diff --git a/example/curves.cpp b/example/curves.cpp index 8ca67bed..0d090e97 100644 --- a/example/curves.cpp +++ b/example/curves.cpp @@ -32,6 +32,7 @@ #include #include +//#include #include #include #include @@ -192,6 +193,16 @@ int main() { std::cout << "----------------------------" << std::endl; + /*std::cout << "BN128-254 curve g1 group basic math:" << std::endl; + fp_curve_group_basic_math_examples::g1_type>(); + + std::cout << "----------------------------" << std::endl; + + std::cout << "BN128-254 curve g2 group basic math:" << std::endl; + fp2_curve_group_basic_math_examples::g2_type>(); + + std::cout << "----------------------------" << std::endl;*/ + std::cout << "Edwards curve g1 group basic math:" << std::endl; fp_curve_group_basic_math_examples::g1_type<>>(); diff --git a/include/nil/crypto3/algebra/curves/bn128.hpp b/include/nil/crypto3/algebra/curves/bn128.hpp new file mode 100644 index 00000000..0241b563 --- /dev/null +++ b/include/nil/crypto3/algebra/curves/bn128.hpp @@ -0,0 +1,99 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// Copyright (c) 2020 Ilias Khairullin +// +// 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 +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_CURVES_BN128_HPP +#define CRYPTO3_ALGEBRA_CURVES_BN128_HPP + +#include +#include + +#include +#include +#include + +//#include + +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace curves { + + /* + The curve equation for a BN curve is: + + E/Fp: y^2 = x^3 + b. + */ + + /* + Over Fp12_2over3over2 + y^2 = x^3 + b + u^2 = -1 + xi = xi_a + xi_b u + v^3 = xi + w^2 = v + */ + template + struct bn128 { }; + + template<> + struct bn128<254> { + constexpr static const std::size_t base_field_bits = 254; + typedef fields::bn128_base_field base_field_type; + typedef typename base_field_type::modulus_type number_type; + typedef typename base_field_type::extended_modulus_type extended_number_type; + + constexpr static const number_type base_field_modulus = base_field_type::modulus; + + constexpr static const std::size_t scalar_field_bits = 254; + typedef fields::bn128_fr scalar_field_type; + constexpr static const number_type scalar_field_modulus = scalar_field_type::modulus; + + typedef typename detail::bn128_g1<254> g1_type; + typedef typename detail::bn128_g2<254> g2_type; + + // typedef typename pairing::pairing_policy> pairing_policy; + + typedef typename fields::fp12_2over3over2 gt_type; + + constexpr static const number_type p = base_field_modulus; + constexpr static const number_type q = scalar_field_modulus; + + constexpr static const number_type a = 0; + constexpr static const number_type b = 0x03; + constexpr static const number_type x = 0x09; + constexpr static const number_type y = 0x01; + }; + + typedef bn128<254> bn128_254; + + } // namespace curves + } // namespace algebra + } // namespace crypto3 +} // namespace nil + +#endif // CRYPTO3_ALGEBRA_CURVES_BN128_HPP diff --git a/include/nil/crypto3/algebra/curves/detail/bn128/g1.hpp b/include/nil/crypto3/algebra/curves/detail/bn128/g1.hpp new file mode 100755 index 00000000..758e9d44 --- /dev/null +++ b/include/nil/crypto3/algebra/curves/detail/bn128/g1.hpp @@ -0,0 +1,331 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// Copyright (c) 2020 Ilias Khairullin +// +// 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 +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_CURVES_BN128_G1_HPP +#define CRYPTO3_ALGEBRA_CURVES_BN128_G1_HPP + +#include + +#include +#include +#include + +#include +#include + +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace curves { + namespace detail { + + using namespace nil::crypto3::algebra; + + template + struct bn128_g1 { + + constexpr static const std::size_t g1_field_bits = ModulusBits; + typedef typename fields::bn128_fq::value_type g1_field_type_value; + + constexpr static const std::size_t g2_field_bits = ModulusBits; + typedef typename fields::fp2>::value_type g2_field_type_value; + + using underlying_field_value_type = g1_field_type_value; + + // constexpr static const std::size_t value_bits = policy_type::g1_field_type::value_bits; + + underlying_field_value_type X; + underlying_field_value_type Y; + underlying_field_value_type Z; + + /************************* Constructors and zero/one ***********************************/ + + bn128_g1() : + bn128_g1(underlying_field_value_type::one(), underlying_field_value_type::one(), + underlying_field_value_type::zero()) {}; + // must be + // bn128_g1() : bn128_g1(zero_fill[0], zero_fill[1], zero_fill[2]) {}; + // when constexpr fields will be finished + + bn128_g1(underlying_field_value_type X, + underlying_field_value_type Y, + underlying_field_value_type Z) { + this->X = X; + this->Y = Y; + this->Z = Z; + }; + + static bn128_g1 zero() { + return bn128_g1(); + } + + static bn128_g1 one() { + return bn128_g1(underlying_field_value_type(1), underlying_field_value_type(2), + underlying_field_value_type(1)); + // must be + // return bn128_g1(one_fill[0], one_fill[1], one_fill[2]); + // when constexpr fields will be finished + } + + /************************* Comparison operations ***********************************/ + + bool operator==(const bn128_g1 &other) const { + if (this->is_zero()) { + return other.is_zero(); + } + + if (other.is_zero()) { + return false; + } + + /* now neither is O */ + + underlying_field_value_type Z1sq, Z2sq, lhs, rhs; + Z1sq = (this->Z).squared(); + Z2sq = other.Z.squared(); + lhs = Z2sq * this->X; + rhs = Z1sq * other.X; + + if (lhs != rhs) { + return false; + } + + underlying_field_value_type Z1cubed, Z2cubed; + Z1cubed = Z1sq * this->Z; + Z2cubed = Z2sq * other.Z; + lhs = Z2cubed * this->Y; + rhs = Z1cubed * other.Y; + + return (lhs == rhs); + } + + bool operator!=(const bn128_g1 &other) const { + return !operator==(other); + } + + bool is_zero() const { + return Z.is_zero(); + } + + bool is_special() const { + return (this->is_zero() || this->Z == 1); + } + + /************************* Arithmetic operations ***********************************/ + + bn128_g1 operator=(const bn128_g1 &other) { + // handle special cases having to do with O + this->X = other.X; + this->Y = other.Y; + this->Z = other.Z; + + return *this; + } + + /* + Jacobi coordinate + (p_out[0], p_out[1], p_out[2]) = (X, Y, Z) + (other.X, other.Y, other.Z) + */ + bn128_g1 operator+(const bn128_g1 &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); + } + + bn128_g1 operator-(const bn128_g1 &other) const { + return *this + (-other); + } + + bn128_g1 operator-() const { + return bn128_g1(X, -Y, Z); + } + + /* + Jacobi coordinate + (p_out[0], p_out[1], p_out[2]) = 2(X, Y, Z) + */ + bn128_g1 doubled() const { + underlying_field_value_type p_out[3]; + + underlying_field_value_type A, B, C, D, E; + A = X.squared(); + B = Y.squared(); + C = B.squared(); + D = ((X + B).squared() - A - C).doubled(); + E = A.doubled() + A; + + p_out[0] = E.squared() - D.doubled(); + p_out[1] = E * (D - p_out[0]) - C.doubled().doubled().doubled(); + p_out[2] = (Y * Z).doubled(); + + return bn128_g1(p_out[0], p_out[1], p_out[2]); + } + + bn128_g1 mixed_add(const bn128_g1 &other) const { + if (this->is_zero()) { + return other; + } + + if (other.is_zero()) { + return *this; + } + + // no need to handle points of order 2,4 + // (they cannot exist in a prime-order subgroup) + + // check for doubling case + + // using Jacobian pinates so: + // (X1:Y1:Z1) = (X2:Y2:Z2) + // iff + // X1/Z1^2 == X2/Z2^2 and Y1/Z1^3 == Y2/Z2^3 + // iff + // X1 * Z2^2 == X2 * Z1^2 and Y1 * Z2^3 == Y2 * Z1^3 + + // we know that Z2 = 1 + + underlying_field_value_type Z1Z1 = this->Z.squared(); + + underlying_field_value_type U2 = other.X * Z1Z1; + + underlying_field_value_type S2 = other.Y * this->Z * Z1Z1; + ; // S2 = Y2*Z1*Z1Z1 + + if (this->X == U2 && this->Y == S2) { + // dbl case; nothing of above can be reused + return this->doubled(); + } + + bn128_g1 result; + underlying_field_value_type H, HH, I, J, r, V; + // H = U2-X1 + H = U2 - this->X; + // HH = H^2 + HH = H.squared(); + // I = 4*HH + I = HH.doubled().doubled(); + // J = H*I + J = H * I; + // r = 2*(S2-Y1) + r = (S2 - this->Y).doubled(); + // V = X1*I + V = this->X * I; + // X3 = r^2-J-2*V + result.X = r.squared() - J - V.doubled(); + // Y3 = r*(V-X3)-2*Y1*J + result.Y = r * (V - result.X) - (this->Y * J).doubled(); + // Z3 = (Z1+H)^2-Z1Z1-HH + result.Z = (this->Z + H).squared() - Z1Z1 - HH; + + return result; + } + + template + bn128_g1 operator*(const NumberType &other) const { + return scalar_mul(*this, other); + } + + private: + bn128_g1 add(const bn128_g1 &other) const { // unfinished + + underlying_field_value_type Z1Z1, Z2Z2, U1, U2, S1, S2, H, I, J, t3, r, V; + + underlying_field_value_type X_out, Y_out, Z_out; + + Z1Z1 = Z.squared(); + Z2Z2 = other.Z.squared(); + U1 = X * Z2Z2; + U2 = other.X * Z1Z1; + + S1 = Y * other.Z * Z2Z2; + S2 = other.Y * Z * Z1Z1; + + H = U2 - U1; + t3 = S2 - S1; + + I = H.doubled().squared(); + J = H * I; + r = t3.doubled(); + V = U1 * I; + + X_out = r.squared() - J - V.doubled(); + Y_out = r * (V - X_out) - (S1 * J).doubled(); + Z_out = ((Z + other.Z).squared() - Z1Z1 - Z2Z2) * H; + + return bn128_g1(X_out, Y_out, Z_out); + } + + public: + /************************* Reducing operations ***********************************/ + + bn128_g1 to_affine_coordinates() const { + underlying_field_value_type p_out[3]; + + if (is_zero() || Z == 1) + return *this; + underlying_field_value_type r, r2; + r = Z.inversed(); + r2 = r.squared(); + p_out[0] = X * r2; // r2 + p_out[1] = Y * r * r2; // r3 + p_out[2] = underlying_field_value_type::one(); + + return bn128_g1(p_out[0], p_out[1], p_out[2]); + } + + bn128_g1 to_special() const { + return this->to_affine_coordinates(); + } + + private: + /*constexpr static const std::array zero_fill = { + underlying_field_value_type::one(), underlying_field_value_type::one(), + underlying_field_value_type::zero()};*/ + + /*constexpr static const std::array one_fill = { + underlying_field_value_type(1), underlying_field_value_type(2), + underlying_field_value_type(1)};*/ + }; + + } // namespace detail + } // namespace curves + } // namespace algebra + } // namespace crypto3 +} // namespace nil +#endif // CRYPTO3_ALGEBRA_CURVES_BN128_G1_HPP diff --git a/include/nil/crypto3/algebra/curves/detail/bn128/g2.hpp b/include/nil/crypto3/algebra/curves/detail/bn128/g2.hpp new file mode 100755 index 00000000..46ecfa19 --- /dev/null +++ b/include/nil/crypto3/algebra/curves/detail/bn128/g2.hpp @@ -0,0 +1,341 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// Copyright (c) 2020 Ilias Khairullin +// +// 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 +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_CURVES_BN128_G2_HPP +#define CRYPTO3_ALGEBRA_CURVES_BN128_G2_HPP + +#include + +#include +#include +#include + +#include +#include + +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace curves { + namespace detail { + + using namespace nil::crypto3::algebra; + + template + struct bn128_g2 { + + constexpr static const std::size_t g1_field_bits = ModulusBits; + typedef typename fields::bn128_fq::value_type g1_field_type_value; + + constexpr static const std::size_t g2_field_bits = ModulusBits; + typedef typename fields::fp2>::value_type g2_field_type_value; + + using underlying_field_value_type = g2_field_type_value; + + // constexpr static const std::size_t value_bits = policy_type::g2_field_type::value_bits; + + underlying_field_value_type X; + underlying_field_value_type Y; + underlying_field_value_type Z; + + /************************* Constructors and zero/one ***********************************/ + + bn128_g2() : + bn128_g2(underlying_field_value_type::one(), underlying_field_value_type::one(), + underlying_field_value_type::zero()) {}; + // must be + // bn128_g2() : bn128_g2(zero_fill[0], zero_fill[1], zero_fill[2]) {}; + // when constexpr fields will be finished + + bn128_g2(underlying_field_value_type X, + underlying_field_value_type Y, + underlying_field_value_type Z) { + this->X = X; + this->Y = Y; + this->Z = Z; + }; + + static bn128_g2 zero() { + return bn128_g2(); + } + + static bn128_g2 one() { + return bn128_g2( + underlying_field_value_type( + 0x21C1452BAD76CBAFD56F91BF61C4C7A4764793ABC7E62D2EB2382A21D01014DA_cppui254, + 0x13F9579708C580632ECD7DCD6EE2E6FC20F597815A2792CC5128240A38EEBC15_cppui254), + underlying_field_value_type( + 0x16CFE76F05CE1E4C043A5A50EE37E9B0ADD1E47D95E5250BA20538A3680892C_cppui254, + 0x2D6532096CCA63300C3BA564B9BD9949DCDFB32C84AC6E2A065FD2334A7D09BE_cppui254), + underlying_field_value_type::one()); + // must be + // return bn128_g2(one_fill[0], one_fill[1], one_fill[2]); + // when constexpr fields will be finished + } + + /************************* Comparison operations ***********************************/ + + bool operator==(const bn128_g2 &other) const { + if (this->is_zero()) { + return other.is_zero(); + } + + if (other.is_zero()) { + return false; + } + + /* now neither is O */ + + underlying_field_value_type Z1sq, Z2sq, lhs, rhs; + Z1sq = (this->Z).squared(); + Z2sq = other.Z.squared(); + lhs = Z2sq * this->X; + rhs = Z1sq * other.X; + + if (lhs != rhs) { + return false; + } + + underlying_field_value_type Z1cubed, Z2cubed; + Z1cubed = Z1sq * this->Z; + Z2cubed = Z2sq * other.Z; + lhs = Z2cubed * this->Y; + rhs = Z1cubed * other.Y; + + return (lhs == rhs); + } + + bool operator!=(const bn128_g2 &other) const { + return !operator==(other); + } + + bool is_zero() const { + return Z.is_zero(); + } + + bool is_special() const { + return (this->is_zero() || this->Z == 1); + } + + /************************* Arithmetic operations ***********************************/ + + bn128_g2 operator=(const bn128_g2 &other) { + // handle special cases having to do with O + this->X = other.X; + this->Y = other.Y; + this->Z = other.Z; + + return *this; + } + + /* + Jacobi coordinate + (p_out[0], p_out[1], p_out[2]) = (X, Y, Z) + (other.X, other.Y, other.Z) + */ + bn128_g2 operator+(const bn128_g2 &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); + } + + bn128_g2 operator-(const bn128_g2 &other) const { + return *this + (-other); + } + + bn128_g2 operator-() const { + return bn128_g2(X, -Y, Z); + } + + /* + Jacobi coordinate + (p_out[0], p_out[1], p_out[2]) = 2(X, Y, Z) + */ + bn128_g2 doubled() const { + underlying_field_value_type p_out[3]; + + underlying_field_value_type A, B, C, D, E; + A = X.squared(); + B = Y.squared(); + C = B.squared(); + D = ((X + B).squared() - A - C).doubled(); + E = A.doubled() + A; + + p_out[0] = E.squared() - D.doubled(); + p_out[1] = E * (D - p_out[0]) - C.doubled().doubled().doubled(); + p_out[2] = (Y * Z).doubled(); + + return bn128_g2(p_out[0], p_out[1], p_out[2]); + } + + bn128_g2 mixed_add(const bn128_g2 &other) const { + if (this->is_zero()) { + return other; + } + + if (other.is_zero()) { + return *this; + } + + // no need to handle points of order 2,4 + // (they cannot exist in a prime-order subgroup) + + // check for doubling case + + // using Jacobian pinates so: + // (X1:Y1:Z1) = (X2:Y2:Z2) + // iff + // X1/Z1^2 == X2/Z2^2 and Y1/Z1^3 == Y2/Z2^3 + // iff + // X1 * Z2^2 == X2 * Z1^2 and Y1 * Z2^3 == Y2 * Z1^3 + + // we know that Z2 = 1 + + underlying_field_value_type Z1Z1 = this->Z.squared(); + + underlying_field_value_type U2 = other.X * Z1Z1; + + underlying_field_value_type S2 = other.Y * this->Z * Z1Z1; + ; // S2 = Y2*Z1*Z1Z1 + + if (this->X == U2 && this->Y == S2) { + // dbl case; nothing of above can be reused + return this->doubled(); + } + + bn128_g2 result; + underlying_field_value_type H, HH, I, J, r, V; + // H = U2-X1 + H = U2 - this->X; + // HH = H^2 + HH = H.squared(); + // I = 4*HH + I = HH.doubled().doubled(); + // J = H*I + J = H * I; + // r = 2*(S2-Y1) + r = (S2 - this->Y).doubled(); + // V = X1*I + V = this->X * I; + // X3 = r^2-J-2*V + result.X = r.squared() - J - V.doubled(); + // Y3 = r*(V-X3)-2*Y1*J + result.Y = r * (V - result.X) - (this->Y * J).doubled(); + // Z3 = (Z1+H)^2-Z1Z1-HH + result.Z = (this->Z + H).squared() - Z1Z1 - HH; + + return result; + } + + template + bn128_g2 operator*(const NumberType &other) const { + return scalar_mul(*this, other); + } + + private: + bn128_g2 add(const bn128_g2 &other) const { // unfinished + + underlying_field_value_type Z1Z1, Z2Z2, U1, U2, S1, S2, H, I, J, t3, r, V; + + underlying_field_value_type X_out, Y_out, Z_out; + + Z1Z1 = Z.squared(); + Z2Z2 = other.Z.squared(); + U1 = X * Z2Z2; + U2 = other.X * Z1Z1; + + S1 = Y * other.Z * Z2Z2; + S2 = other.Y * Z * Z1Z1; + + H = U2 - U1; + t3 = S2 - S1; + + I = H.doubled().squared(); + J = H * I; + r = t3.doubled(); + V = U1 * I; + X_out = r.squared() - J - V.doubled(); + Y_out = r * (V - X_out) - (S1 * J).doubled(); + Z_out = ((Z + other.Z).squared() - Z1Z1 - Z2Z2) * H; + + return bn128_g2(X_out, Y_out, Z_out); + } + + public: + /************************* Reducing operations ***********************************/ + + bn128_g2 to_affine_coordinates() const { + underlying_field_value_type p_out[3]; + + if (is_zero() || Z.is_one()) + return *this; + underlying_field_value_type r, r2; + r = Z.inversed(); + r2 = r.squared(); + p_out[0] = X * r2; // r2 + p_out[1] = Y * r * r2; // r3 + p_out[2] = underlying_field_value_type::one(); + + return bn128_g2(p_out[0], p_out[1], p_out[2]); + } + + bn128_g2 to_special() const { + return this->to_affine_coordinates(); + } + + private: + /*constexpr static const underlying_field_value_type zero_fill = { + underlying_field_value_type::one(), underlying_field_value_type::one(), + underlying_field_value_type::zero()};*/ + + /*constexpr static const underlying_field_value_type one_fill = { + underlying_field_value_type( + 0x21C1452BAD76CBAFD56F91BF61C4C7A4764793ABC7E62D2EB2382A21D01014DA_cppui254, + 0x13F9579708C580632ECD7DCD6EE2E6FC20F597815A2792CC5128240A38EEBC15_cppui254), + underlying_field_value_type( + 0x16CFE76F05CE1E4C043A5A50EE37E9B0ADD1E47D95E5250BA20538A3680892C_cppui254, + 0x2D6532096CCA63300C3BA564B9BD9949DCDFB32C84AC6E2A065FD2334A7D09BE_cppui254), + underlying_field_value_type::one()};*/ + }; + + } // namespace detail + } // namespace curves + } // namespace algebra + } // namespace crypto3 +} // namespace nil +#endif // CRYPTO3_ALGEBRA_CURVES_BN128_G2_HPP diff --git a/include/nil/crypto3/algebra/curves/detail/weierstrass.hpp b/include/nil/crypto3/algebra/curves/detail/weierstrass.hpp new file mode 100644 index 00000000..20c3318e --- /dev/null +++ b/include/nil/crypto3/algebra/curves/detail/weierstrass.hpp @@ -0,0 +1,116 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020-2021 Mikhail Komarov +// Copyright (c) 2020-2021 Ilias Khairullin +// Copyright (c) 2020-2021 Nikita Kaskov +// +// 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 +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_CURVES_WEIERSTRASS_HPP +#define CRYPTO3_ALGEBRA_CURVES_WEIERSTRASS_HPP + +#include + +#include + +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace curves { + /** + * For short Weierstrass curves y^2 = x^3 + b mod r, if there exists a cube root of unity mod r, + * we can take advantage of an enodmorphism to decompose a 254 bit scalar into 2 128 bit scalars. + * \beta = cube root of 1, mod q (q = order of fq) + * \lambda = cube root of 1, mod r (r = order of fr) + * + * For a point P1 = (X, Y), where Y^2 = X^3 + b, we know that + * the point P2 = (X * \beta, Y) is also a point on the curve + * We can represent P2 as a scalar multiplication of P1, where P2 = \lambda * P1 + * + * For a generic multiplication of P1 by a 254 bit scalar k, we can decompose k + * into 2 127 bit scalars (k1, k2), such that k = k1 - (k2 * \lambda) + * + * We can now represent (k * P1) as (k1 * P1) - (k2 * P2), where P2 = (X * \beta, Y). + * As k1, k2 have half the bit length of k, we have reduced the number of loop iterations of our + * scalar multiplication algorithm in half + * + * To find k1, k2, We use the extended euclidean algorithm to find 4 short scalars [a1, a2], [b1, b2] + * such that modulus = (a1 * b2) - (b1 * a2) We then compute scalars c1 = round(b2 * k / r), c2 = + * round(b1 * k / r), where k1 = (c1 * a1) + (c2 * a2), k2 = -((c1 * b1) + (c2 * b2)) We pre-compute + * scalars g1 = (2^256 * b1) / n, g2 = (2^256 * b2) / n, to avoid having to perform long division on + * 512-bit scalars + **/ + template + static void split_into_endomorphism_scalars(const typename FieldType::value_type &k, + typename FieldType::value_type &k1, + typename FieldType::value_type &k2) { + typedef typename FieldType::value_type value_type; + + value_type input = k.reduce_once(); + // uint64_t lambda_reduction[4] = { 0 }; + // __to_montgomery_form(lambda, lambda_reduction); + + // TODO: these parameters only work for the bn254 coordinate field. + // Need to shift into Params and calculate correct constants for the subgroup field + constexpr value_type endo_g1 = {Params::endo_g1_lo, Params::endo_g1_mid, Params::endo_g1_hi, 0}; + + constexpr value_type endo_g2 = {Params::endo_g2_lo, Params::endo_g2_mid, 0, 0}; + + constexpr value_type endo_minus_b1 = {Params::endo_minus_b1_lo, Params::endo_minus_b1_mid, 0, 0}; + + constexpr value_type endo_b2 = {Params::endo_b2_lo, Params::endo_b2_mid, 0, 0}; + + // compute c1 = (g2 * k) >> 256 + wide_array c1 = endo_g2.mul_512(input); + // compute c2 = (g1 * k) >> 256 + wide_array c2 = endo_g1.mul_512(input); + + // (the bit shifts are implicit, as we only utilize the high limbs of c1, c2 + + // TODO remove data duplication + value_type c1_hi = {c1.data[4], c1.data[5], c1.data[6], + c1.data[7]}; // *(field*)((uintptr_t)(&c1) + (4 * sizeof(uint64_t))); + value_type c2_hi = {c2.data[4], c2.data[5], c2.data[6], + c2.data[7]}; // *(field*)((uintptr_t)(&c2) + (4 * sizeof(uint64_t))); + + // compute q1 = c1 * -b1 + wide_array q1 = c1_hi.mul_512(endo_minus_b1); + // compute q2 = c2 * b2 + wide_array q2 = c2_hi.mul_512(endo_b2); + + // TODO: this doesn't have to be a 512-bit multiply... + value_type q1_lo {q1.data[0], q1.data[1], q1.data[2], q1.data[3]}; + value_type q2_lo {q2.data[0], q2.data[1], q2.data[2], q2.data[3]}; + + value_type t1 = (q2_lo - q1_lo).reduce_once(); + value_type t2 = (t1 * beta() + input).reduce_once(); + k2.data[0] = t1.data[0]; + k2.data[1] = t1.data[1]; + k1.data[0] = t2.data[0]; + k1.data[1] = t2.data[1]; + } + } // namespace curves + } // namespace algebra + } // namespace crypto3 +} // namespace nil +#endif // CRYPTO3_ALGEBRA_CURVES_SCALAR_MUL_HPP diff --git a/include/nil/crypto3/algebra/fields/detail/double_element/double_element.hpp b/include/nil/crypto3/algebra/fields/detail/double_element/double_element.hpp new file mode 100644 index 00000000..0481f304 --- /dev/null +++ b/include/nil/crypto3/algebra/fields/detail/double_element/double_element.hpp @@ -0,0 +1,29 