using System; using System.Diagnostics; using Org.BouncyCastle.Crypto.Utilities; namespace Org.BouncyCastle.Math.EC.Custom.Sec { internal abstract class Nat224 { 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; c += (ulong)x[4] + y[4]; z[4] = (uint)c; c >>= 32; c += (ulong)x[5] + y[5]; z[5] = (uint)c; c >>= 32; c += (ulong)x[6] + y[6]; z[6] = (uint)c; c >>= 32; return (uint)c; } public static uint Add(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff) { ulong c = 0; c += (ulong)x[xOff + 0] + y[yOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; c += (ulong)x[xOff + 1] + y[yOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; c += (ulong)x[xOff + 2] + y[yOff + 2]; z[zOff + 2] = (uint)c; c >>= 32; c += (ulong)x[xOff + 3] + y[yOff + 3]; z[zOff + 3] = (uint)c; c >>= 32; c += (ulong)x[xOff + 4] + y[yOff + 4]; z[zOff + 4] = (uint)c; c >>= 32; c += (ulong)x[xOff + 5] + y[yOff + 5]; z[zOff + 5] = (uint)c; c >>= 32; c += (ulong)x[xOff + 6] + y[yOff + 6]; z[zOff + 6] = (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; c += (ulong)x[4] + y[4] + z[4]; z[4] = (uint)c; c >>= 32; c += (ulong)x[5] + y[5] + z[5]; z[5] = (uint)c; c >>= 32; c += (ulong)x[6] + y[6] + z[6]; z[6] = (uint)c; c >>= 32; return (uint)c; } public static uint AddBothTo(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff) { ulong c = 0; c += (ulong)x[xOff + 0] + y[yOff + 0] + z[zOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; c += (ulong)x[xOff + 1] + y[yOff + 1] + z[zOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; c += (ulong)x[xOff + 2] + y[yOff + 2] + z[zOff + 2]; z[zOff + 2] = (uint)c; c >>= 32; c += (ulong)x[xOff + 3] + y[yOff + 3] + z[zOff + 3]; z[zOff + 3] = (uint)c; c >>= 32; c += (ulong)x[xOff + 4] + y[yOff + 4] + z[zOff + 4]; z[zOff + 4] = (uint)c; c >>= 32; c += (ulong)x[xOff + 5] + y[yOff + 5] + z[zOff + 5]; z[zOff + 5] = (uint)c; c >>= 32; c += (ulong)x[xOff + 6] + y[yOff + 6] + z[zOff + 6]; z[zOff + 6] = (uint)c; c >>= 32; return (uint)c; } // TODO Re-write to allow full range for x? public static uint AddDWord(ulong x, uint[] z, int zOff) { Debug.Assert(zOff <= 5); ulong c = x; c += (ulong)z[zOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; c += (ulong)z[zOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; return c == 0 ? 0 : Inc(z, zOff + 2); } public static uint AddExt(uint[] xx, uint[] yy, uint[] zz) { ulong c = 0; for (int i = 0; i < 14; ++i) { c += (ulong)xx[i] + yy[i]; zz[i] = (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; c += (ulong)x[xOff + 4] + z[zOff + 4]; z[zOff + 4] = (uint)c; c >>= 32; c += (ulong)x[xOff + 5] + z[zOff + 5]; z[zOff + 5] = (uint)c; c >>= 32; c += (ulong)x[xOff + 6] + z[zOff + 6]; z[zOff + 6] = (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; c += (ulong)u[uOff + 4] + v[vOff + 4]; u[uOff + 4] = (uint)c; v[vOff + 4] = (uint)c; c >>= 32; c += (ulong)u[uOff + 5] + v[vOff + 5]; u[uOff + 5] = (uint)c; v[vOff + 5] = (uint)c; c >>= 32; c += (ulong)u[uOff + 6] + v[vOff + 6]; u[uOff + 6] = (uint)c; v[vOff + 6] = (uint)c; c >>= 32; return (uint)c; } public static uint AddWord(uint x, uint[] z, int zOff) { Debug.Assert(zOff <= 6); ulong c = (ulong)x + z[zOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; return c == 0 ? 0 : Inc(z, zOff + 1); } public static uint AddWordExt(uint x, uint[] zz, int zzOff) { Debug.Assert(zzOff <= 13); ulong c = (ulong)x + zz[zzOff + 0]; zz[zzOff + 0] = (uint)c; c >>= 32; return c == 0 ? 0 : IncExt(zz, zzOff + 1); } public static void Copy(uint[] x, uint[] z) { z[0] = x[0]; z[1] = x[1]; z[2] = x[2]; z[3] = x[3]; z[4] = x[4]; z[5] = x[5]; z[6] = x[6]; } public static uint[] Create() { return new uint[7]; } public static uint[] CreateExt() { return new uint[14]; } public static int Dec(uint[] z, int zOff) { Debug.Assert(zOff <= 7); for (int i = zOff; i < 7; ++i) { if (--z[i] != uint.MaxValue) { return 0; } } return -1; } public static int DecExt(uint[] zz, int zzOff) { Debug.Assert(zzOff <= 14); for (int i = zzOff; i < 14; ++i) { if (--zz[i] != uint.MaxValue) { return 0; } } return -1; } 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 uint[] FromBigInteger(BigInteger x) { if (x.SignValue < 0 || x.BitLength > 224) 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 uint GetBit(uint[] x, int bit) { if (bit == 0) { return x[0] & 1; } int w = bit >> 5; if (w < 0 || w >= 7) { return 0; } int b = bit & 31; return (x[w] >> b) & 1; } public static bool Gte(uint[] x, uint[] y) { for (int i = 6; 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 = 6; 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 GteExt(uint[] xx, uint[] yy) { for (int i = 13; i >= 0; --i) { uint xx_i = xx[i], yy_i = yy[i]; if (xx_i < yy_i) return false; if (xx_i > yy_i) return true; } return true; } public static uint Inc(uint[] z, int zOff) { Debug.Assert(zOff <= 7); for (int i = zOff; i < 7; ++i) { if (++z[i] != uint.MinValue) { return 0; } } return 1; } public static uint IncExt(uint[] zz, int zzOff) { Debug.Assert(zzOff <= 14); for (int i = zzOff; i < 14; ++i) { if (++zz[i] != uint.MinValue) { return 0; } } return 1; } public static bool IsOne(uint[] x) { if (x[0] != 1) { return false; } for (int i = 1; i < 7; ++i) { if (x[i] != 0) { return false; } } return true; } public static bool IsZero(uint[] x) { for (int i = 0; i < 7; ++i) { if (x[i] != 0) { return false; } } return true; } public static bool IsZeroExt(uint[] xx) { for (int i = 0; i < 14; ++i) { if (xx[i] != 0) { 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 y_4 = y[4]; ulong y_5 = y[5]; ulong y_6 = y[6]; { 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; c += x_0 * y_4; zz[4] = (uint)c; c >>= 32; c += x_0 * y_5; zz[5] = (uint)c; c >>= 32; c += x_0 * y_6; zz[6] = (uint)c; c >>= 32; zz[7] = (uint)c; } for (int i = 1; i < 7; ++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 += x_i * y_4 + zz[i + 4]; zz[i + 4] = (uint)c; c >>= 32; c += x_i * y_5 + zz[i + 5]; zz[i + 5] = (uint)c; c >>= 32; c += x_i * y_6 + zz[i + 6]; zz[i + 6] = (uint)c; c >>= 32; zz[i + 7] = (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 y_4 = y[yOff + 4]; ulong y_5 = y[yOff + 5]; ulong y_6 = y[yOff + 6]; { 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; c += x_0 * y_4; zz[zzOff + 4] = (uint)c; c >>= 32; c += x_0 * y_5; zz[zzOff + 5] = (uint)c; c >>= 32; c += x_0 * y_6; zz[zzOff + 6] = (uint)c; c >>= 32; zz[zzOff + 7] = (uint)c; } for (int i = 1; i < 7; ++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; c += x_i * y_4 + zz[zzOff + 4]; zz[zzOff + 4] = (uint)c; c >>= 32; c += x_i * y_5 + zz[zzOff + 5]; zz[zzOff + 5] = (uint)c; c >>= 32; c += x_i * y_6 + zz[zzOff + 6]; zz[zzOff + 6] = (uint)c; c >>= 32; zz[zzOff + 7] = (uint)c; } } public static uint MulAdd(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 y_4 = y[yOff + 4]; ulong y_5 = y[yOff + 5]; ulong y_6 = y[yOff + 6]; ulong zc = 0; for (int i = 0; i < 7; ++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 += x_i * y_4 + zz[zzOff + 4]; zz[zzOff + 4] = (uint)c; c >>= 32; c += x_i * y_5 + zz[zzOff + 5]; zz[zzOff + 5] = (uint)c; c >>= 32; c += x_i * y_6 + zz[zzOff + 6]; zz[zzOff + 6] = (uint)c; c >>= 32; c += zc + zz[zzOff + 7]; zz[zzOff + 7] = (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; ulong x4 = x[xOff + 4]; c += wVal * x4 + x3 + y[yOff + 4]; z[zOff + 4] = (uint)c; c >>= 32; ulong x5 = x[xOff + 5]; c += wVal * x5 + x4 + y[yOff + 5]; z[zOff + 5] = (uint)c; c >>= 32; ulong x6 = x[xOff + 6]; c += wVal * x6 + x5 + y[yOff + 6]; z[zOff + 6] = (uint)c; c >>= 32; c += x6; return c; } public static uint MulByWord(uint x, uint[] z) { ulong c = 0, xVal = x; c += xVal * (ulong)z[0]; z[0] = (uint)c; c >>= 32; c += xVal * (ulong)z[1]; z[1] = (uint)c; c >>= 32; c += xVal * (ulong)z[2]; z[2] = (uint)c; c >>= 32; c += xVal * (ulong)z[3]; z[3] = (uint)c; c >>= 32; c += xVal * (ulong)z[4]; z[4] = (uint)c; c >>= 32; c += xVal * (ulong)z[5]; z[5] = (uint)c; c >>= 32; c += xVal * (ulong)z[6]; z[6] = (uint)c; c >>= 32; return (uint)c; } public static uint MulByWordAddTo(uint x, uint[] y, uint[] z) { ulong c = 0, xVal = x; c += xVal * (ulong)z[0] + y[0]; z[0] = (uint)c; c >>= 32; c += xVal * (ulong)z[1] + y[1]; z[1] = (uint)c; c >>= 32; c += xVal * (ulong)z[2] + y[2]; z[2] = (uint)c; c >>= 32; c += xVal * (ulong)z[3] + y[3]; z[3] = (uint)c; c >>= 32; c += xVal * (ulong)z[4] + y[4]; z[4] = (uint)c; c >>= 32; c += xVal * (ulong)z[5] + y[5]; z[5] = (uint)c; c >>= 32; c += xVal * (ulong)z[6] + y[6]; z[6] = (uint)c; c >>= 32; return (uint)c; } public static uint MulWordAddTo(uint x, uint[] y, int yOff, uint[] z, int zOff) { ulong c = 0, xVal = x; c += xVal * y[yOff + 0] + z[zOff + 0]; z[zOff + 0] = (uint)c; c >>= 32; c += xVal * y[yOff + 1] + z[zOff + 1]; z[zOff + 1] = (uint)c; c >>= 32; c += xVal * y[yOff + 2] + z[zOff + 2]; z[zOff + 2] = (uint)c; c >>= 32; c += xVal * y[yOff + 3] + z[zOff + 3]; z[zOff + 3] = (uint)c; c >>= 32; c += xVal * y[yOff + 4] + z[zOff + 4]; z[zOff + 4] = (uint)c; c >>= 32; c += xVal * y[yOff + 5] + z[zOff + 5]; z[zOff + 5] = (uint)c; c >>= 32; c += xVal * y[yOff + 6] + z[zOff + 6]; z[zOff + 6] = (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 <= 3); 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 c == 0 ? 0 : Inc(z, zOff + 4); } public static uint Mul33WordAdd(uint x, uint y, uint[] z, int zOff) { Debug.Assert(x >> 31 == 0); Debug.Assert(zOff <= 4); 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 : Inc(z, zOff + 3); } public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff) { Debug.Assert(zOff <= 4); 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 : Inc(z, zOff + 3); } 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 < 7); return (uint)c; } public static uint ShiftDownBit(uint[] x, int xLen, uint c) { int i = xLen; while (--i >= 0) { uint next = x[i]; x[i] = (next >> 1) | (c << 31); c = next; } return c << 31; } public static uint ShiftDownBit(uint[] x, uint c, uint[] z) { int i = 7; while (--i >= 0) { uint next = x[i]; z[i] = (next >> 1) | (c << 31); c = next; } return c << 31; } public static uint ShiftDownBits(uint[] x, int xLen, int bits, uint c) { Debug.Assert(bits > 0 && bits < 32); int i = xLen; while (--i >= 0) { uint next = x[i]; x[i] = (next >> bits) | (c << -bits); c = next; } return c << -bits; } public static uint ShiftDownWord(uint[] x, int xLen, uint c) { int i = xLen; while (--i >= 0) { uint next = x[i]; x[i] = c; c = next; } return c; } public static uint ShiftUpBit(uint[] x, int xLen, uint c) { for (int i = 0; i < xLen; ++i) { uint next = x[i]; x[i] = (next << 1) | (c >> 31); c = next; } return c >> 31; } public static uint ShiftUpBit(uint[] x, int xOff, int xLen, uint c) { for (int i = 0; i < xLen; ++i) { uint next = x[xOff + i]; x[xOff + i] = (next << 1) | (c >> 31); c = next; } return c >> 31; } public static uint ShiftUpBit(uint[] x, uint c, uint[] z) { for (int i = 0; i < 7; ++i) { uint next = x[i]; z[i] = (next << 1) | (c >> 31); c = next; } return c >> 31; } public static void Square(uint[] x, uint[] zz) { ulong x_0 = x[0]; ulong zz_1; { uint c = 0; int i = 6, j = 14; 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 >> 1); } } ulong x_1 = x[1]; ulong zz_2 = zz[2]; { zz_1 += x_1 * x_0; zz[1] = (uint)zz_1; 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; zz[2] = (uint)zz_2; 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; zz[3] = (uint)zz_3; zz_4 += (zz_3 >> 32) + x_3 * x_1; zz_5 += (zz_4 >> 32) + x_3 * x_2; zz_4 &= M; zz_6 += zz_5 >> 32; zz_5 &= M; } ulong x_4 = x[4]; ulong zz_7 = zz[7]; ulong zz_8 = zz[8]; { zz_4 += x_4 * x_0; zz[4] = (uint)zz_4; zz_5 += (zz_4 >> 32) + x_4 * x_1; zz_6 += (zz_5 >> 32) + x_4 * x_2; zz_5 &= M; zz_7 += (zz_6 >> 32) + x_4 * x_3; zz_6 &= M; zz_8 += zz_7 >> 32; zz_7 &= M; } ulong x_5 = x[5]; ulong zz_9 = zz[9]; ulong zz_10 = zz[10]; { zz_5 += x_5 * x_0; zz[5] = (uint)zz_5; zz_6 += (zz_5 >> 32) + x_5 * x_1; zz_7 += (zz_6 >> 32) + x_5 * x_2; zz_6 &= M; zz_8 += (zz_7 >> 32) + x_5 * x_3; zz_7 &= M; zz_9 += (zz_8 >> 32) + x_5 * x_4; zz_8 &= M; zz_10 += zz_9 >> 32; zz_9 &= M; } ulong x_6 = x[6]; ulong zz_11 = zz[11]; ulong zz_12 = zz[12]; { zz_6 += x_6 * x_0; zz[6] = (uint)zz_6; zz_7 += (zz_6 >> 32) + x_6 * x_1; zz_8 += (zz_7 >> 32) + x_6 * x_2; zz_9 += (zz_8 >> 32) + x_6 * x_3; zz_10 += (zz_9 >> 32) + x_6 * x_4; zz_11 += (zz_10 >> 32) + x_6 * x_5; zz_12 += zz_11 >> 32; } zz[7] = (uint)zz_7; zz[8] = (uint)zz_8; zz[9] = (uint)zz_9; zz[10] = (uint)zz_10; zz[11] = (uint)zz_11; zz[12] = (uint)zz_12; zz[13] += (uint)(zz_12 >> 32); ShiftUpBit(zz, 14, (uint)x_0 << 31); } public static void Square(uint[] x, int xOff, uint[] zz, int zzOff) { ulong x_0 = x[xOff + 0]; ulong zz_1; { uint c = 0; int i = 6, j = 14; 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 >> 1); } } ulong x_1 = x[xOff + 1]; ulong zz_2 = zz[zzOff + 2]; { zz_1 += x_1 * x_0; zz[zzOff + 1] = (uint)zz_1; 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; zz[zzOff + 2] = (uint)zz_2; 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; zz[zzOff + 3] = (uint)zz_3; zz_4 += (zz_3 >> 32) + x_3 * x_1; zz_5 += (zz_4 >> 32) + x_3 * x_2; zz_4 &= M; zz_6 += zz_5 >> 32; zz_5 &= M; } ulong x_4 = x[xOff + 4]; ulong zz_7 = zz[zzOff + 7]; ulong zz_8 = zz[zzOff + 8]; { zz_4 += x_4 * x_0; zz[zzOff + 4] = (uint)zz_4; zz_5 += (zz_4 >> 32) + x_4 * x_1; zz_6 += (zz_5 >> 32) + x_4 * x_2; zz_5 &= M; zz_7 += (zz_6 >> 32) + x_4 * x_3; zz_6 &= M; zz_8 += zz_7 >> 32; zz_7 &= M; } ulong x_5 = x[xOff + 5]; ulong zz_9 = zz[zzOff + 9]; ulong zz_10 = zz[zzOff + 10]; { zz_5 += x_5 * x_0; zz[zzOff + 5] = (uint)zz_5; zz_6 += (zz_5 >> 32) + x_5 * x_1; zz_7 += (zz_6 >> 32) + x_5 * x_2; zz_6 &= M; zz_8 += (zz_7 >> 32) + x_5 * x_3; zz_7 &= M; zz_9 += (zz_8 >> 32) + x_5 * x_4; zz_8 &= M; zz_10 += zz_9 >> 32; zz_9 &= M; } ulong x_6 = x[xOff + 6]; ulong zz_11 = zz[zzOff + 11]; ulong zz_12 = zz[zzOff + 12]; { zz_6 += x_6 * x_0; zz[zzOff + 6] = (uint)zz_6; zz_7 += (zz_6 >> 32) + x_6 * x_1; zz_8 += (zz_7 >> 32) + x_6 * x_2; zz_9 += (zz_8 >> 32) + x_6 * x_3; zz_10 += (zz_9 >> 32) + x_6 * x_4; zz_11 += (zz_10 >> 32) + x_6 * x_5; zz_12 += zz_11 >> 32; } zz[zzOff + 7] = (uint)zz_7; zz[zzOff + 8] = (uint)zz_8; zz[zzOff + 9] = (uint)zz_9; zz[zzOff + 10] = (uint)zz_10; zz[zzOff + 11] = (uint)zz_11; zz[zzOff + 12] = (uint)zz_12; zz[zzOff + 13] += (uint)(zz_12 >> 32); ShiftUpBit(zz, zzOff, 16, (uint)x_0 << 31); } 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; c += (long)x[4] - y[4]; z[4] = (uint)c; c >>= 32; c += (long)x[5] - y[5]; z[5] = (uint)c; c >>= 32; c += (long)x[6] - y[6]; z[6] = (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; c += (long)x[xOff + 4] - y[yOff + 4]; z[zOff + 4] = (uint)c; c >>= 32; c += (long)x[xOff + 5] - y[yOff + 5]; z[zOff + 5] = (uint)c; c >>= 32; c += (long)x[xOff + 6] - y[yOff + 6]; z[zOff + 6] = (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; c += (long)z[4] - x[4] - y[4]; z[4] = (uint)c; c >>= 32; c += (long)z[5] - x[5] - y[5]; z[5] = (uint)c; c >>= 32; c += (long)z[6] - x[6] - y[6]; z[6] = (uint)c; c >>= 32; return (int)c; } // TODO Re-write to allow full range for x? public static int SubDWord(ulong x, uint[] z) { long c = -(long)x; c += (long)z[0]; z[0] = (uint)c; c >>= 32; c += (long)z[1]; z[1] = (uint)c; c >>= 32; return c == 0 ? 0 : Dec(z, 2); } public static int SubExt(uint[] xx, uint[] yy, uint[] zz) { long c = 0; for (int i = 0; i < 14; ++i) { c += (long)xx[i] - yy[i]; zz[i] = (uint)c; c >>= 32; } return (int)c; } public static int SubFromExt(uint[] x, int xOff, uint[] zz, int zzOff) { Debug.Assert(zzOff <= 7); long c = 0; c += (long)zz[zzOff + 0] - x[xOff + 0]; zz[zzOff + 0] = (uint)c; c >>= 32; c += (long)zz[zzOff + 1] - x[xOff + 1]; zz[zzOff + 1] = (uint)c; c >>= 32; c += (long)zz[zzOff + 2] - x[xOff + 2]; zz[zzOff + 2] = (uint)c; c >>= 32; c += (long)zz[zzOff + 3] - x[xOff + 3]; zz[zzOff + 3] = (uint)c; c >>= 32; c += (long)zz[zzOff + 4] - x[xOff + 4]; zz[zzOff + 4] = (uint)c; c >>= 32; c += (long)zz[zzOff + 5] - x[xOff + 5]; zz[zzOff + 5] = (uint)c; c >>= 32; c += (long)zz[zzOff + 6] - x[xOff + 6]; zz[zzOff + 6] = (uint)c; c >>= 32; return (int)c; } public static int SubWord(uint x, uint[] z, int zOff) { Debug.Assert(zOff <= 6); long c = (long)z[zOff + 0] - x; z[zOff + 0] = (uint)c; c >>= 32; return c == 0 ? 0 : Dec(z, zOff + 1); } public static int SubWordExt(uint x, uint[] zz, int zzOff) { Debug.Assert(zzOff <= 13); long c = (long)zz[zzOff + 0] - x; zz[zzOff + 0] = (uint)c; c >>= 32; return c == 0 ? 0 : DecExt(zz, zzOff + 1); } public static BigInteger ToBigInteger(uint[] x) { byte[] bs = new byte[28]; for (int i = 0; i < 7; ++i) { uint x_i = x[i]; if (x_i != 0) { Pack.UInt32_To_BE(x_i, bs, (6 - i) << 2); } } return new BigInteger(1, bs); } public static void Zero(uint[] z) { z[0] = 0; z[1] = 0; z[2] = 0; z[3] = 0; z[4] = 0; z[5] = 0; z[6] = 0; } } }