// Copyright (c) 2023 Espresso Systems (espressosys.com)
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// This file is part of the HyperPlonk library.
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// You should have received a copy of the MIT License
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// along with the HyperPlonk library. If not, see <https://mit-license.org/>.
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//! Main module for the Permutation Check protocol
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use self::util::computer_nums_and_denoms;
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use crate::{
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pcs::PolynomialCommitmentScheme,
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poly_iop::{errors::PolyIOPErrors, prelude::ProductCheck, PolyIOP},
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};
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use ark_ec::pairing::Pairing;
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use ark_poly::DenseMultilinearExtension;
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use ark_std::{end_timer, start_timer};
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use std::sync::Arc;
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use transcript::IOPTranscript;
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/// A permutation subclaim consists of
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/// - the SubClaim from the ProductCheck
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/// - Challenges beta and gamma
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#[derive(Clone, Debug, Default, PartialEq)]
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pub struct PermutationCheckSubClaim<E, PCS, PC>
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where
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E: Pairing,
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PC: ProductCheck<E, PCS>,
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PCS: PolynomialCommitmentScheme<E>,
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{
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/// the SubClaim from the ProductCheck
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pub product_check_sub_claim: PC::ProductCheckSubClaim,
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/// Challenges beta and gamma
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pub challenges: (E::ScalarField, E::ScalarField),
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}
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pub mod util;
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/// A PermutationCheck w.r.t. `(fs, gs, perms)`
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/// proves that (g1, ..., gk) is a permutation of (f1, ..., fk) under
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/// permutation `(p1, ..., pk)`
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/// It is derived from ProductCheck.
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///
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/// A Permutation Check IOP takes the following steps:
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///
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/// Inputs:
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/// - fs = (f1, ..., fk)
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/// - gs = (g1, ..., gk)
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/// - permutation oracles = (p1, ..., pk)
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pub trait PermutationCheck<E, PCS>: ProductCheck<E, PCS>
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where
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E: Pairing,
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PCS: PolynomialCommitmentScheme<E>,
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{
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type PermutationCheckSubClaim;
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type PermutationProof;
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/// Initialize the system with a transcript
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///
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/// This function is optional -- in the case where a PermutationCheck is
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/// an building block for a more complex protocol, the transcript
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/// may be initialized by this complex protocol, and passed to the
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/// PermutationCheck prover/verifier.
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fn init_transcript() -> Self::Transcript;
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/// Inputs:
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/// - fs = (f1, ..., fk)
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/// - gs = (g1, ..., gk)
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/// - permutation oracles = (p1, ..., pk)
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/// Outputs:
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/// - a permutation check proof proving that gs is a permutation of fs under
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/// permutation
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/// - the product polynomial built during product check
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/// - the fractional polynomial built during product check
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///
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/// Cost: O(N)
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#[allow(clippy::type_complexity)]
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fn prove(
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pcs_param: &PCS::ProverParam,
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fxs: &[Self::MultilinearExtension],
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gxs: &[Self::MultilinearExtension],
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perms: &[Self::MultilinearExtension],
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transcript: &mut IOPTranscript<E::ScalarField>,
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) -> Result<
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(
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Self::PermutationProof,
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Self::MultilinearExtension,
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Self::MultilinearExtension,
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),
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PolyIOPErrors,
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>;
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/// Verify that (g1, ..., gk) is a permutation of
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/// (f1, ..., fk) over the permutation oracles (perm1, ..., permk)
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fn verify(
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proof: &Self::PermutationProof,
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aux_info: &Self::VPAuxInfo,
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transcript: &mut Self::Transcript,
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) -> Result<Self::PermutationCheckSubClaim, PolyIOPErrors>;
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}
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impl<E, PCS> PermutationCheck<E, PCS> for PolyIOP<E::ScalarField>
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where
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E: Pairing,
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PCS: PolynomialCommitmentScheme<E, Polynomial = Arc<DenseMultilinearExtension<E::ScalarField>>>,
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{
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type PermutationCheckSubClaim = PermutationCheckSubClaim<E, PCS, Self>;
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type PermutationProof = Self::ProductCheckProof;
