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verifier.rs
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verifier.rs
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use ff::Field;
use super::super::{
commitment::{Guard, Params, MSM},
Error,
};
use super::{
construct_intermediate_sets, ChallengeX1, ChallengeX2, ChallengeX3, ChallengeX4,
CommitmentReference, Query, VerifierQuery,
};
use crate::arithmetic::{eval_polynomial, lagrange_interpolate, CurveAffine};
use crate::transcript::{EncodedChallenge, TranscriptRead};
/// Verify a multi-opening proof
pub fn verify_proof<
'r,
'params: 'r,
I,
C: CurveAffine,
E: EncodedChallenge<C>,
T: TranscriptRead<C, E>,
>(
params: &'params Params<C>,
transcript: &mut T,
queries: I,
mut msm: MSM<'params, C>,
) -> Result<Guard<'params, C, E>, Error>
where
I: IntoIterator<Item = VerifierQuery<'r, 'params, C>> + Clone,
{
// Sample x_1 for compressing openings at the same point sets together
let x_1: ChallengeX1<_> = transcript.squeeze_challenge_scalar();
// Sample a challenge x_2 for keeping the multi-point quotient
// polynomial terms linearly independent.
let x_2: ChallengeX2<_> = transcript.squeeze_challenge_scalar();
let (commitment_map, point_sets) = construct_intermediate_sets(queries);
// Compress the commitments and expected evaluations at x together.
// using the challenge x_1
let mut q_commitments: Vec<_> = vec![
(params.empty_msm(), C::Scalar::ONE); // (accumulator, next x_1 power).
point_sets.len()];
// A vec of vecs of evals. The outer vec corresponds to the point set,
// while the inner vec corresponds to the points in a particular set.
let mut q_eval_sets = Vec::with_capacity(point_sets.len());
for point_set in point_sets.iter() {
q_eval_sets.push(vec![C::Scalar::ZERO; point_set.len()]);
}
{
let mut accumulate = |set_idx: usize, new_commitment, evals: Vec<C::Scalar>| {
let (q_commitment, x_1_power) = &mut q_commitments[set_idx];
match new_commitment {
CommitmentReference::Commitment(c) => {
q_commitment.append_term(*x_1_power, *c);
}
CommitmentReference::MSM(msm) => {
let mut msm = msm.clone();
msm.scale(*x_1_power);
q_commitment.add_msm(&msm);
}
}
for (eval, set_eval) in evals.iter().zip(q_eval_sets[set_idx].iter_mut()) {
*set_eval += (*eval) * (*x_1_power);
}
*x_1_power *= *x_1;
};
// Each commitment corresponds to evaluations at a set of points.
// For each set, we collapse each commitment's evals pointwise.
// Run in order of increasing x_1 powers.
for commitment_data in commitment_map.into_iter().rev() {
accumulate(
commitment_data.set_index, // set_idx,
commitment_data.commitment, // commitment,
commitment_data.evals, // evals
);
}
}
// Obtain the commitment to the multi-point quotient polynomial f(X).
let q_prime_commitment = transcript.read_point().map_err(|_| Error::SamplingError)?;
// Sample a challenge x_3 for checking that f(X) was committed to
// correctly.
let x_3: ChallengeX3<_> = transcript.squeeze_challenge_scalar();
// u is a vector containing the evaluations of the Q polynomial
// commitments at x_3
let mut u = Vec::with_capacity(q_eval_sets.len());
for _ in 0..q_eval_sets.len() {
u.push(transcript.read_scalar().map_err(|_| Error::SamplingError)?);
}
// We can compute the expected msm_eval at x_3 using the u provided
// by the prover and from x_2
let msm_eval = point_sets
.iter()
.zip(q_eval_sets.iter())
.zip(u.iter())
.fold(
C::Scalar::ZERO,
|msm_eval, ((points, evals), proof_eval)| {
let r_poly = lagrange_interpolate(points, evals);
let r_eval = eval_polynomial(&r_poly, *x_3);
let eval = points.iter().fold(*proof_eval - &r_eval, |eval, point| {
eval * &(*x_3 - point).invert().unwrap()
});
msm_eval * &(*x_2) + &eval
},
);
// Sample a challenge x_4 that we will use to collapse the openings of
// the various remaining polynomials at x_3 together.
let x_4: ChallengeX4<_> = transcript.squeeze_challenge_scalar();
// Compute the final commitment that has to be opened
msm.append_term(C::Scalar::ONE, q_prime_commitment);
let (msm, v) = q_commitments.into_iter().zip(u.iter()).fold(
(msm, msm_eval),
|(mut msm, msm_eval), ((q_commitment, _), q_eval)| {
msm.scale(*x_4);
msm.add_msm(&q_commitment);
(msm, msm_eval * &(*x_4) + q_eval)
},
);
// Verify the opening proof
super::commitment::verify_proof(params, msm, transcript, *x_3, v)
}
impl<'a, 'b, C: CurveAffine> Query<C::Scalar> for VerifierQuery<'a, 'b, C> {
type Commitment = CommitmentReference<'a, 'b, C>;
type Eval = C::Scalar;
fn get_point(&self) -> C::Scalar {
self.point
}
fn get_eval(&self) -> C::Scalar {
self.eval
}
fn get_commitment(&self) -> Self::Commitment {
self.commitment
}
}