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// +// Distributed under the Boost Software License, Version 1.0 +// See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_FIELDS_DOUBLE_ELEMENT_HPP +#define CRYPTO3_ALGEBRA_FIELDS_DOUBLE_ELEMENT_HPP + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace fields { + namespace detail { + + template + struct double_element { + typedef extension_params params_type; + }; + + } // namespace detail + } // namespace fields + } // namespace algebra + } // namespace crypto3 +} // namespace nil +#endif // ALGEBRA_FIELDS_DOUBLE_ELEMENT_HPP diff --git a/include/nil/crypto3/algebra/fields/detail/double_element/fp.hpp b/include/nil/crypto3/algebra/fields/detail/double_element/fp.hpp new file mode 100644 index 00000000..1119d62c --- /dev/null +++ b/include/nil/crypto3/algebra/fields/detail/double_element/fp.hpp @@ -0,0 +1,104 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// +// Distributed under the Boost Software License, Version 1.0 +// See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_FIELDS_FP_DOUBLE_HPP +#define CRYPTO3_ALGEBRA_FIELDS_FP_DOUBLE_HPP + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace fields { + namespace detail { + + template + struct double_element_fp : public double_element> { + + typedef params_type::double_number_type number_type; + + number_type data; + + double_element_fp(number_type data) : data(data); + + inline static double_element_fp zero() const { + return double_element_fp(type(0)); + } + + inline static double_element_fp one() const { + return double_element_fp(type(1)); + } + + bool is_zero() const { + return data == type(0); + } + + bool is_one() const { + return data == type(1); + } + + bool operator==(const double_element_fp &B) const { + return data == B.data; + } + + bool operator!=(const double_element_fp &B) const { + return data != B.data; + } + + double_element_fp operator+(const double_element_fp &B) const { + return data + B.data; + } + + double_element_fp operator-(const double_element_fp &B) const { + return data - B.data; + } + + double_element_fp operator-() const { + return -data; + } + + // data + data + double_element_fp doubled() const { + return data + data; + } + + double_element_fp subOpt1() const { + } + + element_fp mod() { + } + }; + + double_element_fp addNC(const double_element_fp &A, const double_element_fp &B) { + return {addNC(data[0] + B.data[0]), addNC(data[1] + B.data[1])}; + } + + double_element_fp subNC(const double_element_fp &A, const double_element_fp &B) { + return {subNC(data[0] + B.data[0]), subNC(data[1] + B.data[1])}; + } + + double_element_fp mul(const element_fp &A, const element_fp &B) { + } + + double_element_fp squared(const element_fp &B) { + { + element_fp t0, t1; + t0 = addNC(x.b_, x.b_); + z.b_ = mul(t0, x.a_); + t1 = addNC(x.a_, Fp::getDirectP(1)); // RRR + t1 = subNC(t1, x.b_); + t0 = addNC(x.a_, x.b_); + z.a_ = mul(t0, t1); + } + } + } // namespace detail + } // namespace fields + } // namespace algebra + } // namespace crypto3 +} // namespace nil + +#endif // ALGEBRA_FIELDS_FP_DOUBLE_HPP diff --git a/include/nil/crypto3/algebra/fields/detail/double_element/fp12_2over3over2.hpp b/include/nil/crypto3/algebra/fields/detail/double_element/fp12_2over3over2.hpp new file mode 100644 index 00000000..c408a1be --- /dev/null +++ b/include/nil/crypto3/algebra/fields/detail/double_element/fp12_2over3over2.hpp @@ -0,0 +1,272 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// +// Distributed under the Boost Software License, Version 1.0 +// See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_FILEDS_FP12_2OVER3OVER2_DOUBLE_HPP +#define CRYPTO3_ALGEBRA_FILEDS_FP12_2OVER3OVER2_DOUBLE_HPP + +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace fields { + namespace detail { + + template + struct double_element_fp12_2over3over2 + : public double_element> { + + using underlying_type = double_element_fp6_3over2; + + using value_type = std::array; + + value_type data; + + double_element_fp12_2over3over2(type data) : data(data); + + inline static double_element_fp12_2over3over2 zero() const { + return {underlying_type::zero(), underlying_type::zero()}; + } + + bool operator==(const double_element_fp12_2over3over2 &B) const { + return (data[0] == B.data[0]) && (data[1] == B.data[1]); + } + + bool operator!=(const double_element_fp12_2over3over2 &B) const { + return (data[0] != B.data[0]) || (data[1] != B.data[1]); + } + + double_element_fp12_2over3over2 operator+(const double_element_fp12_2over3over2 &B) const { + return {data[0] + B.data[0], data[1] + B.data[1]}; + } + + double_element_fp12_2over3over2 operator-(const double_element_fp12_2over3over2 &B) const { + return {data[0] - B.data[0], data[1] - B.data[1]}; + } + + double_element_fp12_2over3over2 operator-() const { + return zero() - data; + } + + // data + data + double_element_fp12_2over3over2 doubled() const { + return {data[0].doubled(), data[1].doubled()}; + } + + double_element_fp12_2over3over2 addNC(const double_element_fp12_2over3over2 &B) { + return {addNC(data[0] + B.data[0]), addNC(data[1] + B.data[1])}; + } + + double_element_fp12_2over3over2 subNC(const double_element_fp12_2over3over2 &B) { + return {subNC(data[0] + B.data[0]), subNC(data[1] + B.data[1])}; + } + + element mod() { + return {data[0].mod(), data[1].mod()}; + } + }; + + double_element_fp12_2over3over2 mul(const element &A, + const element &B) { + } + + /* + z *= x, + position: 0 1 2 3 4 5 + x = (l00, 0, l02) + (0, l11, 0)*w + x is represented as: + (x.a_, x.b_, x.c_) = (l00, l11, l02) + 4800clk * 66 + */ + /* + Operation Count: + + 13 * Fp2Dbl::mulOpt2 + 6 * Fp2Dbl::mod + 10 * Fp2::add/sub + 19 * Fp2Dbl::add/sub == 19 * (2 * Fp2::add/sub) == 38 * Fp2::add/sub + 4 * Fp2Dbl::mul_xi == 4 * (2 * Fp2::add/sub) == 8 * Fp2::add/sub + + Total: + + 13 * Fp2Dbl::mulOpt2 + 6 * Fp2Dbl::mod + 56 * Fp2::add/sub + */ + double_element_fp12_2over3over2 mul_Fp2_024(const element_fp6_3over2 &B) { + element &z0 = z.a_.a_; + element &z1 = z.a_.b_; + element &z2 = z.a_.c_; + element &z3 = z.b_.a_; + element &z4 = z.b_.b_; + element &z5 = z.b_.c_; + const element &x0 = x.a_; + const element &x2 = x.c_; + const element &x4 = x.b_; + element t0, t1, t2; + element s0; + + double_element T3, T4; + double_element D0, D2, D4; + double_element S1; + + D0 = mulOpt2(z0, x0); + D2 = mulOpt2(z2, x2); + D4 = mulOpt2(z4, x4); + + t2 = z0 + z4; + t1 = z0 + z2; + s0 = z1 + z3 + z5; + // For z.a_.a_ = z0. + S1 = mulOpt2(z1, x2); + T4 = (S1 + D4).mul_xi() + D0; + z0 = T4.mod(); + // For z.a_.b_ = z1. + T3 = mulOpt2(z5, x4); + S1 += T3; + T3 += D2; + T4 = T3.mul_xi(); + T3 = mulOpt2(z1, x0); + S1 += T3; + T4 += T3; + z1 = T4.mod(); + // For z.a_.c_ = z2. + t0 = x0 + x2; + T3 = mulOpt2(t1, t0) - D0 - D2; + T4 = mulOpt2(z3, x4); + S1 += T4; + T3 += T4; + // z3 needs z2. + // For z.b_.a_ = z3. + t0 = z2 + z4; + z2 = T3.mod(); + t1 = x2 + x4; + T3 = mulOpt2(t0, t1) - D2 - D4; + T4 = T3.mul_xi(); + T3 = mulOpt2(z3, x0); + S1 += T3; + T4 += T3; + z3 = T4.mod(); + // For z.b_.b_ = z4. + T3 = mulOpt2(z5, x2); + S1 += T3; + T4 = T3.mul_xi() + mulOpt2(t2, x0 + x4) - D0 - D4; + z4 = T4.mod(); + // For z.b_.c_ = z5. + z5 = (mulOpt2(s0, x0 + x2 + x4) - S1).mod(); + } + + /* + z = cv2 * cv3, + position:0 1 2 3 4 5 + cv2 = (l00, 0, l02) + (0, l11, 0)*w + cv3 = (l00, 0, l02) + (0, l11, 0)*w + these are represented as: + (cv*.a_, cv*.b_, cv*.c_) = (l00, l11, l02) + */ + /* + Operation Count: + + 6 * Fp2Dbl::mulOpt2 + 5 * Fp2Dbl::mod + 6 * Fp2::add/sub + 7 * Fp2Dbl::add/sub == 7 * (2 * Fp2::add/sub) == 14 * Fp2::add/sub + 3 * Fp2Dbl::mul_xi == 3 * (2 * Fp2::add/sub) == 6 * Fp2::add/sub + + Total: + + 6 * Fp2Dbl::mulOpt2 + 5 * Fp2Dbl::mod + 26 * Fp2::add/sub + call:2 + */ + double_element_fp12_2over3over2 mul_Fp2_024_Fp2_024(const element_fp6_3over2 &B1, + const element_fp6_3over2 &B2) { + element &z0 = z.a_.a_; + element &z1 = z.a_.b_; + element &z2 = z.a_.c_; + element &z3 = z.b_.a_; + element &z4 = z.b_.b_; + element &z5 = z.b_.c_; + const element &x0 = cv2.a_; + const element &x2 = cv2.c_; + const element &x4 = cv2.b_; + const element &y0 = cv3.a_; + const element &y2 = cv3.c_; + const element &y4 = cv3.b_; + double_element T00, T22, T44, T02, T24, T40; + + T00 = mulOpt2(x0, y0); + T22 = mulOpt2(x2, y2); + T44 = mulOpt2(x4, y4); + z0 = x0 + x2; + z1 = y0 + y2; + T02 = mulOpt2(z0, z1); + T02 -= T00; + T02 -= T22; + z2 = T02.mod(); + z0 = x2 + x4; + z1 = y2 + y4; + T24 = mulOpt2(z0, z1); + T24 -= T22; + T24 -= T44; + T02 = T24.mul_xi(); + z3 = T02.mod(); + z0 = x4 + x0; + z1 = y4 + y0; + T40 = mulOpt2(z0, z1); + T40 -= T00; + T40 -= T44; + z4 = T40.mod(); + T02 = T22.mul_xi(); + z1 = T02.mod(); + T02 = T44.mul_xi(); + T02 += T00; + z0 = T02.mod(); + z5.clear(); + } + + /* + square over Fp4 + Operation Count: + + 3 * Fp2Dbl::square + 2 * Fp2Dbl::mod + 1 * Fp2Dbl::mul_xi == 1 * (2 * Fp2::add/sub) == 2 * Fp2::add/sub + 3 * Fp2Dbl::add/sub == 3 * (2 * Fp2::add/sub) == 6 * Fp2::add/sub + 1 * Fp2::add/sub + + Total: + + 3 * Fp2Dbl::square + 2 * Fp2Dbl::mod + 9 * Fp2::add/sub + */ + static inline void sq_Fp4UseDbl(Fp2 &z0, Fp2 &z1, const Fp2 &x0, const Fp2 &x1) { + Fp2Dbl T0, T1, T2; + T0 = x0.squared(); + T1 = x1.squared(); + Fp2Dbl::mul_xi(T2, T1); + T2 += T0; + z1 = x0 + x1; + Fp2Dbl::mod(z0, T2); + // overwrite z[0] (position 0). + T2 = z1.squared(); + T2 -= T0; + T2 -= T1; + Fp2Dbl::mod(z1, T2); + } + + } // namespace detail + } // namespace fields + } // namespace algebra + } // namespace crypto3 +} // namespace nil + +#endif // ALGEBRA_FILEDS_FP12_2OVER3OVER2_DOUBLE_HPP diff --git a/include/nil/crypto3/algebra/fields/detail/double_element/fp2.hpp b/include/nil/crypto3/algebra/fields/detail/double_element/fp2.hpp new file mode 100644 index 00000000..14a54e28 --- /dev/null +++ b/include/nil/crypto3/algebra/fields/detail/double_element/fp2.hpp @@ -0,0 +1,140 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// +// Distributed under the Boost Software License, Version 1.0 +// See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_FILEDS_FP2_DOUBLE_HPP +#define CRYPTO3_ALGEBRA_FILEDS_FP2_DOUBLE_HPP + +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace fields { + namespace detail { + + template + struct double_element_fp2 : public double_element> { + + using underlying_type = double_element_fp; + + using value_type = std::array; + + value_type data; + + double_element_fp2(type data) : data(data); + + inline static double_element_fp2 zero() const { + return {underlying_type::zero(), underlying_type::zero()}; + } + + bool is_zero() const { + return (data[0] == underlying_type::zero()) && (data[1] == underlying_type::zero()); + } + + bool operator==(const double_element_fp2 &B) const { + return (data[0] == B.data[0]) && (data[1] == B.data[1]); + } + + bool operator!=(const double_element_fp2 &B) const { + return (data[0] != B.data[0]) || (data[1] != B.data[1]); + } + + double_element_fp2 operator+(const double_element_fp2 &B) const { + return {data[0] + B.data[0], data[1] + B.data[1]}; + } + + double_element_fp2 operator-(const double_element_fp2 &B) const { + return {data[0] - B.data[0], data[1] - B.data[1]}; + } + + double_element_fp2 operator-() const { + return zero() - data; + } + + // data + data + double_element_fp2 doubled() const { + return {data[0].doubled(), data[1].doubled()}; + } + + double_element_fp2 subOpt1() const { + return {mod(data[0]), mod(data[1])}; + } + + /* + XITAG + u^2 = -1 + xi = 9 + u + (a + bu)(9 + u) = (9a - b) + (a + 9b)u + */ + double_element_fp2 mul_xi() { + return {data[0].doubled().doubled().doubled() + data[0] - data[1], + data[1].doubled().doubled().doubled() + data[1] + data[0]}; + } + + element_fp2 mod() { + return {data[0].mod(), data[1].mod()}; + } + }; + + double_element_fp2 addNC(const double_element_fp2 &A, const double_element_fp2 &B) { + return {addNC(data[0] + B.data[0]), addNC(data[1] + B.data[1])}; + } + + double_element_fp2 subNC(const double_element_fp2 &A, const double_element_fp2 &B) { + return {subNC(data[0] + B.data[0]), subNC(data[1] + B.data[1])}; + } + + double_element_fp2 mulOpt(const element_fp2 &A, const element_fp2 &B, int mode) { + double_element d0; + double_element_fp2 z; + element s, t; + + s = addNC(A.data[0], A.data[1]); + t = addNC(B.data[0], B.data[1]); + d0 = mul(A.data[1], B.data[1]); + + z.data[0] = mul(A.data[0], B.data[0]); + + z.data[1] = mul(s, t); + z.data[1] = subNC(z.data[1], z.data[0]); + z.data[1] = subNC(z.data[1], d0); + + if (mode == 1) { + z.data[0] = subOpt1(z.data[0], d0); + + } else { + z.data[0] = z.data[0] - d0; + } + } + + double_element_fp2 mulOpt1(const element_fp2 &A, const element_fp2 &B) { + return mulOpt(A, B, 1); + } + + double_element_fp2 mulOpt2(const element_fp2 &A, const element_fp2 &B) { + return mulOpt(A, B, 2); + } + + double_element_fp2 squared(const element_fp2 &B) { + element_fp t0, t1; + t0 = addNC(x.b_, x.b_); + z.b_ = mul(t0, x.a_); + t1 = addNC(x.a_, Fp::getDirectP(1)); // RRR + t1 = subNC(t1, x.b_); + t0 = addNC(x.a_, x.b_); + z.a_ = mul(t0, t1); + } + + } // namespace detail + } // namespace fields + } // namespace algebra + } // namespace crypto3 +} // namespace nil + +#endif // ALGEBRA_FILEDS_FP2_DOUBLE_HPP diff --git a/include/nil/crypto3/algebra/fields/detail/double_element/fp6_3over2.hpp b/include/nil/crypto3/algebra/fields/detail/double_element/fp6_3over2.hpp new file mode 100644 index 00000000..5b98f574 --- /dev/null +++ b/include/nil/crypto3/algebra/fields/detail/double_element/fp6_3over2.hpp @@ -0,0 +1,280 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// +// Distributed under the Boost Software License, Version 1.0 +// See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_FIELDS_FP6_3OVER2_DOUBLE_HPP +#define CRYPTO3_ALGEBRA_FIELDS_FP6_3OVER2_DOUBLE_HPP + +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace fields { + namespace detail { + + template + struct double_element_fp6_3over2 : public double_element> { + + using underlying_type = double_element_fp2; + + using value_type = std::array; + + value_type data; + + double_element_fp6_3over2(type data) : data(data); + + inline static double_element_fp6_3over2 zero() const { + return {underlying_type::zero(), underlying_type::zero(), underlying_type::zero()}; + } + + bool operator==(const double_element_fp6_3over2 &B) const { + return (data[0] == B.data[0]) && (data[1] == B.data[1]) && (data[2] == B.data[2]); + } + + bool operator!