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Vanishing polynomial evaluator #35

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Feb 22, 2022
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Vanishing polynomial evaluator #35

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22 changes: 2 additions & 20 deletions halo2_proofs/src/arithmetic.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -402,26 +402,8 @@ pub fn lagrange_interpolate<F: FieldExt>(points: &[F], evals: &[F]) -> Vec<F> {
}
}

/// Given roots [a_0, a_1, ... a_n] returns vanishing polynomials
/// (x - a_0) * (x - a_1) * ... * (x - a_n)
pub fn vanishing_polynomial<F: FieldExt>(roots: &[F]) -> Vec<F> {
fn mul_with<F: FieldExt>(coeffs: Vec<F>, root: &F) -> Vec<F> {
let mut ret = vec![F::zero(); coeffs.len() + 1];

for (i, coeff) in coeffs.iter().enumerate() {
ret[i] -= *coeff * root;
ret[i + 1] += coeff;
}

ret
}

let mut coeffs = vec![F::one()];
for root in roots {
coeffs = mul_with(coeffs, root);
}

coeffs
pub(crate) fn evaluate_vanishing_polynomial<F: FieldExt>(roots: &[F], z: F) -> F {
roots.iter().fold(F::one(), |acc, point| (z - point) * acc)
}

#[cfg(test)]
Expand Down
11 changes: 5 additions & 6 deletions halo2_proofs/src/poly/multiopen/shplonk/prover.rs
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Expand Up @@ -2,8 +2,8 @@ use super::{
construct_intermediate_sets, ChallengeU, ChallengeV, ChallengeY, Commitment, Query, RotationSet,
};
use crate::arithmetic::{
eval_polynomial, kate_division, lagrange_interpolate, vanishing_polynomial, CurveAffine,
FieldExt,
eval_polynomial, evaluate_vanishing_polynomial, kate_division, lagrange_interpolate,
CurveAffine, FieldExt,
};
use crate::poly::multiopen::ProverQuery;
use crate::poly::{commitment::Params, Coeff, Error, Polynomial};
Expand Down Expand Up @@ -156,14 +156,13 @@ where
transcript.write_point(h)?;
let u: ChallengeU<_> = transcript.squeeze_challenge_scalar();

let zt_x = vanishing_polynomial(&super_point_set[..]);
let zt_eval = eval_polynomial(&zt_x[..], *u);
let zt_eval = evaluate_vanishing_polynomial(&super_point_set[..], *u);

let linearisation_contribution =
|rotation_set: RotationSetExtension<C>| -> Polynomial<C::Scalar, Coeff> {
// calculate difference vanishing polynomial evaluation
let z_diff = vanishing_polynomial(&rotation_set.diffs[..]);
let z_i = eval_polynomial(&z_diff[..], *u);

let z_i = evaluate_vanishing_polynomial(&rotation_set.diffs[..], *u);

// inner linearisation contibutions are
// [P_i_0(X) - r_i_0, P_i_1(X) - r_i_1, ... ] where
Expand Down
10 changes: 4 additions & 6 deletions halo2_proofs/src/poly/multiopen/shplonk/verifier.rs
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
use super::{construct_intermediate_sets, ChallengeU, ChallengeV, ChallengeY};
use crate::arithmetic::{
eval_polynomial, lagrange_interpolate, vanishing_polynomial, CurveAffine, Engine, FieldExt,
MillerLoopResult, MultiMillerLoop,
eval_polynomial, evaluate_vanishing_polynomial, lagrange_interpolate, CurveAffine, Engine,
FieldExt, MillerLoopResult, MultiMillerLoop,
};
use crate::poly::{
commitment::{Params, ParamsVerifier},
Expand Down Expand Up @@ -47,14 +47,12 @@ where
let u: ChallengeU<_> = transcript.squeeze_challenge_scalar();
let h2 = transcript.read_point().map_err(|_| Error::SamplingError)?;

let zt_x = vanishing_polynomial(&super_point_set[..]);
let zt_eval = eval_polynomial(&zt_x[..], *u);
let zt_eval = evaluate_vanishing_polynomial(&super_point_set[..], *u);

let mut outer_msm: PreMSM<C> = PreMSM::new();

for rotation_set in rotation_sets.iter() {
let z_diff = vanishing_polynomial(&rotation_set.diffs[..]);
let z_i = eval_polynomial(&z_diff[..], *u);
let z_i = evaluate_vanishing_polynomial(&rotation_set.diffs[..], *u);

let mut inner_msm: ProjectiveMSM<C> = ProjectiveMSM::new();
for commitment_data in rotation_set.commitments.iter() {
Expand Down