2020-11-30 23:22:11 -08:00
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use super::super::{
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2021-02-10 06:57:08 -08:00
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circuit::Expression, ChallengeBeta, ChallengeGamma, ChallengeTheta, ChallengeX, Error,
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ProvingKey,
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};
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2020-12-23 12:03:31 -08:00
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use super::Argument;
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2020-11-30 23:22:11 -08:00
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use crate::{
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arithmetic::{eval_polynomial, parallelize, CurveAffine},
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poly::{
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self,
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2020-11-30 23:22:11 -08:00
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commitment::{Blind, Params},
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2020-12-01 00:46:11 -08:00
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multiopen::ProverQuery,
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2020-11-30 23:22:11 -08:00
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Coeff, EvaluationDomain, ExtendedLagrangeCoeff, LagrangeCoeff, Polynomial, Rotation,
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},
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2021-04-30 18:28:50 -07:00
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transcript::{EncodedChallenge, TranscriptWrite},
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2020-11-30 23:22:11 -08:00
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};
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2022-11-29 21:05:37 -08:00
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use ff::WithSmallOrderMulGroup;
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use group::{
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ff::{BatchInvert, Field},
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Curve,
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};
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2022-01-20 08:16:48 -08:00
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use rand_core::RngCore;
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2021-02-10 06:57:08 -08:00
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use std::{
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collections::BTreeMap,
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iter,
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ops::{Mul, MulAssign},
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};
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2020-11-30 22:53:20 -08:00
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2020-12-02 19:56:22 -08:00
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#[derive(Debug)]
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2022-01-13 04:17:48 -08:00
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pub(in crate::plonk) struct Permuted<C: CurveAffine, Ev> {
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compressed_input_expression: Polynomial<C::Scalar, LagrangeCoeff>,
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permuted_input_expression: Polynomial<C::Scalar, LagrangeCoeff>,
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compressed_input_coset: poly::Ast<Ev, C::Scalar, ExtendedLagrangeCoeff>,
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permuted_input_poly: Polynomial<C::Scalar, Coeff>,
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permuted_input_coset: poly::AstLeaf<Ev, ExtendedLagrangeCoeff>,
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permuted_input_blind: Blind<C::Scalar>,
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compressed_table_expression: Polynomial<C::Scalar, LagrangeCoeff>,
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compressed_table_coset: poly::Ast<Ev, C::Scalar, ExtendedLagrangeCoeff>,
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permuted_table_expression: Polynomial<C::Scalar, LagrangeCoeff>,
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permuted_table_poly: Polynomial<C::Scalar, Coeff>,
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permuted_table_coset: poly::AstLeaf<Ev, ExtendedLagrangeCoeff>,
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permuted_table_blind: Blind<C::Scalar>,
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}
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2020-12-02 19:56:22 -08:00
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#[derive(Debug)]
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pub(in crate::plonk) struct Committed<C: CurveAffine, Ev> {
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permuted: Permuted<C, Ev>,
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product_poly: Polynomial<C::Scalar, Coeff>,
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product_coset: poly::AstLeaf<Ev, ExtendedLagrangeCoeff>,
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2020-11-30 22:53:20 -08:00
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product_blind: Blind<C::Scalar>,
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}
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2020-12-03 17:18:28 -08:00
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pub(in crate::plonk) struct Constructed<C: CurveAffine> {
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2020-11-30 22:53:20 -08:00
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permuted_input_poly: Polynomial<C::Scalar, Coeff>,
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permuted_input_blind: Blind<C::Scalar>,
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permuted_table_poly: Polynomial<C::Scalar, Coeff>,
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permuted_table_blind: Blind<C::Scalar>,
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product_poly: Polynomial<C::Scalar, Coeff>,
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product_blind: Blind<C::Scalar>,
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}
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2020-12-03 17:18:28 -08:00
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pub(in crate::plonk) struct Evaluated<C: CurveAffine> {
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2020-11-30 22:53:20 -08:00
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constructed: Constructed<C>,
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}
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2020-11-30 23:22:11 -08:00
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2022-11-29 21:05:37 -08:00
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impl<F: WithSmallOrderMulGroup<3>> Argument<F> {
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/// Given a Lookup with input expressions [A_0, A_1, ..., A_{m-1}] and table expressions
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2020-12-05 14:58:48 -08:00
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/// [S_0, S_1, ..., S_{m-1}], this method
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/// - constructs A_compressed = \theta^{m-1} A_0 + theta^{m-2} A_1 + ... + \theta A_{m-2} + A_{m-1}
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/// and S_compressed = \theta^{m-1} S_0 + theta^{m-2} S_1 + ... + \theta S_{m-2} + S_{m-1},
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/// - permutes A_compressed and S_compressed using permute_expression_pair() helper,
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2020-11-30 23:22:11 -08:00
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/// obtaining A' and S', and
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/// - constructs Permuted<C> struct using permuted_input_value = A', and
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/// permuted_table_expression = S'.
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2020-11-30 23:22:11 -08:00
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/// The Permuted<C> struct is used to update the Lookup, and is then returned.