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fn init_transcript() -> Self::Transcript {
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IOPTranscript::<E::ScalarField>::new(b"Initializing PermutationCheck transcript")
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}
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fn prove(
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pcs_param: &PCS::ProverParam,
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fxs: &[Self::MultilinearExtension],
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gxs: &[Self::MultilinearExtension],
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perms: &[Self::MultilinearExtension],
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transcript: &mut IOPTranscript<E::ScalarField>,
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) -> Result<
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(
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Self::PermutationProof,
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Self::MultilinearExtension,
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Self::MultilinearExtension,
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),
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PolyIOPErrors,
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> {
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let start = start_timer!(|| "Permutation check prove");
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if fxs.is_empty() {
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return Err(PolyIOPErrors::InvalidParameters("fxs is empty".to_string()));
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}
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if (fxs.len() != gxs.len()) || (fxs.len() != perms.len()) {
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return Err(PolyIOPErrors::InvalidProof(format!(
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"fxs.len() = {}, gxs.len() = {}, perms.len() = {}",
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fxs.len(),
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gxs.len(),
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perms.len(),
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)));
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}
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let num_vars = fxs[0].num_vars;
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for ((fx, gx), perm) in fxs.iter().zip(gxs.iter()).zip(perms.iter()) {
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if (fx.num_vars != num_vars) || (gx.num_vars != num_vars) || (perm.num_vars != num_vars)
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{
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return Err(PolyIOPErrors::InvalidParameters(
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"number of variables unmatched".to_string(),
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));
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}
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}
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// generate challenge `beta` and `gamma` from current transcript
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let beta = transcript.get_and_append_challenge(b"beta")?;
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let gamma = transcript.get_and_append_challenge(b"gamma")?;
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let (numerators, denominators) = computer_nums_and_denoms(&beta, &gamma, fxs, gxs, perms)?;
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// invoke product check on numerator and denominator
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let (proof, prod_poly, frac_poly) = <Self as ProductCheck<E, PCS>>::prove(
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pcs_param,
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&numerators,
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&denominators,
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transcript,
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)?;
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end_timer!(start);
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Ok((proof, prod_poly, frac_poly))
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}
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fn verify(
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proof: &Self::PermutationProof,
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aux_info: &Self::VPAuxInfo,
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transcript: &mut Self::Transcript,
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) -> Result<Self::PermutationCheckSubClaim, PolyIOPErrors> {
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let start = start_timer!(|| "Permutation check verify");
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let beta = transcript.get_and_append_challenge(b"beta")?;
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let gamma = transcript.get_and_append_challenge(b"gamma")?;
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// invoke the zero check on the iop_proof
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let product_check_sub_claim =
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<Self as ProductCheck<E, PCS>>::verify(proof, aux_info, transcript)?;
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end_timer!(start);
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Ok(PermutationCheckSubClaim {
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product_check_sub_claim,
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challenges: (beta, gamma),
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})
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}
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}
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#[cfg(test)]
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mod test {
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use super::PermutationCheck;
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use crate::{
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pcs::{prelude::MultilinearKzgPCS, PolynomialCommitmentScheme},
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poly_iop::{errors::PolyIOPErrors, PolyIOP},
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};
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use arithmetic::{evaluate_opt, identity_permutation_mles, random_permutation_mles, VPAuxInfo};
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use ark_bls12_381::Bls12_381;
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use ark_ec::pairing::Pairing;
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use ark_poly::{DenseMultilinearExtension, MultilinearExtension};
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use ark_std::test_rng;
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use std::{marker::PhantomData, sync::Arc};
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type Kzg = MultilinearKzgPCS<Bls12_381>;
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fn test_permutation_check_helper<E, PCS>(
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pcs_param: &PCS::ProverParam,
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fxs: &[Arc<DenseMultilinearExtension<E::ScalarField>>],
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gxs: &[Arc<DenseMultilinearExtension<E::ScalarField>>],
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perms: &[Arc<DenseMultilinearExtension<E::ScalarField>>],
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) -> Result<(), PolyIOPErrors>
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where
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E: Pairing,
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PCS: PolynomialCommitmentScheme<
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E,
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Polynomial = Arc<DenseMultilinearExtension<E::ScalarField>>,
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>,
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{
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let nv = fxs[0].num_vars;
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// what's AuxInfo used for?
