mirror of https://github.com/zcash/halo2.git
372 lines
14 KiB
Rust
372 lines
14 KiB
Rust
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use ff::Field;
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use std::iter;
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use super::Proof;
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use crate::{
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arithmetic::{eval_polynomial, parallelize, BatchInvert, Curve, CurveAffine, FieldExt},
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plonk::{Error, ProvingKey},
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poly::{
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commitment::{Blind, Params},
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multiopen::ProverQuery,
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Coeff, ExtendedLagrangeCoeff, LagrangeCoeff, Polynomial, Rotation,
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},
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transcript::{Hasher, Transcript},
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};
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#[derive(Clone)]
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pub(crate) struct Committed<C: CurveAffine> {
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permutation_product_polys: Vec<Polynomial<C::Scalar, Coeff>>,
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permutation_product_cosets: Vec<Polynomial<C::Scalar, ExtendedLagrangeCoeff>>,
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permutation_product_cosets_inv: Vec<Polynomial<C::Scalar, ExtendedLagrangeCoeff>>,
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permutation_product_blinds: Vec<Blind<C::Scalar>>,
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permutation_product_commitments: Vec<C>,
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}
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pub(crate) struct Constructed<C: CurveAffine> {
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permutation_product_polys: Vec<Polynomial<C::Scalar, Coeff>>,
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permutation_product_blinds: Vec<Blind<C::Scalar>>,
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permutation_product_commitments: Vec<C>,
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}
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pub(crate) struct Evaluated<C: CurveAffine> {
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constructed: Constructed<C>,
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permutation_product_evals: Vec<C::Scalar>,
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permutation_product_inv_evals: Vec<C::Scalar>,
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permutation_evals: Vec<Vec<C::Scalar>>,
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}
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impl<C: CurveAffine> Proof<C> {
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pub(crate) fn commit<HBase: Hasher<C::Base>, HScalar: Hasher<C::Scalar>>(
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params: &Params<C>,
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pk: &ProvingKey<C>,
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advice: &[Polynomial<C::Scalar, LagrangeCoeff>],
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x_0: C::Scalar,
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x_1: C::Scalar,
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transcript: &mut Transcript<C, HBase, HScalar>,
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) -> Result<Committed<C>, Error> {
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let domain = &pk.vk.domain;
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// Compute permutation product polynomial commitment
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let mut permutation_product_polys = vec![];
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let mut permutation_product_cosets = vec![];
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let mut permutation_product_cosets_inv = vec![];
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let mut permutation_product_commitments_projective = vec![];
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let mut permutation_product_blinds = vec![];
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// Iterate over each permutation
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let mut permutation_modified_advice = pk
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.vk
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.cs
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.permutations
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.iter()
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.zip(pk.permutations.iter())
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// Goal is to compute the products of fractions
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//
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// (p_j(\omega^i) + \delta^j \omega^i \beta + \gamma) /
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// (p_j(\omega^i) + \beta s_j(\omega^i) + \gamma)
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//
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// where p_j(X) is the jth advice column in this permutation,
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// and i is the ith row of the column.
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.map(|(columns, permuted_values)| {
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let mut modified_advice = vec![C::Scalar::one(); params.n as usize];
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// Iterate over each column of the permutation
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for (&column, permuted_column_values) in columns.iter().zip(permuted_values.iter())
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{
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parallelize(&mut modified_advice, |modified_advice, start| {
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for ((modified_advice, advice_value), permuted_advice_value) in
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modified_advice
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.iter_mut()
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.zip(advice[column.index()][start..].iter())
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.zip(permuted_column_values[start..].iter())
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{
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*modified_advice *=
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&(x_0 * permuted_advice_value + &x_1 + advice_value);
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}
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});
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}
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modified_advice
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})
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.collect::<Vec<_>>();
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// Batch invert to obtain the denominators for the permutation product
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// polynomials
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permutation_modified_advice
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.iter_mut()
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.flat_map(|v| v.iter_mut())
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.batch_invert();
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for (columns, mut modified_advice) in pk
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.vk
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.cs
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.permutations
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.iter()
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.zip(permutation_modified_advice.into_iter())
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{
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// Iterate over each column again, this time finishing the computation
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// of the entire fraction by computing the numerators
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let mut deltaomega = C::Scalar::one();
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for &column in columns.iter() {
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let omega = domain.get_omega();
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parallelize(&mut modified_advice, |modified_advice, start| {
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let mut deltaomega = deltaomega * &omega.pow_vartime(&[start as u64, 0, 0, 0]);
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for (modified_advice, advice_value) in modified_advice
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.iter_mut()
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.zip(advice[column.index()][start..].iter())
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{
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// Multiply by p_j(\omega^i) + \delta^j \omega^i \beta