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2022-09-09 11:15:10 -07:00
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#[allow(clippy::too_many_arguments)]
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2021-04-30 18:28:50 -07:00
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pub(in crate::plonk) fn commit_permuted<
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'a,
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C,
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E: EncodedChallenge<C>,
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Ev: Copy + Send + Sync,
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Ec: Copy + Send + Sync,
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2021-12-25 05:36:41 -08:00
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R: RngCore,
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2021-05-07 07:21:54 -07:00
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T: TranscriptWrite<C, E>,
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2021-04-30 18:28:50 -07:00
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>(
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2020-11-30 23:22:11 -08:00
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&self,
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pk: &ProvingKey<C>,
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params: &Params<C>,
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domain: &EvaluationDomain<C::Scalar>,
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2021-12-29 18:12:49 -08:00
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value_evaluator: &poly::Evaluator<Ev, C::Scalar, LagrangeCoeff>,
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2022-01-13 04:17:48 -08:00
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coset_evaluator: &mut poly::Evaluator<Ec, C::Scalar, ExtendedLagrangeCoeff>,
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2020-12-23 12:03:31 -08:00
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theta: ChallengeTheta<C>,
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2021-12-29 18:12:49 -08:00
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advice_values: &'a [poly::AstLeaf<Ev, LagrangeCoeff>],
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fixed_values: &'a [poly::AstLeaf<Ev, LagrangeCoeff>],
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instance_values: &'a [poly::AstLeaf<Ev, LagrangeCoeff>],
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advice_cosets: &'a [poly::AstLeaf<Ec, ExtendedLagrangeCoeff>],
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fixed_cosets: &'a [poly::AstLeaf<Ec, ExtendedLagrangeCoeff>],
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instance_cosets: &'a [poly::AstLeaf<Ec, ExtendedLagrangeCoeff>],
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2021-12-25 05:36:41 -08:00
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mut rng: R,
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2020-12-23 12:03:31 -08:00
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transcript: &mut T,
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2022-01-13 04:17:48 -08:00
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) -> Result<Permuted<C, Ec>, Error>
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2021-02-10 06:57:08 -08:00
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where
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2021-02-22 11:02:53 -08:00
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C: CurveAffine<ScalarExt = F>,
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2021-02-22 10:39:14 -08:00
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C::Curve: Mul<F, Output = C::Curve> + MulAssign<F>,
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2021-02-10 06:57:08 -08:00
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{
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2021-02-11 18:24:55 -08:00
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// Closure to get values of expressions and compress them
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let compress_expressions = |expressions: &[Expression<C::Scalar>]| {
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// Values of input expressions involved in the lookup
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let unpermuted_expressions: Vec<_> = expressions
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2021-02-10 06:57:08 -08:00
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.iter()
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2021-02-11 18:24:55 -08:00
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.map(|expression| {
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expression.evaluate(
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2021-12-29 18:12:49 -08:00
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&|scalar| poly::Ast::ConstantTerm(scalar),
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2021-07-21 11:55:19 -07:00
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&|_| panic!("virtual selectors are removed during optimization"),
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2023-02-21 09:37:35 -08:00
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#[cfg(feature = "unstable-dynamic-lookups")]
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&|_| panic!("virtual table tags are removed during optimization"),
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2022-06-28 08:56:09 -07:00
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&|query| {
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fixed_values[query.column_index]
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.with_rotation(query.rotation)
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.into()
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2021-02-10 06:57:08 -08:00
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},
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2022-06-28 08:56:09 -07:00
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&|query| {
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advice_values[query.column_index]
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.with_rotation(query.rotation)
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.into()
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2021-02-10 06:57:08 -08:00
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},
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2022-06-28 08:56:09 -07:00
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&|query| {
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instance_values[query.column_index]
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.with_rotation(query.rotation)
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.into()
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2021-02-10 06:57:08 -08:00
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},
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2021-07-25 13:24:49 -07:00
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&|a| -a,
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2021-12-29 18:12:49 -08:00
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&|a, b| a + b,
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&|a, b| a * b,
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2021-02-10 06:57:08 -08:00
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&|a, scalar| a * scalar,
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)
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})
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.collect();
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2021-02-11 18:24:55 -08:00
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let unpermuted_cosets: Vec<_> = expressions
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2020-12-02 21:40:35 -08:00
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.iter()
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2021-02-11 18:24:55 -08:00
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.map(|expression| {
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expression.evaluate(
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2021-12-29 18:12:49 -08:00
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&|scalar| poly::Ast::ConstantTerm(scalar),
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2021-07-24 09:27:50 -07:00
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&|_| panic!("virtual selectors are removed during optimization"),
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2023-02-21 09:37:35 -08:00
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#[cfg(feature = "unstable-dynamic-lookups")]
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&|_| panic!("virtual table tags are removed during optimization"),
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2022-06-28 08:56:09 -07:00
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&|query| {
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fixed_cosets[query.column_index]
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.with_rotation(query.rotation)
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.into()
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2021-07-12 11:53:12 -07:00
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},
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2022-06-28 08:56:09 -07:00
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&|query| {
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advice_cosets[query.column_index]
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.with_rotation(query.rotation)
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.into()
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2021-07-12 11:53:12 -07:00
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},
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2022-06-28 08:56:09 -07:00
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&|query| {
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instance_cosets[query.column_index]
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.with_rotation(query.rotation)
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.into()
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2021-07-12 11:53:12 -07:00
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},
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2021-07-25 13:24:49 -07:00
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&|a| -a,
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2021-12-29 18:12:49 -08:00
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&|a, b| a + b,
