Browse Source
spark-based commitments to R1CS matrices (#152)
* spark-based commitments to R1CS matrices * small fixesmain
Srinath Setty
1 year ago
committed by
GitHub
GitHub
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GPG Key ID: 4AEE18F83AFDEB23
20 changed files with 1758 additions and 98 deletions
Unified View
Diff Options
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+1 -1Cargo.toml
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+5 -3benches/compressed-snark.rs
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+5 -3examples/minroot.rs
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+1 -2src/bellperson/mod.rs
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+6 -10src/bellperson/r1cs.rs
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+2 -2src/circuit.rs
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+6 -0src/errors.rs
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+3 -6src/gadgets/ecc.rs
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+103 -13src/lib.rs
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+2 -3src/nifs.rs
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+6 -2src/provider/ipa_pc.rs
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+5 -2src/r1cs.rs
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+30 -0src/spartan/math.rs
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+124 -46src/spartan/mod.rs
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+20 -2src/spartan/polynomial.rs
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+220 -0src/spartan/spark/mod.rs
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+477 -0src/spartan/spark/product.rs
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+732 -0src/spartan/spark/sparse.rs
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+6 -2src/spartan/sumcheck.rs
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+4 -1src/traits/snark.rs
@ -0,0 +1,30 @@ |
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pub trait Math {
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fn pow2(self) -> usize;
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fn get_bits(self, num_bits: usize) -> Vec<bool>;
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fn log_2(self) -> usize;
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}
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impl Math for usize {
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#[inline]
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fn pow2(self) -> usize {
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let base: usize = 2;
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base.pow(self as u32)
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}
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/// Returns the num_bits from n in a canonical order
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fn get_bits(self, num_bits: usize) -> Vec<bool> {
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(0..num_bits)
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.map(|shift_amount| ((self & (1 << (num_bits - shift_amount - 1))) > 0))
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.collect::<Vec<bool>>()
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}
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fn log_2(self) -> usize {
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assert_ne!(self, 0);
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if self.is_power_of_two() {
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(1usize.leading_zeros() - self.leading_zeros()) as usize
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} else {
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(0usize.leading_zeros() - self.leading_zeros()) as usize
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}
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}
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}
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@ -0,0 +1,220 @@ |
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//! This module implements `CompCommitmentEngineTrait` using Spartan's SPARK compiler
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//! We also provide a trivial implementation that has the verifier evaluate the sparse polynomials
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use crate::{
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errors::NovaError,
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r1cs::R1CSShape,
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spartan::{math::Math, CompCommitmentEngineTrait},
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traits::{evaluation::EvaluationEngineTrait, Group, TranscriptReprTrait},
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CommitmentKey,
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};
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use core::marker::PhantomData;
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use serde::{Deserialize, Serialize};
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/// A trivial implementation of `ComputationCommitmentEngineTrait`
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pub struct TrivialCompComputationEngine<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> {
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_p: PhantomData<G>,
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_p2: PhantomData<EE>,
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}
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/// Provides an implementation of a trivial commitment
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#[derive(Clone, Debug, Serialize, Deserialize)]
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#[serde(bound = "")]
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pub struct TrivialCommitment<G: Group> {
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S: R1CSShape<G>,
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}
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/// Provides an implementation of a trivial decommitment
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#[derive(Clone, Debug, Serialize, Deserialize)]
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#[serde(bound = "")]
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pub struct TrivialDecommitment<G: Group> {
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_p: PhantomData<G>,
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}
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/// Provides an implementation of a trivial evaluation argument
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#[derive(Clone, Debug, Serialize, Deserialize)]
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#[serde(bound = "")]
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pub struct TrivialEvaluationArgument<G: Group> {
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_p: PhantomData<G>,
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}
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impl<G: Group> TranscriptReprTrait<G> for TrivialCommitment<G> {
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fn to_transcript_bytes(&self) -> Vec<u8> {
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self.S.to_transcript_bytes()
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}
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}
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impl<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> CompCommitmentEngineTrait<G, EE>
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for TrivialCompComputationEngine<G, EE>
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{
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type Decommitment = TrivialDecommitment<G>;
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type Commitment = TrivialCommitment<G>;
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type EvaluationArgument = TrivialEvaluationArgument<G>;
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/// commits to R1CS matrices
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fn commit(
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_ck: &CommitmentKey<G>,
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S: &R1CSShape<G>,
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) -> Result<(Self::Commitment, Self::Decommitment), NovaError> {
