#pragma once #include namespace nall { namespace EllipticCurve { static const uint256_t P = (1_u256 << 255) - 19; static const uint256_t L = (1_u256 << 252) + 27742317777372353535851937790883648493_u256; static BarrettReduction modP{P}; static BarrettReduction modL{L}; struct Modulo25519; auto cmove(bool move, Modulo25519& l, const Modulo25519& r) -> void; auto cswap(bool swap, Modulo25519& l, Modulo25519& r) -> void; struct Modulo25519 { using type = Modulo25519; #define Mask ((1ull << 51) - 1) inline Modulo25519() = default; inline Modulo25519(const Modulo25519&) = default; inline Modulo25519(uint64_t a, uint64_t b = 0, uint64_t c = 0, uint64_t d = 0, uint64_t e = 0) : l{a, b, c, d, e} {} inline Modulo25519(uint256_t n) { l[0] = n >> 0 & Mask; l[1] = n >> 51 & Mask; l[2] = n >> 102 & Mask; l[3] = n >> 153 & Mask; l[4] = n >> 204 & Mask; } inline auto operator()() const -> uint256_t { return operator uint256_t(); } inline auto& operator[](uint index) { return l[index]; } inline auto operator[](uint index) const { return l[index]; } inline explicit operator bool() const { return operator uint256_t(); } inline operator uint256_t() const { type o = *this; o[1] += (o[0] >> 51); o[0] &= Mask; o[2] += (o[1] >> 51); o[1] &= Mask; o[3] += (o[2] >> 51); o[2] &= Mask; o[4] += (o[3] >> 51); o[3] &= Mask; o[0] += 19 * (o[4] >> 51); o[4] &= Mask; o[1] += (o[0] >> 51); o[0] &= Mask; o[2] += (o[1] >> 51); o[1] &= Mask; o[3] += (o[2] >> 51); o[2] &= Mask; o[4] += (o[3] >> 51); o[3] &= Mask; o[0] += 19 * (o[4] >> 51); o[4] &= Mask; o[0] += 19; o[1] += (o[0] >> 51); o[0] &= Mask; o[2] += (o[1] >> 51); o[1] &= Mask; o[3] += (o[2] >> 51); o[2] &= Mask; o[4] += (o[3] >> 51); o[3] &= Mask; o[0] += 19 * (o[4] >> 51); o[4] &= Mask; o[0] += Mask - 18; o[1] += Mask; o[2] += Mask; o[3] += Mask; o[4] += Mask; o[1] += o[0] >> 51; o[0] &= Mask; o[2] += o[1] >> 51; o[1] &= Mask; o[3] += o[2] >> 51; o[2] &= Mask; o[4] += o[3] >> 51; o[3] &= Mask; o[4] &= Mask; return (uint256_t)o[0] << 0 | (uint256_t)o[1] << 51 | (uint256_t)o[2] << 102 | (uint256_t)o[3] << 153 | (uint256_t)o[4] << 204; } inline auto operator!=(type r) const -> bool { bool e = 1; e &= l[0] == r[0]; e &= l[1] == r[1]; e &= l[2] == r[2]; e &= l[3] == r[3]; e &= l[4] == r[4]; return e == 0; } inline auto operator-() const -> type { //P - l type o; uint64_t c; o[0] = 0xfffffffffffda - l[0]; c = o[0] >> 51; o[0] &= Mask; o[1] = 0xffffffffffffe - l[1] + c; c = o[1] >> 51; o[1] &= Mask; o[2] = 0xffffffffffffe - l[2] + c; c = o[2] >> 51; o[2] &= Mask; o[3] = 0xffffffffffffe - l[3] + c; c = o[3] >> 51; o[3] &= Mask; o[4] = 0xffffffffffffe - l[4] + c; c = o[4] >> 51; o[4] &= Mask; o[0] += c * 19; return o; } inline auto operator+(type r) const -> type { type o; uint64_t c; o[0] = l[0] + r[0]; c = o[0] >> 51; o[0] &= Mask; o[1] = l[1] + r[1] + c; c = o[1] >> 51; o[1] &= Mask; o[2] = l[2] + r[2] + c; c = o[2] >> 51; o[2] &= Mask; o[3] = l[3] + r[3] + c; c = o[3] >> 51; o[3] &= Mask; o[4] = l[4] + r[4] + c; c = o[4] >> 51; o[4] &= Mask; o[0] += c * 19; return o; } inline auto operator-(type r) const -> type { type o; uint64_t c; o[0] = l[0] + 0x1fffffffffffb4 - r[0]; c = o[0] >> 51; o[0] &= Mask; o[1] = l[1] + 0x1ffffffffffffc - r[1] + c; c = o[1] >> 51; o[1] &= Mask; o[2] = l[2] + 0x1ffffffffffffc - r[2] + c; c = o[2] >> 51; o[2] &= Mask; o[3] = l[3] + 0x1ffffffffffffc - r[3] + c; c = o[3] >> 51; o[3] &= Mask; o[4] = l[4] + 0x1ffffffffffffc - r[4] + c; c = o[4] >> 51; o[4] &= Mask; o[0] += c * 19; return o; } inline auto operator*(uint64_t scalar) const -> type { type o; uint128_t a; a = (uint128_t)l[0] * scalar; o[0] = a & Mask; a = (uint128_t)l[1] * scalar + (a >> 51 & Mask); o[1] = a & Mask; a = (uint128_t)l[2] * scalar + (a >> 51 & Mask); o[2] = a & Mask; a = (uint128_t)l[3] * scalar + (a >> 51 & Mask); o[3] = a & Mask; a = (uint128_t)l[4] * scalar + (a >> 51 & Mask); o[4] = a & Mask; o[0] += (a >> 51) * 19; return o; } inline auto operator*(type r) const -> type { uint128_t t[] = { (uint128_t)r[0] * l[0], (uint128_t)r[0] * l[1] + (uint128_t)r[1] * l[0], (uint128_t)r[0] * l[2] + (uint128_t)r[1] * l[1] + (uint128_t)r[2] * l[0], (uint128_t)r[0] * l[3] + (uint128_t)r[1] * l[2] + (uint128_t)r[2] * l[1] + (uint128_t)r[3] * l[0], (uint128_t)r[0] * l[4] + (uint128_t)r[1] * l[3] + (uint128_t)r[2] * l[2] + (uint128_t)r[3] * l[1] + (uint128_t)r[4] * l[0] }; r[1] *= 19, r[2] *= 19, r[3] *= 19, r[4] *= 19; t[0] += (uint128_t)r[4] * l[1] + (uint128_t)r[3] * l[2] + (uint128_t)r[2] * l[3] + (uint128_t)r[1] * l[4]; t[1] += (uint128_t)r[4] * l[2] + (uint128_t)r[3] * l[3] + (uint128_t)r[2] * l[4]; t[2] += (uint128_t)r[4] * l[3] + (uint128_t)r[3] * l[4]; t[3] += (uint128_t)r[4] * l[4]; uint64_t c; r[0] = t[0] & Mask; c = (uint64_t)(t[0] >> 51); t[1] += c; r[1] = t[1] & Mask; c = (uint64_t)(t[1] >> 51); t[2] += c; r[2] = t[2] & Mask; c = (uint64_t)(t[2] >> 51); t[3] += c; r[3] = t[3] & Mask; c = (uint64_t)(t[3] >> 51); t[4] += c; r[4] = t[4] & Mask; c = (uint64_t)(t[4] >> 51); r[0] += c * 19; c = r[0] >> 51; r[0] &= Mask; r[1] += c; c = r[1] >> 51; r[1] &= Mask; r[2] += c; return r; } inline auto square() const -> type { type r{*this}; type d{r[0] * 2, r[1] * 2, r[2] * 2 * 19, r[4] * 19, r[4] * 19 * 2}; uint128_t t[5]; t[0] = (uint128_t)r[0] * r[0] + (uint128_t)d[4] * r[1] + (uint128_t)d[2] * r[3]; t[1] = (uint128_t)d[0] * r[1] + (uint128_t)d[4] * r[2] + (uint128_t)r[3] * r[3] * 19; t[2] = (uint128_t)d[0] * r[2] + (uint128_t)r[1] * r[1] + (uint128_t)d[4] * r[3]; t[3] = (uint128_t)d[0] * r[3] + (uint128_t)d[1] * r[2] + (uint128_t)r[4] * d[3]; t[4] = (uint128_t)d[0] * r[4] + (uint128_t)d[1] * r[3] + (uint128_t)r[2] * r[2]; uint64_t c; r[0] = t[0] & Mask; c = (uint64_t)(t[0] >> 51); t[1] += c; r[1] = t[1] & Mask; c = (uint64_t)(t[1] >> 51); t[2] += c; r[2] = t[2] & Mask; c = (uint64_t)(t[2] >> 51); t[3] += c; r[3] = t[3] & Mask; c = (uint64_t)(t[3] >> 51); t[4] += c; r[4] = t[4] & Mask; c = (uint64_t)(t[4] >> 51); r[0] += c * 19; c = r[0] >> 51; r[0] &= Mask; r[1] += c; c = r[1] >> 51; r[1] &= Mask; r[2] += c; return r; } inline auto expmod(uint256_t e) const -> type { type x = 1, y; for(uint n : rrange(256)) { x = x.square(); y = operator*(x); cmove(e >> n & 1, x, y); } return x; } inline auto reciprocal() const -> type { return expmod(P - 2); } inline auto squareRoot() const -> type { static const type i = type(2).expmod((P - 1) >> 2); //i == sqrt(-1) type x = expmod((P + 3) >> 3); type y = x * i; cmove(operator!=(x.square()), x, y); y = -x; cmove(x() & 1, x, y); return x; } private: uint64_t l[5]; //51-bits per limb; 255-bits total #undef Mask }; inline auto cmove(bool move, Modulo25519& l, const Modulo25519& r) -> void { uint64_t mask = -move; l[0] ^= mask & (l[0] ^ r[0]); l[1] ^= mask & (l[1] ^ r[1]); l[2] ^= mask & (l[2] ^ r[2]); l[3] ^= mask & (l[3] ^ r[3]); l[4] ^= mask & (l[4] ^ r[4]); } inline auto cswap(bool swap, Modulo25519& l, Modulo25519& r) -> void { uint64_t mask = -swap, x; x = mask & (l[0] ^ r[0]); l[0] ^= x; r[0] ^= x; x = mask & (l[1] ^ r[1]); l[1] ^= x; r[1] ^= x; x = mask & (l[2] ^ r[2]); l[2] ^= x; r[2] ^= x; x = mask & (l[3] ^ r[3]); l[3] ^= x; r[3] ^= x; x = mask & (l[4] ^ r[4]); l[4] ^= x; r[4] ^= x; } }}