2020-11-30 23:22:11 -08:00
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use super::super::{
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circuit::{Advice, Any, Aux, Column, Fixed},
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Error, ProvingKey,
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};
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use super::Argument;
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use crate::{
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arithmetic::{eval_polynomial, parallelize, BatchInvert, Curve, CurveAffine, FieldExt},
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poly::{
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commitment::{Blind, Params},
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Coeff, EvaluationDomain, ExtendedLagrangeCoeff, LagrangeCoeff, Polynomial, Rotation,
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},
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transcript::{Hasher, Transcript},
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};
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use ff::Field;
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use std::collections::BTreeMap;
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2020-11-30 22:53:20 -08:00
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#[derive(Clone, Debug)]
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pub(crate) struct Permuted<C: CurveAffine> {
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permuted_input_value: Polynomial<C::Scalar, LagrangeCoeff>,
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permuted_input_poly: Polynomial<C::Scalar, Coeff>,
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permuted_input_coset: Polynomial<C::Scalar, ExtendedLagrangeCoeff>,
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permuted_input_inv_coset: Polynomial<C::Scalar, ExtendedLagrangeCoeff>,
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permuted_input_blind: Blind<C::Scalar>,
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permuted_input_commitment: C,
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permuted_table_value: Polynomial<C::Scalar, LagrangeCoeff>,
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permuted_table_poly: Polynomial<C::Scalar, Coeff>,
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permuted_table_coset: Polynomial<C::Scalar, ExtendedLagrangeCoeff>,
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permuted_table_blind: Blind<C::Scalar>,
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permuted_table_commitment: C,
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}
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#[derive(Clone, Debug)]
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pub(crate) struct Product<C: CurveAffine> {
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product_poly: Polynomial<C::Scalar, Coeff>,
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product_coset: Polynomial<C::Scalar, ExtendedLagrangeCoeff>,
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product_inv_coset: Polynomial<C::Scalar, ExtendedLagrangeCoeff>,
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product_blind: Blind<C::Scalar>,
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product_commitment: C,
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}
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#[derive(Clone, Debug)]
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pub(crate) struct Committed<C: CurveAffine> {
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permuted: Permuted<C>,
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product: Product<C>,
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}
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pub(crate) struct Constructed<C: CurveAffine> {
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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_input_commitment: C,
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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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permuted_table_commitment: C,
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product_poly: Polynomial<C::Scalar, Coeff>,
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product_blind: Blind<C::Scalar>,
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product_commitment: 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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pub product_eval: C::Scalar,
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pub product_inv_eval: C::Scalar,
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pub permuted_input_eval: C::Scalar,
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pub permuted_input_inv_eval: C::Scalar,
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pub permuted_table_eval: C::Scalar,
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}
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2020-11-30 23:22:11 -08:00
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impl Argument {
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/// Given a Lookup with input columns [A_0, A_1, ..., A_m] and table columns
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/// [S_0, S_1, ..., S_m], this method
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/// - constructs A_compressed = A_0 + theta A_1 + theta^2 A_2 + ... and
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/// S_compressed = S_0 + theta S_1 + theta^2 S_2 + ...,
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/// - permutes A_compressed and S_compressed using permute_column_pair() helper,
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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_value = S'.
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/// The Permuted<C> struct is used to update the Lookup, and is then returned.