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Ok((
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TrivialCommitment { S: S.clone() },
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TrivialDecommitment {
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_p: Default::default(),
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},
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))
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}
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/// proves an evaluation of R1CS matrices viewed as polynomials
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fn prove(
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_ck: &CommitmentKey<G>,
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_ek: &EE::ProverKey,
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_S: &R1CSShape<G>,
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_decomm: &Self::Decommitment,
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_comm: &Self::Commitment,
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_r: &(&[G::Scalar], &[G::Scalar]),
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_transcript: &mut G::TE,
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) -> Result<Self::EvaluationArgument, NovaError> {
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Ok(TrivialEvaluationArgument {
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_p: Default::default(),
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})
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}
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/// verifies an evaluation of R1CS matrices viewed as polynomials
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fn verify(
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_vk: &EE::VerifierKey,
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comm: &Self::Commitment,
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r: &(&[G::Scalar], &[G::Scalar]),
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_arg: &Self::EvaluationArgument,
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_transcript: &mut G::TE,
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) -> Result<(G::Scalar, G::Scalar, G::Scalar), NovaError> {
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let (r_x, r_y) = r;
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let evals = SparsePolynomial::<G>::multi_evaluate(&[&comm.S.A, &comm.S.B, &comm.S.C], r_x, r_y);
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Ok((evals[0], evals[1], evals[2]))
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}
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}
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mod product;
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mod sparse;
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use sparse::{SparseEvaluationArgument, SparsePolynomial, SparsePolynomialCommitment};
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/// A non-trivial implementation of `CompCommitmentEngineTrait` using Spartan's SPARK compiler
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pub struct SparkEngine<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> {
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_p: PhantomData<G>,
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_p2: PhantomData<EE>,
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}
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/// An implementation of Spark decommitment
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#[derive(Clone, Serialize, Deserialize)]
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#[serde(bound = "")]
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pub struct SparkDecommitment<G: Group> {
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A: SparsePolynomial<G>,
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B: SparsePolynomial<G>,
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C: SparsePolynomial<G>,
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}
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impl<G: Group> SparkDecommitment<G> {
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fn new(S: &R1CSShape<G>) -> Self {
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let ell = (S.num_cons.log_2(), S.num_vars.log_2() + 1);
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let A = SparsePolynomial::new(ell, &S.A);
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let B = SparsePolynomial::new(ell, &S.B);
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let C = SparsePolynomial::new(ell, &S.C);
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Self { A, B, C }
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}
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fn commit(&self, ck: &CommitmentKey<G>) -> SparkCommitment<G> {
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let comm_A = self.A.commit(ck);
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let comm_B = self.B.commit(ck);
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let comm_C = self.C.commit(ck);
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SparkCommitment {
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comm_A,
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comm_B,
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comm_C,
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}
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}
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}
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/// An implementation of Spark commitment
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#[derive(Clone, Serialize, Deserialize)]
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#[serde(bound = "")]
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pub struct SparkCommitment<G: Group> {
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comm_A: SparsePolynomialCommitment<G>,
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comm_B: SparsePolynomialCommitment<G>,
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comm_C: SparsePolynomialCommitment<G>,
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}
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impl<G: Group> TranscriptReprTrait<G> for SparkCommitment<G> {
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fn to_transcript_bytes(&self) -> Vec<u8> {
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let mut bytes = self.comm_A.to_transcript_bytes();
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bytes.extend(self.comm_B.to_transcript_bytes());
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bytes.extend(self.comm_C.to_transcript_bytes());
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bytes
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}
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}
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/// Provides an implementation of a trivial evaluation argument
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#[derive(Clone, Serialize, Deserialize)]
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#[serde(bound = "")]
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pub struct SparkEvaluationArgument<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> {
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arg_A: SparseEvaluationArgument<G, EE>,
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arg_B: SparseEvaluationArgument<G, EE>,
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arg_C: SparseEvaluationArgument<G, EE>,
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}
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impl<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> CompCommitmentEngineTrait<G, EE>
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for SparkEngine<G, EE>
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{
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type Decommitment = SparkDecommitment<G>;
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type Commitment = SparkCommitment<G>;
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type EvaluationArgument = SparkEvaluationArgument<G, EE>;
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/// commits to R1CS matrices
