using System; using System.Diagnostics; using Org.BouncyCastle.Crypto.Utilities; namespace Org.BouncyCastle.Math.Raw { internal abstract class Nat128 { private const ulong M = 0xFFFFFFFFUL; public static uint Add(uint[] x, uint[] y, uint[] z) { ulong c = 0; c += (ulong)x[0] + y[0]; z[0] = (uint)c; c >>= 32; c += (ulong)x[1] + y[1]; z[1] = (uint)c; c >>= 32; c += (ulong)x[2] + y[2]; z[2] = (uint)c; c >>= 32; c += (ulong)x[3] + y[3]; z[3] = (uint)c; c >>= 32; return (uint)c; } public static uint AddBothTo(uint[] x, uint[] y, uint[] z) { ulong c = 0; c += (ulong)x[0] + y[0] + z[0]; z[0] = (uint)c; c >>= 32; c += (ulong)x[1] + y[1] + z[1]; z[1] = (uint)c; c >>= 32; c += (ulong)x[2] + y[2] + z[2]; z[2] = (uint)c; c >>= 32; c += (ulong)x[3] + y[3] + z[3]; z[3] = (uint)c; c >>= 32; return (uint)c; } public static uint AddTo(uint[] x, uint[] z) { ulong c = 0; c += (ulong)x[0] + z[0]; z[0] = (uint)c; c >>= 32; c += (ulong)x[1] + z[1]; z[1] = (uint)c; c >>= 32; c += (ulong)x[2] + z[2]; z[2] = (uint)c; c >>= 32; c += (ulong)x[3] + z[3]; z[3] = (uint)c; c >>= 32; return (uint)c; } public static uint AddTo(uint[] x, int xOff, uint[] z, int zOff, uint cIn) { ulong c = cIn; c += (ulong)x[xOff + 0] + z[zOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; c += (ulong)x[xOff + 1] + z[zOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; c += (ulong)x[xOff + 2] + z[zOff + 2]; z[zOff + 2] = (uint)c; c >>= 32; c += (ulong)x[xOff + 3] + z[zOff + 3]; z[zOff + 3] = (uint)c; c >>= 32; return (uint)c; } public static uint AddToEachOther(uint[] u, int uOff, uint[] v, int vOff) { ulong c = 0; c += (ulong)u[uOff + 0] + v[vOff + 0]; u[uOff + 0] = (uint)c; v[vOff + 0] = (uint)c; c >>= 32; c += (ulong)u[uOff + 1] + v[vOff + 1]; u[uOff + 1] = (uint)c; v[vOff + 1] = (uint)c; c >>= 32; c += (ulong)u[uOff + 2] + v[vOff + 2]; u[uOff + 2] = (uint)c; v[vOff + 2] = (uint)c; c >>= 32; c += (ulong)u[uOff + 3] + v[vOff + 3]; u[uOff + 3] = (uint)c; v[vOff + 3] = (uint)c; c >>= 32; return (uint)c; } public static void Copy(uint[] x, uint[] z) { z[0] = x[0]; z[1] = x[1]; z[2] = x[2]; z[3] = x[3]; } public static void Copy64(ulong[] x, ulong[] z) { z[0] = x[0]; z[1] = x[1]; } public static uint[] Create() { return new uint[4]; } public static ulong[] Create64() { return new ulong[2]; } public static uint[] CreateExt() { return new uint[8]; } public static ulong[] CreateExt64() { return new ulong[4]; } public static bool Diff(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff) { bool pos = Gte(x, xOff, y, yOff); if (pos) { Sub(x, xOff, y, yOff, z, zOff); } else { Sub(y, yOff, x, xOff, z, zOff); } return pos; } public static bool Eq(uint[] x, uint[] y) { for (int i = 3; i >= 0; --i) { if (x[i] != y[i]) return false; } return true; } public static bool Eq64(ulong[] x, ulong[] y) { for (int i = 1; i >= 0; --i) { if (x[i] != y[i]) return false; } return true; } public static uint[] FromBigInteger(BigInteger