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pub(in crate::plonk) fn commit_permuted<
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C: CurveAffine,
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HBase: Hasher<C::Base>,
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HScalar: Hasher<C::Scalar>,
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>(
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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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theta: C::Scalar,
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advice_values: &[Polynomial<C::Scalar, LagrangeCoeff>],
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fixed_values: &[Polynomial<C::Scalar, LagrangeCoeff>],
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aux_values: &[Polynomial<C::Scalar, LagrangeCoeff>],
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transcript: &mut Transcript<C, HBase, HScalar>,
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) -> Result<Permuted<C>, Error> {
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// Values of input columns involved in the lookup
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let unpermuted_input_values: Vec<Polynomial<C::Scalar, LagrangeCoeff>> = self
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.input_columns
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.iter()
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.map(|&input| match input.column_type() {
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Any::Advice => advice_values[input.index()].clone(),
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Any::Fixed => fixed_values[input.index()].clone(),
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Any::Aux => aux_values[input.index()].clone(),
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})
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.collect();
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// Compressed version of input columns
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let compressed_input_value = unpermuted_input_values
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.iter()
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.fold(domain.empty_lagrange(), |acc, input| acc * theta + input);
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// Values of table columns involved in the lookup
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let unpermuted_table_values: Vec<Polynomial<C::Scalar, LagrangeCoeff>> = self
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.table_columns
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.iter()
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.map(|&table| match table.column_type() {
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Any::Advice => advice_values[table.index()].clone(),
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Any::Fixed => fixed_values[table.index()].clone(),
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Any::Aux => aux_values[table.index()].clone(),
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})
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.collect();
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// Compressed version of table columns
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let compressed_table_value = unpermuted_table_values
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.iter()
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.fold(domain.empty_lagrange(), |acc, table| acc * theta + table);
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// Permute compressed (InputColumn, TableColumn) pair
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let (permuted_input_value, permuted_table_value) =
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permute_column_pair::<C>(domain, &compressed_input_value, &compressed_table_value)?;
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// Construct Permuted struct
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let permuted_input_poly = pk.vk.domain.lagrange_to_coeff(permuted_input_value.clone());
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let permuted_input_coset = pk
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.vk
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.domain
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.coeff_to_extended(permuted_input_poly.clone(), Rotation::default());
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let permuted_input_inv_coset = pk
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.vk
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.domain
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.coeff_to_extended(permuted_input_poly.clone(), Rotation(-1));
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let permuted_input_blind = Blind(C::Scalar::rand());
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let permuted_input_commitment = params
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.commit_lagrange(&permuted_input_value, permuted_input_blind)
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.to_affine();
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let permuted_table_poly = pk.vk.domain.lagrange_to_coeff(permuted_table_value.clone());
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let permuted_table_coset = pk
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.vk
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.domain
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.coeff_to_extended(permuted_table_poly.clone(), Rotation::default());
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let permuted_table_blind = Blind(C::Scalar::rand());
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let permuted_table_commitment = params
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.commit_lagrange(&permuted_table_value, permuted_table_blind)
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.to_affine();
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// Hash each permuted input commitment
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transcript
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.absorb_point(&permuted_input_commitment)
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.map_err(|_| Error::TranscriptError)?;
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// Hash each permuted table commitment
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transcript
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.absorb_point(&permuted_table_commitment)
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.map_err(|_| Error::TranscriptError)?;
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Ok(Permuted {
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permuted_input_value,
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permuted_input_poly,
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permuted_input_coset,
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permuted_input_inv_coset,
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permuted_input_blind,
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permuted_input_commitment,
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permuted_table_value,
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permuted_table_poly,
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permuted_table_coset,
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permuted_table_blind,
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permuted_table_commitment,
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})
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}
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2020-11-30 23:30:52 -08:00
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/// Given a Lookup with input columns, table columns, and the permuted
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/// input column and permuted table column, this method constructs the
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/// grand product polynomial over the lookup. The grand product polynomial
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/// is used to populate the Product<C> struct. The Product<C> struct is
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/// added to the Lookup and finally returned by the method.
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pub(in crate::plonk) fn commit_product<
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C: CurveAffine,
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HBase: Hasher<C::Base>,
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HScalar: Hasher<C::Scalar>,
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>(
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&self,
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permuted: &Permuted<C>,
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pk: &ProvingKey<C>,
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params: &Params<C>,
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theta: C::Scalar,
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beta: C::Scalar,
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gamma: C::Scalar,
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advice_values: &[Polynomial<C::Scalar, LagrangeCoeff>],
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fixed_values: &[Polynomial<C::Scalar, LagrangeCoeff>],
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aux_values: &[Polynomial<C::Scalar, LagrangeCoeff>],
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transcript: &mut Transcript<C, HBase, HScalar>,
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) -> Result<Product<C>, Error> {
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let permuted = permuted.clone();
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let unpermuted_input_values: Vec<Polynomial<C::Scalar, LagrangeCoeff>> = self
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.input_columns
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.iter()
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.map(|&input| match input.column_type() {
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Any::Advice => advice_values[input.index()].clone(),
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Any::Fixed => fixed_values[input.index()].clone(),
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Any::Aux => aux_values[input.index()].clone(),
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})
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.collect();
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let unpermuted_table_values: Vec<Polynomial<C::Scalar, LagrangeCoeff>> = self
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.table_columns
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.iter()
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.map(|&table| match table.column_type() {
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Any::Advice => advice_values[table.index()].clone(),
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Any::Fixed => fixed_values[table.index()].clone(),
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Any::Aux => aux_values[table.index()].clone(),
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})
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.collect();
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// Goal is to compute the products of fractions
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//
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// (a_1(\omega^i) + \theta a_2(\omega^i) + ... + beta)(s_1(\omega^i) + \theta(\omega^i) + ... + \gamma) /
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// (a'(\omega^i) + \beta)(s'(\omega^i) + \gamma)
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//
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// where a_j(X) is the jth input column in this lookup,
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// where a'(X) is the compression of the permuted input columns,
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// s_j(X) is the jth table column in this lookup,
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// s'(X) is the compression of the permuted table columns,
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// and i is the ith row of the column.
