kzg.hpp

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// === AUDIT STATUS ===
// internal:    { status: Complete, auditors: [Khashayar], commit: }
// external_1:  { status: not started, auditors: [], commit: }
// external_2:  { status: not started, auditors: [], commit: }
// =====================
 
#pragma once
 
#include "barretenberg/commitment_schemes/claim.hpp"
#include "barretenberg/commitment_schemes/commitment_key.hpp"
#include "barretenberg/commitment_schemes/pairing_points.hpp"
#include "barretenberg/commitment_schemes/verification_key.hpp"
#include "barretenberg/stdlib/primitives/pairing_points.hpp"
#include "barretenberg/transcript/transcript.hpp"
 
#include <memory>
#include <utility>
 
namespace bb {
 
template <typename Curve_> class KZG {
  public:
    using Curve = Curve_;
    using CK = CommitmentKey<Curve>;
    using VK = VerifierCommitmentKey<Curve>;
    using Fr = typename Curve::ScalarField;
    using Commitment = typename Curve::AffineElement;
    using GroupElement = typename Curve::Element;
    using Polynomial = bb::Polynomial<Fr>;
    using PairingPointsType =
        std::conditional_t<Curve::is_stdlib_type, stdlib::recursion::PairingPoints<Curve>, bb::PairingPoints<Curve>>;
 
    template <typename Transcript>
    static void compute_opening_proof(const CK& ck,
                                      const ProverOpeningClaim<Curve>& opening_claim,
                                      const std::shared_ptr<Transcript>& prover_trancript)
    {
        Polynomial quotient = opening_claim.polynomial;
        OpeningPair<Curve> pair = opening_claim.opening_pair;
        Commitment quotient_commitment;
 
        if (opening_claim.polynomial.is_empty()) {
            // We treat the empty polynomial as the zero polynomial
            quotient_commitment = Commitment::infinity();
        } else {
            quotient.at(0) = quotient[0] - pair.evaluation;
            // Computes the coefficients for the quotient polynomial q(X) = (p(X) - v) / (X - r) through an FFT
            quotient.factor_roots(pair.challenge);
            quotient_commitment = ck.commit(quotient);
        }
 
        // TODO(#479): for now we compute the KZG commitment directly to unify the KZG and IPA interfaces but in the
        // future we might need to adjust this to use the incoming alternative to work queue (i.e. variation of
        // pthreads) or even the work queue itself
        prover_trancript->send_to_verifier("KZG:W", quotient_commitment);
 
        // Masking challenge is used in the recursive setting to perform batch_mul. This is not used
        // by the prover directly, we just need it for consistent transcript state with the verifier.
        prover_trancript->template get_challenge<Fr>("KZG:masking_challenge");
    };
 
    template <typename Transcript>
    static PairingPointsType reduce_verify(const OpeningClaim<Curve>& claim,
                                           const std::shared_ptr<Transcript>& verifier_transcript)
    {
        auto quotient_commitment = verifier_transcript->template receive_from_prover<Commitment>("KZG:W");
 
        // Note: The pairing check can be expressed naturally as
        // e(C - v * [1]_1, [1]_2) = e([W]_1, [X - r]_2) where C =[p(X)]_1. This can be rearranged (e.g. see the plonk
        // paper) as e(C + r*[W]_1 - v*[1]_1, [1]_2) * e(-[W]_1, [X]_2) = 1, or e(P_0, [1]_2) * e(P_1, [X]_2) = 1
        GroupElement P_0;
        if constexpr (Curve::is_stdlib_type) {
            // Express operation as a batch_mul in order to use Goblinization if available
            auto builder = quotient_commitment.get_context();
            auto one = Fr(builder, 1);
            std::vector<GroupElement> commitments = { claim.commitment,
                                                      quotient_commitment,
                                                      GroupElement::one(builder) };
            std::vector<Fr> scalars = { one, claim.opening_pair.challenge, -claim.opening_pair.evaluation };
            P_0 = GroupElement::batch_mul(commitments, scalars);
 
        } else {
            P_0 = claim.commitment;
            P_0 += quotient_commitment * claim.opening_pair.challenge;
            P_0 -= GroupElement::one() * claim.opening_pair.evaluation;
        }
 
        auto P_1 = -quotient_commitment;
        return PairingPointsType(P_0, P_1);
    };
 
    template <typename Transcript>
    static PairingPointsType reduce_verify_batch_opening_claim(BatchOpeningClaim<Curve>&& batch_opening_claim,
                                                               const std::shared_ptr<Transcript>& transcript,
                                                               const size_t expected_final_msm_size = 0)
    {
        auto quotient_commitment = transcript->template receive_from_prover<Commitment>("KZG:W");
 
        // This challenge is used to compute offset generators in the batch_mul call below
        const Fr masking_challenge = transcript->template get_challenge<Fr>("KZG:masking_challenge");
 
        // The pairing check can be expressed as
        // e(C + [W]₁ ⋅ z, [1]₂) * e(−[W]₁, [X]₂) = 1, where C = ∑ commitmentsᵢ ⋅ scalarsᵢ.
        GroupElement P_0;
        // Place the commitment to W to 'commitments'
        batch_opening_claim.commitments.emplace_back(quotient_commitment);
        // Update the scalars by adding the Shplonk evaluation challenge z
        batch_opening_claim.scalars.emplace_back(batch_opening_claim.evaluation_point);
 
        // Validate the final MSM size if expected size is provided
        if (expected_final_msm_size != 0) {
            BB_ASSERT_EQ(batch_opening_claim.commitments.size(), expected_final_msm_size);
        }
 
        // Compute C + [W]₁ ⋅ z
        P_0 = GroupElement::batch_mul(batch_opening_claim.commitments,
                                      batch_opening_claim.scalars,
                                      /*max_num_bits=*/0,
                                      /*with_edgecases=*/true,
                                      /*masking_scalar=*/masking_challenge);
        auto P_1 = -quotient_commitment;
 
        return PairingPointsType(P_0, P_1);
    }
};
 
} // namespace bb