short_weierstrass/element_g1_affine.hpp

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//---------------------------------------------------------------------------//
// Copyright (c) 2020-2021 Mikhail Komarov <nemo@nil.foundation>
// Copyright (c) 2020-2021 Nikita Kaskov <nbering@nil.foundation>
// Copyright (c) 2020-2021 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
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// The above copyright notice and this permission notice shall be included in all
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//---------------------------------------------------------------------------//
 
#ifndef CRYPTO3_ALGEBRA_CURVES_SHORT_WEIERSTRASS_G1_ELEMENT_HPP
#define CRYPTO3_ALGEBRA_CURVES_SHORT_WEIERSTRASS_G1_ELEMENT_HPP
 
#include <nil/crypto3/algebra/curves/detail/scalar_mul.hpp>
#include <nil/crypto3/algebra/curves/forms.hpp>
 
#include <nil/crypto3/algebra/curves/detail/forms/short_weierstrass/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::short_weierstrass, 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::short_weierstrass;
                        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;
                        };
 
                        constexpr static curve_element zero() {
                            return curve_element();
                        }
 
                        constexpr 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[0];
                        }
 
                        /*************************  Reducing operations  ***********************************/
 
                        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
                        }
 
                        /*************************  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 &other) const {
                            return (*this) + (-other);
                        }
 
                        constexpr curve_element doubled() const {
 
                            if (this->is_zero()) {
                                return (*this);
                            } else {
                                field_value_type Xsquared = X.squared();
                                field_value_type Xsquared3pa = Xsquared.doubled() + Xsquared + params_type::a;
                                field_value_type Xsquared3pasquared = Xsquared3pa.squared();
                                field_value_type Y2squared = Y.doubled().squared();
 
                                field_value_type X3 = Xsquared3pasquared * Y2squared.inversed() - X - X;
                                field_value_type Y3 = (X.doubled() + X) * Xsquared3pa * Y.doubled().inversed() -
                                                      Xsquared3pasquared * Xsquared3pa * Y2squared * (Y.doubled()) - Y;
                            }
                        }
 
                    private:
                        curve_element add(const curve_element &other) const {
                            field_value_type Y2mY1 = other.Y - this->Y;
                            field_value_type Y2mY1squared = Y2mY1.squared();
                            field_value_type X2mX1 = other.X - this->X;
                            field_value_type X2mX1squared = X2mX1.squared();
 
                            field_value_type X3 = Y2mY1squared * X2mX1squared.inversed() - this->X - other.X;
                            field_value_type Y3 = ((this - X).doubled() + other.X) * Y2mY1 * X2mX1.inversed() -
                                                  Y2mY1 * Y2mY1squared * (X2mX1 * X2mX1squared).inversed() - this->Y;
 
                            return curve_element(X3, Y3);
                        }
                    };
 
                }    // namespace detail
            }        // namespace curves
        }            // namespace algebra
    }                // namespace crypto3
}    // namespace nil
#endif    // CRYPTO3_ALGEBRA_CURVES_SHORT_WEIERSTRASS_G1_ELEMENT_HPP