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Merge pull request #3695 from kevaundray/kw/fix-kzg-multi-comment

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chore: Fixes and elaborates on comments for `compute_kzg_proof_multi`
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Hsiao-Wei Wang 2024-04-19 15:32:09 +09:00 committed by GitHub
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specs/_features/eip7594/polynomial-commitments-sampling.md
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@ -308,18 +308,26 @@ def compute_kzg_proof_multi_impl(
polynomial_coeff: PolynomialCoeff, polynomial_coeff: PolynomialCoeff,
zs: Sequence[BLSFieldElement]) -> Tuple[KZGProof, Sequence[BLSFieldElement]]: zs: Sequence[BLSFieldElement]) -> Tuple[KZGProof, Sequence[BLSFieldElement]]:
""" """
Helper function that computes multi-evaluation KZG proofs. Compute a KZG multi-evaluation proof for a set of `k` points.
This is done by committing to the following quotient polynomial:
Q(X) = f(X) - r(X) / Z(X)
Where:
- r(X) is the degree `k-1` polynomial that agrees with f(x) at all `k` points
- Z(X) is the degree `k` polynomial that evaluates to zero on all `k` points
""" """
# For all x_i, compute p(x_i) - p(z) # For all points, compute the evaluation of those points
ys = [evaluate_polynomialcoeff(polynomial_coeff, z) for z in zs] ys = [evaluate_polynomialcoeff(polynomial_coeff, z) for z in zs]
# Compute r(X)
interpolation_polynomial = interpolate_polynomialcoeff(zs, ys) interpolation_polynomial = interpolate_polynomialcoeff(zs, ys)
# Compute f(X) - r(X)
polynomial_shifted = add_polynomialcoeff(polynomial_coeff, neg_polynomialcoeff(interpolation_polynomial)) polynomial_shifted = add_polynomialcoeff(polynomial_coeff, neg_polynomialcoeff(interpolation_polynomial))
# For all x_i, compute (x_i - z) # Compute Z(X)
denominator_poly = vanishing_polynomialcoeff(zs) denominator_poly = vanishing_polynomialcoeff(zs)
# Compute the quotient polynomial directly in evaluation form # Compute the quotient polynomial directly in monomial form
quotient_polynomial = divide_polynomialcoeff(polynomial_shifted, denominator_poly) quotient_polynomial = divide_polynomialcoeff(polynomial_shifted, denominator_poly)
return KZGProof(g1_lincomb(KZG_SETUP_G1_MONOMIAL[:len(quotient_polynomial)], quotient_polynomial)), ys return KZGProof(g1_lincomb(KZG_SETUP_G1_MONOMIAL[:len(quotient_polynomial)], quotient_polynomial)), ys