multilinear_batching_verifier.cpp

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// === AUDIT STATUS ===
// internal:    { status: Complete, auditors: [Sergei], commit: }
// external_1:  { status: not started, auditors: [], commit: }
// external_2:  { status: not started, auditors: [], commit: }
// =====================
 
#include "multilinear_batching_verifier.hpp"
#include "barretenberg/flavor/mega_recursive_flavor.hpp"
#include "barretenberg/flavor/multilinear_batching_flavor.hpp"
#include "barretenberg/flavor/multilinear_batching_recursive_flavor.hpp"
#include "barretenberg/stdlib/primitives/circuit_builders/circuit_builders_fwd.hpp"
#include "barretenberg/sumcheck/sumcheck_output.hpp"
 
namespace bb {
 
template <typename Flavor_>
MultilinearBatchingVerifier<Flavor_>::MultilinearBatchingVerifier(const std::shared_ptr<Transcript>& transcript)
    : transcript(transcript)
{}
 
template <typename Flavor_>
MultilinearBatchingVerifier<Flavor_>::FF MultilinearBatchingVerifier<Flavor_>::compute_new_target_sum(
    const FF& alpha,
    SumcheckOutput<InstanceFlavor>& instance_sumcheck,
    const std::vector<InstanceFF>& unshifted_challenges,
    const std::vector<InstanceFF>& shifted_challenges,
    const FF& accumulator_non_shifted_evaluation,
    const FF& accumulator_shifted_evaluation) const
{
    // Compute new target sum as:
    //   accumulator_non_shifted_evaluation
    // + alpha   * accumulator_shifted_evaluation
    // + alpha^2 * sum(instance_sumcheck.claimed_unshifted_evals * unshifted_challenges)
    // + alpha^3 * sum(instance_sumcheck.claimed_shifted_evals * shifted_challenges)
    FF target_sum(0);
    for (auto [eval, challenge] : zip_view(instance_sumcheck.claimed_evaluations.get_shifted(), shifted_challenges)) {
        target_sum += eval * challenge;
    }
    target_sum *= alpha;
 
    for (auto [eval, challenge] :
         zip_view(instance_sumcheck.claimed_evaluations.get_unshifted(), unshifted_challenges)) {
        target_sum += eval * challenge;
    }
    target_sum *= alpha;
    target_sum += accumulator_shifted_evaluation; // Accumulator shifted evaluation
    target_sum *= alpha;
    target_sum += accumulator_non_shifted_evaluation; // Accumulator non-shifted evaluation
 
    return target_sum;
}
 
template <typename Flavor_>
template <size_t N>
MultilinearBatchingVerifier<Flavor_>::Commitment MultilinearBatchingVerifier<
    Flavor_>::batch_instance_commitments_with_accumulator(RefArray<Commitment, N> instance_commitments,
                                                          const std::vector<FF>& instance_batching_scalars,
                                                          const Commitment& accumulator_commitment,
                                                          const FF& batching_challenge)
{
    std::vector<Commitment> commitments;
    commitments.reserve(N + 1);
    for (const auto& commitment : instance_commitments) {
        commitments.emplace_back(commitment);
    }
    commitments.emplace_back(accumulator_commitment);
 
    std::vector<FF> scalars(instance_batching_scalars);
    scalars.emplace_back(batching_challenge);
 
    return Curve::Element::batch_mul(commitments, scalars);
}
 
template <typename Flavor_>
MultilinearBatchingVerifier<Flavor_>::VerifierClaim MultilinearBatchingVerifier<Flavor_>::compute_new_claim(
    const SumcheckOutput<Flavor>& sumcheck_result,
    InstanceCommitments& verifier_commitments,
    const std::vector<InstanceFF>& unshifted_challenges,
    const std::vector<InstanceFF>& shifted_challenges,
    const Commitment& non_shifted_accumulator_commitment,
    const Commitment& shifted_accumulator_commitment,
    const FF& batching_challenge)
{
    // Compute new claim as instance + challenge * accumulator
    Commitment non_shifted_commitment =
        batch_instance_commitments_with_accumulator<NUM_UNSHIFTED_ENTITIES>(verifier_commitments.get_unshifted(),
                                                                            unshifted_challenges,
                                                                            non_shifted_accumulator_commitment,
                                                                            batching_challenge);
    Commitment shifted_commitment =
        batch_instance_commitments_with_accumulator<NUM_SHIFTED_ENTITIES>(verifier_commitments.get_to_be_shifted(),
                                                                          shifted_challenges,
                                                                          shifted_accumulator_commitment,
                                                                          batching_challenge);
 
