affine_ate_precompute_g2.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_SHORT_WEIERSTRASS_PROJECTIVE_AFFINE_ATE_PRECOMPUTE_G2_HPP
#define CRYPTO3_ALGEBRA_PAIRING_SHORT_WEIERSTRASS_PROJECTIVE_AFFINE_ATE_PRECOMPUTE_G2_HPP
 
#include <nil/crypto3/multiprecision/number.hpp>
#include <nil/crypto3/multiprecision/cpp_int.hpp>
 
#include <nil/crypto3/algebra/pairing/detail/forms/short_weierstrass/projective/types.hpp>
 
namespace nil {
    namespace crypto3 {
        namespace algebra {
            namespace pairing {
 
                template<typename CurveType>
                class short_weierstrass_projective_affine_ate_precompute_g2 {
                    using curve_type = CurveType;
 
                    using params_type = detail::pairing_params<curve_type>;
                    typedef detail::short_weierstrass_projective_types_policy<curve_type> policy_type;
 
                    using base_field_type = typename curve_type::base_field_type;
                    using g2_type = typename curve_type::template g2_type<>;
                    using g2_affine_type = typename curve_type::template g2_type<curves::coordinates::affine>;
 
                    using g2_field_type_value = typename g2_type::field_type::value_type;
 
                public:
                    using g2_precomputed_type = typename policy_type::affine_ate_g2_precomputation;
 
                    static g2_precomputed_type process(const typename g2_type::value_type &Q) {
 
                        typename g2_affine_type::value_type Qcopy = Q.to_affine();
 
                        g2_precomputed_type result;
                        result.QX = Qcopy.X;
                        result.QY = Qcopy.Y;
 
                        g2_field_type_value RX = Qcopy.X;
                        g2_field_type_value RY = Qcopy.Y;
                        bool found_nonzero = false;
 
                        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;
                            }
 
                            typename policy_type::affine_ate_coeffs c;
                            c.old_RX = RX;
                            c.old_RY = RY;
                            g2_field_type_value old_RX_2 = c.old_RX.squared();
                            c.gamma = (old_RX_2 + old_RX_2 + old_RX_2 + params_type::twist_coeff_a) *
                                      (c.old_RY + c.old_RY).inversed();
                            c.gamma_twist = c.gamma * params_type::twist;
 
                            c.gamma_X = c.gamma * c.old_RX;
                            result.coeffs.push_back(c);
 
                            RX = c.gamma.squared() - (c.old_RX + c.old_RX);
                            RY = c.gamma * (c.old_RX - RX) - c.old_RY;
 
                            if (NAF[i] != 0) {
                                typename policy_type::affine_ate_coeffs c;
                                c.old_RX = RX;
                                c.old_RY = RY;
                                if (NAF[i] > 0) {
                                    c.gamma = (c.old_RY - result.QY) * (c.old_RX - result.QX).inversed();
                                } else {
                                    c.gamma = (c.old_RY + result.QY) * (c.old_RX - result.QX).inversed();
                                }
                                c.gamma_twist = c.gamma * params_type::twist;
 
                                c.gamma_X = c.gamma * result.QX;
                                result.coeffs.push_back(c);
 
                                RX = c.gamma.squared() - (c.old_RX + result.QX);
                                RY = c.gamma * (c.old_RX - RX) - c.old_RY;
                            }
                        }
 
                        return result;
                    }
                };
            }    // namespace pairing
        }        // namespace algebra
    }            // namespace crypto3
}    // namespace nil
#endif    // CRYPTO3_ALGEBRA_PAIRING_SHORT_WEIERSTRASS_PROJECTIVE_AFFINE_ATE_PRECOMPUTE_G2_HPP