twisted_edwards/element_g1_affine.hpp

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//---------------------------------------------------------------------------//
// Copyright (c) 2021 Mikhail Komarov <nemo@nil.foundation>
// Copyright (c) 2021 Nikita Kaskov <nbering@nil.foundation>
// Copyright (c) 2021 Ilias Khairullin <ilias@nil.foundation>
//
// MIT License
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//---------------------------------------------------------------------------//
 
#ifndef CRYPTO3_ALGEBRA_CURVES_TWISTED_EDWARDS_G1_ELEMENT_AFFINE_HPP
#define CRYPTO3_ALGEBRA_CURVES_TWISTED_EDWARDS_G1_ELEMENT_AFFINE_HPP
 
#include <nil/crypto3/algebra/curves/detail/scalar_mul.hpp>
#include <nil/crypto3/algebra/curves/forms.hpp>
#include <nil/crypto3/algebra/curves/detail/forms/twisted_edwards/coordinates.hpp>
#include <nil/crypto3/algebra/curves/detail/forms/montgomery/coordinates.hpp>
 
namespace nil {
    namespace crypto3 {
        namespace algebra {
            namespace curves {
                namespace detail {
                    template<typename CurveParams, typename Form, typename Coordinates>
                    struct curve_element;
 
                    template<typename CurveParams>
                    struct curve_element<CurveParams, forms::twisted_edwards, coordinates::affine> {
 
                        using field_type = typename CurveParams::field_type;
 
                    private:
                        using params_type = CurveParams;
                        using field_value_type = typename field_type::value_type;
 
                    public:
                        using form = forms::twisted_edwards;
                        using coordinates = coordinates::affine;
 
                        using group_type = typename params_type::template group_type<coordinates>;
 
                        field_value_type X;
                        field_value_type Y;
 
                        /*************************  Constructors and zero/one  ***********************************/
                        constexpr curve_element() :
                            curve_element(params_type::zero_fill[0], params_type::zero_fill[1]) {};
 
                        constexpr curve_element(field_value_type in_X, field_value_type in_Y) {
                            this->X = in_X;
                            this->Y = in_Y;
                        };
 
                        static curve_element zero() {
                            return curve_element();
                        }
                        static curve_element one() {
                            return curve_element(params_type::one_fill[0], params_type::one_fill[1]);
                        }
 
                        /*************************  Comparison operations  ***********************************/
 
                        constexpr bool operator==(const curve_element &other) const {
                            if (this->is_zero()) {
                                return other.is_zero();
                            }
 
                            if (other.is_zero()) {
                                return false;
                            }
 
                            /* now neither is O */
 
                            if (this->X != other.X) {
                                return false;
                            }
 
                            if (this->Y != other.Y) {
                                return false;
                            }
 
                            return true;
                        }
 
                        constexpr bool operator!=(const curve_element &other) const {
                            return !(operator==(other));
                        }
                        constexpr bool is_zero() const {
                            return X == params_type::zero_fill[0] && Y == params_type::zero_fill[1];
                        }
 
                        constexpr bool is_well_formed() const {
                            if (this->is_zero()) {
                                return true;
                            } else {
 
                                field_value_type XX = this->X.squared();
                                field_value_type YY = this->Y.squared();
 
                                return (field_value_type(params_type::a) * XX + YY ==
                                        field_value_type::one() + field_value_type(params_type::d) * XX * YY);
                            }
                        }
 
                        /*************************  Reducing operations  ***********************************/
 
                        // /** @brief
                        //  *
                        //  * @return return the corresponding element from affine coordinates to
                        //  * projective coordinates
                        //  */
                        // constexpr curve_element<
                        //     params_type,
                        //     form,
                        //     typename curves::coordinates::projective> to_projective () const {
 
                        //     using result_type = curve_element<params_type,
                        //         form, typename curves::coordinates::projective>;
 
                        //     return result_type(X, Y, result_type::field_type::value_type::one()); // X = x, Y = y, Z
                        //     = 1
                        // }
 
                        constexpr curve_element<params_type, form, typename curves::coordinates::inverted>
                            to_inverted() const {
 
                            using result_type =
                                curve_element<params_type, form, typename curves::coordinates::inverted>;
 
