algebra/include/nil/crypto3/algebra/curves/detail/forms/twisted_edwards/extended_with_a_minus_1/element_g1.hpp

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//---------------------------------------------------------------------------//
// Copyright (c) 2021 Mikhail Komarov <nemo@nil.foundation>
// Copyright (c) 2021 Ilias Khairullin <ilias@nil.foundation>
//
// MIT License
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#ifndef CRYPTO3_ALGEBRA_CURVES_TWISTED_EDWARDS_G1_ELEMENT_EXTENDED_WITH_A_MINUS_1_HPP
#define CRYPTO3_ALGEBRA_CURVES_TWISTED_EDWARDS_G1_ELEMENT_EXTENDED_WITH_A_MINUS_1_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/twisted_edwards/extended_with_a_minus_1/add_2008_hwcd_3.hpp>
#include <nil/crypto3/algebra/curves/detail/forms/twisted_edwards/extended_with_a_minus_1/dbl_2008_hwcd.hpp>
#include <nil/crypto3/algebra/curves/detail/forms/twisted_edwards/extended_with_a_minus_1/madd_2008_hwcd_2.hpp>
#include <nil/crypto3/algebra/curves/detail/forms/twisted_edwards/element_g1_affine.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::extended_with_a_minus_1> {
 
                        using params_type = CurveParams;
                        using field_type = typename params_type::field_type;
 
                    private:
                        using field_value_type = typename field_type::value_type;
 
                        using common_addition_processor =
                            twisted_edwards_element_g1_extended_with_a_minus_1_add_2008_hwcd_3;
                        using common_doubling_processor =
                            twisted_edwards_element_g1_extended_with_a_minus_1_dbl_2008_hwcd;
                        using mixed_addition_processor =
                            twisted_edwards_element_g1_extended_with_a_minus_1_madd_2008_hwcd_2;
 
                    public:
                        using form = forms::twisted_edwards;
                        using coordinates = coordinates::extended_with_a_minus_1;
 
                        using group_type = typename params_type::template group_type<coordinates>;
 
                        field_value_type X;
                        field_value_type Y;
                        field_value_type T;
                        field_value_type Z;
 
                        /*************************  Constructors and zero/one  ***********************************/
 
                        constexpr curve_element() :
                            curve_element(params_type::zero_fill[0],
                                          params_type::zero_fill[1],
                                          field_value_type::zero(),
                                          field_value_type::one()) {};
 
                        constexpr curve_element(field_value_type X,
                                                field_value_type Y,
                                                field_value_type T,
                                                field_value_type Z) {
                            this->X = X;
                            this->Y = Y;
                            this->T = T;
                            this->Z = Z;
                        };
 
                        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],
                                                 params_type::one_fill[0] * params_type::one_fill[1],
                                                 field_value_type::one());
                        }
 
                        /*************************  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 */
 
                            // X1/Z1 = X2/Z2 <=> X1*Z2 = X2*Z1
                            if ((this->X * other.Z) != (other.X * this->Z)) {
                                return false;
                            }
 
                            // Y1/Z1 = Y2/Z2 <=> Y1*Z2 = Y2*Z1
                            if ((this->Y * other.Z) != (other.Y * this->Z)) {
                                return false;
                            }
 
                            // T1/Z1 = T2/Z2 <=> T1*Z2 = T2*Z1
                            if ((this->T * other.Z) != (other.T * this->Z)) {
                                return false;
                            }
 
                            return true;
                        }
 
                        constexpr bool operator!=(const curve_element &other) const {
                            return !(operator==(other));
                        }
                        constexpr bool is_zero() const {
                            return (this->X.is_zero() && this->T.is_zero() && this->Z.is_zero());
                        }
 
                        constexpr bool is_well_formed() const {
                            assert(false && "Not implemented yet.");
                            return true;
                        }
 
                        /*************************  Reducing operations  ***********************************/
 
                        constexpr curve_element<params_type, form, curves::coordinates::affine> to_affine() const {
 
                            using result_type = curve_element<params_type, form, curves::coordinates::affine>;
 
                            if (is_zero()) {
                                return result_type::zero();
                            }
 
                            // assert((X/Z)*(Y/Z) == (T/Z));
                            return result_type(X / Z, Y / Z);    //  x=X/Z, y=Y/Z
                        }
 
                        /*************************  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;
                            this->T = other.T;
                            this->Z = other.Z;
 
                            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 common_addition_processor::process(*this, other);
                        }
 
                        constexpr curve_element operator-() const {
                            return curve_element(-X, Y, -T, Z);
                        }
 
                        constexpr curve_element operator-(const curve_element &other) const {
                            return (*this) + (-other);
                        }
 
                        constexpr curve_element doubled() const {
                            return common_doubling_processor::process(*this);
                        }
 
                        curve_element mixed_add(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;
                            }
 
                            return mixed_addition_processor::process(*this, other);
                        }
                    };
 
                }    // namespace detail
            }        // namespace curves
        }            // namespace algebra
    }                // namespace crypto3
}    // namespace nil
#endif    // CRYPTO3_ALGEBRA_CURVES_TWISTED_EDWARDS_G1_ELEMENT_EXTENDED_WITH_A_MINUS_1_HPP