crypto-lab-grover

What It Is

Grover's algorithm (Lov Grover, 1996) is a quantum search algorithm that finds a marked item in an unstructured search space of N items using O(√N) queries — a quadratic speedup over classical brute force. This demo classically simulates the complete amplitude amplification process with exact mathematical formulas: oracle phase kickback, inversion-about-mean diffusion, and probability oscillation including overshoot past optimal iterations. The security model is symmetric cryptography — Grover is the quantum threat to AES, SHA, and HMAC that Shor's algorithm does not touch. Grover's speedup is provably optimal (BBBV lower bound); no quantum algorithm can search faster than O(√N).

When to Use It

• Understanding why AES-256 retains strong post-quantum security margins while AES-128 is weakened — Under idealized Grover assumptions, effective key length is halved: AES-128 drops to ~2^64 effective operations (potentially feasible), while AES-256 drops to ~2^128 (still strong). In practice, circuit depth makes the real cost far higher than these headline figures.
• Visualizing the oracle-and-diffusion loop — The amplitude bar chart shows probability concentrating on the target state in real time, making the quadratic speedup intuitive.
• Teaching the overshoot phenomenon — The probability curve shows why running more Grover iterations past k* = π/4·√N actually decreases success probability.
• Comparing Grover and Shor as complementary quantum threats — The side-by-side comparison table clarifies which algorithms each one breaks and what the mitigation is.
• Do not use this for public-key cryptography threats — Grover does not affect RSA, ECC, or Diffie-Hellman; that is Shor's domain.

Live Demo

https://systemslibrarian.github.io/crypto-lab-grover/

Adjust the qubit count (n = 2–20) to resize the search space, step through Grover iterations one at a time or auto-run, and watch amplitude concentrate on the target state. The demo also shows AES-128/192/256 quantum impact analysis with an interactive key-size selector, a hash function security table (MD5 through SHA3-512), and a classical-vs-quantum search race animation.

How to Run Locally

git clone https://github.com/systemslibrarian/crypto-lab-grover
cd crypto-lab-grover
npm install
npm run dev

Part of the Crypto-Lab Suite

One of 60+ live browser demos at systemslibrarian.github.io/crypto-lab — spanning Atbash (600 BCE) through NIST FIPS 203/204/205 (2024).

Sources

1. Grover, L. K. (1996). "A fast quantum mechanical algorithm for database search." Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 212–219.
2. Bennett, C. H., Bernstein, E., Brassard, G., & Vazirani, U. (1997). "Strengths and weaknesses of quantum computing." SIAM Journal on Computing, 26(5), pp. 1510–1523. (BBBV lower bound — proves Grover's O(√N) is optimal.)
3. Grassl, M., Langenberg, B., Roetteler, M., & Steinwandt, R. (2016). "Applying Grover's algorithm to AES: Quantum resource estimates." Post-Quantum Cryptography (PQCrypto 2016), LNCS 9606, pp. 29–43. (Source for AES circuit depth and qubit cost estimates.)
4. NIST (2024). CNSA 2.0 and post-quantum cryptography transition guidance. Recommends AES-256 for post-quantum symmetric security.
5. Nielsen, M. A. & Chuang, I. L. (2010). Quantum Computation and Quantum Information. Cambridge University Press. (Standard reference for amplitude amplification.)

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