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fn commit(
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ck: &CommitmentKey<G>,
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S: &R1CSShape<G>,
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) -> Result<(Self::Commitment, Self::Decommitment), NovaError> {
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let sparse = SparkDecommitment::new(S);
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let comm = sparse.commit(ck);
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Ok((comm, sparse))
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}
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/// proves an evaluation of R1CS matrices viewed as polynomials
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fn prove(
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ck: &CommitmentKey<G>,
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pk_ee: &EE::ProverKey,
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S: &R1CSShape<G>,
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decomm: &Self::Decommitment,
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comm: &Self::Commitment,
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r: &(&[G::Scalar], &[G::Scalar]),
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transcript: &mut G::TE,
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) -> Result<Self::EvaluationArgument, NovaError> {
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let arg_A =
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SparseEvaluationArgument::prove(ck, pk_ee, &decomm.A, &S.A, &comm.comm_A, r, transcript)?;
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let arg_B =
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SparseEvaluationArgument::prove(ck, pk_ee, &decomm.B, &S.B, &comm.comm_B, r, transcript)?;
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let arg_C =
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SparseEvaluationArgument::prove(ck, pk_ee, &decomm.C, &S.C, &comm.comm_C, r, transcript)?;
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Ok(SparkEvaluationArgument {
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arg_A,
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arg_B,
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arg_C,
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})
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}
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/// verifies an evaluation of R1CS matrices viewed as polynomials
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fn verify(
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vk_ee: &EE::VerifierKey,
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comm: &Self::Commitment,
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|
r: &(&[G::Scalar], &[G::Scalar]),
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arg: &Self::EvaluationArgument,
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transcript: &mut G::TE,
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) -> Result<(G::Scalar, G::Scalar, G::Scalar), NovaError> {
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let eval_A = arg.arg_A.verify(vk_ee, &comm.comm_A, r, transcript)?;
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let eval_B = arg.arg_B.verify(vk_ee, &comm.comm_B, r, transcript)?;
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let eval_C = arg.arg_C.verify(vk_ee, &comm.comm_C, r, transcript)?;
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Ok((eval_A, eval_B, eval_C))
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}
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}
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@ -0,0 +1,477 @@ |
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use crate::{
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errors::NovaError,
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spartan::{
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math::Math,
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polynomial::{EqPolynomial, MultilinearPolynomial},
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sumcheck::{CompressedUniPoly, SumcheckProof, UniPoly},
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},
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traits::{Group, TranscriptEngineTrait},
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};
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use core::marker::PhantomData;
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use ff::{Field, PrimeField};
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use serde::{Deserialize, Serialize};
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pub(crate) struct IdentityPolynomial<Scalar: PrimeField> {
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ell: usize,
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_p: PhantomData<Scalar>,
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}
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|
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impl<Scalar: PrimeField> IdentityPolynomial<Scalar> {
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pub fn new(ell: usize) -> Self {
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IdentityPolynomial {
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ell,
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_p: Default::default(),
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}
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}
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|
|
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pub fn evaluate(&self, r: &[Scalar]) -> Scalar {
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assert_eq!(self.ell, r.len());
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(0..self.ell)
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.map(|i| Scalar::from(2_usize.pow((self.ell - i - 1) as u32) as u64) * r[i])
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.fold(Scalar::zero(), |acc, item| acc + item)
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}
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}
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|
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impl<G: Group> SumcheckProof<G> {
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pub fn prove_cubic<F>(
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claim: &G::Scalar,
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num_rounds: usize,
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poly_A: &mut MultilinearPolynomial<G::Scalar>,
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poly_B: &mut MultilinearPolynomial<G::Scalar>,
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|
poly_C: &mut MultilinearPolynomial<G::Scalar>,
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|
comb_func: F,
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|
transcript: &mut G::TE,
|
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|
) -> Result<(Self, Vec<G::Scalar>, Vec<G::Scalar>), NovaError>
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|
where
|
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|
F: Fn(&G::Scalar, &G::Scalar, &G::Scalar) -> G::Scalar,
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|
{
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let mut e = *claim;
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let mut r: Vec<G::Scalar> = Vec::new();
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|
let mut cubic_polys: Vec<CompressedUniPoly<G>> = Vec::new();
|
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|
for _j in 0..num_rounds {
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|
let mut eval_point_0 = G::Scalar::zero();
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|
let mut eval_point_2 = G::Scalar::zero();
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|
let mut eval_point_3 = G::Scalar::zero();
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|
|
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|
let len = poly_A.len() / 2;
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|
for i in 0..len {
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|
// eval 0: bound_func is A(low)
