GF(2) field

src/field.rs

@@ -10,6 +10,7 @@ pub mod crypto_bigint_const_monty;
 pub(crate) mod crypto_bigint_helpers;
 #[cfg(feature = "crypto_bigint")]
 pub mod crypto_bigint_monty;
+pub mod f2;
 
 use crate::{ConstSemiring, ring::Ring};
 use core::{
@@ -40,6 +41,11 @@ pub trait Field:
     /// Underlying representation of an element
     type Inner: Debug + Eq + Clone + Sync + Send;
 
+    /// Type used to represent the modulus. Usually the same as `Self::Inner`,
+    /// but may differ when the modulus doesn't fit in the element representation
+    /// (e.g. F2 where elements are `bool` but the modulus is `2: u8`).
+    type Modulus: Debug + Eq + Clone + Sync + Send;
+
     fn inner(&self) -> &Self::Inner;
     fn inner_mut(&mut self) -> &mut Self::Inner;
     fn into_inner(self) -> Self::Inner;
@@ -63,11 +69,11 @@ pub trait PrimeField: Field {
     // Note: Not using `&self` to avoid conflicts with `Zero` trait.
     fn is_zero(value: &Self) -> bool;
 
-    fn modulus(&self) -> Self::Inner;
+    fn modulus(&self) -> Self::Modulus;
 
     fn modulus_minus_one_div_two(&self) -> Self::Inner;
 
-    fn make_cfg(modulus: &Self::Inner) -> Result<Self::Config, FieldError>;
+    fn make_cfg(modulus: &Self::Modulus) -> Result<Self::Config, FieldError>;
 
     /// Creates a new instance of a prime field element from
     /// an arbitrary element of `Self::Inner`. The method
@@ -92,7 +98,7 @@ pub trait PrimeField: Field {
 pub trait ConstPrimeField:
     Field + ConstSemiring + Inv<Output = Option<Self>> + From<u64> + From<u128> + From<Self::Inner>
 {
-    const MODULUS: Self::Inner;
+    const MODULUS: Self::Modulus;
     const MODULUS_MINUS_ONE_DIV_TWO: Self::Inner;
 
     /// Creates a new instance of a prime field element from
@@ -124,7 +130,7 @@ impl<T: ConstPrimeField> PrimeField for T {
     }
 
     #[inline(always)]
-    fn modulus(&self) -> Self::Inner {
+    fn modulus(&self) -> Self::Modulus {
         Self::MODULUS
     }
 
@@ -133,7 +139,7 @@ impl<T: ConstPrimeField> PrimeField for T {
         Self::MODULUS_MINUS_ONE_DIV_TWO
     }
 
-    fn make_cfg(modulus: &Self::Inner) -> Result<Self::Config, FieldError> {
+    fn make_cfg(modulus: &Self::Modulus) -> Result<Self::Config, FieldError> {
         if *modulus == Self::MODULUS {
             Ok(())
         } else {

src/field/ark_ff_field.rs

@@ -400,6 +400,7 @@ impl<F: ArkWrappedField> Ring for ArkField<F> {}
 
 impl<F: ArkWrappedField> Field for ArkField<F> {
     type Inner = F;
+    type Modulus = <F::BasePrimeField as ark_ff::PrimeField>::BigInt;
 
     #[inline(always)]
     fn inner(&self) -> &Self::Inner {

src/field/ark_ff_fp.rs

@@ -491,6 +491,7 @@ impl<P: FpConfig<N>, const N: usize> IntRing for Fp<P, N> {
 
 impl<P: FpConfig<N>, const N: usize> Field for Fp<P, N> {
     type Inner = BigInt<N>;
+    type Modulus = Self::Inner;
 
     #[inline(always)]
     fn inner(&self) -> &Self::Inner {
@@ -510,7 +511,7 @@ impl<P: FpConfig<N>, const N: usize> Field for Fp<P, N> {
 
