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ArkLib.CommitmentScheme.KZG.Sampling

Sampling Support for KZG-Style Setup #

This file contains small shared probabilistic helpers used by KZG setup and its reductions.

Notation #

source
def Groups.sampleNonzeroZMod {p : outParam ℕ} [Fact (Nat.Prime p)] :
ProbComp (ZMod p)

Uniformly sample a nonzero element of ZMod p.

The implementation samples an index in {0, ..., p - 2} and shifts it by one, so the support is exactly the canonical representatives 1, ..., p - 1 modulo p.

Instances For
    source
    theorem Groups.simulateQ_randomOracle_sampleNonzeroZMod {p : outParam ℕ} [Fact (Nat.Prime p)] :
    (simulateQ OracleSpec.randomOracle sampleNonzeroZMod).run' ∅ = sampleNonzeroZMod

    Simulating the random oracle leaves the nonzero SRS trapdoor sampler unchanged.