short_weierstrass/jacobian_with_a4_0/madd_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>
//
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#ifndef CRYPTO3_ALGEBRA_CURVES_SHORT_WEIERSTRASS_G1_ELEMENT_JACOBIAN_WITH_A4_0_MADD_2007_BL_HPP
#define CRYPTO3_ALGEBRA_CURVES_SHORT_WEIERSTRASS_G1_ELEMENT_JACOBIAN_WITH_A4_0_MADD_2007_BL_HPP
 
namespace nil {
    namespace crypto3 {
        namespace algebra {
            namespace curves {
                namespace detail {
 
                    struct short_weierstrass_element_g1_jacobian_with_a4_0_madd_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;
 
                            // Because for some reasons it's not so
                            // assert(second.Z == field_value_type::one());
 
                            const field_value_type Z1Z1 = (first.Z).squared();            // Z1Z1 = Z1^2
                            const field_value_type U2 = second.X * Z1Z1;                  // X2*Z1Z1
                            const field_value_type S2 = second.Y * first.Z * Z1Z1;        // S2 = Y2 * Z1 * Z1Z1
                            const field_value_type H = U2 - (first.X);                    // H = U2-X1
                            const field_value_type HH = H.squared();                      // HH = H^2
                            const field_value_type I = HH.doubled().doubled();            // I = 4*HH
                            const field_value_type J = H * I;                             // J = H*I
                            const field_value_type r = (S2 - (first.Y)).doubled();        // r = 2*(S2-Y1)
                            const field_value_type V = first.X * I;                       // V = X1*I
                            const field_value_type X3 = r.squared() - J - V.doubled();    // X3 = r^2-J-2*V
                            const field_value_type Y3 =
                                r * (V - X3) - (first.Y * J).doubled();                         // Y3 = r*(V-X3)-2*Y1*J
                            const field_value_type Z3 = (first.Z + H).squared() - Z1Z1 - HH;    // Z3 = (Z1+H)^2-Z1Z1-HH
 
                            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_MADD_2007_BL_HPP