diff options
| author | Peter Dettman <peter.dettman@bouncycastle.org> | 2018-07-08 16:30:26 +0700 |
|---|---|---|
| committer | Peter Dettman <peter.dettman@bouncycastle.org> | 2018-07-08 16:30:26 +0700 |
| commit | 5268ce495106a67a3e167559b78c6dc1f857a423 (patch) | |
| tree | 1b18df57d8e9dd6cf327f53608f9d1e228711332 /crypto/src/math/ec | |
| parent | Improved performance for BigInteger.ToString(int) (diff) | |
| download | BouncyCastle.NET-ed25519-5268ce495106a67a3e167559b78c6dc1f857a423.tar.xz | |
Add Ed25519 and Ed448 from RFC 8032
Diffstat (limited to 'crypto/src/math/ec')
| -rw-r--r-- | crypto/src/math/ec/rfc7748/X25519.cs | 4 | ||||
| -rw-r--r-- | crypto/src/math/ec/rfc7748/X25519Field.cs | 147 | ||||
| -rw-r--r-- | crypto/src/math/ec/rfc7748/X448.cs | 8 | ||||
| -rw-r--r-- | crypto/src/math/ec/rfc7748/X448Field.cs | 123 | ||||
| -rw-r--r-- | crypto/src/math/ec/rfc8032/Ed25519.cs | 937 | ||||
| -rw-r--r-- | crypto/src/math/ec/rfc8032/Ed448.cs | 1067 |
6 files changed, 2253 insertions, 33 deletions
diff --git a/crypto/src/math/ec/rfc7748/X25519.cs b/crypto/src/math/ec/rfc7748/X25519.cs index 16f680d90..a10d53da5 100644 --- a/crypto/src/math/ec/rfc7748/X25519.cs +++ b/crypto/src/math/ec/rfc7748/X25519.cs @@ -10,10 +10,10 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 private const int C_A24 = (C_A + 2)/4; // 0x1 - //private static readonly int[] S_x = new int[] { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; + //private static readonly int[] S_x = { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; // 0x215132111D8354CB52385F46DCA2B71D440F6A51EB4D1207816B1E0137D48290 - private static readonly int[] PsubS_x = new int[]{ 0x03D48290, 0x02C7804D, 0x01207816, 0x028F5A68, 0x00881ED4, 0x00A2B71D, + private static readonly int[] PsubS_x = { 0x03D48290, 0x02C7804D, 0x01207816, 0x028F5A68, 0x00881ED4, 0x00A2B71D, 0x0217D1B7, 0x014CB523, 0x0088EC1A, 0x0042A264 }; private static int[] precompBase = null; diff --git a/crypto/src/math/ec/rfc7748/X25519Field.cs b/crypto/src/math/ec/rfc7748/X25519Field.cs index 282f41628..fd5599657 100644 --- a/crypto/src/math/ec/rfc7748/X25519Field.cs +++ b/crypto/src/math/ec/rfc7748/X25519Field.cs @@ -11,6 +11,9 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 private const int M25 = 0x01FFFFFF; private const int M26 = 0x03FFFFFF; + private static readonly int[] RootNegOne = { 0x020EA0B0, 0x0386C9D2, 0x00478C4E, 0x0035697F, 0x005E8630, + 0x01FBD7A7, 0x0340264F, 0x01F0B2B4, 0x00027E0E, 0x00570649 }; + private X25519Field() {} public static void Add(int[] x, int[] y, int[] z) @@ -21,6 +24,16 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 } } + public static void AddOne(int[] z) + { + z[0] += 1; + } + + public static void AddOne(int[] z, int zOff) + { + z[zOff] += 1; + } + public static void Apm(int[] x, int[] y, int[] zp, int[] zm) { for (int i = 0; i < Size; ++i) @@ -54,6 +67,17 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 z[5] = z5; z[6] = z6; z[7] = z7; z[8] = z8; z[9] = z9; } + public static void CNegate(int negate, int[] z) + { + Debug.Assert(negate >> 1 == 0); + + int mask = 0 - negate; + for (int i = 0; i < Size; ++i) + { + z[i] = (z[i] ^ mask) - mask; + } + } + public static void Copy(int[] x, int xOff, int[] z, int zOff) { for (int i = 0; i < Size; ++i) @@ -67,6 +91,11 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 return new int[Size]; } + public static int[] CreateTable(int n) + { + return new int[Size * n]; + } + public static void CSwap(int swap, int[] a, int[] b) { Debug.Assert(swap >> 1 == 0); @@ -143,24 +172,23 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 // (250 1s) (1 0s) (1 1s) (1 0s) (2 1s) // Addition chain: [1] [2] 3 5 10 15 25 50 75 125 [250] - int[] x2 = Create(); Sqr(x, x2); Mul(x, x2, x2); - int[] x3 = Create(); Sqr(x2, x3); Mul(x, x3, x3); - int[] x5 = x3; Sqr(x3, 2, x5); Mul(x2, x5, x5); - int[] x10 = Create(); Sqr(x5, 5, x10); Mul(x5, x10, x10); - int[] x15 = Create(); Sqr(x10, 5, x15); Mul(x5, x15, x15); - int[] x25 = x5; Sqr(x15, 10, x25); Mul(x10, x25, x25); - int[] x50 = x10; Sqr(x25, 25, x50); Mul(x25, x50, x50); - int[] x75 = x15; Sqr(x50, 25, x75); Mul(x25, x75, x75); - int[] x125 = x25; Sqr(x75, 50, x125); Mul(x50, x125, x125); - int[] x250 = x50; Sqr(x125, 125, x250); Mul(x125, x250, x250); - - int[] t = x125; - Sqr(x250, 2, t); - Mul(t, x, t); + int[] x2 = Create(); + int[] t = Create(); + PowPm5d8(x, x2, t); Sqr(t, 3, t); Mul(t, x2, z); } + public static bool IsZeroVar(int[] x) + { + int d = 0; + for (int i = 0; i < Size; ++i) + { + d |= x[i]; + } + return d == 0; + } + public static void Mul(int[] x, int y, int[] z) { int x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4]; @@ -345,6 +373,14 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 z[9] = z9 + (int)t; } + public static void Negate(int[] x, int[] z) + { + for (int i = 0; i < Size; ++i) + { + z[i] = -x[i]; + } + } + public static void Normalize(int[] z) { int x = (z[9] >> 23) & 1; @@ -353,6 +389,37 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 Debug.Assert(z[9] >> 24 == 0); } + public static void One(int[] z) + { + z[0] = 1; + for (int i = 1; i < Size; ++i) + { + z[i] = 0; + } + } + + private static void PowPm5d8(int[] x, int[] rx2, int[] rz) + { + // z = x^((p-5)/8) = x^FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD + // (250 1s) (1 0s) (1 1s) + // Addition chain: [1] 2 3 5 10 15 25 50 75 125 [250] + + int[] x2 = rx2; Sqr(x, x2); Mul(x, x2, x2); + int[] x3 = Create(); Sqr(x2, x3); Mul(x, x3, x3); + int[] x5 = x3; Sqr(x3, 2, x5); Mul(x2, x5, x5); + int[] x10 = Create(); Sqr(x5, 5, x10); Mul(x5, x10, x10); + int[] x15 = Create(); Sqr(x10, 5, x15); Mul(x5, x15, x15); + int[] x25 = x5; Sqr(x15, 10, x25); Mul(x10, x25, x25); + int[] x50 = x10; Sqr(x25, 25, x50); Mul(x25, x50, x50); + int[] x75 = x15; Sqr(x50, 25, x75); Mul(x25, x75, x75); + int[] x125 = x25; Sqr(x75, 50, x125); Mul(x50, x125, x125); + int[] x250 = x50; Sqr(x125, 125, x250); Mul(x125, x250, x250); + + int[] t = x125; + Sqr(x250, 2, t); + Mul(t, x, rz); + } + private static void Reduce(int[] z, int c) { int z9 = z[9], t = z9; @@ -509,6 +576,45 