    FF shifted_evaluation = sumcheck_result.claimed_evaluations.batched_shifted_instance +
                            sumcheck_result.claimed_evaluations.batched_shifted_accumulator * batching_challenge;
    FF non_shifted_evaluation = sumcheck_result.claimed_evaluations.batched_unshifted_instance +
                                sumcheck_result.claimed_evaluations.batched_unshifted_accumulator * batching_challenge;
    std::vector<FF> challenge = sumcheck_result.challenge;
 
    return VerifierClaim{
        .challenge = challenge,
        .non_shifted_evaluation = non_shifted_evaluation,
        .shifted_evaluation = shifted_evaluation,
        .non_shifted_commitment = non_shifted_commitment,
        .shifted_commitment = shifted_commitment,
    };
};
 
template <typename Flavor_>
std::pair<bool, typename MultilinearBatchingVerifier<Flavor_>::VerifierClaim> MultilinearBatchingVerifier<
    Flavor_>::verify_proof(SumcheckOutput<InstanceFlavor>& instance_sumcheck,
                           InstanceCommitments& verifier_commitments,
                           const std::vector<InstanceFF>& unshifted_challenges,
                           const std::vector<InstanceFF>& shifted_challenges)
{
    // Receive commitments
    auto non_shifted_accumulator_commitment =
        transcript->template receive_from_prover<Commitment>("non_shifted_accumulator_commitment");
    auto shifted_accumulator_commitment =
        transcript->template receive_from_prover<Commitment>("shifted_accumulator_commitment");
 
    // Receive challenges and evaluations
    std::vector<FF> accumulator_challenges(Flavor::VIRTUAL_LOG_N);
    std::vector<FF> accumulator_evaluations(Flavor::NUM_ACCUMULATOR_EVALUATIONS);
    for (size_t i = 0; i < Flavor::VIRTUAL_LOG_N; i++) {
        accumulator_challenges[i] =
            transcript->template receive_from_prover<FF>("accumulator_challenge_" + std::to_string(i));
    }
    for (size_t i = 0; i < Flavor::NUM_ACCUMULATOR_EVALUATIONS; i++) {
        accumulator_evaluations[i] =
            transcript->template receive_from_prover<FF>("accumulator_evaluation_" + std::to_string(i));
    }
 
    // Run sumcheck
    const FF alpha = transcript->template get_challenge<FF>("Sumcheck:alpha");
 
    FF target_sum = compute_new_target_sum(alpha,
                                           instance_sumcheck,
                                           unshifted_challenges,
                                           shifted_challenges,
                                           accumulator_evaluations[0],
                                           accumulator_evaluations[1]);
 
    Sumcheck sumcheck(transcript, alpha, Flavor::VIRTUAL_LOG_N, target_sum);
    // MultilinearBatchingFlavor doesn't use gate challenges
    const auto sumcheck_result = sumcheck.verify({}, {});
 
    // Construct new claim
    auto claim_batching_challenge = transcript->template get_challenge<FF>("claim_batching_challenge");
    VerifierClaim verifier_claim = compute_new_claim(sumcheck_result,
                                                     verifier_commitments,
                                                     unshifted_challenges,
                                                     shifted_challenges,
                                                     non_shifted_accumulator_commitment,
                                                     shifted_accumulator_commitment,
                                                     claim_batching_challenge);
 
    bool eq_consistent = check_eq_consistency(sumcheck_result, accumulator_challenges, instance_sumcheck.challenge);
    bool verified = sumcheck_result.verified && eq_consistent;
 
    return { verified, verifier_claim };
}
 
template <typename Flavor_>
bool MultilinearBatchingVerifier<Flavor_>::check_eq_consistency(const SumcheckOutput<Flavor>& sumcheck_result,
                                                                const std::vector<FF>& accumulator_challenges,
                                                                const std::vector<InstanceFF>& instance_challenges)
{
    auto accumulator_eq_check = sumcheck_result.claimed_evaluations.eq_accumulator ==
                                VerifierEqPolynomial<FF>::eval(accumulator_challenges, sumcheck_result.challenge);
    auto instance_eq_check = sumcheck_result.claimed_evaluations.eq_instance ==
                             VerifierEqPolynomial<FF>::eval(instance_challenges, sumcheck_result.challenge);
 
    if constexpr (IsRecursiveFlavor<Flavor>) {
        const auto equality_verified = accumulator_eq_check && instance_eq_check;
        bool equality_verified_value = equality_verified.get_value();
        equality_verified.assert_equal(stdlib::bool_t(equality_verified.get_context(), true));
        return equality_verified_value;
    } else {
        return accumulator_eq_check && instance_eq_check;
    }
}
 
template class MultilinearBatchingVerifier<MultilinearBatchingFlavor>;
template class MultilinearBatchingVerifier<MultilinearBatchingRecursiveFlavor>;
 
} // namespace bb