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This commit is contained in:
wborgeaud 2021-05-05 18:32:24 +02:00
parent 1f3f7d5b70
commit 5e06c014c8
1 changed files with 27 additions and 17 deletions
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44
src/polynomial/commitment.rs
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@ -73,35 +73,21 @@ impl<F: Field> ListPolynomialCommitment<F> {
challenger.observe_hash(&self.merkle_tree.root);
let alpha = challenger.get_challenge();
// Scale polynomials by `alpha`.
let scaled_poly = self
.polynomials
.iter()
.rev()
.map(|p| p.clone().into())
.fold(Polynomial::empty(), |acc, p| acc.scalar_mul(alpha).add(&p));
// Scale evaluations by `alpha`.
let scaled_evals = evaluations
.iter()
.map(|e| reduce_with_powers(e, alpha))
.collect::<Vec<_>>();
let pairs = points
.iter()
.zip(&scaled_evals)
.map(|(&x, &e)| (x, e))
.collect::<Vec<_>>();
debug_assert!(pairs.iter().all(|&(x, e)| scaled_poly.eval(x) == e));
let quotient = Self::compute_quotient(points, &scaled_evals, &scaled_poly);
let interpolant: Polynomial<F> = interpolant(&pairs).into();
let denominator = points
.iter()
.fold(Polynomial::from(vec![F::ONE]), |acc, &x| {
acc.mul(&vec![-x, F::ONE].into())
});
let numerator = scaled_poly.add(&interpolant.neg());
let (mut quotient, rem) = numerator.polynomial_division(&denominator);
debug_assert!(rem.is_zero());
quotient.pad((quotient.degree() + 1).next_power_of_two());
let lde_quotient = PolynomialCoeffs::from(quotient.clone()).lde(self.fri_config.rate_bits);
let lde_quotient_values = lde_quotient
.clone()
@ -122,6 +108,30 @@ impl<F: Field> ListPolynomialCommitment<F> {
quotient_degree: quotient.len(),
}
}
/// Given `points=(x_i)`, `evals=(y_i)` and `poly=P` with `P(x_i)=y_i`, computes the polynomial
/// `Q=(P-I)/Z` where `I` interpolates `(x_i, y_i)` and `Z` is the vanishing polynomial on `(x_i)`.
fn compute_quotient(points: &[F], evals: &[F], poly: &Polynomial<F>) -> Polynomial<F> {
let pairs = points
.iter()
.zip(evals)
.map(|(&x, &e)| (x, e))
.collect::<Vec<_>>();
debug_assert!(pairs.iter().all(|&(x, e)| poly.eval(x) == e));
let interpolant: Polynomial<F> = interpolant(&pairs).into();
let denominator = points
.iter()
.fold(Polynomial::from(vec![F::ONE]), |acc, &x| {
acc.mul(&vec![-x, F::ONE].into())
});
let numerator = poly.add(&interpolant.neg());
let (mut quotient, rem) = numerator.polynomial_division(&denominator);
debug_assert!(rem.is_zero());
quotient.pad((quotient.degree() + 1).next_power_of_two());
quotient
}
}
pub struct OpeningProof<F: Field> {