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*modified_advice *= &(deltaomega * &x_0 + &x_1 + advice_value);
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deltaomega *= ω
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}
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});
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deltaomega *= &C::Scalar::DELTA;
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}
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// The modified_advice vector is a vector of products of fractions
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// of the form
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//
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// (p_j(\omega^i) + \delta^j \omega^i \beta + \gamma) /
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// (p_j(\omega^i) + \beta s_j(\omega^i) + \gamma)
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//
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// where i is the index into modified_advice, for the jth column in
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// the permutation
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// Compute the evaluations of the permutation product polynomial
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// over our domain, starting with z[0] = 1
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let mut z = vec![C::Scalar::one()];
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for row in 1..(params.n as usize) {
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let mut tmp = z[row - 1];
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tmp *= &modified_advice[row];
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z.push(tmp);
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}
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let z = domain.lagrange_from_vec(z);
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let blind = Blind(C::Scalar::rand());
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permutation_product_commitments_projective.push(params.commit_lagrange(&z, blind));
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permutation_product_blinds.push(blind);
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let z = domain.lagrange_to_coeff(z);
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permutation_product_polys.push(z.clone());
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permutation_product_cosets
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.push(domain.coeff_to_extended(z.clone(), Rotation::default()));
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permutation_product_cosets_inv.push(domain.coeff_to_extended(z, Rotation(-1)));
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}
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let mut permutation_product_commitments =
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vec![C::zero(); permutation_product_commitments_projective.len()];
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C::Projective::batch_to_affine(
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&permutation_product_commitments_projective,
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&mut permutation_product_commitments,
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);
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let permutation_product_commitments = permutation_product_commitments;
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drop(permutation_product_commitments_projective);
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// Hash each permutation product commitment
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for c in &permutation_product_commitments {
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transcript
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.absorb_point(c)
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.map_err(|_| Error::TranscriptError)?;
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}
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Ok(Committed {
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permutation_product_polys,
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permutation_product_cosets,
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permutation_product_cosets_inv,
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permutation_product_blinds,
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permutation_product_commitments,
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})
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}
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}
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impl<C: CurveAffine> Committed<C> {
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pub(crate) fn construct<'a>(
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self,
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pk: &'a ProvingKey<C>,
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advice_cosets: &'a [Polynomial<C::Scalar, ExtendedLagrangeCoeff>],
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x_0: C::Scalar,
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x_1: C::Scalar,
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) -> Result<
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(
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Constructed<C>,
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impl Iterator<Item = Polynomial<C::Scalar, ExtendedLagrangeCoeff>> + 'a,
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),
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Error,
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> {
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let domain = &pk.vk.domain;
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let permutation_product_cosets_owned = self.permutation_product_cosets.clone();
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let permutation_product_cosets = self.permutation_product_cosets;
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let permutation_product_cosets_inv = self.permutation_product_cosets_inv;
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let expressions = iter::empty()
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// l_0(X) * (1 - z(X)) = 0
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.chain(
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permutation_product_cosets_owned
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.into_iter()
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.map(move |coset| Polynomial::one_minus(coset) * &pk.l0),
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)
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// z(X) \prod (p(X) + \beta s_i(X) + \gamma) - z(omega^{-1} X) \prod (p(X) + \delta^i \beta X + \gamma)
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.chain(pk.vk.cs.permutations.iter().enumerate().map(
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move |(permutation_index, columns)| {
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let mut left = permutation_product_cosets[permutation_index].clone();
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for (advice, permutation) in columns
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.iter()
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.map(|&column| &advice_cosets[pk.vk.cs.get_advice_query_index(column, 0)])
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.zip(pk.permutation_cosets[permutation_index].iter())
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{
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parallelize(&mut left, |left, start| {
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for ((left, advice), permutation) in left
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.iter_mut()
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.zip(advice[start..].iter())
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.zip(permutation[start..].iter())
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{
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*left *= &(*advice + &(x_0 * permutation) + &x_1);
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}
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});
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}
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let mut right = permutation_product_cosets_inv[permutation_index].clone();
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let mut current_delta = x_0 * &C::Scalar::ZETA;
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let step = domain.get_extended_omega();
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for advice in columns
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.iter()
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.map(|&column| &advice_cosets[pk.vk.cs.get_advice_query_index(column, 0)])
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{
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parallelize(&mut right, move |right, start| {
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let mut beta_term =
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current_delta * &step.pow_vartime(&[start as u64, 0, 0, 0]);
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for (right, advice) in right.iter_mut().zip(advice[start..].iter()) {