=(const double_element_fp6_3over2 &B) const { + return (data[0] != B.data[0]) || (data[1] != B.data[1]) || (data[2] != B.data[2]); + } + + double_element_fp6_3over2 operator+(const double_element_fp6_3over2 &B) const { + return {data[0] + B.data[0], data[1] + B.data[1], data[2] + B.data[2]}; + } + + double_element_fp6_3over2 operator-(const double_element_fp6_3over2 &B) const { + return {data[0] - B.data[0], data[1] - B.data[1], data[2] - B.data[2]}; + } + + double_element_fp6_3over2 operator-() const { + return zero() - data; + } + + // data + data + double_element_fp6_3over2 doubled() const { + return {data[0].doubled(), data[1].doubled(), data[2].doubled()}; + } + + double_element_fp6_3over2 addNC(const double_element_fp6_3over2 &B) { + return {addNC(data[0] + B.data[0]), addNC(data[1] + B.data[1]), addNC(data[2] + B.data[2])}; + } + + double_element_fp6_3over2 subNC(const double_element_fp6_3over2 &B) { + return {subNC(data[0] + B.data[0]), subNC(data[1] + B.data[1]), subNC(data[2] + B.data[2])}; + } + + element_fp6_3over2 mod() { + return {data[0].mod(), data[1].mod(), B.data[2].mod()}; + } + }; + + double_element_fp6_3over2 mul(const element &A, const element &B) { + Fp2 t0, t1; + Fp2Dbl T0, T1, T2; + // # 1 + T0 = mulOpt1(x.a_, y.a_); + T1 = mulOpt1(x.b_, y.b_); + T2 = mulOpt1(x.c_, y.c_); + // # 2 + t0 = addNC(x.b_, x.c_); + t1 = addNC(y.b_, y.c_); + // # 3 + z.c_ = mulOpt2(t0, t1); + // # 4 + z.b_ = addNC(T1, T2); + // # 5 + z.c_.a_ = z.c_.a_ - z.b_.a_; + // # 6 + z.c_.b_ = subNC(z.c_.b_, z.b_.b_); + // # 7 + z.b_ = z.c_.mul_xi(); + // # 8 + z.a_ = z.b_ + T0; + // # 9 + t0 = addNC(x.a_, x.b_); + t1 = addNC(y.a_, y.b_); + // # 10 + z.c_ = mulOpt2(t0, t1); + // # 11 + z.b_ = addNC(T0, T1); + // # 12 + z.c_.a_ = z.c_.a_ - z.b_.a_; + // # 13 + z.c_.b_ = subNC(z.c_.b_, z.b_.b_); + /// c1 except xi * t2 term + // # 14, 15 + z.b_ = T2.mul_xi(); // store xi * t2 term + // # 16 + z.b_ = z.b_ + z.c_; + // # 17 + t0 = addNC(x.a_, x.c_); + t1 = addNC(y.a_, y.c_); + // # 18 + z.c_ = mulOpt2(t0, t1); + // # 19 + T2 = addNC(T2, T0); + // # 20 + z.c_.a_ = z.c_.a_ - T2.a_; + // # 22 + z.c_.a_ = z.c_.a_ + T1.a_; + // # 21 + z.c_.b_ = subNC(z.c_.b_, T2.b_); + // # 23 + z.c_.b_ = addNC(z.c_.b_, T1.b_); + } + + /* + Algorithm 11 in App.B of Aranha et al. ePrint 2010/526 + + NOTE: + The original version uses precomputed and stored value of -P[1]. + But, we do not use that, this algorithm always calculates it. + + input P[0..2], R[0..2] + R <- [2]R, + (l00, 0, l02, 0, l11, 0) = f_{R,R}(P), + l = (a,b,c) = (l00, l11, l02) + where P[2] == 1 + */ + double_element_fp6_3over2 pointDblLineEvalWithoutP(element_fp2 *R) { + element_fp2 t0, t1, t2, t3, t4, t5; + double_element_fp2 T0, T1, T2; + // X1, Y1, Z1 == R[0], R[1], R[2] + // xp, yp = P[0], P[1] + + // # 1 + t0 = R[2].squared(); + t4 = R[0] * R[1]; + t1 = R[1].squared(); + // # 2 + t3 = t0.doubled(); + t4 = t4.divBy2(); + t5 = t0 + t1; + // # 3 + t0 += t3; + // # 4 + + if (ParamT::b == 82) { + // (a + bu) * (9 - u) = (9a + b) + (9b - a)u + t3.a_ = t0.b_; + t3.b_ = t0.a_; + t0 = t3.mul_xi(); + t2.a_ = t0.b_; + t2.b_ = t0.a_; + } else { + // (a + bu) * binv_xi + t2 = t0 * ParamT::b_invxi; + } + // # 5 + t0 = R[0].squared(); + t3 = t2.doubled(); + // ## 6 + t3 += t2; + l.c_ = addNC(t0, t0); + // ## 7 + R[0] = t1 - t3; + l.c_ = addNC(l.c_, t0); + t3 += t1; + // # 8 + R[0] *= t4; + t3 = t3.divBy2(); + // ## 9 + T0 = t3.squared(); + T1 = t2.squared(); + // # 10 + T2 = addNC(T1, T1); + t3 = R[1] + R[2]; + // # 11 + T2 = T2 + T1; + + t3 = t3.squared(); + // # 12 + t3 -= t5; + // # 13 + T0 -= T2; + // # 14 + R[1] = T0.mod(); + R[2] = t1 * t3; + t2 -= t1; + // # 15 + l.a_ = t2.mul_xi(); + l.b_ = -t3; + } + + double_element_fp6_3over2 pointDblLineEval(element_fp2 *R, element_fp2 *P) { + return pointDblLineEvalWithoutP(R).mulFp6_24_Fp_01(P); + } + + /* + Algorithm 12 in App.B of Aranha et al. ePrint 2010/526 + + input : P[0..1], Q[0..1], R[0..2] + R <- R + Q + (l00, 0, l02, 0, l11, 0) = f_{R,Q}(P), + l = (a,b,c) = (l00, l11, l02) + where Q[2] == 1, and P[2] == 1 + */ + double_element_fp6_3over2 pointAddLineEvalWithoutP(element_fp2 *R, const element_fp2 *Q) { + element_fp2 t1, t2, t3, t4; + double_element_fp2 T1, T2; + // # 1 + t1 = R[2] * Q[0]; + t2 = R[2] * Q[1]; + // # 2 + t1 = R[0] - t1; + t2 = R[1] - t2; + // # 3 + t3 = t1.squared(); + // # 4 + R[0] = t3 * R[0]; + t4 = t2.squared(); + // # 5 + t3 *= t1; + t4 *= R[2]; + // # 6 + t4 += t3; + // # 7 + t4 -= R[0]; + // # 8 + t4 -= R[0]; + // # 9 + R[0] -= t4; + // # 10 + T1 = mulOpt1(t2, R[0]); + T2 = mulOpt1(t3, R[1]); + // # 11 + T2 = T1 - T2; + // # 12 + R[1] = T2.mod(); + R[0] = t1 * t4; + R[2] = t3 * R[2]; + // # 14 + l.c_ = -t2; + // # 15 + T1 = mulOpt1(t2, Q[0]); + T2 = mulOpt1(t1, Q[1]); + // # 16 + T1 = T1 - T2; + // # 17 + t2 = T1.mod(); + // ### @note: Be careful, below fomulas are typo. + // # 18 + l.a_ = t2.mul_xi(); + l.b_ = t1; + } + + double_element_fp6_3over2 pointAddLineEval(element_fp2 *R, const element_fp2 *Q, + const element *P) { + return pointAddLineEvalWithoutP(R, Q).mulFp6_24_Fp_01(P); + } + + } // namespace detail + } // namespace fields + } // namespace algebra + } // namespace crypto3 +} // namespace nil + +#endif // ALGEBRA_FF_FP6_3OVER2_DOUBLE_HPP diff --git a/include/nil/crypto3/algebra/pairing/bn128.hpp b/include/nil/crypto3/algebra/pairing/bn128.hpp new file mode 100644 index 00000000..1a06a260 --- /dev/null +++ b/include/nil/crypto3/algebra/pairing/bn128.hpp @@ -0,0 +1,49 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// +// Distributed under the Boost Software License, Version 1.0 +// See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_PAIRING_BN128_POLICY_HPP +#define CRYPTO3_ALGEBRA_PAIRING_BN128_POLICY_HPP + +#include +#include + +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace curves { + template + struct bn128; + } // namespace curves + namespace pairing { + + using namespace nil::crypto3::algebra; + + template + struct pairing_policy> { + + using g1_precomp = detail::bn128_ate_g1_precomp; + using g2_precomp = detail::bn128_ate_g2_precomp; + + using precompute_g1 = detail::bn128_ate_precompute_g1; + using precompute_g2 = detail::bn128_ate_precompute_g2; + + using reduced_pairing = detail::reduced_pairing; + using pairing = detail::pairing; + + using miller_loop = detail::bn128_ate_miller_loop; + using double_miller_loop = detail::bn128_double_ate_miller_loop; + using final_exponentiation = detail::bn128_final_exponentiation; + }; + } // namespace pairing + } // namespace algebra + } // namespace crypto3 +} // namespace nil +#endif // ALGEBRA_PAIRING_BN128_POLICY_HPP \ No newline at end of file diff --git a/include/nil/crypto3/algebra/pairing/detail/bn128/ate.hpp b/include/nil/crypto3/algebra/pairing/detail/bn128/ate.hpp new file mode 100644 index 00000000..c96d4501 --- /dev/null +++ b/include/nil/crypto3/algebra/pairing/detail/bn128/ate.hpp @@ -0,0 +1,262 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// +// Distributed under the Boost Software License, Version 1.0 +// See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_PAIRING_ATE_HPP +#define CRYPTO3_ALGEBRA_PAIRING_ATE_HPP + +#include +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace pairing { + namespace detail { + /* + calc optimal ate pairing + @param f [out] e(Q, P) + @param Q [in] affine coord. (Q[0], Q[1]) + @param P [in] affine coord. (P[0], P[1]) + @note not defined for infinity point + */ + template + void opt_atePairing(element_fp12 &f, const element_fp2 Q[2], + const element_fp P[2]) { + element_fp2 T[3]; + T[0] = Q[0]; + T[1] = Q[1]; + T[2] = element_fp2({1, 0}); + element_fp2 Qneg[2]; + + if (useNAF) { + Qneg[0] = Q[0]; + Qneg[1] = -Q[1]; + } + // at 1. + element_fp6 d; + d = fields::detail::pointDblLineEval(T, P); + element_fp6 e; + assert(Param::siTbl[1] == 1); + e = fields::detail::pointAddLineEval(T, Q, P); + f = fields::detail::mul_Fp2_024_Fp2_024(d, e); + // loop from 2. + element_fp6 l; + // 844kclk + for (size_t i = 2; i < Param::siTbl.size(); i++) { + // 3.6k x 63 + l = fields::detail::pointDblLineEval(T, P); + // 4.7k x 63 + f = f.squared(); + // 4.48k x 63 + f = mul_Fp2_024(l); + + if (Param::siTbl[i] > 0) { + // 9.8k x 3 + // 5.1k + l = pointAddLineEval(T, Q, P); + f = mul_Fp2_024(l); + } else if (Param::siTbl[i] < 0) { + l = pointAddLineEval(T, Qneg, P); + f = mul_Fp2_024(l); + } + } + + // addition step + element_fp2 Q1[2]; + detail::FrobEndOnTwist_1(Q1, Q); + element_fp2 Q2[2]; + + detail::FrobEndOnTwist_2(Q2, Q); + Q2[1] = -Q2[1]; + + element_fp12 ft; + d = pointAddLineEval(T, Q1, P); // 5k + e = pointAddLineEval(T, Q2, P); // 5k + ft = mul_Fp2_024_Fp2_024(d, e); // 2.7k + f = f * ft; // 6.4k + // final exponentiation + f.final_exp(); + } + + /* + opt_atePairingJac is a wrapper function of opt_atePairing + @param f [out] e(Q, P) + @param Q [in] Jacobi coord. (_Q[0], _Q[1], _Q[2]) + @param _P [in] Jacobi coord. (_P[0], _P[1], _P[2]) + output : e(Q, P) + */ + void opt_atePairingJac(element_fp12 &f, const element_fp2 _Q[3], const element_fp _P[3]) { + if (_Q[2] == 0 || _P[2] == 0) { + f = 1; + return; + } + + element_fp2 Q[3]; + element_fp P[3]; + detail::NormalizeJac(Q, _Q); + detail::NormalizeJac(P, _P); + opt_atePairing(f, Q, P); + } + + inline void opt_atePairing(Fp12 &f, const Ec2 &Q, const Ec1 &P) { + Q.normalize(); + P.normalize(); + if (Q.is_zero() || P.is_zero()) { + f = 1; + return; + } + opt_atePairing(f, Q.p, P.p); + } + /* + inQ[3] : permit not-normalized + */ + inline void precomputeG2(std::vector &coeff, element_fp2 Q[3], + const element_fp2 inQ[3]) { + detail::NormalizeJac(Q, inQ); + + element_fp2 T[3]; + T[0] = Q[0]; + T[1] = Q[1]; + T[2] = element_fp2({1, 0}); + element_fp2 Qneg[2]; + if (Param::useNAF) { + Qneg[0] = Q[0]; + Qneg[1] = -Q[1]; + } + + coeff.push_back(fields::detail::pointDblLineEvalWithoutP(T)); + coeff.push_back(pointAddLineEvalWithoutP(T, Q)); + + for (size_t i = 2; i < Param::siTbl.size(); i++) { + coeff.push_back(fields::detail::pointDblLineEvalWithoutP(T)); + + if (Param::siTbl[i] > 0) { + coeff.push_back(pointAddLineEvalWithoutP(T, Q)); + } else if (Param::siTbl[i] < 0) { + coeff.push_back(pointAddLineEvalWithoutP(T, Qneg)); + } + } + + // addition step + element_fp2 Q1[2]; + detail::FrobEndOnTwist_1(Q1, Q); + element_fp2 Q2[2]; + + detail::FrobEndOnTwist_2(Q2, Q); + Q2[1] = -Q2[1]; + + coeff.push_back(pointAddLineEvalWithoutP(T, Q1)); + coeff.push_back(pointAddLineEvalWithoutP(T, Q2)); + } + + /* + precP : normalized point + */ + inline void millerLoop(Fp12 &f, const std::vector &Qcoeff, const element_fp precP[2]) { + + size_t idx = 0; + + element_fp6_3over2 d = Qcoeff[idx]; + d = d.mulFp6_24_Fp_01(precP); + idx++; + + element_fp6_3over2 e = Qcoeff[idx]; + e = e.mulFp6_24_Fp_01(precP); + f = mul_Fp2_024_Fp2_024(d, e); + + idx++; + element_fp6 l; + for (size_t i = 2; i < Param::siTbl.size(); i++) { + l = Qcoeff[idx].mulFp6_24_Fp_01(precP); + idx++; + f = f.squared(); + + f = mul_Fp2_024(l); + + if (Param::siTbl[i]) { + l = Qcoeff[idx]; + idx++; + l = l.mulFp6_24_Fp_01(precP); + f = mul_Fp2_024(l); + } + } + + element_fp12_2over3over2 ft; + + d = Qcoeff[idx].mulFp6_24_Fp_01(precP); + idx++; + + e = Qcoeff[idx].mulFp6_24_Fp_01(precP); + + ft = mul_Fp2_024_Fp2_024(d, e); + f *= ft; + } + + inline void millerLoop2(Fp12 &f, const std::vector &Q1coeff, const element_fp precP1[2], + const std::vector &Q2coeff, const element_fp precP2[2]) { + assert(Param::siTbl[1] == 1); + size_t idx = 0; + + element_fp6 d1 = Q1coeff[idx].mulFp6_24_Fp_01(precP1); + element_fp6 d2 = Q2coeff[idx].mulFp6_24_Fp_01(precP2); + idx++; + + element_fp12 f1; + element_fp6 e1 = Q1coeff[idx].mulFp6_24_Fp_01(precP1); + f1 = fields::detail::mul_Fp2_024_Fp2_024(d1, e1); + + element_fp12 f2; + element_fp6 e2 = Q2coeff[idx].mulFp6_24_Fp_01(precP2); + f2 = fields::detail::mul_Fp2_024_Fp2_024(d2, e2); + f = f1 * f2; + + idx++; + element_fp6 l1, l2; + for (size_t i = 2; i < Param::siTbl.size(); i++) { + l1 = Q1coeff[idx]; + l2 = Q2coeff[idx]; + idx++; + f = f.squared(); + + l1 = l1.mulFp6_24_Fp_01(precP1); + l2 = l2.mulFp6_24_Fp_01(precP2); + + f1 = mul_Fp2_024_Fp2_024(l1, l2); + f = f * f1; + + if (Param::siTbl[i]) { + l1 = Q1coeff[idx]; + l2 = Q2coeff[idx]; + idx++; + + l1 = l1.mulFp6_24_Fp_01(precP1); + l2 = l2.mulFp6_24_Fp_01(precP2); + f1 = mul_Fp2_024_Fp2_024(l1, l2); + f = f * f1; + } + } + + d1 = Q1coeff[idx].mulFp6_24_Fp_01(precP1); + d2 = Q2coeff[idx].mulFp6_24_Fp_01(precP2); + idx++; + + e1 = Q1coeff[idx].mulFp6_24_Fp_01(precP1); + e2 = Q2coeff[idx].mulFp6_24_Fp_01(precP2); + + f1 = mul_Fp2_024_Fp2_024(d1, e1); + f2 = mul_Fp2_024_Fp2_024(d2, e2); + f *= f1; + f *= f2; + } + } // namespace detail + } // namespace pairing + } // namespace algebra + } // namespace crypto3 +} // namespace nil +#endif // ALGEBRA_PAIRING_ATE_HPP diff --git a/include/nil/crypto3/algebra/pairing/detail/bn128/basic_functions.hpp b/include/nil/crypto3/algebra/pairing/detail/bn128/basic_functions.hpp new file mode 100644 index 00000000..d9042407 --- /dev/null +++ b/include/nil/crypto3/algebra/pairing/detail/bn128/basic_functions.hpp @@ -0,0 +1,280 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// +// Distributed under the Boost Software License, Version 1.0 +// See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_PAIRING_BN128_BASIC_FUNCTIONS_HPP +#define CRYPTO3_ALGEBRA_PAIRING_BN128_BASIC_FUNCTIONS_HPP + +#include +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace pairing { + namespace detail { + + /* + square over Fp4 + Operation Count: + + 3 * Fp2Dbl::square + 2 * Fp2Dbl::mod + 1 * Fp2Dbl::mul_xi == 1 * (2 * Fp2::add/sub) == 2 * Fp2::add/sub + 3 * Fp2Dbl::add/sub == 3 * (2 * Fp2::add/sub) == 6 * Fp2::add/sub + 1 * Fp2::add/sub + + Total: + + 3 * Fp2Dbl::square + 2 * Fp2Dbl::mod + 9 * Fp2::add/sub + */ + template + element_fp4 + sq_Fp4UseDbl(const element_fp4 &B) { + double_element_fp2 T0, T1, T2; + element_fp2 z0, z1; + T0 = x0.squared(); + T1 = x1.squared(); + T2 = T1.mul_xi(); + T2 += T0; + z1 = x0 + x1; + z0 = T2.mod(); + // overwrite z[0] (position 0). + T2 = z1.squared(); + T2 -= T0; + T2 -= T1; + z1 = T2.mod(); + return {z0, z1}; + } + + /* + Final exponentiation based on: + - Laura Fuentes-Casta{\~n}eda, Edward Knapp, and Francisco + Rodr\'{\i}guez-Henr\'{\i}quez. + Faster hashing to $\mathbb{G}_2$. + SAC 2011, pp. 412--430. doi:10.1007/978-3-642-28496-0_25. + + *this = final_exp(*this) + */ + template + element_fp12_2over3over2 + pow_neg_t(const element_fp12_2over3over2 &A) { + element_fp12_2over3over2 out = A; + element_fp12_2over3over2 inConj; + inConj.a_ = A.a_; + inConj.b_ = -A.b_; // in^-1 == in^(p^6) + + for (size_t i = 1; i < Param::zReplTbl.size(); i++) { + out.sqru(); + if (Param::zReplTbl[i] > 0) { + out = out * in; + } else if (Param::zReplTbl[i] < 0) { + out = out * inConj; + } + } + // invert by conjugation + out.b_ = -out.b_; + } + + /* + @note destory *this + */ + template + element_fp12_2over3over2 + mapToCyclo(element_fp12_2over3over2 A) { + // (a + b*i) -> ((a - b*i) * (a + b*i)^(-1))^(q^2+1) + // + // See Beuchat page 9: raising to 6-th power is the same as + // conjugation, so this entire function computes + // z^((p^6-1) * (p^2+1)) + z.a_ = A.a_; + z.b_ - A.b_; + data = A.data.inversed(); + z *= A; + z.Frobenius2(A); + z *= A; + } + + template + element_fp12_2over3over2 + final_exp(element_fp12_2over3over2 A) { + element_fp12_2over3over2 f, f2z, f6z, f6z2, f12z3; + element_fp12_2over3over2 a, b; + element_fp12_2over3over2 &z = A; + f = mapToCyclo(f); + + f2z = pow_neg_t(f); + f2z = f2z.sqru(); // f2z = f^(-2*z) + f6z = f2z.sqru(); + f6z *= f2z; // f6z = f^(-6*z) + f6z2 = pow_neg_t(f6z); + // A variable a is unnecessary only here. + a = f6z2.sqru(); + // Compress::fixed_power(f12z3, a); // f12z3 = f^(-12*z^3) + f12z3 = pow_neg_t(a); + // It will compute inversion of f2z, thus, conjugation free. + f6z.b_ = -f6z.b_; // f6z = f^(6z) + f12z3.b_ = -f12z3.b_; // f12z3 = f^(12*z^3) + // Computes a and b. + a = f12z3 * f6z2; // a = f^(12*z^3 + 6z^2) + a *= f6z; // a = f^(12*z^3 + 6z^2 + 6z) + b = a * f2z; // b = f^(12*z^3 + 6z^2 + 4z)w + // @note f2z, f6z, and f12z are unnecessary from here. + // Last part. + z = a * f6z2; // z = f^(12*z^3 + 12z^2 + 6z) + z *= f; // z = f^(12*z^3 + 12z^2 + 6z + 1) + f2z = b.Frobenius(); // f2z = f^(q(12*z^3 + 6z^2 + 4z)) + z *= f2z; // z = f^(q(12*z^3 + 6z^2 + 4z) + (12*z^3 + 12z^2 + 6z + 1)) + f2z = a.Frobenius2(); // f2z = f^(q^2(12*z^3 + 6z^2 + 6z)) + z *= f2z; // z = f^(q^2(12*z^3 + 6z^2 + 6z) + q(12*z^3 + 6z^2 + 4z) + (12*z^3 + 12z^2 + 6z + + // 1)) + f.b_ = -f.b_; // f = -f + b *= f; // b = f^(12*z^3 + 6z^2 + 4z - 1) + f2z = b.Frobenius3(); // f2z = f^(q^3(12*z^3 + 6z^2 + 4z - 1)) + z *= f2z; + // z = f^(q^3(12*z^3 + 6z^2 + 4z - 1) + + // q^2(12*z^3 + 6z^2 + 6z) + + // q(12*z^3 + 6z^2 + 4z) + + // (12*z^3 + 12z^2 + 6z + 1)) + // see page 6 in the "Faster hashing to G2" paper + } + + /* + @memo Jacobian coordinates: Y^2 = X^3 + b*Z^6 + */ + template + inline bool isOnECJac3(const Fp *P) { + typedef ParamT Param; + if (P[2] == 0) + return true; + + element_fp Z6p_2; + Z6p_2 = P[2].squared(); + Z6p_2 *= P[2]; + Z6p_2 = Z6p_2.squared(); + Z6p_2 *= Param::b; + return P[1] * P[1] == P[0] * P[0] * P[0] + Z6p_2; + } + + /* + @memo Y^2=X^3+b + Homogeneous. + */ + template + inline bool isOnECHom2(const Fp *P) { + typedef ParamT Param; + return P[1] * P[1] == P[0] * P[0] * P[0] + Param::b; + } + + /* + @memo Y^2=X^3+b + Homogeneous. + */ + template + inline bool isOnECHom3(const Fp *P) { + typedef ParamT Param; + if (P[2] == 0) + return true; + + return P[1] * P[1] * P[2] == P[0] * P[0] * P[0] + P[2].squared() * P[2] * Param::b; + } + + /* + @memo Y^2=X^3+b/xi + */ + template + inline bool isOnTwistECJac3(const Fp2 *P) { + typedef ParamT Param; + + if (P[2] == 0) + return true; + + return P[1] * P[1] == P[0] * P[0] * P[0] + ((P[2].squared() * P[2]).squared()) * Param::b_invxi; + } + + /* + @memo Y^2=X^3+b/xi + Homogeneous. + */ + template + inline bool isOnTwistECHom2(const Fp2 *P) { + typedef ParamT Param; + return P[1] * P[1] == (P[0] * P[0] * P[0] + Param::b_invxi); + } + + /* + @memo Y^2=X^3+b/xi + Homogeneous. + */ + template + inline bool isOnTwistECHom3(const Fp2 *P) { + typedef ParamT Param; + if (P[2] == 0) + return true; + return P[1] * P[1] * P[2] == (P[0] * P[0] * P[0] + Param::b_invxi * P[2] * P[2] * P[2]); + } + + /* + For Jacobian coordinates + */ + template + inline void NormalizeJac(FF *out, const FF *in) { + if (in[2] == 0) { + out[0].clear(); + out[1].clear(); + out[2].clear(); + } else if (in[2] == 1) { + copy(out, in); + } else { + FF A, AA; + + A = in[2].inversed(); + AA = A.squared(); + + out[0] = in[0] * AA; + out[1] = in[1] * AA * A; + out[2] = 1; + } + } + + /* + For Homogeneous + */ + template + inline void NormalizeHom(FF *out, const FF *in) { + if (in[2] == 0) { + out[0].clear(); + out[1].clear(); + out[2].clear(); + } else if (in[2] == 1) { + copy(out, in); + } else { + FF A = in[2]; + A = A.inversed(); + out[0] = in[0] * A; + out[1] = in[1] * A; + out[2] = 1; + } + } + + inline bool Ec2::isValid() const { + return isOnTwistECJac3(p); + } + + inline bool Ec1::isValid() const { + return isOnECJac3(p); + } + } // namespace detail + } // namespace pairing + } // namespace algebra + } // namespace crypto3 +} // namespace nil + +#endif // ALGEBRA_PAIRING_BN128_BASIC_FUNCTIONS_HPP diff --git a/include/nil/crypto3/algebra/pairing/detail/bn128/functions.hpp b/include/nil/crypto3/algebra/pairing/detail/bn128/functions.hpp new file mode 100644 index 00000000..60ad163f --- /dev/null +++ b/include/nil/crypto3/algebra/pairing/detail/bn128/functions.hpp @@ -0,0 +1,155 @@ +//---------------------------------------------------------------------------// +// Copyright (c) 2020 Mikhail Komarov +// Copyright (c) 2020 Nikita Kaskov +// +// Distributed under the Boost Software License, Version 1.0 +// See accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt +//---------------------------------------------------------------------------// + +#ifndef CRYPTO3_ALGEBRA_PAIRING_BN128_FUNCTIONS_HPP +#define CRYPTO3_ALGEBRA_PAIRING_BN128_FUNCTIONS_HPP + +#include + +#include +#include +#include + +#include + +#include + +namespace nil { + namespace crypto3 { + namespace algebra { + namespace pairing { + namespace detail { + + using nil::crypto3::algebra; + + template + using bn128_Fq6 = fields::fp6_3over2 >> ::value_type; + + template + struct bn128_ate_g1_precomp { + typename curves::bn128_g1::underlying_field_type_value X; + typename curves::bn128_g1::underlying_field_type_value Y; + typename curves::bn128_g1::underlying_field_type_value Z; + + bool operator==(const bn128_ate_g1_precomp &other) const { + return (X == other.X && Y == other.Y && Z == other.Z); + } + }; + + template + typedef bn128_Fq6 bn128_ate_ell_coeffs; + + template + struct bn128_ate_g2_precomp { + typename curves::bn128_g2::underlying_field_type_value q[3]; + + std::vector> coeffs; + + bool operator==(const bn128_ate_g2_precomp &other) const { + if (!(q[0] == other.q[0] && q[1] == other.q[1] && q[2] == other.q[2] && + coeffs.size() == other.coeffs.size())) { + return false; + } + + /* work around for upstream serialization bug */ + for (size_t i = 0; i < coeffs.size(); ++i) { + std::stringstream this_ss, other_ss; + this_ss << coeffs[i]; + other_ss << other.coeffs[i]; + if (this_ss.str() != other_ss.str()) { + return false; + } + } + + return true; + } + }; + + template + bn128_ate_g1_precomp + bn128_ate_precompute_g1(const curves::bn128_g1 &P) { + + bn128_ate_g1_precomp result; + detail::NormalizeJac(result.P, P.p); + + return result; + } + + template + bn128_ate_g2_precomp + bn128_ate_precompute_g2(const curves::bn128_g2 &Q) { + + bn128_ate_g2_precomp result; + detail::precomputeg2(result.coeffs, result.Q, Q.coord); + + return result; + } + + template + curves::bn128_gt + bn128_double_ate_miller_loop(const bn128_ate_g1_precomp &prec_P1, + const bn128_ate_g2_precomp &prec_Q1, + const bn128_ate_g1_precomp &prec_P2, + const bn128_ate_g2_precomp &prec_Q2) { + curves::bn128_gt f; + + millerLoop2(f.elem, prec_Q1.coeffs, prec_P1.P, prec_Q2.coeffs, prec_P2.P); + return f; + } + + template + curves::bn128_gt + bn128_ate_miller_loop(const bn128_ate_g1_precomp &prec_P, + const bn128_ate_g2_precomp &prec_Q) { + curves::bn128_gt f; + millerLoop(f.elem, prec_Q.coeffs, prec_P.P); + return f; + } + + template + curves::bn128_gt + bn128_final_exponentiation(const curves::bn128_gt &elt) { + curves::bn128_gt eltcopy = elt; + eltcopy.elem.final_exp(); + return eltcopy; + } + + /*template + static curves::bn128_gt bn128_final_exponentiation (const + curves::bn128_gt &elt) { return bn128_final_exponentiation(elt); + } + + template + static curves::bn128_gt bn128_miller_loop (const + bn128_ate_g1_precomp &prec_P, const bn128_ate_g2_precomp &prec_Q) { + + curves::bn128_gt result = bn128_ate_miller_loop(prec_P, prec_Q); + + return result; + } + + template + static curves::bn128_gt bn128_double_miller_loop (const + bn128_ate_g1_precomp &prec_P1, const bn128_ate_g2_precomp &prec_Q1, const bn128_ate_g1_precomp &prec_P2, const + bn128_ate_g2_precomp &prec_Q2) { + + curves::bn128_gt result = bn128_double_ate_miller_loop(prec_P1, + prec_Q1, prec_P2, prec_Q2); + + return result; + }*/ + + } // namespace detail + } // namespace pairing + } // namespace algebra + } // namespace crypto3 +} // namespace nil +#endif // ALGEBRA_PAIRING_BN128_FUNCTIONS_HPP diff 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