diff options
Diffstat (limited to 'crypto/src/math/raw')
| -rw-r--r-- | crypto/src/math/raw/Interleave.cs | 70 | ||||
| -rw-r--r-- | crypto/src/math/raw/Mod.cs | 184 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat.cs | 1053 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat128.cs | 856 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat160.cs | 874 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat192.cs | 1048 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat224.cs | 1176 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat256.cs | 1387 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat320.cs | 98 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat384.cs | 46 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat448.cs | 100 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat512.cs | 46 | ||||
| -rw-r--r-- | crypto/src/math/raw/Nat576.cs | 102 |
13 files changed, 7040 insertions, 0 deletions
diff --git a/crypto/src/math/raw/Interleave.cs b/crypto/src/math/raw/Interleave.cs new file mode 100644 index 000000000..9755c9d6f --- /dev/null +++ b/crypto/src/math/raw/Interleave.cs @@ -0,0 +1,70 @@ +using System; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Interleave + { + /* + * This expands 8 bit indices into 16 bit contents (high bit 14), by inserting 0s between bits. + * In a binary field, this operation is the same as squaring an 8 bit number. + */ + private static readonly ushort[] INTERLEAVE2_TABLE = new ushort[] + { + 0x0000, 0x0001, 0x0004, 0x0005, 0x0010, 0x0011, 0x0014, 0x0015, + 0x0040, 0x0041, 0x0044, 0x0045, 0x0050, 0x0051, 0x0054, 0x0055, + 0x0100, 0x0101, 0x0104, 0x0105, 0x0110, 0x0111, 0x0114, 0x0115, + 0x0140, 0x0141, 0x0144, 0x0145, 0x0150, 0x0151, 0x0154, 0x0155, + 0x0400, 0x0401, 0x0404, 0x0405, 0x0410, 0x0411, 0x0414, 0x0415, + 0x0440, 0x0441, 0x0444, 0x0445, 0x0450, 0x0451, 0x0454, 0x0455, + 0x0500, 0x0501, 0x0504, 0x0505, 0x0510, 0x0511, 0x0514, 0x0515, + 0x0540, 0x0541, 0x0544, 0x0545, 0x0550, 0x0551, 0x0554, 0x0555, + 0x1000, 0x1001, 0x1004, 0x1005, 0x1010, 0x1011, 0x1014, 0x1015, + 0x1040, 0x1041, 0x1044, 0x1045, 0x1050, 0x1051, 0x1054, 0x1055, + 0x1100, 0x1101, 0x1104, 0x1105, 0x1110, 0x1111, 0x1114, 0x1115, + 0x1140, 0x1141, 0x1144, 0x1145, 0x1150, 0x1151, 0x1154, 0x1155, + 0x1400, 0x1401, 0x1404, 0x1405, 0x1410, 0x1411, 0x1414, 0x1415, + 0x1440, 0x1441, 0x1444, 0x1445, 0x1450, 0x1451, 0x1454, 0x1455, + 0x1500, 0x1501, 0x1504, 0x1505, 0x1510, 0x1511, 0x1514, 0x1515, + 0x1540, 0x1541, 0x1544, 0x1545, 0x1550, 0x1551, 0x1554, 0x1555, + 0x4000, 0x4001, 0x4004, 0x4005, 0x4010, 0x4011, 0x4014, 0x4015, + 0x4040, 0x4041, 0x4044, 0x4045, 0x4050, 0x4051, 0x4054, 0x4055, + 0x4100, 0x4101, 0x4104, 0x4105, 0x4110, 0x4111, 0x4114, 0x4115, + 0x4140, 0x4141, 0x4144, 0x4145, 0x4150, 0x4151, 0x4154, 0x4155, + 0x4400, 0x4401, 0x4404, 0x4405, 0x4410, 0x4411, 0x4414, 0x4415, + 0x4440, 0x4441, 0x4444, 0x4445, 0x4450, 0x4451, 0x4454, 0x4455, + 0x4500, 0x4501, 0x4504, 0x4505, 0x4510, 0x4511, 0x4514, 0x4515, + 0x4540, 0x4541, 0x4544, 0x4545, 0x4550, 0x4551, 0x4554, 0x4555, + 0x5000, 0x5001, 0x5004, 0x5005, 0x5010, 0x5011, 0x5014, 0x5015, + 0x5040, 0x5041, 0x5044, 0x5045, 0x5050, 0x5051, 0x5054, 0x5055, + 0x5100, 0x5101, 0x5104, 0x5105, 0x5110, 0x5111, 0x5114, 0x5115, + 0x5140, 0x5141, 0x5144, 0x5145, 0x5150, 0x5151, 0x5154, 0x5155, + 0x5400, 0x5401, 0x5404, 0x5405, 0x5410, 0x5411, 0x5414, 0x5415, + 0x5440, 0x5441, 0x5444, 0x5445, 0x5450, 0x5451, 0x5454, 0x5455, + 0x5500, 0x5501, 0x5504, 0x5505, 0x5510, 0x5511, 0x5514, 0x5515, + 0x5540, 0x5541, 0x5544, 0x5545, 0x5550, 0x5551, 0x5554, 0x5555 + }; + + internal static uint Expand8to16(uint x) + { + return INTERLEAVE2_TABLE[x & 0xFF]; + } + + internal static uint Expand16to32(uint x) + { + return (uint)(INTERLEAVE2_TABLE[x & 0xFF] | INTERLEAVE2_TABLE[(x >> 8) & 0xFF] << 16); + } + + internal static ulong Expand32to64(uint x) + { + uint r00 = (uint)(INTERLEAVE2_TABLE[x & 0xFF] | INTERLEAVE2_TABLE[(x >> 8) & 0xFF] << 16); + uint r32 = (uint)(INTERLEAVE2_TABLE[(x >> 16) & 0xFF] | INTERLEAVE2_TABLE[x >> 24] << 16); + return (ulong)r32 << 32 | (ulong)r00; + } + + internal static void Expand64To128(ulong x, ulong[] z, int zOff) + { + z[zOff ] = Expand32to64((uint)x); + z[zOff + 1] = Expand32to64((uint)(x >> 32)); + } + } +} diff --git a/crypto/src/math/raw/Mod.cs b/crypto/src/math/raw/Mod.cs new file mode 100644 index 000000000..63467e668 --- /dev/null +++ b/crypto/src/math/raw/Mod.cs @@ -0,0 +1,184 @@ +using System; +using System.Diagnostics; + +using Org.BouncyCastle.Crypto.Utilities; +using Org.BouncyCastle.Utilities; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Mod + { + public static void Invert(uint[] p, uint[] x, uint[] z) + { + int len = p.Length; + if (Nat.IsZero(len, x)) + throw new ArgumentException("cannot be 0", "x"); + if (Nat.IsOne(len, x)) + { + Array.Copy(x, 0, z, 0, len); + return; + } + + uint[] u = Nat.Copy(len, x); + uint[] a = Nat.Create(len); + a[0] = 1; + int ac = 0; + + if ((u[0] & 1) == 0) + { + InversionStep(p, u, len, a, ref ac); + } + if (Nat.IsOne(len, u)) + { + InversionResult(p, ac, a, z); + return; + } + + uint[] v = Nat.Copy(len, p); + uint[] b = Nat.Create(len); + int bc = 0; + + int uvLen = len; + + for (;;) + { + while (u[uvLen - 1] == 0 && v[uvLen - 1] == 0) + { + --uvLen; + } + + if (Nat.Gte(len, u, v)) + { + Nat.SubFrom(len, v, u); + Debug.Assert((u[0] & 1) == 0); + ac += Nat.SubFrom(len, b, a) - bc; + InversionStep(p, u, uvLen, a, ref ac); + if (Nat.IsOne(len, u)) + { + InversionResult(p, ac, a, z); + return; + } + } + else + { + Nat.SubFrom(len, u, v); + Debug.Assert((v[0] & 1) == 0); + bc += Nat.SubFrom(len, a, b) - ac; + InversionStep(p, v, uvLen, b, ref bc); + if (Nat.IsOne(len, v)) + { + InversionResult(p, bc, b, z); + return; + } + } + } + } + + public static uint[] Random(uint[] p) + { + int len = p.Length; + Random rand = new Random(); + uint[] s = Nat.Create(len); + + uint m = p[len - 1]; + m |= m >> 1; + m |= m >> 2; + m |= m >> 4; + m |= m >> 8; + m |= m >> 16; + + do + { + byte[] bytes = new byte[len << 2]; + rand.NextBytes(bytes); + Pack.BE_To_UInt32(bytes, 0, s); + s[len - 1] &= m; + } + while (Nat.Gte(len, s, p)); + + return s; + } + + public static void Add(uint[] p, uint[] x, uint[] y, uint[] z) + { + int len = p.Length; + uint c = Nat.Add(len, x, y, z); + if (c != 0) + { + Nat.SubFrom(len, p, z); + } + } + + public static void Subtract(uint[] p, uint[] x, uint[] y, uint[] z) + { + int len = p.Length; + int c = Nat.Sub(len, x, y, z); + if (c != 0) + { + Nat.AddTo(len, p, z); + } + } + + private static void InversionResult(uint[] p, int ac, uint[] a, uint[] z) + { + if (ac < 0) + { + Nat.Add(p.Length, a, p, z); + } + else + { + Array.Copy(a, 0, z, 0, p.Length); + } + } + + private static void InversionStep(uint[] p, uint[] u, int uLen, uint[] x, ref int xc) + { + int len = p.Length; + int count = 0; + while (u[0] == 0) + { + Nat.ShiftDownWord(uLen, u, 0); + count += 32; + } + + { + int zeroes = GetTrailingZeroes(u[0]); + if (zeroes > 0) + { + Nat.ShiftDownBits(uLen, u, zeroes, 0); + count += zeroes; + } + } + + for (int i = 0; i < count; ++i) + { + if ((x[0] & 1) != 0) + { + if (xc < 0) + { + xc += (int)Nat.AddTo(len, p, x); + } + else + { + xc += Nat.SubFrom(len, p, x); + } + } + + Debug.Assert(xc == 0 || xc == -1); + Nat.ShiftDownBit(len, x, (uint)xc); + } + } + + private static int GetTrailingZeroes(uint x) + { + Debug.Assert(x != 0); + int count = 0; + while ((x & 1) == 0) + { + x >>= 1; + ++count; + } + return count; + } + } +} diff --git a/crypto/src/math/raw/Nat.cs b/crypto/src/math/raw/Nat.cs new file mode 100644 index 000000000..1f9ab00ec --- /dev/null +++ b/crypto/src/math/raw/Nat.cs @@ -0,0 +1,1053 @@ +using System; +using System.Diagnostics; + +using Org.BouncyCastle.Crypto.Utilities; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Nat + { + private const ulong M = 0xFFFFFFFFUL; + + public static uint Add(int