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&|a, b| a * b,
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2021-02-10 06:57:08 -08:00
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&|a, scalar| a * scalar,
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)
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2020-12-02 21:40:35 -08:00
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})
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2021-02-10 06:57:08 -08:00
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.collect();
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2020-12-02 21:40:35 -08:00
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2021-02-11 18:24:55 -08:00
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// Compressed version of expressions
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2021-12-29 18:12:49 -08:00
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let compressed_expression = unpermuted_expressions.iter().fold(
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2022-11-29 21:05:37 -08:00
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poly::Ast::ConstantTerm(C::Scalar::ZERO),
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2021-12-29 18:12:49 -08:00
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|acc, expression| &(acc * *theta) + expression,
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);
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2020-12-02 21:40:35 -08:00
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2022-09-28 06:12:10 -07:00
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// Compressed version of cosets
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let compressed_coset = unpermuted_cosets.iter().fold(
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2022-11-29 21:05:37 -08:00
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poly::Ast::<_, _, ExtendedLagrangeCoeff>::ConstantTerm(C::Scalar::ZERO),
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2022-09-28 06:12:10 -07:00
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|acc, eval| acc * poly::Ast::ConstantTerm(*theta) + eval.clone(),
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);
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2021-02-11 18:24:55 -08:00
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(
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2022-09-28 06:12:10 -07:00
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compressed_coset,
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2021-12-29 18:12:49 -08:00
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value_evaluator.evaluate(&compressed_expression, domain),
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2021-02-11 18:24:55 -08:00
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)
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2020-12-02 21:40:35 -08:00
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};
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|
2021-02-11 18:24:55 -08:00
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|
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// Get values of input expressions involved in the lookup and compress them
|
2022-09-28 06:12:10 -07:00
|
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|
|
let (compressed_input_coset, compressed_input_expression) =
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2021-02-11 18:24:55 -08:00
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compress_expressions(&self.input_expressions);
|
2020-12-02 21:40:35 -08:00
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|
2021-02-11 18:24:55 -08:00
|
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|
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// Get values of table expressions involved in the lookup and compress them
|
2022-09-28 06:12:10 -07:00
|
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|
|
let (compressed_table_coset, compressed_table_expression) =
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2021-02-11 18:24:55 -08:00
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|
|
compress_expressions(&self.table_expressions);
|
2020-11-30 23:22:11 -08:00
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|
2021-02-11 18:24:55 -08:00
|
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// Permute compressed (InputExpression, TableExpression) pair
|
2021-12-25 05:36:41 -08:00
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|
let (permuted_input_expression, permuted_table_expression) = permute_expression_pair::<C, _>(
|
2021-07-08 11:46:38 -07:00
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pk,
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params,
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2021-02-11 18:24:55 -08:00
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domain,
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2021-12-25 05:36:41 -08:00
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&mut rng,
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2021-02-11 18:24:55 -08:00
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&compressed_input_expression,
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&compressed_table_expression,
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)?;
|
2020-12-02 21:40:35 -08:00
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2021-12-25 05:36:41 -08:00
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// Closure to construct commitment to vector of values
|
|
|
|
|
let mut commit_values = |values: &Polynomial<C::Scalar, LagrangeCoeff>| {
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|
|
|
|
let poly = pk.vk.domain.lagrange_to_coeff(values.clone());
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|
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|
|
let blind = Blind(C::Scalar::random(&mut rng));
|
|
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|
let commitment = params.commit_lagrange(values, blind).to_affine();
|
|
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|
|
(poly, blind, commitment)
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|
};
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|
2021-02-11 18:24:55 -08:00
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// Commit to permuted input expression
|
2020-12-02 21:40:35 -08:00
|
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|
let (permuted_input_poly, permuted_input_blind, permuted_input_commitment) =
|
2021-02-11 18:24:55 -08:00
|
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|
|
commit_values(&permuted_input_expression);
|
2020-12-02 21:40:35 -08:00
|
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|
2021-02-11 18:24:55 -08:00
|
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|
// Commit to permuted table expression
|
2020-12-02 21:40:35 -08:00
|
|
|
|
let (permuted_table_poly, permuted_table_blind, permuted_table_commitment) =
|
2021-02-11 18:24:55 -08:00
|
|
|
|
commit_values(&permuted_table_expression);
|
2020-12-02 21:40:35 -08:00
|
|
|
|
|
|
|
|
|
// Hash permuted input commitment
|
2021-05-26 14:28:11 -07:00
|
|
|
|
transcript.write_point(permuted_input_commitment)?;
|
2020-12-02 21:40:35 -08:00
|
|
|
|
|
|
|
|
|
// Hash permuted table commitment
|
2021-05-26 14:28:11 -07:00
|
|
|
|
transcript.write_point(permuted_table_commitment)?;
|
2020-11-30 23:22:11 -08:00
|
|
|
|
|
2022-01-13 04:17:48 -08:00
|
|
|
|
let permuted_input_coset = coset_evaluator
|
|
|
|
|
.register_poly(pk.vk.domain.coeff_to_extended(permuted_input_poly.clone()));
|
|
|
|
|
let permuted_table_coset = coset_evaluator
|
|
|
|
|
.register_poly(pk.vk.domain.coeff_to_extended(permuted_table_poly.clone()));
|
2020-11-30 23:22:11 -08:00
|
|
|
|
|
|
|
|
|
Ok(Permuted {
|
2022-09-28 06:12:10 -07:00
|
|
|
|
compressed_input_expression,
|
|
|
|
|
compressed_input_coset,
|
2021-02-11 18:24:55 -08:00
|
|
|
|
permuted_input_expression,
|
2020-11-30 23:22:11 -08:00
|
|
|
|
permuted_input_poly,
|
|
|
|
|
permuted_input_coset,
|
|
|
|
|
permuted_input_blind,
|
2022-09-28 06:12:10 -07:00
|
|
|
|
compressed_table_expression,
|
|
|
|
|
compressed_table_coset,
|
2021-02-11 18:24:55 -08:00
|
|
|
|
permuted_table_expression,
|
2020-11-30 23:22:11 -08:00
|
|
|
|
permuted_table_poly,
|
|
|
|
|
permuted_table_coset,
|
|
|
|
|
permuted_table_blind,
|
|
|
|
|
})
|
|
|
|
|
}
|
2020-12-02 19:56:22 -08:00
|
|
|
|
}
|
2020-11-30 23:30:52 -08:00
|
|
|
|
|
2022-01-13 04:17:48 -08:00
|
|
|
|
impl<C: CurveAffine, Ev: Copy + Send + Sync> Permuted<C, Ev> {
|
2021-02-11 18:24:55 -08:00
|
|
|
|
/// Given a Lookup with input expressions, table expressions, and the permuted
|
|
|
|
|
/// input expression and permuted table expression, this method constructs the
|
2020-11-30 23:30:52 -08:00
|
|
|
|
/// grand product polynomial over the lookup. The grand product polynomial
|
|
|
|
|
/// is used to populate the Product<C> struct. The Product<C> struct is
|
|
|
|
|
/// added to the Lookup and finally returned by the method.
|
2022-09-09 11:15:10 -07:00
|
|
|
|
#[allow(clippy::too_many_arguments)]
|
2021-12-25 05:36:41 -08:00
|
|
|
|
pub(in crate::plonk) fn commit_product<
|
|
|
|
|
E: EncodedChallenge<C>,
|
|
|
|
|
R: RngCore,
|
|
|
|
|
T: TranscriptWrite<C, E>,
|
|
|
|
|
>(
|
2020-12-02 19:56:22 -08:00
|
|
|
|
self,
|
2020-11-30 23:30:52 -08:00
|
|
|
|
pk: &ProvingKey<C>,
|
|
|
|
|
params: &Params<C>,
|
2020-12-23 12:03:31 -08:00
|
|
|
|
beta: ChallengeBeta<C>,
|
|
|
|
|
gamma: ChallengeGamma<C>,
|
2022-01-13 04:17:48 -08:00
|
|
|
|
evaluator: &mut poly::Evaluator<Ev, C::Scalar, ExtendedLagrangeCoeff>,
|
2021-12-25 05:36:41 -08:00
|
|
|
|
mut rng: R,
|
2020-12-23 12:03:31 -08:00
|
|
|
|
transcript: &mut T,
|
2022-01-13 04:17:48 -08:00
|
|
|
|
) -> Result<Committed<C, Ev>, Error> {
|
2021-07-08 11:46:38 -07:00
|
|
|
|
let blinding_factors = pk.vk.cs.blinding_factors();
|
2020-11-30 23:30:52 -08:00
|
|
|
|
// Goal is to compute the products of fractions
|
|
|
|
|
//
|
2020-12-05 14:58:48 -08:00
|
|
|
|
// Numerator: (\theta^{m-1} a_0(\omega^i) + \theta^{m-2} a_1(\omega^i) + ... + \theta a_{m-2}(\omega^i) + a_{m-1}(\omega^i) + \beta)
|
|
|
|
|
// * (\theta^{m-1} s_0(\omega^i) + \theta^{m-2} s_1(\omega^i) + ... + \theta s_{m-2}(\omega^i) + s_{m-1}(\omega^i) + \gamma)
|
|
|
|
|
// Denominator: (a'(\omega^i) + \beta) (s'(\omega^i) + \gamma)
|
2020-11-30 23:30:52 -08:00
|
|
|
|
//
|
2021-02-11 18:24:55 -08:00
|
|
|
|
// where a_j(X) is the jth input expression in this lookup,
|
|
|
|
|
// where a'(X) is the compression of the permuted input expressions,
|
|
|
|
|
// s_j(X) is the jth table expression in this lookup,
|
|
|
|
|
// s'(X) is the compression of the permuted table expressions,
|
|
|
|
|
// and i is the ith row of the expression.