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let mut lookup_product = vec![C::Scalar::one(); params.n as usize];
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// Denominator uses the permuted input column and permuted table column
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parallelize(&mut lookup_product, |lookup_product, start| {
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for ((lookup_product, permuted_input_value), permuted_table_value) in lookup_product
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.iter_mut()
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.zip(permuted.permuted_input_value[start..].iter())
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.zip(permuted.permuted_table_value[start..].iter())
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{
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*lookup_product *= &(beta + permuted_input_value);
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*lookup_product *= &(gamma + permuted_table_value);
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}
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});
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// Batch invert to obtain the denominators for the lookup product
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// polynomials
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lookup_product.iter_mut().batch_invert();
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// Finish the computation of the entire fraction by computing the numerators
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// (a_1(X) + \theta a_2(X) + ... + \beta) (s_1(X) + \theta s_2(X) + ... + \gamma)
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// Compress unpermuted input columns
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let mut input_term = vec![C::Scalar::zero(); params.n as usize];
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for unpermuted_input_value in unpermuted_input_values.iter() {
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parallelize(&mut input_term, |input_term, start| {
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for (input_term, input_value) in input_term
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.iter_mut()
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.zip(unpermuted_input_value[start..].iter())
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{
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*input_term *= θ
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*input_term += input_value;
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}
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});
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}
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// Compress unpermuted table columns
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let mut table_term = vec![C::Scalar::zero(); params.n as usize];
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for unpermuted_table_value in unpermuted_table_values.iter() {
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parallelize(&mut table_term, |table_term, start| {
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for (table_term, fixed_value) in table_term
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.iter_mut()
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.zip(unpermuted_table_value[start..].iter())
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{
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*table_term *= θ
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*table_term += fixed_value;
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}
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});
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}
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// Add \beta and \gamma offsets
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parallelize(&mut lookup_product, |product, start| {
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for ((product, input_term), table_term) in product
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.iter_mut()
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.zip(input_term[start..].iter())
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.zip(table_term[start..].iter())
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{
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*product *= &(*input_term + &beta);
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*product *= &(*table_term + &gamma);
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}
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});
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// The product vector is a vector of products of fractions of the form
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//
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// (a_1(\omega^i) + \theta a_2(\omega^i) + ... + \beta)(s_1(\omega^i) + \theta s_2(\omega^i) + ... + \gamma)/
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// (a'(\omega^i) + \beta) (s'(\omega^i) + \gamma)
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//
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// where a_j(\omega^i) is the jth input column in this lookup,
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// a'j(\omega^i) is the permuted input column,
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// s_j(\omega^i) is the jth table column in this lookup,
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// s'(\omega^i) is the permuted table column,
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// and i is the ith row of the column.
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// Compute the evaluations of the lookup 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 *= &lookup_product[row];
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z.push(tmp);
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}
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let z = pk.vk.domain.lagrange_from_vec(z);
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#[cfg(feature = "sanity-checks")]
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// This test works only with intermediate representations in this method.
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// It can be used for debugging purposes.
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{
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// While in Lagrange basis, check that product is correctly constructed
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let n = params.n as usize;
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// z'(X) (a'(X) + \beta) (s'(X) + \gamma)
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// - z'(\omega^{-1} X) (a_1(X) + \theta a_2(X) + ... + \beta) (s_1(X) + \theta s_2(X) + ... + \gamma)
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for i in 0..n {
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let prev_idx = (n + i - 1) % n;
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let mut left = z[i];
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let permuted_input_value = &permuted.permuted_input_value[i];
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let permuted_table_value = &permuted.permuted_table_value[i];
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left *= &(*beta + permuted_input_value);
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left *= &(*gamma + permuted_table_value);
|
|
|
|
|
|
|
|
let mut right = z[prev_idx];
|
|
|
|
let mut input_term = unpermuted_input_values
|
|
|
|
.iter()
|
|
|
|
.fold(C::Scalar::zero(), |acc, input| acc * &theta + &input[i]);
|
|
|
|
|
|
|
|
let mut table_term = unpermuted_table_values
|
|
|
|
.iter()
|
|
|
|
.fold(C::Scalar::zero(), |acc, table| acc * &theta + &table[i]);
|
|
|
|
|
|
|
|
input_term += &(*beta);
|
|
|
|
table_term += &(*gamma);
|
|
|
|
right *= &(input_term * &table_term);
|
|
|
|
|
|
|
|
assert_eq!(left, right);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
let product_blind = Blind(C::Scalar::rand());
|
|
|
|
let product_commitment = params.commit_lagrange(&z, product_blind).to_affine();
|
|
|
|
let z = pk.vk.domain.lagrange_to_coeff(z);
|
|
|
|
let product_coset = pk
|
|
|
|
.vk
|
|
|
|
.domain
|
|
|
|
.coeff_to_extended(z.clone(), Rotation::default());
|
|
|
|
let product_inv_coset = pk.vk.domain.coeff_to_extended(z.clone(), Rotation(-1));
|
|
|
|
|
|
|
|
// Hash each product commitment
|
|
|
|
transcript
|
|
|
|
.absorb_point(&product_commitment)
|
|
|
|
.map_err(|_| Error::TranscriptError)?;
|
|
|
|
|
|
|
|
Ok(Product::<C> {
|
|
|
|
product_poly: z,
|
|
|
|
product_coset,
|
|
|
|
product_inv_coset,
|
|
|
|
product_commitment,
|
|
|
|
product_blind,
|
|
|
|
})
|
|
|
|
}
|
2020-11-30 23:22:11 -08:00
|
|
|
}
|
|
|
|
|
|
|
|
/// Given a column of input values A and a column of table values S,
|
|
|
|
/// 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.
