dbl_2009_l.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_DBL_2009_L_HPP
#define CRYPTO3_ALGEBRA_CURVES_SHORT_WEIERSTRASS_G1_ELEMENT_JACOBIAN_WITH_A4_0_DBL_2009_L_HPP
 
namespace nil {
    namespace crypto3 {
        namespace algebra {
            namespace curves {
                namespace detail {
 
                    struct short_weierstrass_element_g1_jacobian_with_a4_0_dbl_2009_l {
 
                        template<typename ElementType>
                        constexpr static inline ElementType process(const ElementType &first) {
 
                            using field_value_type = typename ElementType::field_type::value_type;
 
                            // handle point at infinity
                            if (first.is_zero()) {
                                return (first);
                            }
 
                            field_value_type A = (first.X).squared();    // A = X1^2
                            field_value_type B = (first.Y).squared();    // B = Y1^2
                            field_value_type C = B.squared();            // C = B^2
                            field_value_type D = (first.X + B).squared() - A - C;
                            D = D + D;                            // D = 2 * ((X1 + B)^2 - A - C)
                            field_value_type E = A + A + A;       // E = 3 * A
                            field_value_type F = E.squared();     // F = E^2
                            field_value_type X3 = F - (D + D);    // X3 = F - 2 D
                            field_value_type eightC = C + C;
                            eightC = eightC + eightC;
                            eightC = eightC + eightC;
                            field_value_type Y3 = E * (D - X3) - eightC;    // Y3 = E * (D - X3) - 8 * C
                            field_value_type Y1Z1 = (first.Y) * (first.Z);
                            field_value_type Z3 = Y1Z1 + Y1Z1;    // Z3 = 2 * Y1 * Z1
 
                            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_DBL_2009_L_HPP