|
2022-11-29 21:05:37 -08:00
|
|
|
|
let mut lookup_product = vec![C::Scalar::ZERO; params.n as usize];
|
2021-02-11 18:24:55 -08:00
|
|
|
|
// Denominator uses the permuted input expression and permuted table expression
|
2020-11-30 23:30:52 -08:00
|
|
|
|
parallelize(&mut lookup_product, |lookup_product, start| {
|
|
|
|
|
for ((lookup_product, permuted_input_value), permuted_table_value) in lookup_product
|
|
|
|
|
.iter_mut()
|
2021-02-11 18:24:55 -08:00
|
|
|
|
.zip(self.permuted_input_expression[start..].iter())
|
|
|
|
|
.zip(self.permuted_table_expression[start..].iter())
|
2020-11-30 23:30:52 -08:00
|
|
|
|
{
|
2020-12-02 20:39:44 -08:00
|
|
|
|
*lookup_product = (*beta + permuted_input_value) * &(*gamma + permuted_table_value);
|
2020-11-30 23:30:52 -08:00
|
|
|
|
}
|
|
|
|
|
});
|
|
|
|
|
|
|
|
|
|
// Batch invert to obtain the denominators for the lookup product
|
|
|
|
|
// polynomials
|
|
|
|
|
lookup_product.iter_mut().batch_invert();
|
|
|
|
|
|
|
|
|
|
// Finish the computation of the entire fraction by computing the numerators
|
2020-12-05 14:58:48 -08:00
|
|
|
|
// (\theta^{m-1} a_0(\omega^i) + \theta^{m-2} a_1(\omega^i) + ... + \theta a_{m-2}(\omega^i) + a_{m-1}(\omega^i) + \beta)
|
|
|
|
|
// * (\theta^{m-1} s_0(\omega^i) + \theta^{m-2} s_1(\omega^i) + ... + \theta s_{m-2}(\omega^i) + s_{m-1}(\omega^i) + \gamma)
|
2020-12-04 20:51:28 -08:00
|
|
|
|
parallelize(&mut lookup_product, |product, start| {
|
2022-09-28 06:12:10 -07:00
|
|
|
|
for ((product, &input_term), &table_term) in product
|
|
|
|
|
.iter_mut()
|
|
|
|
|
.zip(self.compressed_input_expression[start..].iter())
|
|
|
|
|
.zip(self.compressed_table_expression[start..].iter())
|
|
|
|
|
{
|
2021-01-05 16:00:27 -08:00
|
|
|
|
*product *= &(input_term + &*beta);
|
|
|
|
|
*product *= &(table_term + &*gamma);
|
2020-11-30 23:30:52 -08:00
|
|
|
|
}
|
|
|
|
|
});
|
|
|
|
|
|
|
|
|
|
// The product vector is a vector of products of fractions of the form
|
|
|
|
|
//
|
2020-12-05 14:58:48 -08:00
|
|
|
|
// Numerator: (\theta^{m-1} a_0(\omega^i) + \theta^{m-2} a_1(\omega^i) + ... + \theta a_{m-2}(\omega^i) + a_{m-1}(\omega^i) + \beta)
|
|
|
|
|
// * (\theta^{m-1} s_0(\omega^i) + \theta^{m-2} s_1(\omega^i) + ... + \theta s_{m-2}(\omega^i) + s_{m-1}(\omega^i) + \gamma)
|
|
|
|
|
// Denominator: (a'(\omega^i) + \beta) (s'(\omega^i) + \gamma)
|
2020-11-30 23:30:52 -08:00
|
|
|
|
//
|
2021-02-11 18:24:55 -08:00
|
|
|
|
// where there are m input expressions and m table expressions,
|
|
|
|
|
// a_j(\omega^i) is the jth input expression in this lookup,
|
|
|
|
|
// a'j(\omega^i) is the permuted input expression,
|
|
|
|
|
// s_j(\omega^i) is the jth table expression in this lookup,
|
|
|
|
|
// s'(\omega^i) is the permuted table expression,
|
|
|
|
|
// and i is the ith row of the expression.
|
2020-11-30 23:30:52 -08:00
|
|
|
|
|
|
|
|
|
// Compute the evaluations of the lookup product polynomial
|
|
|
|
|
// over our domain, starting with z[0] = 1
|
2022-11-29 21:05:37 -08:00
|
|
|
|
let z = iter::once(C::Scalar::ONE)
|
2021-07-08 11:46:38 -07:00
|
|
|
|
.chain(lookup_product)
|
2022-11-29 21:05:37 -08:00
|
|
|
|
.scan(C::Scalar::ONE, |state, cur| {
|
2020-12-02 20:39:44 -08:00
|
|
|
|
*state *= &cur;
|
|
|
|
|
Some(*state)
|
|
|
|
|
})
|
2021-07-08 11:46:38 -07:00
|
|
|
|
// Take all rows including the "last" row which should
|
|
|
|
|
// be a boolean (and ideally 1, else soundness is broken)
|
|
|
|
|
.take(params.n as usize - blinding_factors)
|
|
|
|
|
// Chain random blinding factors.
|
2021-12-25 05:36:41 -08:00
|
|
|
|
.chain((0..blinding_factors).map(|_| C::Scalar::random(&mut rng)))
|
2020-12-02 20:39:44 -08:00
|
|
|
|
.collect::<Vec<_>>();
|
2021-07-08 11:46:38 -07:00
|
|
|
|
assert_eq!(z.len(), params.n as usize);
|
2020-11-30 23:30:52 -08:00
|
|
|
|
let z = pk.vk.domain.lagrange_from_vec(z);
|
|
|
|
|
|
|
|
|
|
#[cfg(feature = "sanity-checks")]
|
|
|
|
|
// This test works only with intermediate representations in this method.