|
|
|
|
fn permute_column_pair<C: CurveAffine>(
|
|
|
|
domain: &EvaluationDomain<C::Scalar>,
|
|
|
|
input_column: &Polynomial<C::Scalar, LagrangeCoeff>,
|
|
|
|
table_column: &Polynomial<C::Scalar, LagrangeCoeff>,
|
|
|
|
) -> Result<
|
|
|
|
(
|
|
|
|
Polynomial<C::Scalar, LagrangeCoeff>,
|
|
|
|
Polynomial<C::Scalar, LagrangeCoeff>,
|
|
|
|
),
|
|
|
|
Error,
|
|
|
|
> {
|
|
|
|
let mut permuted_input_column = input_column.clone();
|
|
|
|
|
|
|
|
// Sort input lookup column values
|
|
|
|
permuted_input_column.sort();
|
|
|
|
|
|
|
|
// A BTreeMap of each unique element in the table column and its count
|
|
|
|
let mut leftover_table_map: BTreeMap<C::Scalar, u32> =
|
|
|
|
table_column.iter().fold(BTreeMap::new(), |mut acc, coeff| {
|
|
|
|
*acc.entry(*coeff).or_insert(0) += 1;
|
|
|
|
acc
|
|
|
|
});
|
|
|
|
let mut repeated_input_rows = vec![];
|
|
|
|
let mut permuted_table_coeffs = vec![C::Scalar::zero(); table_column.len()];
|
|
|
|
|
|
|
|
for row in 0..permuted_input_column.len() {
|
|
|
|
let input_value = permuted_input_column[row];
|
|
|
|
|
|
|
|
// If this is the first occurence of `input_value` in the input column
|
|
|
|
if row == 0 || input_value != permuted_input_column[row - 1] {
|
|
|
|
permuted_table_coeffs[row] = input_value;
|
|
|
|
// Remove one instance of input_value from leftover_table_map
|
|
|
|
if let Some(count) = leftover_table_map.get_mut(&input_value) {
|
|
|
|
assert!(*count > 0);
|
|
|
|
*count -= 1;
|
|
|
|
} else {
|
|
|
|
// Return error if input_value not found
|
|
|
|
return Err(Error::ConstraintSystemFailure);
|
|
|
|
}
|
|
|
|
// If input value is repeated
|
|
|
|
} else {
|
|
|
|
repeated_input_rows.push(row);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Populate permuted table at unfilled rows with leftover table elements
|
|
|
|
for (coeff, count) in leftover_table_map.iter() {
|
|
|
|
for _ in 0..*count {
|
|
|
|
permuted_table_coeffs[repeated_input_rows.pop().unwrap() as usize] = *coeff;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
assert!(repeated_input_rows.is_empty());
|
|
|
|
|
|
|
|
let mut permuted_table_column = domain.empty_lagrange();
|
|
|
|
parallelize(
|
|
|
|
&mut permuted_table_column,
|
|
|
|
|permuted_table_column, start| {
|
|
|
|
for (permuted_table_value, permuted_table_coeff) in permuted_table_column
|
|
|
|
.iter_mut()
|
|
|
|
.zip(permuted_table_coeffs[start..].iter())
|
|
|
|
{
|
|
|
|
*permuted_table_value += permuted_table_coeff;
|
|
|
|
}
|
|
|
|
},
|
|
|
|
);
|
|
|
|
|
|
|
|
Ok((permuted_input_column, permuted_table_column))
|
|
|
|
}
|