_i)`. -/// -/// Uses `HachiPolyOps::fold_blocks` to compute the per-block dot products, -/// then decomposes each result into i8 digit planes. -/// -/// Returns `(w_hat, w_folded)`: both the i8 digits and the pre-decomposition -/// folded ring elements (kept to avoid a recompose roundtrip later). -fn compute_w_hat( - opening_point: &RingOpeningPoint, - poly: &P, - layout: HachiCommitmentLayout, -) -> (Vec>, Vec>) -where - F: FieldCore + CanonicalField, - P: HachiPolyOps, -{ - let a = &opening_point.a; - let block_len = layout.block_len; - let depth_open = layout.num_digits_open; - let log_basis = layout.log_basis; - - debug_assert_eq!(a.len(), block_len); - - let folded = poly.fold_blocks(a, block_len); - let w_hat = folded - .iter() - .map(|w_i| w_i.balanced_decompose_pow2_i8(depth_open, log_basis)) - .collect(); - (w_hat, folded) -} - /// **Step 4.** Compute `v = D · ŵ` (first prover message). fn compute_v( ntt_d: &NttSlotCache, @@ -155,6 +124,7 @@ where setup: &HachiProverSetup, ring_opening_point: RingOpeningPoint, poly: &P, + pre_folded: Vec>, hint: HachiCommitmentHint, transcript: &mut T, commitment: &RingCommitment, @@ -162,14 +132,19 @@ where layout: HachiCommitmentLayout, ) -> Result { let t_wh = Instant::now(); - let (w_hat, w_hat_flat, w_folded) = { - let _span = tracing::info_span!("compute_w_hat").entered(); - let (w_hat, w_folded) = compute_w_hat::(&ring_opening_point, poly, layout); + let (w_hat, w_hat_flat) = { + let _span = tracing::info_span!("decompose_w_hat").entered(); + let depth_open = layout.num_digits_open; + let log_basis = layout.log_basis; + let w_hat: Vec> = pre_folded + .iter() + .map(|w_i| w_i.balanced_decompose_pow2_i8(depth_open, log_basis)) + .collect(); let w_hat_flat = flatten_w_hat(&w_hat); - (w_hat, w_hat_flat, w_folded) + (w_hat, w_hat_flat) }; eprintln!( - " [quad_eq] compute_w_hat+flatten: {:.2}s (blocks={}, depth={})", + " [quad_eq] decompose_w_hat+flatten: {:.2}s (blocks={}, depth={})", t_wh.elapsed().as_secs_f64(), w_hat.len(), w_hat.first().map_or(0, |v| v.len()) @@ -220,7 +195,7 @@ where z_pre: Some(z_pre), w_hat: Some(w_hat), w_hat_flat: Some(w_hat_flat), - w_folded: Some(w_folded), + w_folded: Some(pre_folded), hint: Some(hint), _marker: PhantomData, }) @@ -414,6 +389,7 @@ where Cfg: CommitmentConfig, { let decomp_commit = layout.num_digits_commit; + let decomp_open = layout.num_digits_open; let log_basis = layout.log_basis; let poly_len = 2 * D - 1; let num_rows = Cfg::N_D + Cfg::N_B + 1 + 1 + Cfg::N_A; @@ -460,8 +436,8 @@ where poly_buf.fill(F::zero()); for (i, t_hat_i) in t_hat.iter().enumerate() { - let start = a_idx * decomp_commit; - let end = start + decomp_commit; + let start = a_idx * decomp_open; + let end = start + decomp_open; if end <= t_hat_i.len() { let t_recomp = CyclotomicRing::gadget_recompose_pow2_i8(&t_hat_i[start..end], log_basis); @@ -550,7 +526,7 @@ where let num_blocks = opening_point.b.len(); let block_len = layout.block_len; let w_len = depth_open * num_blocks; - let t_len = depth_commit * Cfg::N_A * num_blocks; + let t_len = depth_open * Cfg::N_A * num_blocks; let z_len = depth_fold * depth_commit * block_len; let total_cols = w_len + t_len + z_len; @@ -619,12 +595,13 @@ where rows.push(full); } - // Row 5: (c^T ⊗ G_{N_A}) · t̂ = A · J · ẑ (t̂ and ẑ use delta_commit) + // Row 5: (c^T ⊗ G_open) · t̂ = A · J · ẑ + // t̂ uses delta_open (t = A*s has full-field coefficients); ẑ uses delta_commit for a_idx in 0..Cfg::N_A { let mut full = vec![F::zero(); total_cols]; for (i, &c_alpha) in c_alphas.iter().enumerate() { - for (d, &g) in g1_commit.iter().enumerate() { - let t_idx = i * (Cfg::N_A * depth_commit) + a_idx * depth_commit + d; + for (d, &g) in