|
|
|
|
|
// It can be used for debugging purposes.
|
|
|
|
|
{
|
|
|
|
|
// While in Lagrange basis, check that product is correctly constructed
|
2021-07-13 15:12:21 -07:00
|
|
|
|
let u = (params.n as usize) - (blinding_factors + 1);
|
2020-11-30 23:30:52 -08:00
|
|
|
|
|
2021-07-08 11:46:38 -07:00
|
|
|
|
// l_0(X) * (1 - z(X)) = 0
|
2022-11-29 21:05:37 -08:00
|
|
|
|
assert_eq!(z[0], C::Scalar::ONE);
|
2021-07-08 11:46:38 -07:00
|
|
|
|
|
|
|
|
|
// z(\omega X) (a'(X) + \beta) (s'(X) + \gamma)
|
|
|
|
|
// - z(X) (\theta^{m-1} a_0(X) + ... + a_{m-1}(X) + \beta) (\theta^{m-1} s_0(X) + ... + s_{m-1}(X) + \gamma)
|
2021-07-13 15:12:21 -07:00
|
|
|
|
for i in 0..u {
|
2021-07-09 11:41:52 -07:00
|
|
|
|
let mut left = z[i + 1];
|
2021-02-11 18:24:55 -08:00
|
|
|
|
let permuted_input_value = &self.permuted_input_expression[i];
|
2020-11-30 23:30:52 -08:00
|
|
|
|
|
2021-02-11 18:24:55 -08:00
|
|
|
|
let permuted_table_value = &self.permuted_table_expression[i];
|
2020-11-30 23:30:52 -08:00
|
|
|
|
|
|
|
|
|
left *= &(*beta + permuted_input_value);
|
|
|
|
|
left *= &(*gamma + permuted_table_value);
|
|
|
|
|
|
2021-07-08 11:46:38 -07:00
|
|
|
|
let mut right = z[i];
|
2022-09-28 06:12:10 -07:00
|
|
|
|
let mut input_term = self.compressed_input_expression[i];
|
2020-11-30 23:30:52 -08:00
|
|
|
|
|
2022-09-28 06:12:10 -07:00
|
|
|
|
let mut table_term = self.compressed_table_expression[i];
|
2020-11-30 23:30:52 -08:00
|
|
|
|
|
|
|
|
|
input_term += &(*beta);
|
|
|
|
|
table_term += &(*gamma);
|
|
|
|
|
right *= &(input_term * &table_term);
|
|
|
|
|
|
|
|
|
|
assert_eq!(left, right);
|
|
|
|
|
}
|
2021-07-08 11:46:38 -07:00
|
|
|
|
|
|
|
|
|
// l_last(X) * (z(X)^2 - z(X)) = 0
|
|
|
|
|
// Assertion will fail only when soundness is broken, in which
|
2021-07-14 08:46:29 -07:00
|
|
|
|
// case this z[u] value will be zero. (bad!)
|
2022-11-29 21:05:37 -08:00
|
|
|
|
assert_eq!(z[u], C::Scalar::ONE);
|
2020-11-30 23:30:52 -08:00
|
|
|
|
}
|
|
|
|
|
|
2021-12-25 05:36:41 -08:00
|
|
|
|
let product_blind = Blind(C::Scalar::random(rng));
|
2020-11-30 23:30:52 -08:00
|
|
|
|
let product_commitment = params.commit_lagrange(&z, product_blind).to_affine();
|
|
|
|
|
let z = pk.vk.domain.lagrange_to_coeff(z);
|
2022-01-13 04:17:48 -08:00
|
|
|
|
let product_coset = evaluator.register_poly(pk.vk.domain.coeff_to_extended(z.clone()));
|
2020-11-30 23:30:52 -08:00
|
|
|
|
|
2020-12-02 20:39:44 -08:00
|
|
|
|
// Hash product commitment
|
2021-05-26 14:28:11 -07:00
|
|
|
|
transcript.write_point(product_commitment)?;
|
2020-11-30 23:30:52 -08:00
|
|
|
|
|
2022-01-13 04:17:48 -08:00
|
|
|
|
Ok(Committed::<C, _> {
|
2020-12-02 19:56:22 -08:00
|
|
|
|
permuted: self,
|
2020-11-30 23:30:52 -08:00
|
|
|
|
product_poly: z,
|
|
|
|
|
product_coset,
|
|
|
|
|
product_blind,
|
|
|
|
|
})
|
|
|
|
|
}
|
2020-11-30 23:22:11 -08:00
|
|
|
|
}
|
|
|
|
|
|
2022-01-13 04:17:48 -08:00
|
|
|
|
impl<'a, C: CurveAffine, Ev: Copy + Send + Sync + 'a> Committed<C, Ev> {
|
2021-02-11 18:24:55 -08:00
|
|
|
|
/// Given a Lookup with input expressions, table expressions, permuted input
|
|
|
|
|
/// expression, permuted table expression, and grand product polynomial, this
|
2020-12-01 00:19:07 -08:00
|
|
|
|
/// method constructs constraints that must hold between these values.
|
2022-01-13 04:17:48 -08:00
|
|
|
|
/// This method returns the constraints as a vector of ASTs for polynomials in
|
2020-12-01 00:19:07 -08:00
|
|
|
|
/// the extended evaluation domain.