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eval_point_0 += comb_func(&poly_A[i], &poly_B[i], &poly_C[i]);
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|
|
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|
// eval 2: bound_func is -A(low) + 2*A(high)
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|
let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
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|
let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
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|
let poly_C_bound_point = poly_C[len + i] + poly_C[len + i] - poly_C[i];
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|
eval_point_2 += comb_func(
|
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|
&poly_A_bound_point,
|
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|
&poly_B_bound_point,
|
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|
&poly_C_bound_point,
|
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|
);
|
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|
|
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|
// eval 3: bound_func is -2A(low) + 3A(high); computed incrementally with bound_func applied to eval(2)
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|
let poly_A_bound_point = poly_A_bound_point + poly_A[len + i] - poly_A[i];
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|
let poly_B_bound_point = poly_B_bound_point + poly_B[len + i] - poly_B[i];
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|
let poly_C_bound_point = poly_C_bound_point + poly_C[len + i] - poly_C[i];
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|
|
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|
eval_point_3 += comb_func(
|
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|
&poly_A_bound_point,
|
||||
|
&poly_B_bound_point,
|
||||
|
&poly_C_bound_point,
|
||||
|
);
|
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|
}
|
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|
|
||||
|
let evals = vec![eval_point_0, e - eval_point_0, eval_point_2, eval_point_3];
|
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|
let poly = UniPoly::from_evals(&evals);
|
||||
|
|
||||
|
// append the prover's message to the transcript
|
||||
|
transcript.absorb(b"p", &poly);
|
||||
|
|
||||
|
//derive the verifier's challenge for the next round
|
||||
|
let r_i = transcript.squeeze(b"c")?;
|
||||
|
r.push(r_i);
|
||||
|
|
||||
|
// bound all tables to the verifier's challenege
|
||||
|
poly_A.bound_poly_var_top(&r_i);
|
||||
|
poly_B.bound_poly_var_top(&r_i);
|
||||
|
poly_C.bound_poly_var_top(&r_i);
|
||||
|
e = poly.evaluate(&r_i);
|
||||
|
cubic_polys.push(poly.compress());
|
||||
|
}
|
||||
|
|
||||
|
Ok((
|
||||
|
Self::new(cubic_polys),
|
||||
|
r,
|
||||
|
vec![poly_A[0], poly_B[0], poly_C[0]],
|
||||
|
))
|
||||
|
}
|
||||
|
|
||||
|
pub fn prove_cubic_batched<F>(
|
||||
|
claim: &G::Scalar,
|
||||
|
num_rounds: usize,
|
||||
|
poly_vec: (
|
||||
|
&mut Vec<&mut MultilinearPolynomial<G::Scalar>>,
|
||||
|
&mut Vec<&mut MultilinearPolynomial<G::Scalar>>,
|
||||
|
&mut MultilinearPolynomial<G::Scalar>,
|
||||
|
),
|
||||
|
coeffs: &[G::Scalar],
|
||||
|
comb_func: F,
|
||||
|
transcript: &mut G::TE,
|
||||
|
) -> Result<
|
||||
|
(
|
||||
|
Self,
|
||||
|
Vec<G::Scalar>,
|
||||
|
(Vec<G::Scalar>, Vec<G::Scalar>, G::Scalar),
|
||||
|
),
|
||||
|
NovaError,
|
||||
|
>
|
||||
|
where
|
||||
|
F: Fn(&G::Scalar, &G::Scalar, &G::Scalar) -> G::Scalar,
|
||||
|
{
|
||||
|
let (poly_A_vec, poly_B_vec, poly_C) = poly_vec;
|
||||
|
|
||||
|
let mut e = *claim;
|
||||
|
let mut r: Vec<G::Scalar> = Vec::new();
|
||||
|
let mut cubic_polys: Vec<CompressedUniPoly<G>> = Vec::new();
|
||||
|
|
||||
|
for _j in 0..num_rounds {
|
||||
|
let mut evals: Vec<(G::Scalar, G::Scalar, G::Scalar)> = Vec::new();
|
||||
|
|
||||
|
for (poly_A, poly_B) in poly_A_vec.iter().zip(poly_B_vec.iter()) {
|
||||
|
let mut eval_point_0 = G::Scalar::zero();
|
||||
|
let mut eval_point_2 = G::Scalar::zero();
|
||||
|
let mut eval_point_3 = G::Scalar::zero();
|
||||
|
|
||||
|
let len = poly_A.len() / 2;
|
||||
|
for i in 0..len {
|
||||
|
// eval 0: bound_func is A(low)
|
||||
|
eval_point_0 += comb_func(&poly_A[i], &poly_B[i], &poly_C[i]);
|
||||
|
|
||||
|
// eval 2: bound_func is -A(low) + 2*A(high)
|
||||
|
let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
|
||||
|
let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
|
||||
|
let poly_C_bound_point = poly_C[len + i] + poly_C[len + i] - poly_C[i];
|
||||
|
eval_point_2 += comb_func(
|
||||
|
&poly_A_bound_point,
|
||||
|
&poly_B_bound_point,
|
||||
|
&poly_C_bound_point,
|
||||
|
);
|
||||
|
|
||||
|
// eval 3: bound_func is -2A(low) + 3A(high); computed incrementally with bound_func applied to eval(2)
|
||||
|
let poly_A_bound_point = poly_A_bound_point + poly_A[len + i] - poly_A[i];
|
||||
|
let poly_B_bound_point = poly_B_bound_point + poly_B[len + i] - poly_B[i];
|
||||
|
let poly_C_bound_point = poly_C_bound_point + poly_C[len + i] - poly_C[i];
|
||||
|
|
||||
|
eval_point_3 += comb_func(
|
||||
|
&poly_A_bound_point,
|
||||
|
&poly_B_bound_point,
|
||||
|
&poly_C_bound_point,
|
||||
|
);
|
||||
|
}
|
||||
|
|
||||
|
evals.push((eval_point_0, eval_point_2, eval_point_3));
|
||||
|
}
|
||||
|
|
||||
|
let evals_combined_0 = (0..evals.len())
|
||||
|
.map(|i| evals[i].0 * coeffs[i])
|
||||
|
.fold(G::Scalar::zero(), |acc, item| acc + item);
|
||||
|
let evals_combined_2 = (0..evals.len())
|
||||
|
.map(|i| evals[i].1 * coeffs[i])
|
||||
|
.fold(G::Scalar::zero(), |acc, item| acc + item);
|
||||
|
let evals_combined_3 = (0..evals.len())
|
||||
|
.map(|i| evals[i].2 * coeffs[i])
|
||||
|
.fold(G::Scalar::zero(), |acc, item| acc + item);
|
||||
|
|
||||
|
let evals = vec![
|
||||
|
evals_combined_0,
|
||||
|
e - evals_combined_0,
|
||||
|
evals_combined_2,
|
||||
|
evals_combined_3,
|
||||
|
];
|
||||
|
let poly = UniPoly::from_evals(&evals);
|
||||
|
|
||||
|
// append the prover's message to the transcript
|
||||
|
transcript.absorb(b"p", &poly);
|
||||
|
|
||||
|
// derive the verifier's challenge for the next round
|
||||
|
let r_i = transcript.squeeze(b"c")?;
|
||||
|
r.push(r_i);
|
||||
|
|
||||
|
// bound all tables to the verifier's challenege
|
||||
|
for (poly_A, poly_B) in poly_A_vec.iter_mut().zip(poly_B_vec.iter_mut()) {
|
||||
|
poly_A.bound_poly_var_top(&r_i);
|
||||
|
poly_B.bound_poly_var_top(&r_i);
|
||||
|
}
|
||||
|
poly_C.bound_poly_var_top(&r_i);
|
||||
|
|
||||
|
e = poly.evaluate(&r_i);
|
||||
|
cubic_polys.push(poly.compress());
|
||||
|
}
|
||||
|
|
||||
|
let poly_A_final = (0..poly_A_vec.len()).map(|i| poly_A_vec[i][0]).collect();
|
||||
|
let poly_B_final = (0..poly_B_vec.len()).map(|i| poly_B_vec[i][0]).collect();
|
||||
|
let claims_prod = (poly_A_final, poly_B_final, poly_C[0]);
|
||||
|
|
||||
|
Ok((SumcheckProof::new(cubic_polys), r, claims_prod))
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
#[derive(Debug)]
|
||||
|
pub struct ProductArgumentInputs<G: Group> {
|
||||
|
left_vec: Vec<MultilinearPolynomial<G::Scalar>>,
|
||||
|
right_vec: Vec<MultilinearPolynomial<G::Scalar>>,
|
||||
|
}
|
||||
|
|
||||
|
impl<G: Group> ProductArgumentInputs<G> {
|
||||
|
fn compute_layer(
|
||||
|
inp_left: &MultilinearPolynomial<G::Scalar>,
|
||||
|
inp_right: &MultilinearPolynomial<G::Scalar>,
|
||||
|
) -> (
|
||||
|
MultilinearPolynomial<G::Scalar>,
|
||||
|
MultilinearPolynomial<G::Scalar>,
|
||||
|
) {
|
||||
|
let len = inp_left.len() + inp_right.len();
|
||||
|
let outp_left = (0..len / 4)
|
||||
|
.map(|i| inp_left[i] * inp_right[i])
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
let outp_right = (len / 4..len / 2)
|
||||
|
.map(|i| inp_left[i] * inp_right[i])
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
|
||||
|
(
|
||||
|
MultilinearPolynomial::new(outp_left),
|
||||
|
MultilinearPolynomial::new(outp_right),
|
||||
|
)
|
||||
|
}
|
||||
|
|
||||
|
pub fn new(poly: &MultilinearPolynomial<G::Scalar>) -> Self {
|
||||
|
let mut left_vec: Vec<MultilinearPolynomial<G::Scalar>> = Vec::new();
|
||||
|
let mut right_vec: Vec<MultilinearPolynomial<G::Scalar>> = Vec::new();
|
||||
|
let num_layers = poly.len().log_2();
|
||||
|
let (outp_left, outp_right) = poly.split(poly.len() / 2);
|
||||
|
|
||||
|
left_vec.push(outp_left);
|
||||
|
right_vec.push(outp_right);
|
||||
|
|
||||
|
for i in 0..num_layers - 1 {
|
||||
|
