// Copyright 2010 Dolphin Emulator Project // Licensed under GPLv2+ // Refer to the license.txt file included. // Copyright 2007,2008 Segher Boessenkool // Licensed under the terms of the GNU GPL, version 2 // http://www.gnu.org/licenses/old-licenses/gpl-2.0.txt #include #include #include #include #include #include "Common/Common.h" #include "Common/Crypto/bn.h" #include "Common/Crypto/ec.h" #ifdef _MSC_VER #pragma warning(push) #pragma warning(disable : 4505) #endif namespace Common::ec { static const u8 square[16] = {0x00, 0x01, 0x04, 0x05, 0x10, 0x11, 0x14, 0x15, 0x40, 0x41, 0x44, 0x45, 0x50, 0x51, 0x54, 0x55}; struct Elt; static Elt operator*(const Elt& a, const Elt& b); struct Elt { bool IsZero() const { return std::all_of(data.begin(), data.end(), [](u8 b) { return b == 0; }); } void MulX() { u8 carry = data[0] & 1; u8 x = 0; for (std::size_t i = 0; i < data.size() - 1; i++) { u8 y = data[i + 1]; data[i] = x ^ (y >> 7); x = y << 1; } data[29] = x ^ carry; data[20] ^= carry << 2; } Elt Square() const { std::array wide; for (std::size_t i = 0; i < data.size(); i++) { wide[2 * i] = square[data[i] >> 4]; wide[2 * i + 1] = square[data[i] & 15]; } for (std::size_t i = 0; i < data.size(); i++) { u8 x = wide[i]; wide[i + 19] ^= x >> 7; wide[i + 20] ^= x << 1; wide[i + 29] ^= x >> 1; wide[i + 30] ^= x << 7; } u8 x = wide[30] & ~1; wide[49] ^= x >> 7; wide[50] ^= x << 1; wide[59] ^= x >> 1; wide[30] &= 1; Elt result; std::copy(wide.cbegin() + 30, wide.cend(), result.data.begin()); return result; } Elt ItohTsujii(const Elt& b, std::size_t j) const { Elt t = *this; while (j--) t = t.Square(); return t * b; } Elt Inv() const { Elt t = ItohTsujii(*this, 1); Elt s = t.ItohTsujii(*this, 1); t = s.ItohTsujii(s, 3); s = t.ItohTsujii(*this, 1); t = s.ItohTsujii(s, 7); s = t.ItohTsujii(t, 14); t = s.ItohTsujii(*this, 1); s = t.ItohTsujii(t, 29); t = s.ItohTsujii(s, 58); s = t.ItohTsujii(t, 116); return s.Square(); } std::array data{}; }; static Elt operator+(const Elt& a, const Elt& b) { Elt d; for (std::size_t i = 0; i < std::tuple_size{}; i++) d.data[i] = a.data[i] ^ b.data[i]; return d; } static Elt operator*(const Elt& a, const Elt& b) { Elt d; std::size_t i = 0; u8 mask = 1; for (std::size_t n = 0; n < 233; n++) { d.MulX(); if ((a.data[i] & mask) != 0) d = d + b; mask >>= 1; if (mask == 0) { mask = 0x80; i++; } } return d; } static Elt operator/(const Elt& dividend, const Elt& divisor) { return dividend * divisor.Inv(); } struct Point { Point() = default; constexpr explicit Point(Elt x, Elt y) : m_data{{std::move(x), std::move(y)}} {} explicit Point(const u8* data) { std::copy_n(data, sizeof(m_data), Data()); } bool IsZero() const { return X().IsZero() && Y().IsZero(); } Elt& X() { return m_data[0]; } Elt& Y() { return m_data[1]; } u8* Data() { return m_data[0].data.data(); } const Elt& X() const { return m_data[0]; } const Elt& Y() const { return m_data[1]; } const u8* Data() const { return m_data[0].data.data(); } Point Double() const { Point r; if (X().IsZero()) return r; const auto s = Y() / X() + X(); r.X() = s.Square() + s; r.X().data[29] ^= 1; r.Y() = s * r.X() + r.X() + X().Square(); return r; } private: std::array m_data{}; static_assert(sizeof(decltype(m_data)) == 60, "Wrong size for m_data"); }; // y**2 + x*y = x**3 + x + b UNUSED static const u8 ec_b[30] = {0x00, 0x66, 0x64, 0x7e, 0xde, 0x6c, 0x33, 0x2c, 0x7f, 0x8c, 0x09, 0x23, 0xbb, 