|
2020-12-02 19:56:22 -08:00
|
|
|
|
pub(in crate::plonk) fn construct(
|
2020-12-01 00:19:07 -08:00
|
|
|
|
self,
|
2020-12-23 12:03:31 -08:00
|
|
|
|
beta: ChallengeBeta<C>,
|
|
|
|
|
gamma: ChallengeGamma<C>,
|
2022-01-13 04:17:48 -08:00
|
|
|
|
l0: poly::AstLeaf<Ev, ExtendedLagrangeCoeff>,
|
|
|
|
|
l_blind: poly::AstLeaf<Ev, ExtendedLagrangeCoeff>,
|
|
|
|
|
l_last: poly::AstLeaf<Ev, ExtendedLagrangeCoeff>,
|
2021-01-14 05:29:19 -08:00
|
|
|
|
) -> (
|
|
|
|
|
Constructed<C>,
|
2022-01-13 04:17:48 -08:00
|
|
|
|
impl Iterator<Item = poly::Ast<Ev, C::Scalar, ExtendedLagrangeCoeff>> + 'a,
|
2021-01-14 05:29:19 -08:00
|
|
|
|
) {
|
2020-12-01 00:19:07 -08:00
|
|
|
|
let permuted = self.permuted;
|
|
|
|
|
|
2022-01-13 04:17:48 -08:00
|
|
|
|
let active_rows = poly::Ast::one() - (poly::Ast::from(l_last) + l_blind);
|
|
|
|
|
let beta = poly::Ast::ConstantTerm(*beta);
|
|
|
|
|
let gamma = poly::Ast::ConstantTerm(*gamma);
|
2021-07-08 11:46:38 -07:00
|
|
|
|
|
2020-12-01 00:19:07 -08:00
|
|
|
|
let expressions = iter::empty()
|
2021-07-08 11:46:38 -07:00
|
|
|
|
// l_0(X) * (1 - z(X)) = 0
|
2022-01-13 04:17:48 -08:00
|
|
|
|
.chain(Some((poly::Ast::one() - self.product_coset) * l0))
|
2021-07-08 11:46:38 -07:00
|
|
|
|
// l_last(X) * (z(X)^2 - z(X)) = 0
|
|
|
|
|
.chain(Some(
|
2022-01-13 04:17:48 -08:00
|
|
|
|
(poly::Ast::from(self.product_coset) * self.product_coset - self.product_coset)
|
|
|
|
|
* l_last,
|
2021-07-08 11:46:38 -07:00
|
|
|
|
))
|
2021-07-13 15:30:52 -07:00
|
|
|
|
// (1 - (l_last(X) + l_blind(X))) * (
|
2021-07-08 11:46:38 -07:00
|
|
|
|
// z(\omega X) (a'(X) + \beta) (s'(X) + \gamma)
|
|
|
|
|
// - z(X) (\theta^{m-1} a_0(X) + ... + a_{m-1}(X) + \beta) (\theta^{m-1} s_0(X) + ... + s_{m-1}(X) + \gamma)
|
|
|
|
|
// ) = 0
|
2020-12-01 00:19:07 -08:00
|
|
|
|
.chain({
|
2021-07-08 11:46:38 -07:00
|
|
|
|
// z(\omega X) (a'(X) + \beta) (s'(X) + \gamma)
|
2022-01-13 04:17:48 -08:00
|
|
|
|
let left: poly::Ast<_, _, _> = poly::Ast::<_, C::Scalar, _>::from(
|
|
|
|
|
self.product_coset.with_rotation(Rotation::next()),
|
|
|
|
|
) * (poly::Ast::from(permuted.permuted_input_coset)
|
|
|
|
|
+ beta.clone())
|
|
|
|
|
* (poly::Ast::from(permuted.permuted_table_coset) + gamma.clone());
|
2020-12-01 00:19:07 -08:00
|
|
|
|
|
2021-07-08 11:46:38 -07:00
|
|
|
|
// z(X) (\theta^{m-1} a_0(X) + ... + a_{m-1}(X) + \beta) (\theta^{m-1} s_0(X) + ... + s_{m-1}(X) + \gamma)
|
2022-01-13 04:17:48 -08:00
|
|
|
|
let right: poly::Ast<_, _, _> = poly::Ast::from(self.product_coset)
|
2022-09-28 06:12:10 -07:00
|
|
|
|
* (permuted.compressed_input_coset + beta)
|
|
|
|
|
* (permuted.compressed_table_coset + gamma);
|
2022-01-13 04:17:48 -08:00
|
|
|
|
|
|
|
|
|
Some((left - right) * active_rows.clone())
|
2020-12-01 00:19:07 -08:00
|
|
|
|
})
|
2021-02-11 18:24:55 -08:00
|
|
|
|
// Check that the first values in the permuted input expression and permuted
|
|
|
|
|
// fixed expression are the same.
|
2020-12-01 00:19:07 -08:00
|
|
|
|
// l_0(X) * (a'(X) - s'(X)) = 0
|
|
|
|
|
.chain(Some(
|
2022-01-13 04:17:48 -08:00
|
|
|
|
(poly::Ast::from(permuted.permuted_input_coset) - permuted.permuted_table_coset)
|
|
|
|
|
* l0,
|
2020-12-01 00:19:07 -08:00
|
|
|
|
))
|
2021-02-11 18:24:55 -08:00
|
|
|
|
// Check that each value in the permuted lookup input expression is either
|
2020-12-01 00:19:07 -08:00
|
|
|
|
// equal to the value above it, or the value at the same index in the
|
2021-02-11 18:24:55 -08:00
|
|
|
|
// permuted table expression.
|
2021-07-09 11:44:27 -07:00
|
|
|
|
// (1 - (l_last + l_blind)) * (a′(X) − s′(X))⋅(a′(X) − a′(\omega^{-1} X)) = 0
|
2020-12-01 00:19:07 -08:00
|
|
|
|
.chain(Some(
|
2022-01-13 04:17:48 -08:00
|
|
|
|
(poly::Ast::<_, C::Scalar, _>::from(permuted.permuted_input_coset)
|
|
|
|
|
- permuted.permuted_table_coset)
|
|
|
|
|
* (poly::Ast::from(permuted.permuted_input_coset)
|
|
|
|
|
- permuted
|
|
|
|
|
.permuted_input_coset
|
|
|
|
|
.with_rotation(Rotation::prev()))
|
|
|
|
|
* active_rows,
|
2020-12-01 00:19:07 -08:00
|
|
|
|
));
|
|
|
|
|
|
2021-01-14 05:29:19 -08:00
|
|
|
|
(
|
2020-12-01 00:19:07 -08:00
|
|
|
|
Constructed {
|
|
|
|
|
permuted_input_poly: permuted.permuted_input_poly,
|
|
|
|
|
permuted_input_blind: permuted.permuted_input_blind,
|
|
|
|
|
permuted_table_poly: permuted.permuted_table_poly,
|
|
|
|
|
permuted_table_blind: permuted.permuted_table_blind,
|
2020-12-02 19:56:22 -08:00
|
|
|
|
product_poly: self.product_poly,
|
|
|
|
|