let (outp_left, outp_right) =
|
||||
|
ProductArgumentInputs::<G>::compute_layer(&left_vec[i], &right_vec[i]);
|
||||
|
left_vec.push(outp_left);
|
||||
|
right_vec.push(outp_right);
|
||||
|
}
|
||||
|
|
||||
|
Self {
|
||||
|
left_vec,
|
||||
|
right_vec,
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
pub fn evaluate(&self) -> G::Scalar {
|
||||
|
let len = self.left_vec.len();
|
||||
|
assert_eq!(self.left_vec[len - 1].get_num_vars(), 0);
|
||||
|
assert_eq!(self.right_vec[len - 1].get_num_vars(), 0);
|
||||
|
self.left_vec[len - 1][0] * self.right_vec[len - 1][0]
|
||||
|
}
|
||||
|
}
|
||||
|
#[derive(Clone, Debug, Serialize, Deserialize)]
|
||||
|
#[serde(bound = "")]
|
||||
|
pub struct LayerProofBatched<G: Group> {
|
||||
|
proof: SumcheckProof<G>,
|
||||
|
claims_prod_left: Vec<G::Scalar>,
|
||||
|
claims_prod_right: Vec<G::Scalar>,
|
||||
|
}
|
||||
|
|
||||
|
impl<G: Group> LayerProofBatched<G> {
|
||||
|
pub fn verify(
|
||||
|
&self,
|
||||
|
claim: G::Scalar,
|
||||
|
num_rounds: usize,
|
||||
|
degree_bound: usize,
|
||||
|
transcript: &mut G::TE,
|
||||
|
) -> Result<(G::Scalar, Vec<G::Scalar>), NovaError> {
|
||||
|
self
|
||||
|
.proof
|
||||
|
.verify(claim, num_rounds, degree_bound, transcript)
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
#[derive(Clone, Debug, Serialize, Deserialize)]
|
||||
|
#[serde(bound = "")]
|
||||
|
pub(crate) struct ProductArgumentBatched<G: Group> {
|
||||
|
proof: Vec<LayerProofBatched<G>>,
|
||||
|
}
|
||||
|
|
||||
|
impl<G: Group> ProductArgumentBatched<G> {
|
||||
|
pub fn prove(
|
||||
|
poly_vec: &[&MultilinearPolynomial<G::Scalar>],
|
||||
|
transcript: &mut G::TE,
|
||||
|
) -> Result<(Self, Vec<G::Scalar>, Vec<G::Scalar>), NovaError> {
|
||||
|
let mut prod_circuit_vec: Vec<_> = (0..poly_vec.len())
|
||||
|
.map(|i| ProductArgumentInputs::<G>::new(poly_vec[i]))
|
||||
|
.collect();
|
||||
|
|
||||
|
let mut proof_layers: Vec<LayerProofBatched<G>> = Vec::new();
|
||||
|
let num_layers = prod_circuit_vec[0].left_vec.len();
|
||||
|
let evals = (0..prod_circuit_vec.len())
|
||||
|
.map(|i| prod_circuit_vec[i].evaluate())
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
|
||||
|
let mut claims_to_verify = evals.clone();
|
||||
|
let mut rand = Vec::new();
|
||||
|
for layer_id in (0..num_layers).rev() {
|
||||
|
let len = prod_circuit_vec[0].left_vec[layer_id].len()
|
||||
|
+ prod_circuit_vec[0].right_vec[layer_id].len();
|
||||
|
|
||||
|
let mut poly_C = MultilinearPolynomial::new(EqPolynomial::new(rand.clone()).evals());
|
||||
|
assert_eq!(poly_C.len(), len / 2);
|
||||
|
|
||||
|
let num_rounds_prod = poly_C.len().log_2();
|
||||
|
let comb_func_prod = |poly_A_comp: &G::Scalar,
|
||||
|
poly_B_comp: &G::Scalar,
|
||||
|
poly_C_comp: &G::Scalar|
|
||||
|
-> G::Scalar { *poly_A_comp * *poly_B_comp * *poly_C_comp };
|
||||
|
|
||||
|
let mut poly_A_batched: Vec<&mut MultilinearPolynomial<G::Scalar>> = Vec::new();
|
||||
|
let mut poly_B_batched: Vec<&mut MultilinearPolynomial<G::Scalar>> = Vec::new();
|
||||
|
for prod_circuit in prod_circuit_vec.iter_mut() {
|
||||
|
poly_A_batched.push(&mut prod_circuit.left_vec[layer_id]);
|
||||
|
poly_B_batched.push(&mut prod_circuit.right_vec[layer_id])
|
||||
|
}
|
||||
|
let poly_vec = (&mut poly_A_batched, &mut poly_B_batched, &mut poly_C);
|
||||
|
|
||||
|
// produce a fresh set of coeffs and a joint claim
|
||||
|
let coeff_vec = {
|
||||
|
let s = transcript.squeeze(b"r")?;
|
||||
|
let mut s_vec = vec![s];
|
||||
|
for i in 1..claims_to_verify.len() {
|
||||
|
s_vec.push(s_vec[i - 1] * s);
|
||||
|
}
|
||||
|
s_vec
|
||||
|
};
|
||||
|
|
||||
|
let claim = (0..claims_to_verify.len())
|
||||
|
.map(|i| claims_to_verify[i] * coeff_vec[i])
|
||||
|
.fold(G::Scalar::zero(), |acc, item| acc + item);
|
||||
|
|
||||
|
let (proof, rand_prod, claims_prod) = SumcheckProof::prove_cubic_batched(
|
||||
|
&claim,
|
||||
|
num_rounds_prod,
|
||||
|
poly_vec,
|
||||
|
&coeff_vec,
|
||||
|
comb_func_prod,
|
||||
|
transcript,
|
||||
|
)?;
|
||||
|
|
||||
|
let (claims_prod_left, claims_prod_right, _claims_eq) = claims_prod;
|
||||
|
|
||||
|
let v = {
|
||||
|
let mut v = claims_prod_left.clone();
|
||||
|
v.extend(&claims_prod_right);
|
||||
|
v
|
||||
|
};
|
||||
|
transcript.absorb(b"p", &v.as_slice());
|
||||
|
|
||||
|
// produce a random challenge to condense two claims into a single claim
|
||||
|
let r_layer = transcript.squeeze(b"c")?;
|
||||
|
|
||||
|
claims_to_verify = (0..prod_circuit_vec.len())
|
||||
|
.map(|i| claims_prod_left[i] + r_layer * (claims_prod_right[i] - claims_prod_left[i]))
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
|
||||
|
let mut ext = vec![r_layer];
|
||||
|
ext.extend(rand_prod);
|
||||
|
rand = ext;
|
||||
|
|
||||
|
proof_layers.push(LayerProofBatched {
|
||||
|
proof,
|
||||
|
claims_prod_left,
|
||||
|
claims_prod_right,
|
||||
|
});
|
||||
|
}
|
||||
|
|
||||
|
Ok((
|
||||
|
ProductArgumentBatched {
|
||||
|
proof: proof_layers,
|
||||
|
},
|
||||
|
evals,
|
||||
|
rand,
|
||||
|
))
|
||||
|
}
|
||||
|
|
||||
|
pub fn verify(
|
||||
|
&self,
|
||||
|
claims_prod_vec: &[G::Scalar],
|
||||
|
len: usize,
|
||||
|
transcript: &mut G::TE,
|
||||
|
) -> Result<(Vec<G::Scalar>, Vec<G::Scalar>), NovaError> {
|
||||
|
let num_layers = len.log_2();
|
||||
|
|
||||
|
let mut rand: Vec<G::Scalar> = Vec::new();
|
||||
|
if self.proof.len() != num_layers {
|
||||
|
return Err(NovaError::InvalidProductProof);
|
||||
|
}
|
||||
|
|
||||
|
let mut claims_to_verify = claims_prod_vec.to_owned();
|
||||
|
for (num_rounds, i) in (0..num_layers).enumerate() {
|
||||
|
// produce random coefficients, one for each instance
|
||||
|
let coeff_vec = {
|
||||
|
let s = transcript.squeeze(b"r")?;
|
||||
|
let mut s_vec = vec![s];
|
||||
|
for i in 1..claims_to_verify.len() {
|
||||
|
s_vec.push(s_vec[i - 1] * s);
|
||||
|
}
|
||||
|
s_vec
|
||||
|
};
|
||||
|
|
||||
|
// produce a joint claim
|
||||
|
let claim = (0..claims_to_verify.len())
|
||||
|
.map(|i| claims_to_verify[i] * coeff_vec[i])
|
||||
|
.fold(G::Scalar::zero(), |acc, item| acc + item);
|
||||
|
|
||||
|
let (claim_last, rand_prod) = self.proof[i].verify(claim, num_rounds, 3, transcript)?;
|
||||
|
|
||||
|
let claims_prod_left = &self.proof[i].claims_prod_left;
|
||||
|
let claims_prod_right = &self.proof[i].claims_prod_right;
|
||||
|
if claims_prod_left.len() != claims_prod_vec.len()
|
||||
|
|| claims_prod_right.len() != claims_prod_vec.len()
|
||||
|
{
|
||||
|
return Err(NovaError::InvalidProductProof);
|
||||
|
}
|
||||
|
|
||||
|
let v = {
|
||||
|
let mut v = claims_prod_left.clone();
|
||||
|
v.extend(claims_prod_right);
|
||||
|
v
|
||||
|
};
|
||||
|
transcript.absorb(b"p", &v.as_slice());
|
||||
|
|
||||
|
if rand.len() != rand_prod.len() {
|
||||
|
return Err(NovaError::InvalidProductProof);
|
||||
|
}
|
||||
|
|
||||
|
let eq: G::Scalar = (0..rand.len())
|
||||
|
.map(|i| {
|
||||
|
rand[i] * rand_prod[i] + (G::Scalar::one() - rand[i]) * (G::Scalar::one() - rand_prod[i])
|
||||
|
})
|
||||
|
.fold(G::Scalar::one(), |acc, item| acc * item);
|
||||
|
let claim_expected: G::Scalar = (0..claims_prod_vec.len())
|
||||
|
.map(|i| coeff_vec[i] * (claims_prod_left[i] * claims_prod_right[i] * eq))
|
||||
|
.fold(G::Scalar::zero(), |acc, item| acc + item);
|
||||
|
|
||||
|
if claim_expected != claim_last {
|
||||
|
return Err(NovaError::InvalidProductProof);
|
||||
|
}
|
||||
|
|
||||
|
// produce a random challenge
|
||||
|
let r_layer = transcript.squeeze(b"c")?;
|
||||
|
|
||||
|
claims_to_verify = (0..claims_prod_left.len())
|
||||
|
.map(|i| claims_prod_left[i] + r_layer * (claims_prod_right[i] - claims_prod_left[i]))
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
|
||||
|
let mut ext = vec![r_layer];
|
||||
|
ext.extend(rand_prod);
|
||||
|
rand = ext;
|
||||
|
}
|
||||
|
Ok((claims_to_verify, rand))
|
||||
|
}
|
||||
|
}
|
||||
@ -0,0 +1,732 @@ |
|||||
|
#![allow(clippy::type_complexity)]
|
||||
|
#![allow(clippy::too_many_arguments)]
|
||||
|
#![allow(clippy::needless_range_loop)]
|
||||
|
use crate::{
|
||||
|
errors::NovaError,
|
||||
|
spartan::{
|
||||
|
math::Math,
|
||||
|
polynomial::{EqPolynomial, MultilinearPolynomial},
|
||||
|
spark::product::{IdentityPolynomial, ProductArgumentBatched},
|
||||
|
SumcheckProof,
|
||||
|
},
|
||||
|
traits::{
|
||||
|
commitment::CommitmentEngineTrait, evaluation::EvaluationEngineTrait, Group,
|
||||