len, uint[] x, uint[] y, uint[] z) + { + ulong c = 0; + for (int i = 0; i < len; ++i) + { + c += (ulong)x[i] + y[i]; + z[i] = (uint)c; + c >>= 32; + } + return (uint)c; + } + + public static uint Add33At(int len, uint x, uint[] z, int zPos) + { + Debug.Assert(zPos <= (len - 2)); + ulong c = (ulong)z[zPos + 0] + x; + z[zPos + 0] = (uint)c; + c >>= 32; + c += (ulong)z[zPos + 1] + 1; + z[zPos + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, zPos + 2); + } + + public static uint Add33At(int len, uint x, uint[] z, int zOff, int zPos) + { + Debug.Assert(zPos <= (len - 2)); + ulong c = (ulong)z[zOff + zPos] + x; + z[zOff + zPos] = (uint)c; + c >>= 32; + c += (ulong)z[zOff + zPos + 1] + 1; + z[zOff + zPos + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, zOff, zPos + 2); + } + + public static uint Add33To(int len, uint x, uint[] z) + { + ulong c = (ulong)z[0] + x; + z[0] = (uint)c; + c >>= 32; + c += (ulong)z[1] + 1; + z[1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, 2); + } + + public static uint Add33To(int len, uint x, uint[] z, int zOff) + { + ulong c = (ulong)z[zOff + 0] + x; + z[zOff + 0] = (uint)c; + c >>= 32; + c += (ulong)z[zOff + 1] + 1; + z[zOff + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, zOff, 2); + } + + public static uint AddBothTo(int len, uint[] x, uint[] y, uint[] z) + { + ulong c = 0; + for (int i = 0; i < len; ++i) + { + c += (ulong)x[i] + y[i] + z[i]; + z[i] = (uint)c; + c >>= 32; + } + return (uint)c; + } + + public static uint AddBothTo(int len, uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff) + { + ulong c = 0; + for (int i = 0; i < len; ++i) + { + c += (ulong)x[xOff + i] + y[yOff + i] + z[zOff + i]; + z[zOff + i] = (uint)c; + c >>= 32; + } + return (uint)c; + } + + public static uint AddDWordAt(int len, ulong x, uint[] z, int zPos) + { + Debug.Assert(zPos <= (len - 2)); + ulong c = (ulong)z[zPos + 0] + (x & M); + z[zPos + 0] = (uint)c; + c >>= 32; + c += (ulong)z[zPos + 1] + (x >> 32); + z[zPos + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, zPos + 2); + } + + public static uint AddDWordAt(int len, ulong x, uint[] z, int zOff, int zPos) + { + Debug.Assert(zPos <= (len - 2)); + ulong c = (ulong)z[zOff + zPos] + (x & M); + z[zOff + zPos] = (uint)c; + c >>= 32; + c += (ulong)z[zOff + zPos + 1] + (x >> 32); + z[zOff + zPos + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, zOff, zPos + 2); + } + + public static uint AddDWordTo(int len, ulong x, uint[] z) + { + ulong c = (ulong)z[0] + (x & M); + z[0] = (uint)c; + c >>= 32; + c += (ulong)z[1] + (x >> 32); + z[1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, 2); + } + + public static uint AddDWordTo(int len, ulong x, uint[] z, int zOff) + { + ulong c = (ulong)z[zOff + 0] + (x & M); + z[zOff + 0] = (uint)c; + c >>= 32; + c += (ulong)z[zOff + 1] + (x >> 32); + z[zOff + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, zOff, 2); + } + + public static uint AddTo(int len, uint[] x, uint[] z) + { + ulong c = 0; + for (int i = 0; i < len; ++i) + { + c += (ulong)x[i] + z[i]; + z[i] = (uint)c; + c >>= 32; + } + return (uint)c; + } + + public static uint AddTo(int len, uint[] x, int xOff, uint[] z, int zOff) + { + ulong c = 0; + for (int i = 0; i < len; ++i) + { + c += (ulong)x[xOff + i] + z[zOff + i]; + z[zOff + i] = (uint)c; + c >>= 32; + } + return (uint)c; + } + + public static uint AddWordAt(int len, uint x, uint[] z, int zPos) + { + Debug.Assert(zPos <= (len - 1)); + ulong c = (ulong)x + z[zPos]; + z[zPos] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, zPos + 1); + } + + public static uint AddWordAt(int len, uint x, uint[] z, int zOff, int zPos) + { + Debug.Assert(zPos <= (len - 1)); + ulong c = (ulong)x + z[zOff + zPos]; + z[zOff + zPos] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, zOff, zPos + 1); + } + + public static uint AddWordTo(int len, uint x, uint[] z) + { + ulong c = (ulong)x + z[0]; + z[0] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, 1); + } + + public static uint AddWordTo(int len, uint x, uint[] z, int zOff) + { + ulong c = (ulong)x + z[zOff]; + z[zOff] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, zOff, 1); + } + + public static void Copy(int len, uint[] x, uint[] z) + { + Array.Copy(x, 0, z, 0, len); + } + + public static uint[] Copy(int len, uint[] x) + { + uint[] z = new uint[len]; + Array.Copy(x, 0, z, 0, len); + return z; + } + + public static uint[] Create(int len) + { + return new uint[len]; + } + + public static ulong[] Create64(int len) + { + return new ulong[len]; + } + + public static int Dec(int len, uint[] z) + { + for (int i = 0; i < len; ++i) + { + if (--z[i] != uint.MaxValue) + { + return 0; + } + } + return -1; + } + + public static int Dec(int len, uint[] x, uint[] z) + { + int i = 0; + while (i < len) + { + uint c = x[i] - 1; + z[i] = c; + ++i; + if (c != uint.MaxValue) + { + while (i < len) + { + z[i] = x[i]; + ++i; + } + return 0; + } + } + return -1; + } + + public static int DecAt(int len, uint[] z, int zPos) + { + Debug.Assert(zPos <= len); + for (int i = zPos; i < len; ++i) + { + if (--z[i] != uint.MaxValue) + { + return 0; + } + } + return -1; + } + + public static int DecAt(int len, uint[] z, int zOff, int zPos) + { + Debug.Assert(zPos <= len); + for (int i = zPos; i < len; ++i) + { + if (--z[zOff + i] != uint.MaxValue) + { + return 0; + } + } + return -1; + } + + public static bool Eq(int len, uint[] x, uint[] y) + { + for (int i = len - 1; i >= 0; --i) + { + if (x[i] != y[i]) + { + return false; + } + } + return true; + } + + public static uint[] FromBigInteger(int bits, BigInteger x) + { + if (x.SignValue < 0 || x.BitLength > bits) + throw new ArgumentException(); + + int len = (bits + 31) >> 5; + uint[] z = Create(len); + 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 >= x.Length) + { + return 0; + } + int b = bit & 31; + return (x[w] >> b) & 1; + } + + public static bool Gte(int len, uint[] x, uint[] y) + { + for (int i = len - 1; 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 uint Inc(int len, uint[] z) + { + for (int i = 0; i < len; ++i) + { + if (++z[i] != uint.MinValue) + { + return 0; + } + } + return 1; + } + + public static uint Inc(int len, uint[] x, uint[] z) + { + int i = 0; + while (i < len) + { + uint c = x[i] + 1; + z[i] = c; + ++i; + if (c != 0) + { + while (i < len) + { + z[i] = x[i]; + ++i; + } + return 0; + } + } + return 1; + } + + public static uint IncAt(int len, uint[] z, int zPos) + { + Debug.Assert(zPos <= len); + for (int i = zPos; i < len; ++i) + { + if (++z[i] != uint.MinValue) + { + return 0; + } + } + return 1; + } + + public static uint IncAt(int len, uint[] z, int zOff, int zPos) + { + Debug.Assert(zPos <= len); + for (int i = zPos; i < len; ++i) + { + if (++z[zOff + i] != uint.MinValue) + { + return 0; + } + } + return 1; + } + + public static bool IsOne(int len, uint[] x) + { + if (x[0] != 1) + { + return false; + } + for (int i = 1; i < len; ++i) + { + if (x[i] != 0) + { + return false; + } + } + return true; + } + + public static bool IsZero(int len, uint[] x) + { + if (x[0] != 0) + { + return false; + } + for (int i = 1; i < len; ++i) + { + if (x[i] != 0) + { + return false; + } + } + return true; + } + + public static void Mul(int len, uint[] x, uint[] y, uint[] zz) + { + zz[len] = (uint)MulWord(len, x[0], y, zz); + + for (int i = 1; i < len; ++i) + { + zz[i + len] = (uint)MulWordAddTo(len, x[i], y, 0, zz, i); + } + } + + public static void Mul(int len, uint[] x, int xOff, uint[] y, int yOff, uint[] zz, int zzOff) + { + zz[zzOff + len] = (uint)MulWord(len, x[xOff], y, yOff, zz, zzOff); + + for (int i = 1; i < len; ++i) + { + zz[zzOff + i + len] = (uint)MulWordAddTo(len, x[xOff + i], y, yOff, zz, zzOff + i); + } + } + + public static uint Mul31BothAdd(int len, uint a, uint[] x, uint b, uint[] y, uint[] z, int zOff) + { + ulong c = 0, aVal = (ulong)a, bVal = (ulong)b; + int i = 0; + do + { + c += aVal * x[i] + bVal * y[i] + z[zOff + i]; + z[zOff + i] = (uint)c; + c >>= 32; + } + while (++i < len); + return (uint)c; + } + + public static uint MulWord(int len, uint x, uint[] y, uint[] z) + { + ulong c = 0, xVal = (ulong)x; + int i = 0; + do + { + c += xVal * y[i]; + z[i] = (uint)c; + c >>= 32; + } + while (++i < len); + return (uint)c; + } + + public static uint MulWord(int len, uint x, uint[] y, int yOff, uint[] z, int zOff) + { + ulong c = 0, xVal = (ulong)x; + int i = 0; + do + { + c += xVal * y[yOff + i]; + z[zOff + i] = (uint)c; + c >>= 32; + } + while (++i < len); + return (uint)c; + } + + public static uint MulWordAddTo(int len, uint x, uint[] y, int yOff, uint[] z, int zOff) + { + ulong c = 0, xVal = (ulong)x; + int i = 0; + do + { + c += xVal * y[yOff + i] + z[zOff + i]; + z[zOff + i] = (uint)c; + c >>= 32; + } + while (++i < len); + return (uint)c; + } + + public static uint MulWordDwordAddAt(int len, uint x, ulong y, uint[] z, int zPos) + { + Debug.Assert(zPos <= (len - 3)); + ulong c = 0, xVal = (ulong)x; + c += xVal * (uint)y + z[zPos + 0]; + z[zPos + 0] = (uint)c; + c >>= 32; + c += xVal * (y >> 32) + z[zPos + 1]; + z[zPos + 1] = (uint)c; + c >>= 32; + c += (ulong)z[zPos + 2]; + z[zPos + 2] = (uint)c; + c >>= 32; + return c == 0 ? 0 : IncAt(len, z, zPos + 3); + } + + public static uint ShiftDownBit(int len, uint[] z, uint c) + { + int i = len; + while (--i >= 0) + { + uint next = z[i]; + z[i] = (next >> 1) | (c << 31); + c = next; + } + return c << 31; + } + + public static uint ShiftDownBit(int len, uint[] z, int zOff, uint c) + { + int i = len; + while (--i >= 0) + { + uint next = z[zOff + i]; + z[zOff + i] = (next >> 1) | (c << 31); + c = next; + } + return c << 31; + } + + public static uint ShiftDownBit(int len, uint[] x, uint c, uint[] z) + { + int i = len; + while (--i >= 0) + { + uint next = x[i]; + z[i] = (next >> 1) | (c << 31); + c = next; + } + return c << 31; + } + + public static uint ShiftDownBit(int len, uint[] x, int xOff, uint c, uint[] z, int zOff) + { + int i = len; + while (--i >= 0) + { + uint next = x[xOff + i]; + z[zOff + i] = (next >> 1) | (c << 31); + c = next; + } + return c << 31; + } + + public static uint ShiftDownBits(int len, uint[] z, int bits, uint c) + { + Debug.Assert(bits > 0 && bits < 32); + int i = len; + while (--i >= 0) + { + uint next = z[i]; + z[i] = (next >> bits) | (c << -bits); + c = next; + } + return c << -bits; + } + + public static uint ShiftDownBits(int len, uint[] z, int zOff, int bits, uint c) + { + Debug.Assert(bits > 0 && bits < 32); + int i = len; + while (--i >= 0) + { + uint next = z[zOff + i]; + z[zOff + i] = (next >> bits) | (c << -bits); + c = next; + } + return c << -bits; + } + + public static uint ShiftDownBits(int len, uint[] x, int bits, uint c, uint[] z) + { + Debug.Assert(bits > 0 && bits < 32); + int i = len; + while (--i >= 0) + { + uint next = x[i]; + z[i] = (next >> bits) | (c << -bits); + c = next; + } + return c << -bits; + } + + public static uint ShiftDownBits(int len, uint[] x, int xOff, int bits, uint c, uint[] z, int zOff) + { + Debug.Assert(bits > 0 && bits < 32); + int i = len; + while (--i >= 0) + { + uint next = x[xOff + i]; + z[zOff + i] = (next >> bits) | (c << -bits); + c = next; + } + return c << -bits; + } + + public static uint ShiftDownWord(int len, uint[] z, uint c) + { + int i = len; + while (--i >= 0) + { + uint next = z[i]; + z[i] = c; + c = next; + } + return c; + } + + public static uint ShiftUpBit(int len, uint[] z, uint c) + { + for (int i = 0; i < len; ++i) + { + uint next = z[i]; + z[i] = (next << 1) | (c >> 31); + c = next; + } + return c >> 31; + } + + public static uint ShiftUpBit(int len, uint[] z, int zOff, uint c) + { + for (int i = 0; i < len; ++i) + { + uint next = z[zOff + i]; + z[zOff + i] = (next << 1) | (c >> 31); + c = next; + } + return c >> 31; + } + + public static uint ShiftUpBit(int len, uint[] x, uint c, uint[] z) + { + for (int i = 0; i < len; ++i) + { + uint next = x[i]; + z[i] = (next << 1) | (c >> 31); + c = next; + } + return c >> 31; + } + + public static uint ShiftUpBit(int len, uint[] x, int xOff, uint c, uint[] z, int zOff) + { + for (int i = 0; i < len; ++i) + { + uint next = x[xOff + i]; + z[zOff + i] = (next << 1) | (c >> 31); + c = next; + } + return c >> 31; + } + + public static ulong ShiftUpBit64(int len, ulong[] x, int xOff, ulong c, ulong[] z, int zOff) + { + for (int i = 0; i < len; ++i) + { + ulong next = x[xOff + i]; + z[zOff + i] = (next << 1) | (c >> 63); + c = next; + } + return c >> 63; + } + + public static uint ShiftUpBits(int len, uint[] z, int bits, uint c) + { + Debug.Assert(bits > 0 && bits < 32); + for (int i = 0; i < len; ++i) + { + uint next = z[i]; + z[i] = (next << bits) | (c >> -bits); + c = next; + } + return c >> -bits; + } + + public static uint ShiftUpBits(int len, uint[] z, int zOff, int bits, uint c) + { + Debug.Assert(bits > 0 && bits < 32); + for (int i = 0; i < len; ++i) + { + uint next = z[zOff + i]; + z[zOff + i] = (next << bits) | (c >> -bits); + c = next; + } + return c >> -bits; + } + + public static ulong ShiftUpBits64(int len, ulong[] z, int zOff, int bits, ulong c) + { + Debug.Assert(bits > 0 && bits < 64); + for (int i = 0; i < len; ++i) + { + ulong next = z[zOff + i]; + z[zOff + i] = (next << bits) | (c >> -bits); + c = next; + } + return c >> -bits; + } + + public static uint ShiftUpBits(int len, uint[] x, int bits, uint c, uint[] z) + { + Debug.Assert(bits > 0 && bits < 32); + for (int i = 0; i < len; ++i) + { + uint next = x[i]; + z[i] = (next << bits) | (c >> -bits); + c = next; + } + return c >> -bits; + } + + public static uint ShiftUpBits(int len, uint[] x, int xOff, int bits, uint c, uint[] z, int zOff) + { + Debug.Assert(bits > 0 && bits < 32); + for (int i = 0; i < len; ++i) + { + uint next = x[xOff + i]; + z[zOff + i] = (next << bits) | (c >> -bits); + c = next; + } + return c >> -bits; + } + + public static ulong ShiftUpBits64(int len, ulong[] x, int xOff, int bits, ulong c, ulong[] z, int zOff) + { + Debug.Assert(bits > 0 && bits < 64); + for (int i = 0; i < len; ++i) + { + ulong next = x[xOff + i]; + z[zOff + i] = (next << bits) | (c >> -bits); + c = next; + } + return c >> -bits; + } + + public static void Square(int len, uint[] x, uint[] zz) + { + int extLen = len << 1; + uint c = 0; + int j = len, k = extLen; + do + { + ulong xVal = (ulong)x[--j]; + ulong p = xVal * xVal; + zz[--k] = (c << 31) | (uint)(p >> 33); + zz[--k] = (uint)(p >> 1); + c = (uint)p; + } + while (j > 0); + + for (int i = 1; i < len; ++i) + { + c = SquareWordAdd(x, i, zz); + AddWordAt(extLen, c, zz, i << 1); + } + + ShiftUpBit(extLen, zz, x[0] << 31); + } + + public static void Square(int len, uint[] x, int xOff, uint[] zz, int zzOff) + { + int extLen = len << 1; + uint c = 0; + int j = len, k = extLen; + do + { + ulong xVal = (ulong)x[xOff + --j]; + ulong p = xVal * xVal; + zz[zzOff + --k] = (c << 31) | (uint)(p >> 33); + zz[zzOff + --k] = (uint)(p >> 1); + c = (uint)p; + } + while (j > 0); + + for (int i = 1; i < len; ++i) + { + c = SquareWordAdd(x, xOff, i, zz, zzOff); + AddWordAt(extLen, c, zz, zzOff, i << 1); + } + + ShiftUpBit(extLen, zz, zzOff, x[xOff] << 31); + } + + public static uint SquareWordAdd(uint[] x, int xPos, uint[] z) + { + ulong c = 0, xVal = (ulong)x[xPos]; + int i = 0; + do + { + c += xVal * x[i] + z[xPos + i]; + z[xPos + i] = (uint)c; + c >>= 32; + } + while (++i < xPos); + return (uint)c; + } + + public static uint SquareWordAdd(uint[] x, int xOff, int xPos, uint[] z, int zOff) + { + ulong c = 0, xVal = (ulong)x[xOff + xPos]; + int i = 0; + do + { + c += xVal * (x[xOff + i] & M) + (z[xPos + zOff] & M); + z[xPos + zOff] = (uint)c; + c >>= 32; + ++zOff; + } + while (++i < xPos); + return (uint)c; + } + + public static int Sub(int len, uint[] x, uint[] y, uint[] z) + { + long c = 0; + for (int i = 0; i < len; ++i) + { + c += (long)x[i] - y[i]; + z[i] = (uint)c; + c >>= 32; + } + return (int)c; + } + + public static int Sub(int len, uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff) + { + long c = 0; + for (int i = 0; i < len; ++i) + { + c += (long)x[xOff + i] - y[yOff + i]; + z[zOff + i] = (uint)c; + c >>= 32; + } + return (int)c; + } + public static int Sub33At(int len, uint x, uint[] z, int zPos) + { + Debug.Assert(zPos <= (len - 2)); + long c = (long)z[zPos + 0] - x; + z[zPos + 0] = (uint)c; + c >>= 32; + c += (long)z[zPos + 1] - 1; + z[zPos + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, zPos + 2); + } + + public static int Sub33At(int len, uint x, uint[] z, int zOff, int zPos) + { + Debug.Assert(zPos <= (len - 2)); + long c = (long)z[zOff + zPos] - x; + z[zOff + zPos] = (uint)c; + c >>= 32; + c += (long)z[zOff + zPos + 1] - 1; + z[zOff + zPos + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, zOff, zPos + 2); + } + + public static int Sub33From(int len, uint x, uint[] z) + { + long c = (long)z[0] - x; + z[0] = (uint)c; + c >>= 32; + c += (long)z[1] - 1; + z[1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, 2); + } + + public static int Sub33From(int len, uint x, uint[] z, int zOff) + { + long c = (long)z[zOff + 0] - x; + z[zOff + 0] = (uint)c; + c >>= 32; + c += (long)z[zOff + 1] - 1; + z[zOff + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, zOff, 2); + } + + public static int SubBothFrom(int len, uint[] x, uint[] y, uint[] z) + { + long c = 0; + for (int i = 0; i < len; ++i) + { + c += (long)z[i] - x[i] - y[i]; + z[i] = (uint)c; + c >>= 32; + } + return (int)c; + } + + public static int SubBothFrom(int len, uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff) + { + long c = 0; + for (int i = 0; i < len; ++i) + { + c += (long)z[zOff + i] - x[xOff + i] - y[yOff + i]; + z[zOff + i] = (uint)c; + c >>= 32; + } + return (int)c; + } + + public static int SubDWordAt(int len, ulong x, uint[] z, int zPos) + { + Debug.Assert(zPos <= (len - 2)); + long c = (long)z[zPos + 0] - (long)(x & M); + z[zPos + 0] = (uint)c; + c >>= 32; + c += (long)z[zPos + 1] - (long)(x >> 32); + z[zPos + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, zPos + 2); + } + + public static int SubDWordAt(int len, ulong x, uint[] z, int zOff, int zPos) + { + Debug.Assert(zPos <= (len - 2)); + long c = (long)z[zOff + zPos] - (long)(x & M); + z[zOff + zPos] = (uint)c; + c >>= 32; + c += (long)z[zOff + zPos + 1] - (long)(x >> 32); + z[zOff + zPos + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, zOff, zPos + 2); + } + + public static int SubDWordFrom(int len, ulong x, uint[] z) + { + long c = (long)z[0] - (long)(x & M); + z[0] = (uint)c; + c >>= 32; + c += (long)z[1] - (long)(x >> 32); + z[1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, 2); + } + + public static int SubDWordFrom(int len, ulong x, uint[] z, int zOff) + { + long c = (long)z[zOff + 0] - (long)(x & M); + z[zOff + 0] = (uint)c; + c >>= 32; + c += (long)z[zOff + 1] - (long)(x >> 32); + z[zOff + 1] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, zOff, 2); + } + + public static int SubFrom(int len, uint[] x, uint[] z) + { + long c = 0; + for (int i = 0; i < len; ++i) + { + c += (long)z[i] - x[i]; + z[i] = (uint)c; + c >>= 32; + } + return (int)c; + } + + public static int SubFrom(int len, uint[] x, int xOff, uint[] z, int zOff) + { + long c = 0; + for (int i = 0; i < len; ++i) + { + c += (long)z[zOff + i] - x[xOff + i]; + z[zOff + i] = (uint)c; + c >>= 32; + } + return (int)c; + } + + public static int SubWordAt(int len, uint x, uint[] z, int zPos) + { + Debug.Assert(zPos <= (len - 1)); + long c = (long)z[zPos] - x; + z[zPos] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, zPos + 1); + } + + public static int SubWordAt(int len, uint x, uint[] z, int zOff, int zPos) + { + Debug.Assert(zPos <= (len - 1)); + long c = (long)z[zOff + zPos] - x; + z[zOff + zPos] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, zOff, zPos + 1); + } + + public static int SubWordFrom(int len, uint x, uint[] z) + { + long c = (long)z[0] - x; + z[0] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, 1); + } + + public static int SubWordFrom(int len, uint x, uint[] z, int zOff) + { + long c = (long)z[zOff + 0] - x; + z[zOff + 0] = (uint)c; + c >>= 32; + return c == 0 ? 0 : DecAt(len, z, zOff, 1); + } + + public static BigInteger ToBigInteger(int len, uint[] x) + { + byte[] bs = new byte[len << 2]; + for (int i = 0; i < len; ++i) + { + uint x_i = x[i]; + if (x_i != 0) + { + Pack.UInt32_To_BE(x_i, bs, (len - 1 - i) << 2); + } + } + return new BigInteger(1, bs); + } + + public static void Zero(int len, uint[] z) + { + for (int i = 0; i < len; ++i) + { + z[i] = 0; + } + } + } +} diff --git a/crypto/src/math/raw/Nat128.cs b/crypto/src/math/raw/Nat128.cs new file mode 100644 index 000000000..819c52062 --- /dev/null +++ b/crypto/src/math/raw/Nat128.cs @@ -0,0 +1,856 @@ +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; + } + } +} diff --git a/crypto/src/math/raw/Nat160.cs b/crypto/src/math/raw/Nat160.cs new file mode 100644 index 000000000..153ac0a43 --- /dev/null +++ b/crypto/src/math/raw/Nat160.cs @@ -0,0 +1,874 @@ +using System; +using System.Diagnostics; + +using Org.BouncyCastle.Crypto.Utilities; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Nat160 + { + 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; + 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; + 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; + c += (ulong)x[4] + z[4]; + z[4] = (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]; + 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; + 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]; + z[4] = x[4]; + } + + public static uint[] Create() + { + return new uint[5]; + } + + public static uint[] CreateExt() + { + return new uint[10]; + } + + 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 = 4; i >= 0; --i) + { + if (x[i] != y[i]) + return false; + } + return true; + } + + public static uint[] FromBigInteger(BigInteger x) + { + if (x.SignValue < 0 || x.BitLength > 160) + 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 >= 5) + { + return 0; + } + int b = bit & 31; + return (x[w] >> b) & 1; + } + + public static bool Gte(uint[] x, uint[] y) + { + for (int i = 4; 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 = 4; 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 < 5; ++i) + { + if (x[i] != 0) + { + return false; + } + } + return true; + } + + public static bool IsZero(uint[] x) + { + for (int i = 0; i < 5; ++i) + { + if (x[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 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; + zz[5] = (uint)c; + } + + for (int i = 1; i < 5; ++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; + zz[i + 5] = (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 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; + zz[zzOff + 5] = (uint)c; + } + + for (int i = 1; i < 5; ++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; + zz[zzOff + 5] = (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 y_4 = y[4]; + + ulong zc = 0; + for (int i = 0; i < 5; ++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 += zc + zz[i + 5]; + zz[i + 5] = (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 y_4 = y[yOff + 4]; + + ulong zc = 0; + for (int i = 0; i < 5; ++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 += zc + zz[zzOff + 5]; + zz[zzOff + 5] = (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; + c += x4; + return c; + } + + public static uint MulWordAddExt(uint x, uint[] yy, int yyOff, uint[] zz, int zzOff) + { + Debug.Assert(yyOff <= 5); + Debug.Assert(zzOff <= 5); + + 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; + c += xVal * yy[yyOff + 4] + zz[zzOff + 4]; + zz[zzOff + 4] = (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 <= 1); + 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 : Nat.IncAt(5, z, zOff, 4); + } + + public static uint Mul33WordAdd(uint x, uint y, uint[] z, int zOff) + { + Debug.Assert(x >> 31 == 