x) { if (x.SignValue < 0 || x.BitLength > 128) throw new ArgumentException(); uint[] z = Create(); int i = 0; while (x.SignValue != 0) { z[i++] = (uint)x.IntValue; x = x.ShiftRight(32); } return z; } public static ulong[] FromBigInteger64(BigInteger x) { if (x.SignValue < 0 || x.BitLength > 128) throw new ArgumentException(); ulong[] z = Create64(); int i = 0; while (x.SignValue != 0) { z[i++] = (ulong)x.LongValue; x = x.ShiftRight(64); } return z; } public static uint GetBit(uint[] x, int bit) { if (bit == 0) { return x[0] & 1; } if ((bit & 127) != bit) { return 0; } int w = bit >> 5; int b = bit & 31; return (x[w] >> b) & 1; } public static bool Gte(uint[] x, uint[] y) { for (int i = 3; i >= 0; --i) { uint x_i = x[i], y_i = y[i]; if (x_i < y_i) return false; if (x_i > y_i) return true; } return true; } public static bool Gte(uint[] x, int xOff, uint[] y, int yOff) { for (int i = 3; i >= 0; --i) { uint x_i = x[xOff + i], y_i = y[yOff + i]; if (x_i < y_i) return false; if (x_i > y_i) return true; } return true; } public static bool IsOne(uint[] x) { if (x[0] != 1) { return false; } for (int i = 1; i < 4; ++i) { if (x[i] != 0) { return false; } } return true; } public static bool IsOne64(ulong[] x) { if (x[0] != 1UL) { return false; } for (int i = 1; i < 2; ++i) { if (x[i] != 0UL) { return false; } } return true; } public static bool IsZero(uint[] x) { for (int i = 0; i < 4; ++i) { if (x[i] != 0) { return false; } } return true; } public static bool IsZero64(ulong[] x) { for (int i = 0; i < 2; ++i) { if (x[i] != 0UL) { return false; } } return true; } public static void Mul(uint[] x, uint[] y, uint[] zz) { ulong y_0 = y[0]; ulong y_1 = y[1]; ulong y_2 = y[2]; ulong y_3 = y[3]; { ulong c = 0, x_0 = x[0]; c += x_0 * y_0; zz[0] = (uint)c; c >>= 32; c += x_0 * y_1; zz[1] = (uint)c; c >>= 32; c += x_0 * y_2; zz[2] = (uint)c; c >>= 32; c += x_0 * y_3; zz[3] = (uint)c; c >>= 32; zz[4] = (uint)c; } for (int i = 1; i < 4; ++i) { ulong c = 0, x_i = x[i]; c += x_i * y_0 + zz[i + 0]; zz[i + 0] = (uint)c; c >>= 32; c += x_i * y_1 + zz[i + 1]; zz[i + 1] = (uint)c; c >>= 32; c += x_i * y_2 + zz[i + 2]; zz[i + 2] = (uint)c; c >>= 32; c += x_i * y_3 + zz[i + 3]; zz[i + 3] = (uint)c; c >>= 32; zz[i + 4] = (uint)c; } } public static void Mul(uint[] x, int xOff, uint[] y, int yOff, uint[] zz, int zzOff) { ulong y_0 = y[yOff + 0]; ulong y_1 = y[yOff + 1]; ulong y_2 = y[yOff + 2]; ulong y_3 = y[yOff + 3]; { ulong c = 0, x_0 = x[xOff + 0]; c += x_0 * y_0; zz[zzOff + 0] = (uint)c; c >>= 32; c += x_0 * y_1; zz[zzOff + 1] = (uint)c; c >>= 32; c += x_0 * y_2; zz[zzOff + 2] = (uint)c; c >>= 32; c += x_0 * y_3; zz[zzOff + 3] = (uint)c; c >>= 32; zz[zzOff + 4] = (uint)c; } for (int i = 1; i < 4; ++i) { ++zzOff; ulong c = 0, x_i = x[xOff + i]; c += x_i * y_0 + zz[zzOff + 0]; zz[zzOff + 0] = (uint)c; c >>= 32; c += x_i * y_1 + zz[zzOff + 1]; zz[zzOff + 1] = (uint)c; c >>= 32; c += x_i * y_2 + zz[zzOff + 2]; zz[zzOff + 2] = (uint)c; c >>= 32; c += x_i * y_3 + zz[zzOff + 3]; zz[zzOff + 3] = (uint)c; c >>= 32; zz[zzOff + 4] = (uint)c; } } public static uint MulAddTo(uint[] x, uint[] y, uint[] zz) { ulong y_0 = y[0]; ulong y_1 = y[1]; ulong y_2 = y[2]; ulong y_3 = y[3]; ulong zc = 0; for (int i = 0; i < 4; ++i) { ulong c = 0, x_i = x[i]; c += x_i * y_0 + zz[i + 0]; zz[i + 0] = (uint)c; c >>= 32; c += x_i * y_1 + zz[i + 1]; zz[i + 1] = (uint)c; c >>= 32; c += x_i * y_2 + zz[i + 2]; zz[i + 2] = (uint)c; c >>= 32; c += x_i * y_3 + zz[i + 3]; zz[i + 3] = (uint)c; c >>= 32; c += zc + zz[i + 4]; zz[i + 4] = (uint)c; zc = c >> 32; } return (uint)zc; } public static uint MulAddTo(uint[] x, int xOff, uint[] y, int yOff, uint[] zz, int zzOff) { ulong y_0 = y[yOff + 0]; ulong y_1 = y[yOff + 1]; ulong y_2 = y[yOff + 2]; ulong y_3 = y[yOff + 3]; ulong zc = 0; for (int i = 0; i < 4; ++i) { ulong c = 0, x_i = x[xOff + i]; c += x_i * y_0 + zz[zzOff + 0]; zz[zzOff + 0] = (uint)c; c >>= 32; c += x_i * y_1 + zz[zzOff + 1]; zz[zzOff + 1] = (uint)c; c >>= 32; c += x_i * y_2 + zz[zzOff + 2]; zz[zzOff + 2] = (uint)c; c >>= 32; c += x_i * y_3 + zz[zzOff + 3]; zz[zzOff + 3] = (uint)c; c >>= 32; c += zc + zz[zzOff + 4]; zz[zzOff + 4] = (uint)c; zc = c >> 32; ++zzOff; } return (uint)zc; } public static ulong Mul33Add(uint w, uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff) { Debug.Assert(w >> 31 == 0); ulong c = 0, wVal = w; ulong x0 = x[xOff + 0]; c += wVal * x0 + y[yOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; ulong x1 = x[xOff + 1]; c += wVal * x1 + x0 + y[yOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; ulong x2 = x[xOff + 2]; c += wVal * x2 + x1 + y[yOff + 2]; z[zOff + 2] = (uint)c; c >>= 32; ulong x3 = x[xOff + 3]; c += wVal * x3 + x2 + y[yOff + 3]; z[zOff + 3] = (uint)c; c >>= 32; c += x3; return c; } public static uint MulWordAddExt(uint x, uint[] yy, int yyOff, uint[] zz, int zzOff) { Debug.Assert(yyOff <= 4); Debug.Assert(zzOff <= 4); ulong c = 0, xVal = x; c += xVal * yy[yyOff + 0] + zz[zzOff + 0]; zz[zzOff + 0] = (uint)c; c >>= 32; c += xVal * yy[yyOff + 1] + zz[zzOff + 1]; zz[zzOff + 1] = (uint)c; c >>= 32; c += xVal * yy[yyOff + 2] + zz[zzOff + 2]; zz[zzOff + 2] = (uint)c; c >>= 32; c += xVal * yy[yyOff + 3] + zz[zzOff + 3]; zz[zzOff + 3] = (uint)c; c >>= 32; return (uint)c; } public static uint Mul33DWordAdd(uint x, ulong y, uint[] z, int zOff) { Debug.Assert(x >> 31 == 0); Debug.Assert(zOff <= 0); ulong c = 0, xVal = x; ulong y00 = y & M; c += xVal * y00 + z[zOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; ulong y01 = y >> 32; c += xVal * y01 + y00 + z[zOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; c += y01 + z[zOff + 2]; z[zOff + 2] = (uint)c; c >>= 32; c += z[zOff + 3]; z[zOff + 3] = (uint)c; c >>= 32; return (uint)c; } public static uint Mul33WordAdd(uint x, uint y, uint[] z, int zOff) { Debug.Assert(x >> 31 == 0); Debug.Assert(zOff <= 1); ulong c = 0, yVal = y; c += yVal * x + z[zOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; c += yVal + z[zOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; c += z[zOff + 2]; z[zOff + 2] = (uint)c; c >>= 32; return c == 0 ? 