mnt4/298/ate_double_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_ATE_DOUBLE_MILLER_LOOP_HPP
#define CRYPTO3_ALGEBRA_PAIRING_MNT4_298_ATE_DOUBLE_MILLER_LOOP_HPP
 
#include <nil/crypto3/multiprecision/number.hpp>
#include <nil/crypto3/multiprecision/cpp_int.hpp>
 
#include <nil/crypto3/algebra/curves/mnt4.hpp>
#include <nil/crypto3/algebra/pairing/detail/mnt4/298/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 mnt4_ate_double_miller_loop;
 
                template<>
                class mnt4_ate_double_miller_loop<298> {
                    using curve_type = curves::mnt4<298>;
 
                    using params_type = detail::pairing_params<curve_type>;
                    typedef detail::short_weierstrass_projective_types_policy<curve_type> policy_type;
 
                    using gt_type = typename curve_type::gt_type;
                    using base_field_type = typename curve_type::base_field_type;
                    using g1_type = typename curve_type::template g1_type<>;
                    using g2_type = typename curve_type::template g2_type<>;
 
                    using g1_field_type_value = typename g1_type::field_type::value_type;
                    using g2_field_type_value = typename g2_type::field_type::value_type;
 
                public:
                    static typename gt_type::value_type
                        process(const typename policy_type::ate_g1_precomputed_type &prec_P1,
                                const typename policy_type::ate_g2_precomputed_type &prec_Q1,
                                const typename policy_type::ate_g1_precomputed_type &prec_P2,
                                const typename policy_type::ate_g2_precomputed_type &prec_Q2) {
 
                        g2_field_type_value L1_coeff1 =
                            g2_field_type_value(prec_P1.PX, g1_field_type_value::zero()) - prec_Q1.QX_over_twist;
                        g2_field_type_value L1_coeff2 =
                            g2_field_type_value(prec_P2.PX, g1_field_type_value::zero()) - prec_Q2.QX_over_twist;
 
                        typename gt_type::value_type f = gt_type::value_type::one();
 
                        bool found_one = false;
                        std::size_t dbl_idx = 0;
                        std::size_t add_idx = 0;
 
                        for (long i = params_type::integral_type_max_bits - 1; i >= 0; --i) {
                            const bool bit = multiprecision::bit_test(params_type::ate_loop_count, i);
 
                            if (!found_one) {
                                /* this skips the MSB itself */
                                found_one |= bit;
                                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::ate_dbl_coeffs dc1 = prec_Q1.dbl_coeffs[dbl_idx];
                            typename policy_type::ate_dbl_coeffs dc2 = prec_Q2.dbl_coeffs[dbl_idx];
                            ++dbl_idx;
 
                            typename gt_type::value_type g_RR_at_P1 = typename gt_type::value_type(
                                -dc1.c_4C - dc1.c_J * prec_P1.PX_twist + dc1.c_L, dc1.c_H * prec_P1.PY_twist);
 
                            typename gt_type::value_type g_RR_at_P2 = typename gt_type::value_type(
                                -dc2.c_4C - dc2.c_J * prec_P2.PX_twist + dc2.c_L, dc2.c_H * prec_P2.PY_twist);
 
                            f = f.squared() * g_RR_at_P1 * g_RR_at_P2;
 
                            if (bit) {
                                typename policy_type::ate_add_coeffs ac1 = prec_Q1.add_coeffs[add_idx];
                                typename policy_type::ate_add_coeffs ac2 = prec_Q2.add_coeffs[add_idx];
                                ++add_idx;
 
                                typename gt_type::value_type g_RQ_at_P1 = typename gt_type::value_type(
                                    ac1.c_RZ * prec_P1.PY_twist,
                                    -(prec_Q1.QY_over_twist * ac1.c_RZ + L1_coeff1 * ac1.c_L1));
                                typename gt_type::value_type g_RQ_at_P2 = typename gt_type::value_type(
                                    ac2.c_RZ * prec_P2.PY_twist,
                                    -(prec_Q2.QY_over_twist * ac2.c_RZ + L1_coeff2 * ac2.c_L1));
 
                                f = f * g_RQ_at_P1 * g_RQ_at_P2;
                            }
                        }
 
                        if (params_type::ate_is_loop_count_neg) {
                            typename policy_type::ate_add_coeffs ac1 = prec_Q1.add_coeffs[add_idx];
                            typename policy_type::ate_add_coeffs ac2 = prec_Q2.add_coeffs[add_idx];
                            ++add_idx;
                            typename gt_type::value_type g_RnegR_at_P1 = typename gt_type::value_type(
                                ac1.c_RZ * prec_P1.PY_twist,
                                -(prec_Q1.QY_over_twist * ac1.c_RZ + L1_coeff1 * ac1.c_L1));
                            typename gt_type::value_type g_RnegR_at_P2 = typename gt_type::value_type(
                                ac2.c_RZ * prec_P2.PY_twist,
                                -(prec_Q2.QY_over_twist * ac2.c_RZ + L1_coeff2 * ac2.c_L1));
 
                            f = (f * g_RnegR_at_P1 * g_RnegR_at_P2).inversed();
                        }
 
                        return f;
                    }
                };
            }    // namespace pairing
        }        // namespace algebra
    }            // namespace crypto3
}    // namespace nil
#endif    // CRYPTO3_ALGEBRA_PAIRING_MNT4_298_ATE_DOUBLE_MILLER_LOOP_HPP