short_weierstrass/jacobian_with_a4_0/add_2007_bl.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_CURVES_SHORT_WEIERSTRASS_G1_ELEMENT_JACOBIAN_WITH_A4_0_ADD_2007_BL_HPP
#define CRYPTO3_ALGEBRA_CURVES_SHORT_WEIERSTRASS_G1_ELEMENT_JACOBIAN_WITH_A4_0_ADD_2007_BL_HPP
 
namespace nil {
    namespace crypto3 {
        namespace algebra {
            namespace curves {
                namespace detail {
 
                    struct short_weierstrass_element_g1_jacobian_with_a4_0_add_2007_bl {
 
                        template<typename ElementType>
                        constexpr static inline ElementType process(const ElementType &first,
                                                                    const ElementType &second) {
 
                            using field_value_type = typename ElementType::field_type::value_type;
 
                            field_value_type Z1Z1 = (first.Z).squared();            // Z1Z1 = Z1^2
                            field_value_type Z2Z2 = (second.Z).squared();           // Z2Z2 = Z2^2
                            field_value_type U1 = (first.X) * Z2Z2;                 // U1 = X1 * Z2Z2
                            field_value_type U2 = (second.X) * Z1Z1;                // U2 = X2 * Z1Z1
                            field_value_type S1 = (first.Y) * (second.Z) * Z2Z2;    // S1 = Y1 * Z2 * Z2Z2
                            field_value_type S2 = (second.Y) * (first.Z) * Z1Z1;    // S2 = Y2 * Z1 * Z1Z1
                            field_value_type H = U2 - U1;                           // H = U2-U1
                            field_value_type S2_minus_S1 = S2 - S1;
                            field_value_type I = (H + H).squared();             // I = (2 * H)^2
                            field_value_type J = H * I;                         // J = H * I
                            field_value_type r = S2_minus_S1 + S2_minus_S1;     // r = 2 * (S2-S1)
                            field_value_type V = U1 * I;                        // V = U1 * I
                            field_value_type X3 = r.squared() - J - (V + V);    // X3 = r^2 - J - 2 * V
                            field_value_type S1_J = S1 * J;
                            field_value_type Y3 = r * (V - X3) - (S1_J + S1_J);    // Y3 = r * (V-X3)-2 S1 J
                            field_value_type Z3 =
                                ((first.Z + second.Z).squared() - Z1Z1 - Z2Z2) * H;    // Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2) * H
 
                            return ElementType(X3, Y3, Z3);
                        }
                    };
 
                }    // namespace detail
            }        // namespace curves
        }            // namespace algebra
    }                // namespace crypto3
}    // namespace nil
#endif    // CRYPTO3_ALGEBRA_CURVES_SHORT_WEIERSTRASS_G1_ELEMENT_JACOBIAN_WITH_A4_0_ADD_2007_BL_HPP