mnt6/298/affine_ate_miller_loop.hpp

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//---------------------------------------------------------------------------//
// Copyright (c) 2020-2021 Mikhail Komarov <nemo@nil.foundation>
// Copyright (c) 2020-2021 Nikita Kaskov <nbering@nil.foundation>
//
// MIT License
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#ifndef CRYPTO3_ALGEBRA_PAIRING_MNT4_298_AFFINE_ATE_MILLER_LOOP_HPP
#define CRYPTO3_ALGEBRA_PAIRING_MNT4_298_AFFINE_ATE_MILLER_LOOP_HPP
 
#include <nil/crypto3/multiprecision/number.hpp>
#include <nil/crypto3/multiprecision/cpp_int.hpp>
 
#include <nil/crypto3/algebra/curves/mnt6.hpp>
#include <nil/crypto3/algebra/pairing/detail/mnt6/298/params.hpp>
#include <nil/crypto3/algebra/pairing/detail/forms/short_weierstrass/projective/types.hpp>
 
namespace nil {
    namespace crypto3 {
        namespace algebra {
            namespace pairing {
 
                template<std::size_t Version = 298>
                class mnt6_affine_ate_miller_loop;
 
                // The only difference between this and mnt4<298> is that they use mul_by_2345 and mul_by_023
                template<>
                class mnt6_affine_ate_miller_loop<298> {
                    using curve_type = curves::mnt6<298>;
 
                    typedef detail::short_weierstrass_projective_types_policy<curve_type> policy_type;
                    using gt_type = typename curve_type::gt_type;
 
                public:
                    static typename gt_type::value_type
                        process(const typename policy_type::affine_ate_g1_precomputation &prec_P,
                                const typename policy_type::affine_ate_g2_precomputation &prec_Q) {
 
                        typename gt_type::value_type f = gt_type::value_type::one();
 
                        bool found_nonzero = false;
                        std::size_t idx = 0;
 
                        std::vector<long> NAF = multiprecision::find_wnaf(1, policy_type::ate_loop_count);
 
                        for (long i = NAF.size() - 1; i >= 0; --i) {
                            if (!found_nonzero) {
                                /* this skips the MSB itself */
                                found_nonzero |= (NAF[i] != 0);
                                continue;
                            }
 
                            /* code below gets executed for all bits (EXCEPT the MSB itself) of
                               param_p (skipping leading zeros) in MSB to LSB
                               order */
                            typename policy_type::affine_ate_coeffs c = prec_Q.coeffs[idx++];
 
                            typename gt_type::value_type g_RR_at_P = typename gt_type::value_type(
                                prec_P.PY_twist_squared, -prec_P.PX * c.gamma_twist + c.gamma_X - c.old_RY);
                            f = f.squared().mul_by_2345(g_RR_at_P);
 
                            if (NAF[i] != 0) {
                                typename policy_type::affine_ate_coeffs c = prec_Q.coeffs[idx++];
                                typename gt_type::value_type g_RQ_at_P;
                                if (NAF[i] > 0) {
                                    g_RQ_at_P = typename gt_type::value_type(
                                        prec_P.PY_twist_squared, -prec_P.PX * c.gamma_twist + c.gamma_X - prec_Q.QY);
                                } else {
                                    g_RQ_at_P = typename gt_type::value_type(
                                        prec_P.PY_twist_squared, -prec_P.PX * c.gamma_twist + c.gamma_X + prec_Q.QY);
                                }
                                f = f.mul_by_2345(g_RQ_at_P);
                            }
                        }
 
                        return f;
                    }
                };
            }    // namespace pairing
        }        // namespace algebra
    }            // namespace crypto3
}    // namespace nil
#endif    // CRYPTO3_ALGEBRA_PAIRING_MNT6_298_AFFINE_ATE_MILLER_LOOP_HPP