|
TranscriptEngineTrait, TranscriptReprTrait,
|
||||
|
},
|
||||
|
Commitment, CommitmentKey,
|
||||
|
};
|
||||
|
use ff::Field;
|
||||
|
use rayon::prelude::*;
|
||||
|
use serde::{Deserialize, Serialize};
|
||||
|
|
||||
|
/// A type that holds a sparse polynomial in dense representation
|
||||
|
#[derive(Clone, Serialize, Deserialize)]
|
||||
|
#[serde(bound = "")]
|
||||
|
pub struct SparsePolynomial<G: Group> {
|
||||
|
ell: (usize, usize), // number of variables in each dimension
|
||||
|
|
||||
|
// dense representation
|
||||
|
row: Vec<G::Scalar>,
|
||||
|
col: Vec<G::Scalar>,
|
||||
|
val: Vec<G::Scalar>,
|
||||
|
|
||||
|
// timestamp polynomials
|
||||
|
row_read_ts: Vec<G::Scalar>,
|
||||
|
row_audit_ts: Vec<G::Scalar>,
|
||||
|
col_read_ts: Vec<G::Scalar>,
|
||||
|
col_audit_ts: Vec<G::Scalar>,
|
||||
|
}
|
||||
|
|
||||
|
/// A type that holds a commitment to a sparse polynomial
|
||||
|
#[derive(Clone, Serialize, Deserialize)]
|
||||
|
#[serde(bound = "")]
|
||||
|
pub struct SparsePolynomialCommitment<G: Group> {
|
||||
|
ell: (usize, usize), // number of variables
|
||||
|
size: usize, // size of the dense representation
|
||||
|
|
||||
|
// commitments to the dense representation
|
||||
|
comm_row: Commitment<G>,
|
||||
|
comm_col: Commitment<G>,
|
||||
|
comm_val: Commitment<G>,
|
||||
|
|
||||
|
// commitments to the timestamp polynomials
|
||||
|
comm_row_read_ts: Commitment<G>,
|
||||
|
comm_row_audit_ts: Commitment<G>,
|
||||
|
comm_col_read_ts: Commitment<G>,
|
||||
|
comm_col_audit_ts: Commitment<G>,
|
||||
|
}
|
||||
|
|
||||
|
impl<G: Group> TranscriptReprTrait<G> for SparsePolynomialCommitment<G> {
|
||||
|
fn to_transcript_bytes(&self) -> Vec<u8> {
|
||||
|
[
|
||||
|
self.comm_row,
|
||||
|
self.comm_col,
|
||||
|
self.comm_val,
|
||||
|
self.comm_row_read_ts,
|
||||
|
self.comm_row_audit_ts,
|
||||
|
self.comm_col_read_ts,
|
||||
|
self.comm_col_audit_ts,
|
||||
|
]
|
||||
|
.as_slice()
|
||||
|
.to_transcript_bytes()
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
impl<G: Group> SparsePolynomial<G> {
|
||||
|
pub fn new(ell: (usize, usize), M: &[(usize, usize, G::Scalar)]) -> Self {
|
||||
|
let mut row = M.iter().map(|(r, _, _)| *r).collect::<Vec<usize>>();
|
||||
|
let mut col = M.iter().map(|(_, c, _)| *c).collect::<Vec<usize>>();
|
||||
|
let mut val = M.iter().map(|(_, _, v)| *v).collect::<Vec<G::Scalar>>();
|
||||
|
|
||||
|
let num_ops = M.len().next_power_of_two();
|
||||
|
let num_cells_row = ell.0.pow2();
|
||||
|
let num_cells_col = ell.1.pow2();
|
||||
|
row.resize(num_ops, 0usize);
|
||||
|
col.resize(num_ops, 0usize);
|
||||
|
val.resize(num_ops, G::Scalar::zero());
|
||||
|
|
||||
|
// timestamp calculation routine
|
||||
|
let timestamp_calc =
|
||||
|
|num_ops: usize, num_cells: usize, addr_trace: &[usize]| -> (Vec<usize>, Vec<usize>) {
|
||||
|
let mut read_ts = vec![0usize; num_ops];
|
||||
|
let mut audit_ts = vec![0usize; num_cells];
|
||||
|
|
||||
|
assert!(num_ops >= addr_trace.len());
|
||||
|
for i in 0..addr_trace.len() {
|
||||
|
let addr = addr_trace[i];
|
||||
|
assert!(addr < num_cells);
|
||||
|
let r_ts = audit_ts[addr];
|
||||
|
read_ts[i] = r_ts;
|
||||
|
|
||||
|
let w_ts = r_ts + 1;
|
||||
|
audit_ts[addr] = w_ts;
|
||||
|
}
|
||||
|
(read_ts, audit_ts)
|
||||
|
};
|
||||
|
|
||||
|
// timestamp polynomials for row
|
||||
|
let (row_read_ts, row_audit_ts) = timestamp_calc(num_ops, num_cells_row, &row);
|
||||
|
let (col_read_ts, col_audit_ts) = timestamp_calc(num_ops, num_cells_col, &col);
|
||||
|
|
||||
|
let to_vec_scalar = |v: &[usize]| -> Vec<G::Scalar> {
|
||||
|
(0..v.len())
|
||||
|
.map(|i| G::Scalar::from(v[i] as u64))
|
||||
|
.collect::<Vec<G::Scalar>>()
|
||||
|
};
|
||||
|
|
||||
|
Self {
|
||||
|
ell,
|
||||
|
// dense representation
|
||||
|
row: to_vec_scalar(&row),
|
||||
|
col: to_vec_scalar(&col),
|
||||
|
val,
|
||||
|
|
||||
|
// timestamp polynomials
|
||||
|
row_read_ts: to_vec_scalar(&row_read_ts),
|
||||
|
row_audit_ts: to_vec_scalar(&row_audit_ts),
|
||||
|
col_read_ts: to_vec_scalar(&col_read_ts),
|
||||
|
col_audit_ts: to_vec_scalar(&col_audit_ts),
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
pub fn commit(&self, ck: &CommitmentKey<G>) -> SparsePolynomialCommitment<G> {
|
||||
|
let comm_vec: Vec<Commitment<G>> = [
|
||||
|
&self.row,
|
||||
|
&self.col,
|
||||
|
&self.val,
|
||||
|
&self.row_read_ts,
|
||||
|
&self.row_audit_ts,
|
||||
|
&self.col_read_ts,
|
||||
|
&self.col_audit_ts,
|
||||
|
]
|
||||
|
.par_iter()
|
||||
|
.map(|v| G::CE::commit(ck, v))
|
||||
|
.collect();
|
||||
|
|
||||
|
SparsePolynomialCommitment {
|
||||
|
ell: self.ell,
|
||||
|
size: self.row.len(),
|
||||
|
comm_row: comm_vec[0],
|
||||
|
comm_col: comm_vec[1],
|
||||
|
comm_val: comm_vec[2],
|
||||
|
comm_row_read_ts: comm_vec[3],
|
||||
|
comm_row_audit_ts: comm_vec[4],
|
||||
|
comm_col_read_ts: comm_vec[5],
|
||||
|
comm_col_audit_ts: comm_vec[6],
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
pub fn multi_evaluate(
|
||||
|
M_vec: &[&[(usize, usize, G::Scalar)]],
|
||||
|
r_x: &[G::Scalar],
|
||||
|
r_y: &[G::Scalar],
|
||||
|
) -> Vec<G::Scalar> {
|
||||
|
let evaluate_with_table =
|
||||
|
|M: &[(usize, usize, G::Scalar)], T_x: &[G::Scalar], T_y: &[G::Scalar]| -> G::Scalar {
|
||||
|
(0..M.len())
|
||||
|
.collect::<Vec<usize>>()
|
||||
|
.par_iter()
|
||||
|
.map(|&i| {
|
||||
|
let (row, col, val) = M[i];
|
||||
|
T_x[row] * T_y[col] * val
|
||||
|
})
|
||||
|
.reduce(G::Scalar::zero, |acc, x| acc + x)
|
||||
|
};
|
||||
|
|
||||
|
let (T_x, T_y) = rayon::join(
|
||||
|
|| EqPolynomial::new(r_x.to_vec()).evals(),
|
||||
|
|| EqPolynomial::new(r_y.to_vec()).evals(),
|
||||
|
);
|
||||
|
|
||||
|
(0..M_vec.len())
|
||||
|
.collect::<Vec<usize>>()
|
||||
|
.par_iter()
|
||||
|
.map(|&i| evaluate_with_table(M_vec[i], &T_x, &T_y))
|
||||
|
.collect()
|
||||
|
}
|
||||
|
|
||||
|
fn evaluation_oracles(
|
||||
|
M: &[(usize, usize, G::Scalar)],
|
||||
|
r_x: &[G::Scalar],
|
||||
|
r_y: &[G::Scalar],
|
||||
|
) -> (
|
||||
|
Vec<G::Scalar>,
|
||||
|
Vec<G::Scalar>,
|
||||
|
Vec<G::Scalar>,
|
||||
|
Vec<G::Scalar>,
|
||||
|
) {
|
||||
|
let evaluation_oracles_with_table = |M: &[(usize, usize, G::Scalar)],
|
||||
|
T_x: &[G::Scalar],
|
||||
|
T_y: &[G::Scalar]|
|
||||
|
-> (Vec<G::Scalar>, Vec<G::Scalar>) {
|
||||
|
(0..M.len())
|
||||
|
.collect::<Vec<usize>>()
|
||||
|
.par_iter()
|
||||
|
.map(|&i| {
|
||||
|
let (row, col, _val) = M[i];
|
||||
|
(T_x[row], T_y[col])
|
||||
|
})
|
||||
|
.collect::<Vec<(G::Scalar, G::Scalar)>>()
|
||||
|
.into_par_iter()
|
||||
|
.unzip()
|
||||
|
};
|
||||
|
|
||||
|
let (T_x, T_y) = rayon::join(
|
||||
|
|| EqPolynomial::new(r_x.to_vec()).evals(),
|
||||
|
|| EqPolynomial::new(r_y.to_vec()).evals(),
|
||||
|
);
|
||||
|
|
||||
|
let (mut E_row, mut E_col) = evaluation_oracles_with_table(M, &T_x, &T_y);
|
||||
|
|
||||
|
// resize the returned vectors
|
||||
|
E_row.resize(M.len().next_power_of_two(), T_x[0]); // we place T_x[0] since resized row is appended with 0s
|
||||
|
E_col.resize(M.len().next_power_of_two(), T_y[0]);
|
||||
|
(E_row, E_col, T_x, T_y)
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
#[derive(Clone, Debug, Serialize, Deserialize)]
|
||||
|
#[serde(bound = "")]
|
||||
|
pub struct SparseEvaluationArgument<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> {
|
||||
|
// claimed evaluation
|
||||
|
eval: G::Scalar,
|
||||
|
|
||||
|
// oracles
|
||||
|
comm_E_row: Commitment<G>,
|
||||
|
comm_E_col: Commitment<G>,
|
||||
|
|
||||
|
// proof of correct evaluation wrt oracles
|
||||
|
sc_proof_eval: SumcheckProof<G>,
|
||||
|
eval_E_row: G::Scalar,
|
||||
|
eval_E_col: G::Scalar,
|
||||
|
eval_val: G::Scalar,
|
||||
|
arg_eval: EE::EvaluationArgument,
|
||||
|
|
||||
|
// proof that E_row is well-formed
|
||||
|
eval_init_row: G::Scalar,
|
||||
|
eval_read_row: G::Scalar,
|
||||
|
eval_write_row: G::Scalar,
|
||||
|
eval_audit_row: G::Scalar,
|
||||
|
eval_init_col: G::Scalar,
|
||||
|
eval_read_col: G::Scalar,
|
||||
|
eval_write_col: G::Scalar,
|
||||
|
eval_audit_col: G::Scalar,
|
||||
|
sc_prod_init_audit_row: ProductArgumentBatched<G>,
|
||||
|
sc_prod_read_write_row_col: ProductArgumentBatched<G>,
|
||||
|
sc_prod_init_audit_col: ProductArgumentBatched<G>,
|
||||
|
eval_row: G::Scalar,
|
||||
|
eval_row_read_ts: G::Scalar,
|
||||
|
eval_E_row2: G::Scalar,
|
||||
|
eval_row_audit_ts: G::Scalar,