 /// ConstPrimeField is only implemented for MontConfig and MontBackend
 impl<M: MontConfig<N>, const N: usize> ConstPrimeField for Fp<MontBackend<M, N>, N> {
-    const MODULUS: Self::Inner = M::MODULUS;
+    const MODULUS: Self::Modulus = M::MODULUS;
     const MODULUS_MINUS_ONE_DIV_TWO: Self::Inner =
         <ArkWrappedFp<MontBackend<M, N>, N> as ArkPrimeField>::MODULUS_MINUS_ONE_DIV_TWO;
 

src/field/crypto_bigint_boxed_monty.rs

@@ -406,6 +406,7 @@ impl Ring for BoxedMontyField {}
 
 impl Field for BoxedMontyField {
     type Inner = BoxedUint;
+    type Modulus = Self::Inner;
 
     #[inline(always)]
     fn inner(&self) -> &Self::Inner {
@@ -440,7 +441,7 @@ impl PrimeField for BoxedMontyField {
         value.0.is_zero().into()
     }
 
-    fn modulus(&self) -> Self::Inner {
+    fn modulus(&self) -> Self::Modulus {
         self.0.params().modulus().clone().get()
     }
 
@@ -450,7 +451,7 @@ impl PrimeField for BoxedMontyField {
         (value - BoxedUint::one()) / NonZero::new(BoxedUint::from(2_u8)).unwrap()
     }
 
-    fn make_cfg(modulus: &Self::Inner) -> Result<Self::Config, FieldError> {
+    fn make_cfg(modulus: &Self::Modulus) -> Result<Self::Config, FieldError> {
         let Some(modulus) = Odd::new(modulus.clone()).into_option() else {
             return Err(FieldError::InvalidModulus);
         };

src/field/crypto_bigint_const_monty.rs

@@ -553,6 +553,7 @@ impl<Mod: Params<LIMBS>, const LIMBS: usize> Ring for ConstMontyField<Mod, LIMBS
 
 impl<Mod: Params<LIMBS>, const LIMBS: usize> Field for ConstMontyField<Mod, LIMBS> {
     type Inner = Uint<LIMBS>;
+    type Modulus = Self::Inner;
 
     #[inline(always)]
     fn inner(&self) -> &Self::Inner {
@@ -571,7 +572,7 @@ impl<Mod: Params<LIMBS>, const LIMBS: usize> Field for ConstMontyField<Mod, LIMB
 }
 
 impl<Mod: Params<LIMBS>, const LIMBS: usize> ConstPrimeField for ConstMontyField<Mod, LIMBS> {
-    const MODULUS: Self::Inner = *Uint::new_ref(Mod::PARAMS.modulus().as_ref());
+    const MODULUS: Self::Modulus = *Uint::new_ref(Mod::PARAMS.modulus().as_ref());
     const MODULUS_MINUS_ONE_DIV_TWO: Self::Inner = {
         let m_minus_one = CBUint::wrapping_sub(Self::MODULUS.inner(), &CBUint::ONE);
         let two = CBUint::<LIMBS>::wrapping_add(&CBUint::ONE, &CBUint::ONE);

src/field/crypto_bigint_monty.rs

@@ -487,6 +487,7 @@ impl<const LIMBS: usize> Ring for MontyField<LIMBS> {}
 
 impl<const LIMBS: usize> Field for MontyField<LIMBS> {
     type Inner = Uint<LIMBS>;
+    type Modulus = Self::Inner;
 
     #[inline(always)]
     fn inner(&self) -> &Self::Inner {
@@ -515,7 +516,7 @@ impl<const LIMBS: usize> PrimeField for MontyField<LIMBS> {
         value.0.as_montgomery().is_zero()
     }
 
-    fn modulus(&self) -> Self::Inner {
+    fn modulus(&self) -> Self::Modulus {
         Uint::new(self.0.params().modulus().get())
     }
 
@@ -528,7 +529,7 @@ impl<const LIMBS: usize> PrimeField for MontyField<LIMBS> {
         )
     }
 
-    fn make_cfg(modulus: &Self::Inner) -> Result<Self::Config, FieldError> {
+    fn make_cfg(modulus: &Self::Modulus) -> Result<Self::Config, FieldError> {
         let Some(modulus) = Odd::new(*modulus.inner()).into_option() else {
             return Err(FieldError::InvalidModulus);
         };