0); + Debug.Assert(zOff <= 2); + 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(5, z, zOff, 3); + } + + public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff) + { + Debug.Assert(zOff <= 2); + 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(5, z, zOff, 3); + } + + public static uint MulWordsAdd(uint x, uint y, uint[] z, int zOff) + { + Debug.Assert(zOff <= 3); + + 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(5, 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 < 5); + 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 = 4, j = 10; + 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_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; + w = (uint)zz_4; + zz[4] = (w << 1) | c; + c = w >> 31; + zz_5 += (zz_4 >> 32) + x_4 * x_1; + zz_6 += (zz_5 >> 32) + x_4 * x_2; + zz_7 += (zz_6 >> 32) + x_4 * x_3; + zz_8 += zz_7 >> 32; + } + + 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 = (uint)zz_7; + zz[7] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_8; + zz[8] = (w << 1) | c; + c = w >> 31; + w = zz[9] + (uint)(zz_8 >> 32); + zz[9] = (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 = 4, j = 10; + 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_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; + w = (uint)zz_4; + zz[zzOff + 4] = (w << 1) | c; + c = w >> 31; + zz_5 += (zz_4 >> 32) + x_4 * x_1; + zz_6 += (zz_5 >> 32) + x_4 * x_2; + zz_7 += (zz_6 >> 32) + x_4 * x_3; + zz_8 += zz_7 >> 32; + } + + 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 = (uint)zz_7; + zz[zzOff + 7] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_8; + zz[zzOff + 8] = (w << 1) | c; + c = w >> 31; + w = zz[zzOff + 9] + (uint)(zz_8 >> 32); + zz[zzOff + 9] = (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; + c += (long)x[4] - y[4]; + z[4] = (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; + 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; + 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; + c += (long)z[4] - x[4]; + z[4] = (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; + c += (long)z[zOff + 4] - x[xOff + 4]; + z[zOff + 4] = (uint)c; + c >>= 32; + return (int)c; + } + + public static BigInteger ToBigInteger(uint[] x) + { + byte[] bs = new byte[20]; + for (int i = 0; i < 5; ++i) + { + uint x_i = x[i]; + if (x_i != 0) + { + Pack.UInt32_To_BE(x_i, bs, (4 - 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; + } + } +} diff --git a/crypto/src/math/raw/Nat192.cs b/crypto/src/math/raw/Nat192.cs new file mode 100644 index 000000000..4797609ee --- /dev/null +++ b/crypto/src/math/raw/Nat192.cs @@ -0,0 +1,1048 @@ +using System; +using System.Diagnostics; + +using Org.BouncyCastle.Crypto.Utilities; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Nat192 + { + 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; + 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; + 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; + c += (ulong)x[4] + z[4]; + z[4] = (uint)c; + c >>= 32; + c += (ulong)x[5] + z[5]; + z[5] = (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; + 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; + 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]; + z[4] = x[4]; + z[5] = x[5]; + } + + public static void Copy64(ulong[] x, ulong[] z) + { + z[0] = x[0]; + z[1] = x[1]; + z[2] = x[2]; + } + + public static uint[] Create() + { + return new uint[6]; + } + + public static ulong[] Create64() + { + return new ulong[3]; + } + + public static uint[] CreateExt() + { + return new uint[12]; + } + + public static ulong[] CreateExt64() + { + return new ulong[6]; + } + + 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 = 5; i >= 0; --i) + { + if (x[i] != y[i]) + return false; + } + return true; + } + + public static bool Eq64(ulong[] x, ulong[] y) + { + for (int i = 2; i >= 0; --i) + { + if (x[i] != y[i]) + { + return false; + } + } + return true; + } + + public static uint[] FromBigInteger(BigInteger x) + { + if (x.SignValue < 0 || x.BitLength > 192) + 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 > 192) + 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; + } + int w = bit >> 5; + if (w < 0 || w >= 6) + { + return 0; + } + int b = bit & 31; + return (x[w] >> b) & 1; + } + + public static bool Gte(uint[] x, uint[] y) + { + for (int i = 5; 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 = 5; 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 < 6; ++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 < 3; ++i) + { + if (x[i] != 0UL) + { + return false; + } + } + return true; + } + + public static bool IsZero(uint[] x) + { + for (int i = 0; i < 6; ++i) + { + if (x[i] != 0) + { + return false; + } + } + return true; + } + + public static bool IsZero64(ulong[] x) + { + for (int i = 0; i < 3; ++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 y_4 = y[4]; + ulong y_5 = y[5]; + + { + 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; + zz[6] = (uint)c; + } + + for (int i = 1; i < 6; ++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; + zz[i + 6] = (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 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; + zz[zzOff + 6] = (uint)c; + } + + for (int i = 1; i < 6; ++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; + zz[zzOff + 6] = (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 y_4 = y[4]; + ulong y_5 = y[5]; + + ulong zc = 0; + for (int i = 0; i < 6; ++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 += zc + zz[i + 6]; + zz[i + 6] = (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 y_4 = y[yOff + 4]; + ulong y_5 = y[yOff + 5]; + + ulong zc = 0; + for (int i = 0; i < 6; ++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 += zc + zz[zzOff + 6]; + zz[zzOff + 6] = (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; + c += x5; + return c; + } + + public static uint MulWordAddExt(uint x, uint[] yy, int yyOff, uint[] zz, int zzOff) + { + Debug.Assert(yyOff <= 6); + Debug.Assert(zzOff <= 6); + 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; + c += xVal * yy[yyOff + 4] + zz[zzOff + 4]; + zz[zzOff + 4] = (uint)c; + c >>= 32; + c += xVal * yy[yyOff + 5] + zz[zzOff + 5]; + zz[zzOff + 5] = (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 <= 2); + 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 : Nat.IncAt(6, z, zOff, 4); + } + + public static uint Mul33WordAdd(uint x, uint y, uint[] z, int zOff) + { + Debug.Assert(x >> 31 == 0); + Debug.Assert(zOff <=3); + 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(6, z, zOff, 3); + } + + public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff) + { + Debug.Assert(zOff <= 3); + 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(6, 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 < 6); + 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 = 5, j = 12; + 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_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; + w = (uint)zz_4; + zz[4] = (w << 1) | c; + c = w >> 31; + 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; + w = (uint)zz_5; + zz[5] = (w << 1) | c; + c = w >> 31; + zz_6 += (zz_5 >> 32) + x_5 * x_1; + zz_7 += (zz_6 >> 32) + x_5 * x_2; + zz_8 += (zz_7 >> 32) + x_5 * x_3; + zz_9 += (zz_8 >> 32) + x_5 * x_4; + zz_10 += zz_9 >> 32; + } + + w = (uint)zz_6; + zz[6] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_7; + zz[7] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_8; + zz[8] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_9; + zz[9] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_10; + zz[10] = (w << 1) | c; + c = w >> 31; + w = zz[11] + (uint)(zz_10 >> 32); + zz[11] = (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 = 5, j = 12; + 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_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; + w = (uint)zz_4; + zz[zzOff + 4] = (w << 1) | c; + c = w >> 31; + 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; + w = (uint)zz_5; + zz[zzOff + 5] = (w << 1) | c; + c = w >> 31; + zz_6 += (zz_5 >> 32) + x_5 * x_1; + zz_7 += (zz_6 >> 32) + x_5 * x_2; + zz_8 += (zz_7 >> 32) + x_5 * x_3; + zz_9 += (zz_8 >> 32) + x_5 * x_4; + zz_10 += zz_9 >> 32; + } + + w = (uint)zz_6; + zz[zzOff + 6] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_7; + zz[zzOff + 7] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_8; + zz[zzOff + 8] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_9; + zz[zzOff + 9] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_10; + zz[zzOff + 10] = (w << 1) | c; + c = w >> 31; + w = zz[zzOff + 11] + (uint)(zz_10 >> 32); + zz[zzOff + 11] = (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; + c += (long)x[4] - y[4]; + z[4] = (uint)c; + c >>= 32; + c += (long)x[5] - y[5]; + z[5] = (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; + 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; + 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; + c += (long)z[4] - x[4]; + z[4] = (uint)c; + c >>= 32; + c += (long)z[5] - x[5]; + z[5] = (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; + c += (long)z[zOff + 4] - x[xOff + 4]; + z[zOff + 4] = (uint)c; + c >>= 32; + c += (long)z[zOff + 5] - x[xOff + 5]; + z[zOff + 5] = (uint)c; + c >>= 32; + return (int)c; + } + + public static BigInteger ToBigInteger(uint[] x) + { + byte[] bs = new byte[24]; + for (int i = 0; i < 6; ++i) + { + uint x_i = x[i]; + if (x_i != 0) + { + Pack.UInt32_To_BE(x_i, bs, (5 - i) << 2); + } + } + return new BigInteger(1, bs); + } + + public static BigInteger ToBigInteger64(ulong[] x) + { + byte[] bs = new byte[24]; + for (int i = 0; i < 3; ++i) + { + ulong x_i = x[i]; + if (x_i != 0L) + { + Pack.UInt64_To_BE(x_i, bs, (2 - 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; + z[4] = 0; + z[5] = 0; + } + } +} diff --git a/crypto/src/math/raw/Nat224.cs b/crypto/src/math/raw/Nat224.cs new file mode 100644 index 000000000..940e930ac --- /dev/null +++ b/crypto/src/math/raw/Nat224.cs @@ -0,0 +1,1176 @@ +using System; +using System.Diagnostics; + +using Org.BouncyCastle.Crypto.Utilities; + +namespace Org.BouncyCastle.Math.Raw +{ + 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; + } + + 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; + c += (ulong)x[4] + z[4]; + z[4] = (uint)c; + c >>= 32; + c += (ulong)x[5] + z[5]; + z[5] = (uint)c; + c >>= 32; + c += (ulong)x[6] + z[6]; + z[6] = (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 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 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 = 6; i >= 0; --i) + { + if (x[i] != y[i]) + return false; + } + return true; + } + + 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 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 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 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 y_4 = y[4]; + ulong y_5 = y[5]; + ulong y_6 = y[6]; + + ulong zc = 0; + for (int i = 0; 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; + c += zc + zz[i + 7]; + zz[i + 7] = (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 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 : Nat.IncAt(7, 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 : Nat.IncAt(7, 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 : Nat.IncAt(7, 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 void Square(uint[] x, uint[] zz) + { + ulong x_0 = x[0]; + ulong zz_1; + + uint c = 0, w; + { + 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; + 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_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; + w = (uint)zz_4; + zz[4] = (w << 1) | c; + c = w >> 31; + 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; + w = (uint)zz_5; + zz[5] = (w << 1) | c; + c = w >> 31; + 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; + w = (uint)zz_6; + zz[6] = (w << 1) | c; + c = w >> 31; + 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; + } + + w = (uint)zz_7; + zz[7] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_8; + zz[8] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_9; + zz[9] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_10; + zz[10] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_11; + zz[11] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_12; + zz[12] = (w << 1) | c; + c = w >> 31; + w = zz[13] + (uint)(zz_12 >> 32); + zz[13] = (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 = 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; + 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_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; + w = (uint)zz_4; + zz[zzOff + 4] = (w << 1) | c; + c = w >> 31; + 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; + w = (uint)zz_5; + zz[zzOff + 5] = (w << 1) | c; + c = w >> 31; + 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; + w = (uint)zz_6; + zz[zzOff + 6] = (w << 1) | c; + c = w >> 31; + 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; + } + + w = (uint)zz_7; + zz[zzOff + 7] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_8; + zz[zzOff + 8] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_9; + zz[zzOff + 9] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_10; + zz[zzOff + 10] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_11; + zz[zzOff + 11] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_12; + zz[zzOff + 12] = (w << 1) | c; + c = w >> 31; + w = zz[zzOff + 13] + (uint)(zz_12 >> 32); + zz[zzOff + 13] = (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; + 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; + } + + 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; + c += (long)z[4] - x[4]; + z[4] = (uint)c; + c >>= 32; + c += (long)z[5] - x[5]; + z[5] = (uint)c; + c >>= 32; + c += (long)z[6] - x[6]; + z[6] = (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; + c += (long)z[zOff + 4] - x[xOff + 4]; + z[zOff + 4] = (uint)c; + c >>= 32; + c += (long)z[zOff + 5] - x[xOff + 5]; + z[zOff + 5] = (uint)c; + c >>= 32; + c += (long)z[zOff + 6] - x[xOff + 6]; + z[zOff + 6] = (uint)c; + c >>= 32; + return (int)c; + } + + 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; + } + } +} diff --git a/crypto/src/math/raw/Nat256.cs b/crypto/src/math/raw/Nat256.cs new file mode 100644 index 000000000..19455031a --- /dev/null +++ b/crypto/src/math/raw/Nat256.cs @@ -0,0 +1,1387 @@ +using System; +using System.Diagnostics; + +using Org.BouncyCastle.Crypto.Utilities; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Nat256 + { + 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; + c += (ulong)x[7] + y[7]; + z[7] = (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; + c += (ulong)x[xOff + 7] + y[yOff + 7]; + z[zOff + 7] = (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; + c += (ulong)x[7] + y[7] + z[7]; + z[7] = (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; + c += (ulong)x[xOff + 7] + y[yOff + 7] + z[zOff + 7]; + z[zOff + 7] = (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; + c += (ulong)x[4] + z[4]; + z[4] = (uint)c; + c >>= 32; + c += (ulong)x[5] + z[5]; + z[5] = (uint)c; + c >>= 32; + c += (ulong)x[6] + z[6]; + z[6] = (uint)c; + c >>= 32; + c += (ulong)x[7] + z[7]; + z[7] = (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; + c += (ulong)x[xOff + 7] + z[zOff + 7]; + z[zOff + 7] = (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; + c += (ulong)u[uOff + 7] + v[vOff + 7]; + u[uOff + 7] = (uint)c; + v[vOff + 7] = (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]; + z[4] = x[4]; + z[5] = x[5]; + z[6] = x[6]; + z[7] = x[7]; + } + + public static void Copy64(ulong[] x, ulong[] z) + { + z[0] = x[0]; + z[1] = x[1]; + z[2] = x[2]; + z[3] = x[3]; + } + + public static uint[] Create() + { + return new uint[8]; + } + + public static ulong[] Create64() + { + return new ulong[4]; + } + + public static uint[] CreateExt() + { + return