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*right *= &(*advice + &beta_term + &x_1);
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beta_term *= &step;
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}
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});
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current_delta *= &C::Scalar::DELTA;
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}
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left - &right
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},
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));
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Ok((
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Constructed {
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permutation_product_polys: self.permutation_product_polys,
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permutation_product_blinds: self.permutation_product_blinds,
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permutation_product_commitments: self.permutation_product_commitments,
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},
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expressions,
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))
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}
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}
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impl<C: CurveAffine> Constructed<C> {
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pub(crate) fn evaluate<HBase: Hasher<C::Base>, HScalar: Hasher<C::Scalar>>(
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self,
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pk: &ProvingKey<C>,
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x_3: C::Scalar,
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transcript: &mut Transcript<C, HBase, HScalar>,
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) -> Evaluated<C> {
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let domain = &pk.vk.domain;
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let permutation_product_evals: Vec<C::Scalar> = self
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.permutation_product_polys
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.iter()
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.map(|poly| eval_polynomial(poly, x_3))
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.collect();
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let permutation_product_inv_evals: Vec<C::Scalar> = self
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.permutation_product_polys
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.iter()
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.map(|poly| eval_polynomial(poly, domain.rotate_omega(x_3, Rotation(-1))))
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.collect();
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let permutation_evals: Vec<Vec<C::Scalar>> = pk
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.permutation_polys
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.iter()
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.map(|polys| {
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polys
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.iter()
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.map(|poly| eval_polynomial(poly, x_3))
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.collect()
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})
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.collect();
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// Hash each advice evaluation
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for eval in permutation_product_evals
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.iter()
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.chain(permutation_product_inv_evals.iter())
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.chain(permutation_evals.iter().flat_map(|evals| evals.iter()))
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{
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transcript.absorb_scalar(*eval);
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}
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Evaluated {
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constructed: self,
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permutation_product_evals,
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permutation_product_inv_evals,
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permutation_evals,
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}
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}
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}
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impl<C: CurveAffine> Evaluated<C> {
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pub fn open<'a>(
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&'a self,
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pk: &'a ProvingKey<C>,
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x_3: C::Scalar,
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) -> impl Iterator<Item = ProverQuery<'a, C>> + Clone {
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let x_3_inv = pk.vk.domain.rotate_omega(x_3, Rotation(-1));
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iter::empty()
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// Open permutation product commitments at x_3
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.chain(
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self.constructed
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.permutation_product_polys
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.iter()
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.zip(self.constructed.permutation_product_blinds.iter())
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.zip(self.permutation_product_evals.iter())
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.map(move |((poly, blind), eval)| ProverQuery {
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point: x_3,
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poly,
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blind: *blind,
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eval: *eval,
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}),
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)
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// Open permutation polynomial commitments at x_3
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.chain(
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pk.permutation_polys
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.iter()
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.zip(self.permutation_evals.iter())
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.flat_map(|(polys, evals)| polys.iter().zip(evals.iter()))
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.map(move |(poly, eval)| ProverQuery {
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point: x_3,
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poly,
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blind: Blind::default(),
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eval: *eval,
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}),
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)
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// Open permutation product commitments at \omega^{-1} x_3
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.chain(
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self.constructed
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.permutation_product_polys
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.iter()
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.zip(self.constructed.permutation_product_blinds.iter())
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.zip(self.permutation_product_inv_evals.iter())
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.map(move |((poly, blind), eval)| ProverQuery {
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point: x_3_inv,
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poly,
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blind: *blind,
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eval: *eval,
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}),
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)
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}
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pub(crate) fn build(self) -> Proof<C> {
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Proof {
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permutation_product_commitments: self.constructed.permutation_product_commitments,
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permutation_product_evals: self.permutation_product_evals,
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permutation_product_inv_evals: self.permutation_product_inv_evals,
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permutation_evals: self.permutation_evals,
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}
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}
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}
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