lib-q-prf

Legendre and Gold (power-residue) pseudorandom functions over prime fields (\mathbb{F}_p), using safe-prime pilot moduli and constant-time arithmetic via crypto_bigint (modular::FixedMontyForm with MontyParams<U256> / MontyParams<U512>).

Scope

• Legendre PRF: (L_K(x)=\left(\frac{x+K}{p}\right)) with explicit PrfError::ZeroInput when (x+K\equiv 0 \pmod p).
• Gold PRF: (\mathrm{Gold}_k(x)=(k+x)^g \bmod p) with pilot (g=(p-1)/2) for safe primes (p=2q+1).
• Key derivation: domain-separated SHAKE256 expansion into ([1,p)) (see shake.rs).

This crate does not implement full anonymous ring signatures; lib-q-ring-sig may compose these PRFs behind the pilot-insecure-prf-transcript feature for non-shipping transcript experiments (see that crate’s module docs).

Features

crypto-bigint/alloc is intentionally not enabled: field elements use fixed-width U256 / U512 only.

Tests and KATs

• tests/reference_vectors.txt — hex KATs; regenerate with scripts/gen_prf_kat.py (requires SymPy).
• SHA-256 fingerprints of modulus encodings catch typos in params.rs.

Documentation

See DESIGN.md for assumptions, extension-field caveats, and safe-prime provenance.