0x58, 0x21, 0x3b, 0x33, 0x3b, 0x20, 0xe9, 0xce, 0x42, 0x81, 0xfe, 0x11, 0x5f, 0x7d, 0x8f, 0x90, 0xad}; // order of the addition group of points static const u8 ec_N[30] = {0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x13, 0xe9, 0x74, 0xe7, 0x2f, 0x8a, 0x69, 0x22, 0x03, 0x1d, 0x26, 0x03, 0xcf, 0xe0, 0xd7}; // base point constexpr Point ec_G{ {{{0x00, 0xfa, 0xc9, 0xdf, 0xcb, 0xac, 0x83, 0x13, 0xbb, 0x21, 0x39, 0xf1, 0xbb, 0x75, 0x5f, 0xef, 0x65, 0xbc, 0x39, 0x1f, 0x8b, 0x36, 0xf8, 0xf8, 0xeb, 0x73, 0x71, 0xfd, 0x55, 0x8b}}}, {{{0x01, 0x00, 0x6a, 0x08, 0xa4, 0x19, 0x03, 0x35, 0x06, 0x78, 0xe5, 0x85, 0x28, 0xbe, 0xbf, 0x8a, 0x0b, 0xef, 0xf8, 0x67, 0xa7, 0xca, 0x36, 0x71, 0x6f, 0x7e, 0x01, 0xf8, 0x10, 0x52}}}}; static Point operator+(const Point& a, const Point& b) { if (a.IsZero()) return b; if (b.IsZero()) return a; Elt u = a.X() + b.X(); if (u.IsZero()) { u = a.Y() + b.Y(); if (u.IsZero()) return a.Double(); return Point{}; } const Elt s = (a.Y() + b.Y()) / u; Elt t = s.Square() + s + b.X(); t.data[29] ^= 1; const Elt rx = t + a.X(); const Elt ry = s * t + a.Y() + rx; return Point{rx, ry}; } static Point operator*(const u8* a, const Point& b) { Point d; for (std::size_t i = 0; i < 30; i++) { for (u8 mask = 0x80; mask != 0; mask >>= 1) { d = d.Double(); if ((a[i] & mask) != 0) d = d + b; } } return d; } static void silly_random(u8* rndArea, u8 count) { u16 i; srand((unsigned)(time(nullptr))); for (i = 0; i < count; i++) { rndArea[i] = rand(); } } std::array Sign(const u8* key, const u8* hash) { u8 e[30]{}; memcpy(e + 10, hash, 20); // Changing random number generator to a lame one... u8 m[30]; silly_random(m, sizeof(m)); // fp = fopen("/dev/random", "rb"); // if (fread(m, sizeof m, 1, fp) != 1) // fatal("reading random"); // fclose(fp); m[0] = 0; Elt r = (m * ec_G).X(); if (bn_compare(r.data.data(), ec_N, 30) >= 0) bn_sub_modulus(r.data.data(), ec_N, 30); // S = m**-1*(e + Rk) (mod N) u8 kk[30]; std::copy_n(key, sizeof(kk), kk); if (bn_compare(kk, ec_N, sizeof(kk)) >= 0) bn_sub_modulus(kk, ec_N, sizeof(kk)); Elt s; bn_mul(s.data.data(), r.data.data(), kk, ec_N, 30); bn_add(kk, s.data.data(), e, ec_N, sizeof(kk)); u8 minv[30]; bn_inv(minv, m, ec_N, sizeof(minv)); bn_mul(s.data.data(), minv, kk, ec_N, 30); std::array signature; std::copy(r.data.cbegin(), r.data.cend(), signature.begin()); std::copy(s.data.cbegin(), s.data.cend(), signature.begin() + 30); return signature; } bool VerifySignature(const u8* public_key, const u8* signature, const u8* hash) { const u8* R = signature; const u8* S = signature + 30; u8 Sinv[30]; bn_inv(Sinv, S, ec_N, 30); u8 e[30]{}; memcpy(e + 10, hash, 20); u8 w1[30], w2[30]; bn_mul(w1, e, Sinv, ec_N, 30); bn_mul(w2, R, Sinv, ec_N, 30); Point r1 = w1 * ec_G + w2 * Point{public_key}; auto& rx = r1.X().data; if (bn_compare(rx.data(), ec_N, 30) >= 0) bn_sub_modulus(rx.data(), ec_N, 30); return (bn_compare(rx.data(), R, 30) == 0); } std::array PrivToPub(const u8* key) { const Point data = key * ec_G; std::array result; std::copy_n(data.Data(), result.size(), result.begin()); return result; } std::array ComputeSharedSecret(const u8* private_key, const u8* public_key) { std::array shared_secret; const Point data = private_key * Point{public_key}; std::copy_n(data.Data(), shared_secret.size(), shared_secret.begin()); return shared_secret; } #ifdef _MSC_VER #pragma warning(pop) #endif } // namespace Common::ec