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let poly_info = VPAuxInfo {
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max_degree: fxs.len() + 1,
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num_variables: nv,
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phantom: PhantomData::default(),
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};
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// prover
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let mut transcript =
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<PolyIOP<E::ScalarField> as PermutationCheck<E, PCS>>::init_transcript();
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transcript.append_message(b"testing", b"initializing transcript for testing")?;
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let (proof, prod_x, _frac_poly) =
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<PolyIOP<E::ScalarField> as PermutationCheck<E, PCS>>::prove(
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pcs_param,
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fxs,
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gxs,
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perms,
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&mut transcript,
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)?;
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// verifier
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let mut transcript =
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<PolyIOP<E::ScalarField> as PermutationCheck<E, PCS>>::init_transcript();
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transcript.append_message(b"testing", b"initializing transcript for testing")?;
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let perm_check_sub_claim = <PolyIOP<E::ScalarField> as PermutationCheck<E, PCS>>::verify(
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&proof,
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&poly_info,
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&mut transcript,
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)?;
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// check product subclaim
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if evaluate_opt(
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&prod_x,
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&perm_check_sub_claim.product_check_sub_claim.final_query.0,
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) != perm_check_sub_claim.product_check_sub_claim.final_query.1
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{
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return Err(PolyIOPErrors::InvalidVerifier("wrong subclaim".to_string()));
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};
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Ok(())
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}
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fn test_permutation_check(nv: usize) -> Result<(), PolyIOPErrors> {
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let mut rng = test_rng();
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let srs = MultilinearKzgPCS::<Bls12_381>::gen_srs_for_testing(&mut rng, nv)?;
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let (pcs_param, _) = MultilinearKzgPCS::<Bls12_381>::trim(&srs, None, Some(nv))?;
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let id_perms = identity_permutation_mles(nv, 2);
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{
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// good path: (w1, w2) is a permutation of (w1, w2) itself under the identify
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// map
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let ws = vec![
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Arc::new(DenseMultilinearExtension::rand(nv, &mut rng)),
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Arc::new(DenseMultilinearExtension::rand(nv, &mut rng)),
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];
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// perms is the identity map
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test_permutation_check_helper::<Bls12_381, Kzg>(&pcs_param, &ws, &ws, &id_perms)?;
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}
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{
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// good path: f = (w1, w2) is a permutation of g = (w2, w1) itself under a map
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let mut fs = vec![
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Arc::new(DenseMultilinearExtension::rand(nv, &mut rng)),
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Arc::new(DenseMultilinearExtension::rand(nv, &mut rng)),
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];
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let gs = fs.clone();
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fs.reverse();
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// perms is the reverse identity map
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let mut perms = id_perms.clone();
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perms.reverse();
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test_permutation_check_helper::<Bls12_381, Kzg>(&pcs_param, &fs, &gs, &perms)?;
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}
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{
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// bad path 1: w is a not permutation of w itself under a random map
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let ws = vec![
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Arc::new(DenseMultilinearExtension::rand(nv, &mut rng)),
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Arc::new(DenseMultilinearExtension::rand(nv, &mut rng)),
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];
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// perms is a random map
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let perms = random_permutation_mles(nv, 2, &mut rng);
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assert!(
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test_permutation_check_helper::<Bls12_381, Kzg>(&pcs_param, &ws, &ws, &perms)
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.is_err()
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);
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}
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{
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// bad path 2: f is a not permutation of g under a identity map
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let fs = vec![
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Arc::new(DenseMultilinearExtension::rand(nv, &mut rng)),
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Arc::new(DenseMultilinearExtension::rand(nv, &mut rng)),
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];
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let gs = vec![
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Arc::new(DenseMultilinearExtension::rand(nv, &mut rng)),
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Arc::new(DenseMultilinearExtension::rand(nv, &mut rng)),
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];
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// s_perm is the identity map
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assert!(test_permutation_check_helper::<Bls12_381, Kzg>(
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&pcs_param, &fs, &gs, &id_perms
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)
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.is_err());
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}
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Ok(())
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}
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#[test]
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fn test_trivial_polynomial() -> Result<(), PolyIOPErrors> {
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test_permutation_check(1)
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}
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#[test]
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fn test_normal_polynomial() -> Result<(), PolyIOPErrors> {
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test_permutation_check(5)
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}
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#[test]
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fn zero_polynomial_should_error() -> Result<(), PolyIOPErrors> {
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assert!(test_permutation_check(0).is_err());
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Ok(())
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}
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}
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