                            return result_type(
                                X.inversed(), Y.inversed(),
                                result_type::field_type::value_type::one());    // X = x^(-1), Y = y^(-1), Z = 1
                        }
 
                        constexpr curve_element<params_type, form,
                                                typename curves::coordinates::extended_with_a_minus_1>
                            to_extended_with_a_minus_1() const {
 
                            using result_type =
                                curve_element<params_type, form, typename curves::coordinates::extended_with_a_minus_1>;
 
                            return result_type(X, Y, X * Y,
                                               result_type::field_type::value_type::one());    // x=X/Z, y=Y/Z, x*y=T/Z
                        }
 
                        constexpr curve_element to_affine() const {
                            return *this;
                        }
 
                        /*************************  Arithmetic operations  ***********************************/
 
                        constexpr curve_element operator=(const curve_element &other) {
                            // handle special cases having to do with O
                            this->X = other.X;
                            this->Y = other.Y;
 
                            return *this;
                        }
 
                        constexpr curve_element operator+(const curve_element &other) const {
                            // handle special cases having to do with O
                            if (this->is_zero()) {
                                return other;
                            }
 
                            if (other.is_zero()) {
                                return (*this);
                            }
 
                            if (*this == other) {
                                return this->doubled();
                            }
 
                            return this->add(other);
                        }
 
                        constexpr curve_element operator-() const {
                            return curve_element(-(this->X), this->Y);
                        }
 
                        constexpr curve_element operator-(const curve_element &B) const {
                            return (*this) + (-B);
                        }
                        constexpr curve_element doubled() const {
 
                            if (this->is_zero()) {
                                return (*this);
                            } else {
 
                                return this->add(*this);    // Temporary intil we find something more efficient
                            }
                        }
 
                    private:
                        curve_element add(const curve_element &other) const {
                            field_value_type XX = (this->X) * (other.X);
                            field_value_type YY = (this->Y) * (other.Y);
                            field_value_type XY = (this->X) * (other.Y);
                            field_value_type YX = (this->Y) * (other.X);
 
                            field_value_type lambda = params_type::d * XX * YY;
                            field_value_type X3 = (XY + YX) * (field_value_type::one() + lambda).inversed();
                            field_value_type Y3 =
                                (YY - params_type::a * XX) * (field_value_type::one() - lambda).inversed();
 
                            return curve_element(X3, Y3);
                        }
 
                    public:
                        /*************************  Reducing operations  ***********************************/
 
                        constexpr auto to_montgomery() const {
                            using result_params =
                                typename group_type::curve_type::template g1_type<curves::coordinates::affine,
                                                                                  forms::montgomery>::params_type;
                            using result_type =
                                typename group_type::curve_type::template g1_type<curves::coordinates::affine,
                                                                                  forms::montgomery>::value_type;
 
                            if (this->is_zero()) {
                                return result_type();
                            }
 
                            assert(static_cast<field_value_type>(result_params::A) ==
                                   static_cast<field_value_type>(2) *
                                       (static_cast<field_value_type>(params_type::a) +
                                        static_cast<field_value_type>(params_type::d)) /
                                       (static_cast<field_value_type>(params_type::a) -
                                        static_cast<field_value_type>(params_type::d)));
 
                            field_value_type s_inv = field_value_type::one();
                            field_value_type B_ =
                                static_cast<field_value_type>(4) / (static_cast<field_value_type>(params_type::a) -
                                                                    static_cast<field_value_type>(params_type::d));
                            if (static_cast<field_value_type>(result_params::B) != B_) {
                                s_inv = (B_ / static_cast<field_value_type>(result_params::B)).sqrt();
                            }
 
                            return result_type((field_value_type::one() + this->Y) /
                                                   (field_value_type::one() - this->Y),
                                               s_inv * ((field_value_type::one() + this->Y) /
                                                        (this->X * (field_value_type::one() - this->Y))));
                        }
                    };
 
                }    // namespace detail
            }        // namespace curves
        }            // namespace algebra
    }                // namespace crypto3
}    // namespace nil
#endif    // CRYPTO3_ALGEBRA_CURVES_TWISTED_EDWARDS_G1_ELEMENT_AFFINE_HPP