new uint[16]; + } + + public static ulong[] CreateExt64() + { + return new ulong[8]; + } + + 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 = 7; i >= 0; --i) + { + if (x[i] != y[i]) + return false; + } + return true; + } + + public static bool Eq64(ulong[] x, ulong[] y) + { + for (int i = 3; i >= 0; --i) + { + if (x[i] != y[i]) + { + return false; + } + } + return true; + } + + public static uint[] FromBigInteger(BigInteger x) + { + if (x.SignValue < 0 || x.BitLength > 256) + 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 > 256) + 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 & 255) != 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 = 7; 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 = 7; 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 < 8; ++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 < 4; ++i) + { + if (x[i] != 0UL) + { + return false; + } + } + return true; + } + + public static bool IsZero(uint[] x) + { + for (int i = 0; i < 8; ++i) + { + if (x[i] != 0) + { + return false; + } + } + return true; + } + + public static bool IsZero64(ulong[] x) + { + for (int i = 0; i < 4; ++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 y_4 = y[4]; + ulong y_5 = y[5]; + ulong y_6 = y[6]; + ulong y_7 = y[7]; + + { + 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; + c += x_0 * y_7; + zz[7] = (uint)c; + c >>= 32; + zz[8] = (uint)c; + } + + for (int i = 1; i < 8; ++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; + c += x_i * y_7 + zz[i + 7]; + zz[i + 7] = (uint)c; + c >>= 32; + zz[i + 8] = (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 y_7 = y[yOff + 7]; + + { + 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; + c += x_0 * y_7; + zz[zzOff + 7] = (uint)c; + c >>= 32; + zz[zzOff + 8] = (uint)c; + } + + for (int i = 1; i < 8; ++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; + c += x_i * y_7 + zz[zzOff + 7]; + zz[zzOff + 7] = (uint)c; + c >>= 32; + zz[zzOff + 8] = (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 y_4 = y[4]; + ulong y_5 = y[5]; + ulong y_6 = y[6]; + ulong y_7 = y[7]; + + ulong zc = 0; + for (int i = 0; i < 8; ++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; + c += x_i * y_7 + zz[i + 7]; + zz[i + 7] = (uint)c; + c >>= 32; + c += zc + zz[i + 8]; + zz[i + 8] = (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 y_4 = y[yOff + 4]; + ulong y_5 = y[yOff + 5]; + ulong y_6 = y[yOff + 6]; + ulong y_7 = y[yOff + 7]; + + ulong zc = 0; + for (int i = 0; i < 8; ++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 += x_i * y_7 + zz[zzOff + 7]; + zz[zzOff + 7] = (uint)c; + c >>= 32; + c += zc + zz[zzOff + 8]; + zz[zzOff + 8] = (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; + ulong x7 = x[xOff + 7]; + c += wVal * x7 + x6 + y[yOff + 7]; + z[zOff + 7] = (uint)c; + c >>= 32; + c += x7; + 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; + c += xVal * (ulong)z[7]; + z[7] = (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; + c += xVal * (ulong)z[7] + y[7]; + z[7] = (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; + c += xVal * y[yOff + 7] + z[zOff + 7]; + z[zOff + 7] = (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 <= 4); + 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 : Nat.IncAt(8, z, zOff, 4); + } + + public static uint Mul33WordAdd(uint x, uint y, uint[] z, int zOff) + { + Debug.Assert(x >> 31 == 0); + Debug.Assert(zOff <= 5); + 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(8, z, zOff, 3); + } + + public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff) + { + Debug.Assert(zOff <= 5); + 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(8, 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 < 8); + 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 = 7, j = 16; + 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_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; + w = (uint)zz_4; + zz[4] = (w << 1) | c; + c = w >> 31; + 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; + w = (uint)zz_5; + zz[5] = (w << 1) | c; + c = w >> 31; + 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; + w = (uint)zz_6; + zz[6] = (w << 1) | c; + c = w >> 31; + zz_7 += (zz_6 >> 32) + x_6 * x_1; + zz_8 += (zz_7 >> 32) + x_6 * x_2; + zz_7 &= M; + zz_9 += (zz_8 >> 32) + x_6 * x_3; + zz_8 &= M; + zz_10 += (zz_9 >> 32) + x_6 * x_4; + zz_9 &= M; + zz_11 += (zz_10 >> 32) + x_6 * x_5; + zz_10 &= M; + zz_12 += zz_11 >> 32; + zz_11 &= M; + } + + ulong x_7 = x[7]; + ulong zz_13 = zz[13]; + ulong zz_14 = zz[14]; + { + zz_7 += x_7 * x_0; + w = (uint)zz_7; + zz[7] = (w << 1) | c; + c = w >> 31; + zz_8 += (zz_7 >> 32) + x_7 * x_1; + zz_9 += (zz_8 >> 32) + x_7 * x_2; + zz_10 += (zz_9 >> 32) + x_7 * x_3; + zz_11 += (zz_10 >> 32) + x_7 * x_4; + zz_12 += (zz_11 >> 32) + x_7 * x_5; + zz_13 += (zz_12 >> 32) + x_7 * x_6; + zz_14 += zz_13 >> 32; + } + + w = (uint)zz_8; + zz[8] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_9; + zz[9] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_10; + zz[10] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_11; + zz[11] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_12; + zz[12] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_13; + zz[13] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_14; + zz[14] = (w << 1) | c; + c = w >> 31; + w = zz[15] + (uint)(zz_14 >> 32); + zz[15] = (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 = 7, j = 16; + 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_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; + w = (uint)zz_4; + zz[zzOff + 4] = (w << 1) | c; + c = w >> 31; + 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; + w = (uint)zz_5; + zz[zzOff + 5] = (w << 1) | c; + c = w >> 31; + 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; + w = (uint)zz_6; + zz[zzOff + 6] = (w << 1) | c; + c = w >> 31; + zz_7 += (zz_6 >> 32) + x_6 * x_1; + zz_8 += (zz_7 >> 32) + x_6 * x_2; + zz_7 &= M; + zz_9 += (zz_8 >> 32) + x_6 * x_3; + zz_8 &= M; + zz_10 += (zz_9 >> 32) + x_6 * x_4; + zz_9 &= M; + zz_11 += (zz_10 >> 32) + x_6 * x_5; + zz_10 &= M; + zz_12 += zz_11 >> 32; + zz_11 &= M; + } + + ulong x_7 = x[xOff + 7]; + ulong zz_13 = zz[zzOff + 13]; + ulong zz_14 = zz[zzOff + 14]; + { + zz_7 += x_7 * x_0; + w = (uint)zz_7; + zz[zzOff + 7] = (w << 1) | c; + c = w >> 31; + zz_8 += (zz_7 >> 32) + x_7 * x_1; + zz_9 += (zz_8 >> 32) + x_7 * x_2; + zz_10 += (zz_9 >> 32) + x_7 * x_3; + zz_11 += (zz_10 >> 32) + x_7 * x_4; + zz_12 += (zz_11 >> 32) + x_7 * x_5; + zz_13 += (zz_12 >> 32) + x_7 * x_6; + zz_14 += zz_13 >> 32; + } + + w = (uint)zz_8; + zz[zzOff + 8] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_9; + zz[zzOff + 9] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_10; + zz[zzOff + 10] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_11; + zz[zzOff + 11] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_12; + zz[zzOff + 12] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_13; + zz[zzOff + 13] = (w << 1) | c; + c = w >> 31; + w = (uint)zz_14; + zz[zzOff + 14] = (w << 1) | c; + c = w >> 31; + w = zz[zzOff + 15] + (uint)(zz_14 >> 32); + zz[zzOff + 15] = (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; + 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; + c += (long)x[7] - y[7]; + z[7] = (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; + c += (long)x[xOff + 7] - y[yOff + 7]; + z[zOff + 7] = (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; + c += (long)z[7] - x[7] - y[7]; + z[7] = (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; + c += (long)z[4] - x[4]; + z[4] = (uint)c; + c >>= 32; + c += (long)z[5] - x[5]; + z[5] = (uint)c; + c >>= 32; + c += (long)z[6] - x[6]; + z[6] = (uint)c; + c >>= 32; + c += (long)z[7] - x[7]; + z[7] = (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; + c += (long)z[zOff + 4] - x[xOff + 4]; + z[zOff + 4] = (uint)c; + c >>= 32; + c += (long)z[zOff + 5] - x[xOff + 5]; + z[zOff + 5] = (uint)c; + c >>= 32; + c += (long)z[zOff + 6] - x[xOff + 6]; + z[zOff + 6] = (uint)c; + c >>= 32; + c += (long)z[zOff + 7] - x[xOff + 7]; + z[zOff + 7] = (uint)c; + c >>= 32; + return (int)c; + } + + public static BigInteger ToBigInteger(uint[] x) + { + byte[] bs = new byte[32]; + for (int i = 0; i < 8; ++i) + { + uint x_i = x[i]; + if (x_i != 0) + { + Pack.UInt32_To_BE(x_i, bs, (7 - i) << 2); + } + } + return new BigInteger(1, bs); + } + + public static BigInteger ToBigInteger64(ulong[] x) + { + byte[] bs = new byte[32]; + for (int i = 0; i < 4; ++i) + { + ulong x_i = x[i]; + if (x_i != 0L) + { + Pack.UInt64_To_BE(x_i, bs, (3 - 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; + z[4] = 0; + z[5] = 0; + z[6] = 0; + z[7] = 0; + } + } +} diff --git a/crypto/src/math/raw/Nat320.cs b/crypto/src/math/raw/Nat320.cs new file mode 100644 index 000000000..c7daa71e2 --- /dev/null +++ b/crypto/src/math/raw/Nat320.cs @@ -0,0 +1,98 @@ +using System; +using System.Diagnostics; + +using Org.BouncyCastle.Crypto.Utilities; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Nat320 + { + public static void Copy64(ulong[] x, ulong[] z) + { + z[0] = x[0]; + z[1] = x[1]; + z[2] = x[2]; + z[3] = x[3]; + z[4] = x[4]; + } + + public static ulong[] Create64() + { + return new ulong[5]; + } + + public static ulong[] CreateExt64() + { + return new ulong[10]; + } + + public static bool Eq64(ulong[] x, ulong[] y) + { + for (int i = 4; i >= 0; --i) + { + if (x[i] != y[i]) + { + return false; + } + } + return true; + } + + public static ulong[] FromBigInteger64(BigInteger x) + { + if (x.SignValue < 0 || x.BitLength > 320) + 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 bool IsOne64(ulong[] x) + { + if (x[0] != 1UL) + { + return false; + } + for (int i = 1; i < 5; ++i) + { + if (x[i] != 0UL) + { + return false; + } + } + return true; + } + + public static bool IsZero64(ulong[] x) + { + for (int i = 0; i < 5; ++i) + { + if (x[i] != 0UL) + { + return false; + } + } + return true; + } + + public static BigInteger ToBigInteger64(ulong[] x) + { + byte[] bs = new byte[40]; + for (int i = 0; i < 5; ++i) + { + ulong x_i = x[i]; + if (x_i != 0L) + { + Pack.UInt64_To_BE(x_i, bs, (4 - i) << 3); + } + } + return new BigInteger(1, bs); + } + } +} diff --git a/crypto/src/math/raw/Nat384.cs b/crypto/src/math/raw/Nat384.cs new file mode 100644 index 000000000..ed1c47e8c --- /dev/null +++ b/crypto/src/math/raw/Nat384.cs @@ -0,0 +1,46 @@ +using System; +using System.Diagnostics; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Nat384 + { + public static void Mul(uint[] x, uint[] y, uint[] zz) + { + Nat192.Mul(x, y, zz); + Nat192.Mul(x, 6, y, 6, zz, 12); + + uint c18 = Nat192.AddToEachOther(zz, 6, zz, 12); + uint c12 = c18 + Nat192.AddTo(zz, 0, zz, 6, 0); + c18 += Nat192.AddTo(zz, 18, zz, 12, c12); + + uint[] dx = Nat192.Create(), dy = Nat192.Create(); + bool neg = Nat192.Diff(x, 6, x, 0, dx, 0) != Nat192.Diff(y, 6, y, 0, dy, 0); + + uint[] tt = Nat192.CreateExt(); + Nat192.Mul(dx, dy, tt); + + c18 += neg ? Nat.AddTo(12, tt, 0, zz, 6) : (uint)Nat.SubFrom(12, tt, 0, zz, 6); + Nat.AddWordAt(24, c18, zz, 18); + } + + public static void Square(uint[] x, uint[] zz) + { + Nat192.Square(x, zz); + Nat192.Square(x, 6, zz, 12); + + uint c18 = Nat192.AddToEachOther(zz, 6, zz, 12); + uint c12 = c18 + Nat192.AddTo(zz, 0, zz, 6, 0); + c18 += Nat192.AddTo(zz, 18, zz, 12, c12); + + uint[] dx = Nat192.Create(); + Nat192.Diff(x, 6, x, 0, dx, 0); + + uint[] m = Nat192.CreateExt(); + Nat192.Square(dx, m); + + c18 += (uint)Nat.SubFrom(12, m, 0, zz, 6); + Nat.AddWordAt(24, c18, zz, 18); + } + } +} diff --git a/crypto/src/math/raw/Nat448.cs b/crypto/src/math/raw/Nat448.cs new file mode 100644 index 000000000..52a253f1b --- /dev/null +++ b/crypto/src/math/raw/Nat448.cs @@ -0,0 +1,100 @@ +using System; +using System.Diagnostics; + +using Org.BouncyCastle.Crypto.Utilities; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Nat448 + { + public static void Copy64(ulong[] x, ulong[] 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 ulong[] Create64() + { + return new ulong[7]; + } + + public static ulong[] CreateExt64() + { + return new ulong[14]; + } + + public static bool Eq64(ulong[] x, ulong[] y) + { + for (int i = 6; i >= 0; --i) + { + if (x[i] != y[i]) + { + return false; + } + } + return true; + } + + public static ulong[] FromBigInteger64(BigInteger x) + { + if (x.SignValue < 0 || x.BitLength > 448) + 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 bool IsOne64(ulong[] x) + { + if (x[0] != 1UL) + { + return false; + } + for (int i = 1; i < 7; ++i) + { + if (x[i] != 0UL) + { + return false; + } + } + return true; + } + + public static bool IsZero64(ulong[] x) + { + for (int i = 0; i < 7; ++i) + { + if (x[i] != 0UL) + { + return false; + } + } + return true; + } + + public static BigInteger ToBigInteger64(ulong[] x) + { + byte[] bs = new byte[56]; + for (int i = 0; i < 7; ++i) + { + ulong x_i = x[i]; + if (x_i != 0L) + { + Pack.UInt64_To_BE(x_i, bs, (6 - i) << 3); + } + } + return new BigInteger(1, bs); + } + } +} diff --git a/crypto/src/math/raw/Nat512.cs b/crypto/src/math/raw/Nat512.cs new file mode 100644 index 000000000..a9ef2b3b6 --- /dev/null +++ b/crypto/src/math/raw/Nat512.cs @@ -0,0 +1,46 @@ +using System; +using System.Diagnostics; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Nat512 + { + public static void Mul(uint[] x, uint[] y, uint[] zz) + { + Nat256.Mul(x, y, zz); + Nat256.Mul(x, 8, y, 8, zz, 16); + + uint c24 = Nat256.AddToEachOther(zz, 8, zz, 16); + uint c16 = c24 + Nat256.AddTo(zz, 0, zz, 8, 0); + c24 += Nat256.AddTo(zz, 24, zz, 16, c16); + + uint[] dx = Nat256.Create(), dy = Nat256.Create(); + bool neg = Nat256.Diff(x, 8, x, 0, dx, 0) != Nat256.Diff(y, 8, y, 0, dy, 0); + + uint[] tt = Nat256.CreateExt(); + Nat256.Mul(dx, dy, tt); + + c24 += neg ? Nat.AddTo(16, tt, 0, zz, 8) : (uint)Nat.SubFrom(16, tt, 0, zz, 8); + Nat.AddWordAt(32, c24, zz, 24); + } + + public static void Square(uint[] x, uint[] zz) + { + Nat256.Square(x, zz); + Nat256.Square(x, 8, zz, 16); + + uint c24 = Nat256.AddToEachOther(zz, 8, zz, 16); + uint c16 = c24 + Nat256.AddTo(zz, 0, zz, 8, 0); + c24 += Nat256.AddTo(zz, 24, zz, 16, c16); + + uint[] dx = Nat256.Create(); + Nat256.Diff(x, 8, x, 0, dx, 0); + + uint[] m = Nat256.CreateExt(); + Nat256.Square(dx, m); + + c24 += (uint)Nat.SubFrom(16, m, 0, zz, 8); + Nat.AddWordAt(32, c24, zz, 24); + } + } +} diff --git a/crypto/src/math/raw/Nat576.cs b/crypto/src/math/raw/Nat576.cs new file mode 100644 index 000000000..813fb86be --- /dev/null +++ b/crypto/src/math/raw/Nat576.cs @@ -0,0 +1,102 @@ +using System; +using System.Diagnostics; + +using Org.BouncyCastle.Crypto.Utilities; + +namespace Org.BouncyCastle.Math.Raw +{ + internal abstract class Nat576 + { + public static void Copy64(ulong[] x, ulong[] 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]; + z[7] = x[7]; + z[8] = x[8]; + } + + public static ulong[] Create64() + { + return new ulong[9]; + } + + public static ulong[] CreateExt64() + { + return new ulong[18]; + } + + public static bool Eq64(ulong[] x, ulong[] y) + { + for (int i = 8; i >= 0; --i) + { + if (x[i] != y[i]) + { + return false; + } + } + return true; + } + + public static ulong[] FromBigInteger64(BigInteger x) + { + if (x.SignValue < 0 || x.BitLength > 576) + 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 bool IsOne64(ulong[] x) + { + if (x[0] != 1UL) + { + return false; + } + for (int i = 1; i < 9; ++i) + { + if (x[i] != 0UL) + { + return false; + } + } + return true; + } + + public static bool IsZero64(ulong[] x) + { + for (int i = 0; i < 9; ++i) + { + if (x[i] != 0UL) + { + return false; + } + } + return true; + } + + public static BigInteger ToBigInteger64(ulong[] x) + { + byte[] bs = new byte[72]; + for (int i = 0; i < 9; ++i) + { + ulong x_i = x[i]; + if (x_i != 0L) + { + Pack.UInt64_To_BE(x_i, bs, (8 - i) << 3); + } + } + return new BigInteger(1, bs); + } + } +} |