|
||||
|
eval_col: G::Scalar,
|
||||
|
eval_col_read_ts: G::Scalar,
|
||||
|
eval_E_col2: G::Scalar,
|
||||
|
eval_col_audit_ts: G::Scalar,
|
||||
|
arg_row_col_joint: EE::EvaluationArgument,
|
||||
|
arg_row_audit_ts: EE::EvaluationArgument,
|
||||
|
arg_col_audit_ts: EE::EvaluationArgument,
|
||||
|
}
|
||||
|
|
||||
|
impl<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> SparseEvaluationArgument<G, EE> {
|
||||
|
pub fn prove(
|
||||
|
ck: &CommitmentKey<G>,
|
||||
|
pk_ee: &EE::ProverKey,
|
||||
|
poly: &SparsePolynomial<G>,
|
||||
|
sparse: &[(usize, usize, G::Scalar)],
|
||||
|
comm: &SparsePolynomialCommitment<G>,
|
||||
|
r: &(&[G::Scalar], &[G::Scalar]),
|
||||
|
transcript: &mut G::TE,
|
||||
|
) -> Result<Self, NovaError> {
|
||||
|
let (r_x, r_y) = r;
|
||||
|
let eval = SparsePolynomial::<G>::multi_evaluate(&[sparse], r_x, r_y)[0];
|
||||
|
|
||||
|
// compute oracles to prove the correctness of `eval`
|
||||
|
let (E_row, E_col, T_x, T_y) = SparsePolynomial::<G>::evaluation_oracles(sparse, r_x, r_y);
|
||||
|
let val = poly.val.clone();
|
||||
|
|
||||
|
// commit to the two oracles
|
||||
|
let comm_E_row = G::CE::commit(ck, &E_row);
|
||||
|
let comm_E_col = G::CE::commit(ck, &E_col);
|
||||
|
|
||||
|
// absorb the commitments and the claimed evaluation
|
||||
|
transcript.absorb(b"E", &vec![comm_E_row, comm_E_col].as_slice());
|
||||
|
transcript.absorb(b"e", &eval);
|
||||
|
|
||||
|
let comb_func_eval = |poly_A_comp: &G::Scalar,
|
||||
|
poly_B_comp: &G::Scalar,
|
||||
|
poly_C_comp: &G::Scalar|
|
||||
|
-> G::Scalar { *poly_A_comp * *poly_B_comp * *poly_C_comp };
|
||||
|
let (sc_proof_eval, r_eval, claims_eval) = SumcheckProof::<G>::prove_cubic(
|
||||
|
&eval,
|
||||
|
E_row.len().log_2(), // number of rounds
|
||||
|
&mut MultilinearPolynomial::new(E_row.clone()),
|
||||
|
&mut MultilinearPolynomial::new(E_col.clone()),
|
||||
|
&mut MultilinearPolynomial::new(val.clone()),
|
||||
|
comb_func_eval,
|
||||
|
transcript,
|
||||
|
)?;
|
||||
|
|
||||
|
// prove evaluations of E_row, E_col and val at r_eval
|
||||
|
let rho = transcript.squeeze(b"r")?;
|
||||
|
let comm_joint = comm_E_row + comm_E_col * rho + comm.comm_val * rho * rho;
|
||||
|
let eval_joint = claims_eval[0] + rho * claims_eval[1] + rho * rho * claims_eval[2];
|
||||
|
let poly_eval = E_row
|
||||
|
.iter()
|
||||
|
.zip(E_col.iter())
|
||||
|
.zip(val.iter())
|
||||
|
.map(|((a, b), c)| *a + rho * *b + rho * rho * *c)
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
let arg_eval = EE::prove(
|
||||
|
ck,
|
||||
|
pk_ee,
|
||||
|
transcript,
|
||||
|
&comm_joint,
|
||||
|
&poly_eval,
|
||||
|
&r_eval,
|
||||
|
&eval_joint,
|
||||
|
)?;
|
||||
|
|
||||
|
// we now need to prove that E_row and E_col are well-formed
|
||||
|
// we use memory checking: H(INIT) * H(WS) =? H(RS) * H(FINAL)
|
||||
|
let gamma_1 = transcript.squeeze(b"g1")?;
|
||||
|
let gamma_2 = transcript.squeeze(b"g2")?;
|
||||
|
|
||||
|
let gamma_1_sqr = gamma_1 * gamma_1;
|
||||
|
let hash_func = |addr: &G::Scalar, val: &G::Scalar, ts: &G::Scalar| -> G::Scalar {
|
||||
|
(*ts * gamma_1_sqr + *val * gamma_1 + *addr) - gamma_2
|
||||
|
};
|
||||
|
|
||||
|
let init_row = (0..T_x.len())
|
||||
|
.map(|i| hash_func(&G::Scalar::from(i as u64), &T_x[i], &G::Scalar::zero()))
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
let read_row = (0..E_row.len())
|
||||
|
.map(|i| hash_func(&poly.row[i], &E_row[i], &poly.row_read_ts[i]))
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
let write_row = (0..E_row.len())
|
||||
|
.map(|i| {
|
||||
|
hash_func(
|
||||
|
&poly.row[i],
|
||||
|
&E_row[i],
|
||||
|
&(poly.row_read_ts[i] + G::Scalar::one()),
|
||||
|
)
|
||||
|
})
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
let audit_row = (0..T_x.len())
|
||||
|
.map(|i| hash_func(&G::Scalar::from(i as u64), &T_x[i], &poly.row_audit_ts[i]))
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
let init_col = (0..T_y.len())
|
||||
|
.map(|i| hash_func(&G::Scalar::from(i as u64), &T_y[i], &G::Scalar::zero()))
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
let read_col = (0..E_col.len())
|
||||
|
.map(|i| hash_func(&poly.col[i], &E_col[i], &poly.col_read_ts[i]))
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
let write_col = (0..E_col.len())
|
||||
|
.map(|i| {
|
||||
|
hash_func(
|
||||
|
&poly.col[i],
|
||||
|
&E_col[i],
|
||||
|
&(poly.col_read_ts[i] + G::Scalar::one()),
|
||||
|
)
|
||||
|
})
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
let audit_col = (0..T_y.len())
|
||||
|
.map(|i| hash_func(&G::Scalar::from(i as u64), &T_y[i], &poly.col_audit_ts[i]))
|
||||
|
.collect::<Vec<G::Scalar>>();
|
||||
|
|
||||
|
let (sc_prod_init_audit_row, eval_init_audit_row, r_init_audit_row) =
|
||||
|
ProductArgumentBatched::prove(
|
||||
|
&[
|
||||
|
&MultilinearPolynomial::new(init_row),
|
||||
|
&MultilinearPolynomial::new(audit_row),
|
||||
|
],
|
||||
|
transcript,
|
||||
|
)?;
|
||||
|
|
||||
|
assert_eq!(init_col.len(), audit_col.len());
|
||||
|
let (sc_prod_init_audit_col, eval_init_audit_col, r_init_audit_col) =
|
||||
|
ProductArgumentBatched::prove(
|
||||
|
&[
|
||||
|
&MultilinearPolynomial::new(init_col),
|
||||
|
&MultilinearPolynomial::new(audit_col),
|
||||
|
],
|
||||
|
transcript,
|
||||
|
)?;
|
||||
|
|
||||
|
assert_eq!(read_row.len(), write_row.len());
|
||||
|
assert_eq!(read_row.len(), read_col.len());
|
||||
|
assert_eq!(read_row.len(), write_col.len());
|
||||
|
|
||||
|
let (sc_prod_read_write_row_col, eval_read_write_row_col, r_read_write_row_col) =
|
||||
|
ProductArgumentBatched::prove(
|
||||
|
&[
|
||||
|
&MultilinearPolynomial::new(read_row),
|
||||
|
&MultilinearPolynomial::new(write_row),
|
||||
|
&MultilinearPolynomial::new(read_col),
|
||||
|
&MultilinearPolynomial::new(write_col),
|
||||
|
],
|
||||
|
transcript,
|
||||
|
)?;
|
||||
|
|
||||
|
// row-related claims of polynomial evaluations to aid the final check of the sum-check
|
||||
|
let eval_row = MultilinearPolynomial::evaluate_with(&poly.row, &r_read_write_row_col);
|
||||
|
let eval_row_read_ts =
|
||||
|
MultilinearPolynomial::evaluate_with(&poly.row_read_ts, &r_read_write_row_col);
|
||||
|
let eval_E_row2 = MultilinearPolynomial::evaluate_with(&E_row, &r_read_write_row_col);
|
||||
|
let eval_row_audit_ts =
|
||||
|
MultilinearPolynomial::evaluate_with(&poly.row_audit_ts, &r_init_audit_row);
|
||||
|
|
||||
|
// col-related claims of polynomial evaluations to aid the final check of the sum-check
|
||||
|
let eval_col = MultilinearPolynomial::evaluate_with(&poly.col, &r_read_write_row_col);
|
||||
|
let eval_col_read_ts =
|
||||
|
MultilinearPolynomial::evaluate_with(&poly.col_read_ts, &r_read_write_row_col);
|
||||
|
let eval_E_col2 = MultilinearPolynomial::evaluate_with(&E_col, &r_read_write_row_col);
|
||||
|
let eval_col_audit_ts =
|
||||
|
MultilinearPolynomial::evaluate_with(&poly.col_audit_ts, &r_init_audit_col);
|
||||
|
|
||||
|
// we can batch prove the first three claims
|
||||
|
transcript.absorb(
|
||||
|
b"e",
|
||||
|
&[
|
||||
|
eval_row,
|
||||
|
eval_row_read_ts,
|
||||
|
eval_E_row2,
|
||||
|
eval_col,
|
||||
|
eval_col_read_ts,
|
||||
|
eval_E_col2,
|
||||
|
]
|
||||
|
.as_slice(),
|
||||
|
);
|
||||
|
let c = transcript.squeeze(b"c")?;
|
||||
|
let eval_joint = eval_row
|
||||
|
+ c * eval_row_read_ts
|
||||
|
+ c * c * eval_E_row2
|
||||
|
+ c * c * c * eval_col
|
||||
|
+ c * c * c * c * eval_col_read_ts
|
||||
|
+ c * c * c * c * c * eval_E_col2;
|
||||
|
let comm_joint = comm.comm_row
|
||||
|
+ comm.comm_row_read_ts * c
|
||||
|
+ comm_E_row * c * c
|
||||
|
+ comm.comm_col * c * c * c
|
||||
|
+ comm.comm_col_read_ts * c * c * c * c
|
||||
|
+ comm_E_col * c * c * c * c * c;
|
||||
|
let poly_joint = poly
|
||||
|
.row
|
||||
|
.iter()
|
||||
|
.zip(poly.row_read_ts.iter())
|
||||
|
.zip(E_row.into_iter())
|
||||
|
.zip(poly.col.iter())
|
||||
|
.zip(poly.col_read_ts.iter())
|
||||
|
.zip(E_col.into_iter())
|
||||
|
.map(|(((((x, y), z), m), n), q)| {
|
||||
|
*x + c * y + c * c * z + c * c * c * m + c * c * c * c * n + c * c * c * c * c * q
|
||||
|
})
|
||||
|
.collect::<Vec<_>>();
|
||||
|
|
||||
|
let arg_row_col_joint = EE::prove(
|
||||
|
ck,
|
||||
|
pk_ee,
|
||||
|
transcript,
|
||||
|
&comm_joint,
|
||||
|
&poly_joint,
|
||||
|
&r_read_write_row_col,
|
||||
|
&eval_joint,
|
||||
|
)?;
|
||||
|
|
||||
|
let arg_row_audit_ts = EE::prove(
|
||||
|