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 } } + public static bool SqrtRatioVar(int[] u, int[] v, int[] z) + { + int[] uv3 = Create(); + int[] uv7 = Create(); + + Mul(u, v, uv3); + Sqr(v, uv7); + Mul(uv3, uv7, uv3); + Sqr(uv7, uv7); + Mul(uv7, uv3, uv7); + + int[] t = Create(); + int[] x = Create(); + PowPm5d8(uv7, t, x); + Mul(x, uv3, x); + + int[] vx2 = Create(); + Sqr(x, vx2); + Mul(vx2, v, vx2); + + Sub(vx2, u, t); + Normalize(t); + if (IsZeroVar(t)) + { + Copy(x, 0, z, 0); + return true; + } + + Add(vx2, u, t); + Normalize(t); + if (IsZeroVar(t)) + { + Mul(x, RootNegOne, z); + return true; + } + + return false; + } + public static void Sub(int[] x, int[] y, int[] z) { for (int i = 0; i < Size; ++i) @@ -516,5 +622,18 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 z[i] = x[i] - y[i]; } } + + public static void SubOne(int[] z) + { + z[0] -= 1; + } + + public static void Zero(int[] z) + { + for (int i = 0; i < Size; ++i) + { + z[i] = 0; + } + } } } diff --git a/crypto/src/math/ec/rfc7748/X448.cs b/crypto/src/math/ec/rfc7748/X448.cs index 32a4a9e2a..88e8a5d76 100644 --- a/crypto/src/math/ec/rfc7748/X448.cs +++ b/crypto/src/math/ec/rfc7748/X448.cs @@ -10,14 +10,14 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 private const uint C_A24 = (C_A + 2)/4; // 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE - private static readonly uint[] S_x = new uint[]{ 0x0FFFFFFEU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, + private static readonly uint[] S_x = { 0x0FFFFFFEU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFEU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU }; // 0xF0FAB725013244423ACF03881AFFEB7BDACDD1031C81B9672954459D84C1F823F1BD65643ACE1B5123AC33FF1C69BAF8ACB1197DC99D2720 - private static readonly uint[] PsubS_x = new uint[]{ 0x099d2720U, 0x0b1197dcU, 0x09baf8acU, 0x033ff1c6U, 0x0b5123acU, - 0x0643ace1U, 0x03f1bd65U, 0x084c1f82U, 0x0954459dU, 0x081b9672U, 0x0dd1031cU, 0x0eb7bdacU, 0x03881affU, 0x0423acf0U, - 0x05013244U, 0x0f0fab72U }; + private static readonly uint[] PsubS_x = { 0x099D2720U, 0x0B1197DCU, 0x09BAF8ACU, 0x033FF1C6U, 0x0B5123ACU, + 0x0643ACE1U, 0x03F1BD65U, 0x084C1F82U, 0x0954459DU, 0x081B9672U, 0x0DD1031CU, 0x0EB7BDACU, 0x03881AFFU, 0x0423ACF0U, + 0x05013244U, 0x0F0FAB72U }; private static uint[] precompBase = null; diff --git a/crypto/src/math/ec/rfc7748/X448Field.cs b/crypto/src/math/ec/rfc7748/X448Field.cs index 0c44f1eb5..5a682714d 100644 --- a/crypto/src/math/ec/rfc7748/X448Field.cs +++ b/crypto/src/math/ec/rfc7748/X448Field.cs @@ -1,6 +1,8 @@ using System; using System.Diagnostics; +using Org.BouncyCastle.Math.Raw; + namespace Org.BouncyCastle.Math.EC.Rfc7748 { [CLSCompliantAttribute(false)] @@ -20,6 +22,16 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 } } + public static void AddOne(uint[] z) + { + z[0] += 1; + } + + public static void AddOne(uint[] z, int zOff) + { + z[zOff] += 1; + } + //public static void Apm(int[] x, int[] y, int[] zp, int[] zm) //{ // for (int i = 0; i < Size; ++i) @@ -62,6 +74,16 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 