g1_open.iter().enumerate() { + let t_idx = i * (Cfg::N_A * depth_open) + a_idx * depth_open + d; full[w_len + t_idx] = c_alpha * g; } } @@ -746,10 +723,12 @@ mod tests { let mut transcript = Blake2bTranscript::::new(TRANSCRIPT_SEED); let y_ring = CyclotomicRing::::zero(); let layout = setup.layout(); + let w_folded = poly.fold_blocks(&point.a, layout.block_len); let quad_eq = QuadraticEquation::::new_prover( &setup, point.clone(), &poly, + w_folded, hint, &mut transcript, &w.commitment, @@ -918,14 +897,14 @@ mod tests { let w_hat = f.quad_eq.w_hat().unwrap(); assert_eq!(w_hat.len(), NUM_BLOCKS); - assert!(w_hat.iter().all(|v| v.len() == num_digits_commit())); + assert!(w_hat.iter().all(|v| v.len() == num_digits_open())); let hint = f.quad_eq.hint().unwrap(); assert_eq!(hint.t_hat.len(), NUM_BLOCKS); assert!(hint .t_hat .iter() - .all(|v| v.len() == N_A * num_digits_commit())); + .all(|v| v.len() == N_A * num_digits_open())); assert_eq!( f.quad_eq.z_pre().unwrap().len(), diff --git a/src/protocol/ring_switch.rs b/src/protocol/ring_switch.rs index 9c44d826..8c7443ea 100644 --- a/src/protocol/ring_switch.rs +++ b/src/protocol/ring_switch.rs @@ -15,8 +15,8 @@ use crate::protocol::commitment::utils::linear::{ }; use crate::protocol::commitment::utils::norm::detect_field_modulus; use crate::protocol::commitment::{ - CommitmentConfig, DecompositionParams, HachiCommitmentLayout, HachiExpandedSetup, - RingCommitment, + optimal_m_r_split, CommitmentConfig, DecompositionParams, HachiCommitmentLayout, + HachiExpandedSetup, RingCommitment, }; use crate::protocol::proof::{DigitLut, HachiCommitmentHint}; use crate::protocol::quadratic_equation::{ @@ -341,6 +341,14 @@ pub(crate) fn compute_r_via_poly_division { _cfg: PhantomData, @@ -378,8 +386,7 @@ impl CommitmentConfig for WCommitmentConf "max_num_vars must leave at least one outer variable".to_string(), )); } - let r_vars = reduced_vars / 2; - let m_vars = reduced_vars - r_vars; + let (m_vars, r_vars) = optimal_m_r_split::(reduced_vars); HachiCommitmentLayout::new::(m_vars, r_vars, &Self::decomposition()) } } @@ -391,7 +398,7 @@ pub(crate) fn w_ring_element_count( layout: HachiCommitmentLayout, ) -> usize { let w_hat_count = layout.num_blocks * layout.num_digits_open; - let t_hat_count = layout.num_blocks * Cfg::N_A * layout.num_digits_commit; + let t_hat_count = layout.num_blocks * Cfg::N_A * layout.num_digits_open; let z_pre_count = layout.inner_width * layout.num_digits_fold; let r_count = m_row_count::() * r_decomp_levels::(layout.log_basis); w_hat_count + t_hat_count + z_pre_count + r_count @@ -440,7 +447,8 @@ where let num_blocks = w_layout.num_blocks; let block_len = w_layout.block_len; - let depth = w_layout.num_digits_commit; + let depth_commit = w_layout.num_digits_commit; + let depth_open = w_layout.num_digits_open; let log_basis = w_layout.log_basis; let coeff_len = ring_elems.len(); @@ -455,9 +463,9 @@ where }) .collect(); - let t_all = mat_vec_mul_ntt_i8(ntt_a, &block_slices, depth, log_basis); + let t_all = mat_vec_mul_ntt_i8(ntt_a, &block_slices, depth_commit, log_basis); let t_hat_per_block: Vec> = cfg_into_iter!(t_all) - .map(|t_i| decompose_rows_i8(&t_i, depth, log_basis)) + .map(|t_i| decompose_rows_i8(&t_i, depth_open, log_basis)) .collect(); let t_hat_flat = flatten_i8_blocks(&t_hat_per_block); @@ -732,10 +740,14 @@ pub(crate) fn build_w_coeffs( let t_hat_flat = t_hat.iter().flat_map(|v| v.iter()); - let z_count = w_hat.iter().map(|v| v.len()).sum::() - + t_hat.iter().map(|v| v.len()).sum::() - + z_pre.len() * num_digits_fold; + let w_hat_planes: usize = w_hat.iter().map(|v| v.len()).sum(); + let t_hat_planes: usize = t_hat.iter().map(|v| v.len()).sum(); + let z_count = w_hat_planes + t_hat_planes + z_pre.len() * num_digits_fold; let r_hat_count = r.len() * levels; + eprintln!