relation_parameters.hpp

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// === AUDIT STATUS ===
// internal:    { status: Planned, auditors: [], commit: }
// external_1:  { status: not started, auditors: [], commit: }
// external_2:  { status: not started, auditors: [], commit: }
// =====================
 
#pragma once
#include "barretenberg/ecc/curves/bn254/fr.hpp"
#include <array>
 
namespace bb {
 
template <typename T> struct RelationParameters {
    using DataType = T;
    static constexpr int NUM_BINARY_LIMBS_IN_GOBLIN_TRANSLATOR = 4;
    static constexpr int NUM_NATIVE_LIMBS_IN_GOBLIN_TRANSLATOR = 1;
    static constexpr int NUM_CHALLENGE_POWERS_IN_GOBLIN_TRANSLATOR = 4;
 
    T eta{ 0 };       // Aux Memory (eta)
    T eta_two{ 0 };   // Aux Memory (eta²)
    T eta_three{ 0 }; // Aux Memory (eta³)
    T beta{ 0 };      // Permutation + Lookup (column batching)
    T gamma{ 0 };     // Permutation + Lookup
 
    T public_input_delta{ 0 }; // Permutation
    T beta_sqr{ 0 };
    T beta_cube{ 0 };
 
    // Compute eta powers from a single eta challenge
    void compute_eta_powers(const T& eta_challenge)
    {
        eta = eta_challenge;
        eta_two = eta * eta;
        eta_three = eta_two * eta;
    }
 
    void compute_beta_powers(const T& beta_challenge)
    {
        beta = beta_challenge;
        beta_sqr = beta * beta;
        beta_cube = beta_sqr * beta;
    }
    // `eccvm_set_permutation_delta` is used in the set membership gadget in eccvm/ecc_set_relation.hpp, specifically to
    // constrain (pc, round, wnaf_slice) to match between the MSM table and the Precomputed table. The number of rows we
    // add per short scalar `mul` is slightly less in the Precomputed table as in the MSM table, so to get the
    // permutation argument to work out, when `precompute_select == 0`, we must implicitly _remove_ (0, 0, 0) as a tuple
    // on the wNAF side. This corresponds to dividing by (γ)·(γ + β²)·(γ + 2β²)·(γ + 3β²).
    //
    // We can remove this by modifying the relation, but this would increase the complexity.
    T eccvm_set_permutation_delta = T(0);
    std::array<T, NUM_BINARY_LIMBS_IN_GOBLIN_TRANSLATOR> accumulated_result = { T(0), T(0), T(0), T(0) }; // Translator
    std::array<T, NUM_BINARY_LIMBS_IN_GOBLIN_TRANSLATOR + NUM_NATIVE_LIMBS_IN_GOBLIN_TRANSLATOR> evaluation_input_x = {
        T(0), T(0), T(0), T(0), T(0)
    }; // Translator
    std::array<std::array<T, NUM_BINARY_LIMBS_IN_GOBLIN_TRANSLATOR + NUM_NATIVE_LIMBS_IN_GOBLIN_TRANSLATOR>,
               NUM_CHALLENGE_POWERS_IN_GOBLIN_TRANSLATOR>
        batching_challenge_v = { { { T(0), T(0), T(0), T(0), T(0) },
                                   { T(0), T(0), T(0), T(0), T(0) },
                                   { T(0), T(0), T(0), T(0), T(0) },
                                   { T(0), T(0), T(0), T(0), T(0) } } };
 
    static RelationParameters get_random()
    {
        RelationParameters result;
        result.compute_eta_powers(T::random_element());  // eta, eta_two = eta², eta_three = eta³
        result.compute_beta_powers(T::random_element()); // beta, beta_sqr = beta², beta_cube = beta³
        result.gamma = T::random_element();
        result.public_input_delta = T::random_element();
        result.eccvm_set_permutation_delta = result.gamma * (result.gamma + result.beta_sqr) *
                                             (result.gamma + result.beta_sqr + result.beta_sqr) *
                                             (result.gamma + result.beta_sqr + result.beta_sqr + result.beta_sqr);
        result.accumulated_result = {
            T::random_element(), T::random_element(), T::random_element(), T::random_element()
        };
 
        result.evaluation_input_x = {
            T::random_element(), T::random_element(), T::random_element(), T::random_element(), T::random_element()
        };
        result.batching_challenge_v = {
            std::array{ T::random_element(),
                        T::random_element(),
                        T::random_element(),
                        T::random_element(),
                        T::random_element() },
            { T::random_element(), T::random_element(), T::random_element(), T::random_element(), T::random_element() },
            { T::random_element(), T::random_element(), T::random_element(), T::random_element(), T::random_element() },
            { T::random_element(), T::random_element(), T::random_element(), T::random_element(), T::random_element() },
        };
 
        return result;
    }
};
} // namespace bb