ck,
|
||||
|
pk_ee,
|
||||
|
transcript,
|
||||
|
&comm.comm_row_audit_ts,
|
||||
|
&poly.row_audit_ts,
|
||||
|
&r_init_audit_row,
|
||||
|
&eval_row_audit_ts,
|
||||
|
)?;
|
||||
|
|
||||
|
let arg_col_audit_ts = EE::prove(
|
||||
|
ck,
|
||||
|
pk_ee,
|
||||
|
transcript,
|
||||
|
&comm.comm_col_audit_ts,
|
||||
|
&poly.col_audit_ts,
|
||||
|
&r_init_audit_col,
|
||||
|
&eval_col_audit_ts,
|
||||
|
)?;
|
||||
|
|
||||
|
Ok(Self {
|
||||
|
// claimed evaluation
|
||||
|
eval,
|
||||
|
|
||||
|
// oracles
|
||||
|
comm_E_row,
|
||||
|
comm_E_col,
|
||||
|
|
||||
|
// proof of correct evaluation wrt oracles
|
||||
|
sc_proof_eval,
|
||||
|
eval_E_row: claims_eval[0],
|
||||
|
eval_E_col: claims_eval[1],
|
||||
|
eval_val: claims_eval[2],
|
||||
|
arg_eval,
|
||||
|
|
||||
|
// proof that E_row and E_row are well-formed
|
||||
|
eval_init_row: eval_init_audit_row[0],
|
||||
|
eval_read_row: eval_read_write_row_col[0],
|
||||
|
eval_write_row: eval_read_write_row_col[1],
|
||||
|
eval_audit_row: eval_init_audit_row[1],
|
||||
|
eval_init_col: eval_init_audit_col[0],
|
||||
|
eval_read_col: eval_read_write_row_col[2],
|
||||
|
eval_write_col: eval_read_write_row_col[3],
|
||||
|
eval_audit_col: eval_init_audit_col[1],
|
||||
|
sc_prod_init_audit_row,
|
||||
|
sc_prod_read_write_row_col,
|
||||
|
sc_prod_init_audit_col,
|
||||
|
eval_row,
|
||||
|
eval_row_read_ts,
|
||||
|
eval_E_row2,
|
||||
|
eval_row_audit_ts,
|
||||
|
eval_col,
|
||||
|
eval_col_read_ts,
|
||||
|
eval_E_col2,
|
||||
|
eval_col_audit_ts,
|
||||
|
arg_row_col_joint,
|
||||
|
arg_row_audit_ts,
|
||||
|
arg_col_audit_ts,
|
||||
|
})
|
||||
|
}
|
||||
|
|
||||
|
pub fn verify(
|
||||
|
&self,
|
||||
|
vk_ee: &EE::VerifierKey,
|
||||
|
comm: &SparsePolynomialCommitment<G>,
|
||||
|
r: &(&[G::Scalar], &[G::Scalar]),
|
||||
|
transcript: &mut G::TE,
|
||||
|
) -> Result<G::Scalar, NovaError> {
|
||||
|
let (r_x, r_y) = r;
|
||||
|
|
||||
|
// append the transcript and scalar
|
||||
|
transcript.absorb(b"E", &vec![self.comm_E_row, self.comm_E_col].as_slice());
|
||||
|
transcript.absorb(b"e", &self.eval);
|
||||
|
|
||||
|
// (1) verify the correct evaluation of sparse polynomial
|
||||
|
let (claim_eval_final, r_eval) = self.sc_proof_eval.verify(
|
||||
|
self.eval,
|
||||
|
comm.size.next_power_of_two().log_2(),
|
||||
|
3,
|
||||
|
transcript,
|
||||
|
)?;
|
||||
|
// verify the last step of the sum-check
|
||||
|
if claim_eval_final != self.eval_E_row * self.eval_E_col * self.eval_val {
|
||||
|
return Err(NovaError::InvalidSumcheckProof);
|
||||
|
}
|
||||
|
|
||||
|
// prove evaluations of E_row, E_col and val at r_eval
|
||||
|
let rho = transcript.squeeze(b"r")?;
|
||||
|
let comm_joint = self.comm_E_row + self.comm_E_col * rho + comm.comm_val * rho * rho;
|
||||
|
let eval_joint = self.eval_E_row + rho * self.eval_E_col + rho * rho * self.eval_val;
|
||||
|
EE::verify(
|
||||
|
vk_ee,
|
||||
|
transcript,
|
||||
|
&comm_joint,
|
||||
|
&r_eval,
|
||||
|
&eval_joint,
|
||||
|
&self.arg_eval,
|
||||
|
)?;
|
||||
|
|
||||
|
// (2) verify if E_row and E_col are well formed
|
||||
|
let gamma_1 = transcript.squeeze(b"g1")?;
|
||||
|
let gamma_2 = transcript.squeeze(b"g2")?;
|
||||
|
|
||||
|
// hash function
|
||||
|
let gamma_1_sqr = gamma_1 * gamma_1;
|
||||
|
let hash_func = |addr: &G::Scalar, val: &G::Scalar, ts: &G::Scalar| -> G::Scalar {
|
||||
|
(*ts * gamma_1_sqr + *val * gamma_1 + *addr) - gamma_2
|
||||
|
};
|
||||
|
|
||||
|
// check the required multiset relationship
|
||||
|
// row
|
||||
|
if self.eval_init_row * self.eval_write_row != self.eval_read_row * self.eval_audit_row {
|
||||
|
return Err(NovaError::InvalidMultisetProof);
|
||||
|
}
|
||||
|
// col
|
||||
|
if self.eval_init_col * self.eval_write_col != self.eval_read_col * self.eval_audit_col {
|
||||
|
return Err(NovaError::InvalidMultisetProof);
|
||||
|
}
|
||||
|
|
||||
|
// verify the product proofs
|
||||
|
let (claim_init_audit_row, r_init_audit_row) = self.sc_prod_init_audit_row.verify(
|
||||
|
&[self.eval_init_row, self.eval_audit_row],
|
||||
|
comm.ell.0.pow2(),
|
||||
|
transcript,
|
||||
|
)?;
|
||||
|
let (claim_init_audit_col, r_init_audit_col) = self.sc_prod_init_audit_col.verify(
|
||||
|
&[self.eval_init_col, self.eval_audit_col],
|
||||
|
comm.ell.1.pow2(),
|
||||
|
transcript,
|
||||
|
)?;
|
||||
|
let (claim_read_write_row_col, r_read_write_row_col) = self.sc_prod_read_write_row_col.verify(
|
||||
|
&[
|
||||
|
self.eval_read_row,
|
||||
|
self.eval_write_row,
|
||||
|
self.eval_read_col,
|
||||
|
self.eval_write_col,
|
||||
|
],
|
||||
|
comm.size,
|
||||
|
transcript,
|
||||
|
)?;
|
||||
|
|
||||
|
// finish the final step of the three sum-checks
|
||||
|
let (claim_init_expected_row, claim_audit_expected_row) = {
|
||||
|
let addr = IdentityPolynomial::new(r_init_audit_row.len()).evaluate(&r_init_audit_row);
|
||||
|
let val = EqPolynomial::new(r_x.to_vec()).evaluate(&r_init_audit_row);
|
||||
|
|
||||
|
(
|
||||
|
hash_func(&addr, &val, &G::Scalar::zero()),
|
||||
|
hash_func(&addr, &val, &self.eval_row_audit_ts),
|
||||
|
)
|
||||
|
};
|
||||
|
|
||||
|
let (claim_read_expected_row, claim_write_expected_row) = {
|
||||
|
(
|
||||
|
hash_func(&self.eval_row, &self.eval_E_row2, &self.eval_row_read_ts),
|
||||
|
hash_func(
|
||||
|
&self.eval_row,
|
||||
|
&self.eval_E_row2,
|
||||
|
&(self.eval_row_read_ts + G::Scalar::one()),
|
||||
|
),
|
||||
|
)
|
||||
|
};
|
||||
|
|
||||
|
// multiset check for the row
|
||||
|
if claim_init_expected_row != claim_init_audit_row[0]
|
||||
|
|| claim_audit_expected_row != claim_init_audit_row[1]
|
||||
|
|| claim_read_expected_row != claim_read_write_row_col[0]
|
||||
|
|| claim_write_expected_row != claim_read_write_row_col[1]
|
||||
|
{
|
||||
|
return Err(NovaError::InvalidSumcheckProof);
|
||||
|
}
|
||||
|
|
||||
|
let (claim_init_expected_col, claim_audit_expected_col) = {
|
||||
|
let addr = IdentityPolynomial::new(r_init_audit_col.len()).evaluate(&r_init_audit_col);
|
||||
|
let val = EqPolynomial::new(r_y.to_vec()).evaluate(&r_init_audit_col);
|
||||
|
|
||||
|
(
|
||||
|
hash_func(&addr, &val, &G::Scalar::zero()),
|
||||
|
hash_func(&addr, &val, &self.eval_col_audit_ts),
|
||||
|
)
|
||||
|
};
|
||||
|
|
||||
|
let (claim_read_expected_col, claim_write_expected_col) = {
|
||||
|
(
|
||||
|
hash_func(&self.eval_col, &self.eval_E_col2, &self.eval_col_read_ts),
|
||||
|
hash_func(
|
||||
|
&self.eval_col,
|
||||
|
&self.eval_E_col2,
|
||||
|
&(self.eval_col_read_ts + G::Scalar::one()),
|
||||
|
),
|
||||
|
)
|
||||
|
};
|
||||
|
|
||||
|
// multiset check for the col
|
||||
|
if claim_init_expected_col != claim_init_audit_col[0]
|
||||
|
|| claim_audit_expected_col != claim_init_audit_col[1]
|
||||
|
|| claim_read_expected_col != claim_read_write_row_col[2]
|
||||
|
|| claim_write_expected_col != claim_read_write_row_col[3]
|
||||
|
{
|
||||
|
return Err(NovaError::InvalidSumcheckProof);
|
||||
|
}
|
||||
|
|
||||
|
transcript.absorb(
|
||||
|
b"e",
|
||||
|
&[
|
||||
|
self.eval_row,
|
||||
|
self.eval_row_read_ts,
|
||||
|
self.eval_E_row2,
|
||||
|
self.eval_col,
|
||||
|
self.eval_col_read_ts,
|
||||
|
self.eval_E_col2,
|
||||
|
]
|
||||
|
.as_slice(),
|
||||
|
);
|
||||
|
let c = transcript.squeeze(b"c")?;
|
||||
|
let eval_joint = self.eval_row
|
||||
|
+ c * self.eval_row_read_ts
|
||||
|
+ c * c * self.eval_E_row2
|
||||
|
+ c * c * c * self.eval_col
|
||||
|
+ c * c * c * c * self.eval_col_read_ts
|
||||
|
+ c * c * c * c * c * self.eval_E_col2;
|
||||
|
let comm_joint = comm.comm_row
|
||||
|
+ comm.comm_row_read_ts * c
|
||||
|
+ self.comm_E_row * c * c
|
||||
|
+ comm.comm_col * c * c * c
|
||||
|
+ comm.comm_col_read_ts * c * c * c * c
|
||||
|
+ self.comm_E_col * c * c * c * c * c;
|
||||
|
|
||||
|
EE::verify(
|
||||
|
vk_ee,
|
||||
|
transcript,
|
||||
|
&comm_joint,
|
||||
|
&r_read_write_row_col,
|
||||
|
&eval_joint,
|
||||
|
&self.arg_row_col_joint,
|
||||
|
)?;
|
||||
|
|
||||
|
EE::verify(
|
||||
|
vk_ee,
|
||||
|
transcript,
|
||||
|
&comm.comm_row_audit_ts,
|
||||
|
&r_init_audit_row,
|
||||
|
&self.eval_row_audit_ts,
|
||||
|
&self.arg_row_audit_ts,
|
||||
|
)?;
|
||||
|
|
||||
|
EE::verify(
|
||||
|
vk_ee,
|
||||
|
transcript,
|
||||
|
&comm.comm_col_audit_ts,
|
||||
|
&r_init_audit_col,
|
||||
|
&self.eval_col_audit_ts,
|
||||
|
&self.arg_col_audit_ts,
|
||||
|
)?;
|
||||
|
|
||||
|
Ok(self.eval)
|
||||
|
}
|
||||
|
}
|
||||