product_blind: self.product_blind,
|
2020-12-01 00:19:07 -08:00
|
|
|
|
},
|
|
|
|
|
expressions,
|
2021-01-14 05:29:19 -08:00
|
|
|
|
)
|
2020-12-01 00:19:07 -08:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2020-12-01 00:33:23 -08:00
|
|
|
|
impl<C: CurveAffine> Constructed<C> {
|
2021-05-07 07:21:54 -07:00
|
|
|
|
pub(in crate::plonk) fn evaluate<E: EncodedChallenge<C>, T: TranscriptWrite<C, E>>(
|
2020-12-01 00:33:23 -08:00
|
|
|
|
self,
|
|
|
|
|
pk: &ProvingKey<C>,
|
2020-12-23 12:03:31 -08:00
|
|
|
|
x: ChallengeX<C>,
|
|
|
|
|
transcript: &mut T,
|
|
|
|
|
) -> Result<Evaluated<C>, Error> {
|
2020-12-01 00:33:23 -08:00
|
|
|
|
let domain = &pk.vk.domain;
|
2021-07-08 11:46:38 -07:00
|
|
|
|
let x_inv = domain.rotate_omega(*x, Rotation::prev());
|
|
|
|
|
let x_next = domain.rotate_omega(*x, Rotation::next());
|
2020-12-01 00:33:23 -08:00
|
|
|
|
|
|
|
|
|
let product_eval = eval_polynomial(&self.product_poly, *x);
|
2021-07-08 11:46:38 -07:00
|
|
|
|
let product_next_eval = eval_polynomial(&self.product_poly, x_next);
|
2020-12-01 00:33:23 -08:00
|
|
|
|
let permuted_input_eval = eval_polynomial(&self.permuted_input_poly, *x);
|
|
|
|
|
let permuted_input_inv_eval = eval_polynomial(&self.permuted_input_poly, x_inv);
|
|
|
|
|
let permuted_table_eval = eval_polynomial(&self.permuted_table_poly, *x);
|
|
|
|
|
|
|
|
|
|
// Hash each advice evaluation
|
|
|
|
|
for eval in iter::empty()
|
|
|
|
|
.chain(Some(product_eval))
|
2021-07-08 11:46:38 -07:00
|
|
|
|
.chain(Some(product_next_eval))
|
2020-12-01 00:33:23 -08:00
|
|
|
|
.chain(Some(permuted_input_eval))
|
|
|
|
|
.chain(Some(permuted_input_inv_eval))
|
|
|
|
|
.chain(Some(permuted_table_eval))
|
|
|
|
|
{
|
2021-05-26 14:28:11 -07:00
|
|
|
|
transcript.write_scalar(eval)?;
|
2020-12-01 00:33:23 -08:00
|
|
|
|
}
|
|
|
|
|
|
2021-01-13 16:22:32 -08:00
|
|
|
|
Ok(Evaluated { constructed: self })
|
2020-12-01 00:33:23 -08:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2020-12-01 00:46:11 -08:00
|
|
|
|
impl<C: CurveAffine> Evaluated<C> {
|
|
|
|
|
pub(in crate::plonk) fn open<'a>(
|
|
|
|
|
&'a self,
|
|
|
|
|
pk: &'a ProvingKey<C>,
|
2020-12-23 12:03:31 -08:00
|
|
|
|
x: ChallengeX<C>,
|
2020-12-01 00:46:11 -08:00
|
|
|
|
) -> impl Iterator<Item = ProverQuery<'a, C>> + Clone {
|
2021-07-08 11:46:38 -07:00
|
|
|
|
let x_inv = pk.vk.domain.rotate_omega(*x, Rotation::prev());
|
|
|
|
|
let x_next = pk.vk.domain.rotate_omega(*x, Rotation::next());
|
2020-12-01 00:46:11 -08:00
|
|
|
|
|
|
|
|
|
iter::empty()
|
|
|
|
|
// Open lookup product commitments at x
|
|
|
|
|
.chain(Some(ProverQuery {
|
|
|
|
|
point: *x,
|
|
|
|
|
poly: &self.constructed.product_poly,
|
|
|
|
|
blind: self.constructed.product_blind,
|
|
|
|
|
}))
|
|
|
|
|
// Open lookup input commitments at x
|
|
|
|
|
.chain(Some(ProverQuery {
|
|
|
|
|
point: *x,
|
|
|
|
|
poly: &self.constructed.permuted_input_poly,
|
|
|
|
|
blind: self.constructed.permuted_input_blind,
|
|
|
|
|
}))
|
|
|
|
|
// Open lookup table commitments at x
|
|
|
|
|
.chain(Some(ProverQuery {
|
|
|
|
|
point: *x,
|
|
|
|
|
poly: &self.constructed.permuted_table_poly,
|
|
|
|
|
blind: self.constructed.permuted_table_blind,
|
|
|
|
|
}))
|
|
|
|
|
// Open lookup input commitments at x_inv
|
|
|
|
|
.chain(Some(ProverQuery {
|
|
|
|
|
point: x_inv,
|
|
|
|
|
poly: &self.constructed.permuted_input_poly,
|
|
|
|
|
blind: self.constructed.permuted_input_blind,
|
|
|
|
|
}))
|
2021-07-08 11:46:38 -07:00
|
|
|
|
// Open lookup product commitments at x_next
|
2020-12-01 00:46:11 -08:00
|
|
|
|
.chain(Some(ProverQuery {
|
2021-07-08 11:46:38 -07:00
|
|
|
|
point: x_next,
|
2020-12-01 00:46:11 -08:00
|
|
|
|
poly: &self.constructed.product_poly,
|
|
|
|
|
blind: self.constructed.product_blind,
|
|
|
|
|
}))
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2021-02-11 18:24:55 -08:00
|
|
|
|
type ExpressionPair<F> = (Polynomial<F, LagrangeCoeff>, Polynomial<F, LagrangeCoeff>);
|
2021-01-14 05:20:54 -08:00
|
|
|
|
|
2021-02-11 18:24:55 -08:00
|
|
|
|
/// Given a vector of input values A and a vector of table values S,
|
2020-11-30 23:22:11 -08:00
|
|
|
|
/// this method permutes A and S to produce A' and S', such that:
|
|
|
|
|
/// - like values in A' are vertically adjacent to each other; and
|
|
|
|
|
/// - the first row in a sequence of like values in A' is the row
|
|
|
|
|
/// that has the corresponding value in S'.
|
|
|
|
|
/// This method returns (A', S') if no errors are encountered.