0 : Nat.IncAt(4, z, zOff, 3); } public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff) { Debug.Assert(zOff <= 1); ulong c = 0, xVal = x; c += xVal * y + z[zOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; c += xVal * (y >> 32) + z[zOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; c += z[zOff + 2]; z[zOff + 2] = (uint)c; c >>= 32; return c == 0 ? 0 : Nat.IncAt(4, z, zOff, 3); } public static uint MulWordsAdd(uint x, uint y, uint[] z, int zOff) { Debug.Assert(zOff <= 2); ulong c = 0, xVal = x, yVal = y; c += yVal * xVal + z[zOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; c += z[zOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; return c == 0 ? 0 : Nat.IncAt(4, z, zOff, 2); } public static uint MulWord(uint x, uint[] y, uint[] z, int zOff) { ulong c = 0, xVal = x; int i = 0; do { c += xVal * y[i]; z[zOff + i] = (uint)c; c >>= 32; } while (++i < 4); return (uint)c; } public static void Square(uint[] x, uint[] zz) { ulong x_0 = x[0]; ulong zz_1; uint c = 0, w; { int i = 3, j = 8; do { ulong xVal = x[i--]; ulong p = xVal * xVal; zz[--j] = (c << 31) | (uint)(p >> 33); zz[--j] = (uint)(p >> 1); c = (uint)p; } while (i > 0); { ulong p = x_0 * x_0; zz_1 = (ulong)(c << 31) | (p >> 33); zz[0] = (uint)p; c = (uint)(p >> 32) & 1; } } ulong x_1 = x[1]; ulong zz_2 = zz[2]; { zz_1 += x_1 * x_0; w = (uint)zz_1; zz[1] = (w << 1) | c; c = w >> 31; zz_2 += zz_1 >> 32; } ulong x_2 = x[2]; ulong zz_3 = zz[3]; ulong zz_4 = zz[4]; { zz_2 += x_2 * x_0; w = (uint)zz_2; zz[2] = (w << 1) | c; c = w >> 31; zz_3 += (zz_2 >> 32) + x_2 * x_1; zz_4 += zz_3 >> 32; zz_3 &= M; } ulong x_3 = x[3]; ulong zz_5 = zz[5]; ulong zz_6 = zz[6]; { zz_3 += x_3 * x_0; w = (uint)zz_3; zz[3] = (w << 1) | c; c = w >> 31; zz_4 += (zz_3 >> 32) + x_3 * x_1; zz_5 += (zz_4 >> 32) + x_3 * x_2; zz_6 += zz_5 >> 32; } w = (uint)zz_4; zz[4] = (w << 1) | c; c = w >> 31; w = (uint)zz_5; zz[5] = (w << 1) | c; c = w >> 31; w = (uint)zz_6; zz[6] = (w << 1) | c; c = w >> 31; w = zz[7] + (uint)(zz_6 >> 32); zz[7] = (w << 1) | c; } public static void Square(uint[] x, int xOff, uint[] zz, int zzOff) { ulong x_0 = x[xOff + 0]; ulong zz_1; uint c = 0, w; { int i = 3, j = 8; do { ulong xVal = x[xOff + i--]; ulong p = xVal * xVal; zz[zzOff + --j] = (c << 31) | (uint)(p >> 33); zz[zzOff + --j] = (uint)(p >> 1); c = (uint)p; } while (i > 0); { ulong p = x_0 * x_0; zz_1 = (ulong)(c << 31) | (p >> 33); zz[zzOff + 0] = (uint)p; c = (uint)(p >> 32) & 1; } } ulong x_1 = x[xOff + 1]; ulong zz_2 = zz[zzOff + 2]; { zz_1 += x_1 * x_0; w = (uint)zz_1; zz[zzOff + 1] = (w << 1) | c; c = w >> 31; zz_2 += zz_1 >> 32; } ulong x_2 = x[xOff + 2]; ulong zz_3 = zz[zzOff + 3]; ulong zz_4 = zz[zzOff + 4]; { zz_2 += x_2 * x_0; w = (uint)zz_2; zz[zzOff + 2] = (w << 1) | c; c = w >> 31; zz_3 += (zz_2 >> 32) + x_2 * x_1; zz_4 += zz_3 >> 32; zz_3 &= M; } ulong x_3 = x[xOff + 3]; ulong zz_5 = zz[zzOff + 5]; ulong zz_6 = zz[zzOff + 6]; { zz_3 += x_3 * x_0; w = (uint)zz_3; zz[zzOff + 3] = (w << 1) | c; c = w >> 31; zz_4 += (zz_3 >> 32) + x_3 * x_1; zz_5 += (zz_4 >> 32) + x_3 * x_2; zz_6 += zz_5 >> 32; } w = (uint)zz_4; zz[zzOff + 4] = (w << 1) | c; c = w >> 31; w = (uint)zz_5; zz[zzOff + 5] = (w << 1) | c; c = w >> 31; w = (uint)zz_6; zz[zzOff + 6] = (w << 1) | c; c = w >> 31; w = zz[zzOff + 7] + (uint)(zz_6 >> 32); zz[zzOff + 7] = (w << 1) | c; } public static int Sub(uint[] x, uint[] y, uint[] z) { long c = 0; c += (long)x[0] - y[0]; z[0] = (uint)c; c >>= 32; c += (long)x[1] - y[1]; z[1] = (uint)c; c >>= 32; c += (long)x[2] - y[2]; z[2] = (uint)c; c >>= 32; c += (long)x[3] - y[3]; z[3] = (uint)c; c >>= 32; return (int)c; } public static int Sub(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff) { long c = 0; c += (long)x[xOff + 0] - y[yOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; c += (long)x[xOff + 1] - y[yOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; c += (long)x[xOff + 2] - y[yOff + 2]; z[zOff + 2] = (uint)c; c >>= 32; c += (long)x[xOff + 3] - y[yOff + 3]; z[zOff + 3] = (uint)c; c >>= 32; return (int)c; } public static int SubBothFrom(uint[] x, uint[] y, uint[] z) { long c = 0; c += (long)z[0] - x[0] - y[0]; z[0] = (uint)c; c >>= 32; c += (long)z[1] - x[1] - y[1]; z[1] = (uint)c; c >>= 32; c += (long)z[2] - x[2] - y[2]; z[2] = (uint)c; c >>= 32; c += (long)z[3] - x[3] - y[3]; z[3] = (uint)c; c >>= 32; return (int)c; } public static int SubFrom(uint[] x, uint[] z) { long c = 0; c += (long)z[0] - x[0]; z[0] = (uint)c; c >>= 32; c += (long)z[1] - x[1]; z[1] = (uint)c; c >>= 32; c += (long)z[2] - x[2]; z[2] = (uint)c; c >>= 32; c += (long)z[3] - x[3]; z[3] = (uint)c; c >>= 32; return (int)c; } public static int SubFrom(uint[] x, int xOff, uint[] z, int zOff) { long c = 0; c += (long)z[zOff + 0] - x[xOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; c += (long)z[zOff + 1] - x[xOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; c += (long)z[zOff + 2] - x[xOff + 2]; z[zOff + 2] = (uint)c; c >>= 32; c += (long)z[zOff + 3] - x[xOff + 3]; z[zOff + 3] = (uint)c; c >>= 32; return (int)c; } public static BigInteger ToBigInteger(uint[] x) { byte[] bs = new byte[16]; for (int i = 0; i < 4; ++i) { uint x_i = x[i]; if (x_i != 0) { Pack.UInt32_To_BE(x_i, bs, (3 - i) << 2); } } return new BigInteger(1, bs); } public static BigInteger ToBigInteger64(ulong[] x) { byte[] bs = new byte[16]; for (int i = 0; i < 2; ++i) { ulong x_i = x[i]; if (x_i != 0UL) { Pack.UInt64_To_BE(x_i, bs, (1 - i) << 3); } } return new BigInteger(1, bs); } public static void Zero(uint[] z) { z[0] = 0; z[1] = 0; z[2] = 0; z[3] = 0; } } }