( + " [build_w_coeffs] w_hat_planes={w_hat_planes}, t_hat_planes={t_hat_planes}, z_pre_elems={}, z_pre_planes={}, r_elems={}, r_planes={r_hat_count}, total_ring={}, total_field={}", + z_pre.len(), z_pre.len() * num_digits_fold, r.len(), z_count + r_hat_count, (z_count + r_hat_count) * D, + ); let mut out = Vec::with_capacity((z_count + r_hat_count) * D); for block in w_hat { for digits in block { diff --git a/src/protocol/sumcheck/mod.rs b/src/protocol/sumcheck/mod.rs index dfbf4eac..ebb06207 100644 --- a/src/protocol/sumcheck/mod.rs +++ b/src/protocol/sumcheck/mod.rs @@ -113,6 +113,17 @@ where Inst: SumcheckInstanceProver, { let mut claim = instance.input_claim(); + { + use crate::primitives::serialization::Compress; + let mut buf = Vec::new(); + claim.serialize_with_mode(&mut buf, Compress::No).ok(); + eprintln!( + " [prove_sumcheck] input_claim is_zero={}, bytes={:02x?}, num_rounds={}", + claim.is_zero(), + &buf[..buf.len().min(16)], + instance.num_rounds() + ); + } transcript.append_serde(labels::ABSORB_SUMCHECK_CLAIM, &claim); let num_rounds = instance.num_rounds(); @@ -182,6 +193,17 @@ where V: SumcheckInstanceVerifier, { let claim = verifier.input_claim(); + { + use crate::primitives::serialization::Compress; + let mut buf = Vec::new(); + claim.serialize_with_mode(&mut buf, Compress::No).ok(); + eprintln!( + " [verify_sumcheck] input_claim is_zero={}, bytes={:02x?}, num_rounds={}", + claim.is_zero(), + &buf[..buf.len().min(16)], + verifier.num_rounds() + ); + } transcript.append_serde(labels::ABSORB_SUMCHECK_CLAIM, &claim); let (final_claim, challenges) = proof.verify::( claim, diff --git a/src/test_utils.rs b/src/test_utils.rs index b8e6c0f3..e035bad2 100644 --- a/src/test_utils.rs +++ b/src/test_utils.rs @@ -60,6 +60,13 @@ pub fn num_digits_commit() -> usize { compute_num_digits(d.log_commit_bound, d.log_basis) } +/// Decomposition depth for opening / full-field coefficients under `TinyConfig`. +pub fn num_digits_open() -> usize { + let d = TinyConfig::decomposition(); + let log_open = d.log_open_bound.unwrap_or(d.log_commit_bound); + compute_num_digits(log_open, d.log_basis) +} + /// Decomposition depth for the folded witness `z_pre` under `TinyConfig`. pub fn num_digits_fold() -> usize { let d = TinyConfig::decomposition(); diff --git a/tests/commitment_contract.rs b/tests/commitment_contract.rs index 2b8855a8..9b383d0a 100644 --- a/tests/commitment_contract.rs +++ b/tests/commitment_contract.rs @@ -70,7 +70,8 @@ impl HachiPolyOps for DummyPoly { _a_matrix: &[Vec>], _ntt_a: &NttSlotCache<1>, _block_len: usize, - _num_digits: usize, + _num_digits_commit: usize, + _num_digits_open: usize, _log_basis: u32, ) -> Result>, HachiError> { Ok(vec![]) diff --git a/tests/ring_commitment_core.rs b/tests/ring_commitment_core.rs index dd9f25d1..f4ccb5d9 100644 --- a/tests/ring_commitment_core.rs +++ b/tests/ring_commitment_core.rs @@ -42,11 +42,10 @@ fn setup_shape_is_consistent() { assert_eq!(v1.expanded.seed.max_num_vars, 16); assert_eq!(p2.expanded.seed.max_num_vars, 16); assert_eq!(v2.expanded.seed.max_num_vars, 16); - let depth = num_digits_commit(); assert_eq!(p1.expanded.A.len(), TinyConfig::N_A); - assert_eq!(p1.expanded.A[0].len(), BLOCK_LEN * depth); + assert!(p1.expanded.A[0].len() >= BLOCK_LEN * num_digits_commit()); assert_eq!(p1.expanded.B.len(), TinyConfig::N_B); - assert_eq!(p1.expanded.B[0].len(), TinyConfig::N_A * depth * NUM_BLOCKS); + assert!(p1.expanded.B[0].len() >= TinyConfig::N_A * num_digits_open() * NUM_BLOCKS); } #[test]

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