|
2021-12-25 05:36:41 -08:00
|
|
|
|
fn permute_expression_pair<C: CurveAffine, R: RngCore>(
|
2021-07-08 11:46:38 -07:00
|
|
|
|
pk: &ProvingKey<C>,
|
|
|
|
|
params: &Params<C>,
|
2020-11-30 23:22:11 -08:00
|
|
|
|
domain: &EvaluationDomain<C::Scalar>,
|
2021-12-25 05:36:41 -08:00
|
|
|
|
mut rng: R,
|
2021-02-11 18:24:55 -08:00
|
|
|
|
input_expression: &Polynomial<C::Scalar, LagrangeCoeff>,
|
|
|
|
|
table_expression: &Polynomial<C::Scalar, LagrangeCoeff>,
|
|
|
|
|
) -> Result<ExpressionPair<C::Scalar>, Error> {
|
2021-07-08 11:46:38 -07:00
|
|
|
|
let blinding_factors = pk.vk.cs.blinding_factors();
|
2021-07-09 11:45:51 -07:00
|
|
|
|
let usable_rows = params.n as usize - (blinding_factors + 1);
|
|
|
|
|
|
2021-07-08 11:46:38 -07:00
|
|
|
|
let mut permuted_input_expression: Vec<C::Scalar> = input_expression.to_vec();
|
2021-07-09 11:45:51 -07:00
|
|
|
|
permuted_input_expression.truncate(usable_rows);
|
2020-11-30 23:22:11 -08:00
|
|
|
|
|
2021-02-11 18:24:55 -08:00
|
|
|
|
// Sort input lookup expression values
|
|
|
|
|
permuted_input_expression.sort();
|
2020-11-30 23:22:11 -08:00
|
|
|
|
|
2021-02-11 18:24:55 -08:00
|
|
|
|
// A BTreeMap of each unique element in the table expression and its count
|
2021-07-08 11:46:38 -07:00
|
|
|
|
let mut leftover_table_map: BTreeMap<C::Scalar, u32> = table_expression
|
|
|
|
|
.iter()
|
2021-07-09 11:45:51 -07:00
|
|
|
|
.take(usable_rows)
|
2021-07-08 11:46:38 -07:00
|
|
|
|
.fold(BTreeMap::new(), |mut acc, coeff| {
|
|
|
|
|
*acc.entry(*coeff).or_insert(0) += 1;
|
|
|
|
|
acc
|
|
|
|
|
});
|
2022-11-29 21:05:37 -08:00
|
|
|
|
let mut permuted_table_coeffs = vec![C::Scalar::ZERO; usable_rows];
|
2021-02-11 18:24:55 -08:00
|
|
|
|
|
|
|
|
|
let mut repeated_input_rows = permuted_input_expression
|
2020-12-02 20:39:44 -08:00
|
|
|
|
.iter()
|
|
|
|
|
.zip(permuted_table_coeffs.iter_mut())
|
|
|
|
|
.enumerate()
|
|
|
|
|
.filter_map(|(row, (input_value, table_value))| {
|
2022-02-03 08:01:22 -08:00
|
|
|
|
// If this is the first occurrence of `input_value` in the input expression
|
2021-02-11 18:24:55 -08:00
|
|
|
|
if row == 0 || *input_value != permuted_input_expression[row - 1] {
|
2020-12-02 20:39:44 -08:00
|
|
|
|
*table_value = *input_value;
|
|
|
|
|
// Remove one instance of input_value from leftover_table_map
|
2021-06-21 10:19:15 -07:00
|
|
|
|
if let Some(count) = leftover_table_map.get_mut(input_value) {
|
2020-12-02 20:39:44 -08:00
|
|
|
|
assert!(*count > 0);
|
|
|
|
|
*count -= 1;
|
|
|
|
|
None
|
|
|
|
|
} else {
|
|
|
|
|
// Return error if input_value not found
|
|
|
|
|
Some(Err(Error::ConstraintSystemFailure))
|
|
|
|
|
}
|
|
|
|
|
// If input value is repeated
|
2020-11-30 23:22:11 -08:00
|
|
|
|
} else {
|
2020-12-02 20:39:44 -08:00
|
|
|
|
Some(Ok(row))
|
2020-11-30 23:22:11 -08:00
|
|
|
|
}
|
2020-12-02 20:39:44 -08:00
|
|
|
|
})
|
|
|
|
|
.collect::<Result<Vec<_>, _>>()?;
|
2020-11-30 23:22:11 -08:00
|
|
|
|
|
|
|
|
|
// Populate permuted table at unfilled rows with leftover table elements
|
|
|
|
|
for (coeff, count) in leftover_table_map.iter() {
|
|
|
|
|
for _ in 0..*count {
|
2022-11-30 07:02:03 -08:00
|
|
|
|
permuted_table_coeffs[repeated_input_rows.pop().unwrap()] = *coeff;
|
2020-11-30 23:22:11 -08:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
assert!(repeated_input_rows.is_empty());
|
|
|
|
|
|
2021-12-25 05:36:41 -08:00
|
|
|
|
permuted_input_expression
|
|
|
|
|
.extend((0..(blinding_factors + 1)).map(|_| C::Scalar::random(&mut rng)));
|
|
|
|
|
permuted_table_coeffs.extend((0..(blinding_factors + 1)).map(|_| C::Scalar::random(&mut rng)));
|
2021-07-08 11:46:38 -07:00
|
|
|
|
assert_eq!(permuted_input_expression.len(), params.n as usize);
|
|
|
|
|
assert_eq!(permuted_table_coeffs.len(), params.n as usize);
|
|
|
|
|
|
|
|
|
|
#[cfg(feature = "sanity-checks")]
|
|
|
|
|
{
|
2021-07-09 11:47:36 -07:00
|
|
|
|
let mut last = None;
|
2021-07-08 11:46:38 -07:00
|
|
|
|
for (a, b) in permuted_input_expression
|
|
|
|
|
.iter()
|
|
|
|
|
.zip(permuted_table_coeffs.iter())
|
2021-07-09 11:45:51 -07:00
|
|
|
|
.take(usable_rows)
|
2021-07-08 11:46:38 -07:00
|
|
|
|
{
|
|
|
|
|
if *a != *b {
|
2021-07-09 11:47:36 -07:00
|
|
|
|
assert_eq!(*a, last.unwrap());
|
2020-11-30 23:22:11 -08:00
|
|
|
|
}
|
2021-07-09 11:47:36 -07:00
|
|
|
|
last = Some(*a);
|
2021-07-08 11:46:38 -07:00
|
|
|
|
}
|
|
|
|
|
}
|
2020-11-30 23:22:11 -08:00
|
|
|
|
|
2021-07-08 11:46:38 -07:00
|
|
|
|
Ok((
|
|
|
|
|
domain.lagrange_from_vec(permuted_input_expression),
|
|
|
|
|
domain.lagrange_from_vec(permuted_table_coeffs),
|
|
|
|
|
))
|
2020-11-30 23:22:11 -08:00
|
|
|
|
}
|