z[8] = z8; z[9] = z9; z[10] = z10; z[11] = z11; z[12] = z12; z[13] = z13; z[14] = z14; z[15] = z15; } + public static void CNegate(int negate, uint[] z) + { + Debug.Assert(negate >> 1 == 0); + + uint[] t = Create(); + Sub(t, z, t); + + Nat.CMov(Size, negate, t, 0, z, 0); + } + public static void Copy(uint[] x, int xOff, uint[] z, int zOff) { for (int i = 0; i < Size; ++i) @@ -166,25 +188,23 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 // z = x^(p-2) = x^(2^448 - 2^224 - 3) // (223 1s) (1 0s) (222 1s) (1 0s) (1 1s) // Addition chain: [1] 2 3 6 9 18 19 37 74 111 [222] [223] - uint[] x2 = Create(); Sqr(x, x2); Mul(x, x2, x2); - uint[] x3 = Create(); Sqr(x2, x3); Mul(x, x3, x3); - uint[] x6 = Create(); Sqr(x3, 3, x6); Mul(x3, x6, x6); - uint[] x9 = Create(); Sqr(x6, 3, x9); Mul(x3, x9, x9); - uint[] x18 = Create(); Sqr(x9, 9, x18); Mul(x9, x18, x18); - uint[] x19 = Create(); Sqr(x18, x19); Mul(x, x19, x19); - uint[] x37 = Create(); Sqr(x19, 18, x37); Mul(x18, x37, x37); - uint[] x74 = Create(); Sqr(x37, 37, x74); Mul(x37, x74, x74); - uint[] x111 = Create(); Sqr(x74, 37, x111); Mul(x37, x111, x111); - uint[] x222 = Create(); Sqr(x111, 111, x222); Mul(x111, x222, x222); - uint[] x223 = Create(); Sqr(x222, x223); Mul(x, x223, x223); uint[] t = Create(); - Sqr(x223, 223, t); - Mul(t, x222, t); + PowPm3d4(x, t); Sqr(t, 2, t); Mul(t, x, z); } + public static bool IsZeroVar(uint[] x) + { + uint d = 0; + for (int i = 0; i < Size; ++i) + { + d |= x[i]; + } + return d == 0U; + } + public static void Mul(uint[] x, uint y, uint[] z) { uint x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4], x5 = x[5], x6 = x[6], x7 = x[7]; @@ -563,6 +583,12 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 z[15] = z15; } + public static void Negate(uint[] x, uint[] z) + { + uint[] zero = Create(); + Sub(zero, x, z); + } + public static void Normalize(uint[] z) { //int x = (z[15] >> (28 - 1)) & 1; @@ -571,6 +597,37 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 Debug.Assert(z[15] >> 28 == 0U); } + public static void One(uint[] z) + { + z[0] = 1U; + for (int i = 1; i < Size; ++i) + { + z[i] = 0; + } + } + + private static void PowPm3d4(uint[] x, uint[] z) + { + // z = x^((p-3)/4) = x^(2^446 - 2^222 - 1) + // (223 1s) (1 0s) (222 1s) + // Addition chain: 1 2 3 6 9 18 19 37 74 111 [222] [223] + uint[] x2 = Create(); Sqr(x, x2); Mul(x, x2, x2); + uint[] x3 = Create(); Sqr(x2, x3); Mul(x, x3, x3); + uint[] x6 = Create(); Sqr(x3, 3, x6); Mul(x3, x6, x6); + uint[] x9 = Create(); Sqr(x6, 3, x9); Mul(x3, x9, x9); + uint[] x18 = Create(); Sqr(x9, 9, x18); Mul(x9, x18, x18); + uint[] x19 = Create(); Sqr(x18, x19); Mul(x, x19, x19); + uint[] x37 = Create(); Sqr(x19, 18, x37); Mul(x18, x37, x37); + uint[] x74 = Create(); Sqr(x37, 37, x74); Mul(x37, x74, x74); + uint[] x111 = Create(); Sqr(x74, 37, x111); Mul(x37, x111, x111); + uint[] x222 = Create(); Sqr(x111, 111, x222); Mul(x111, x222, x222); + uint[] x223 = Create(); Sqr(x222, x223); Mul(x, x223, x223); + + uint[] t = Create(); + Sqr(x223, 223, t); + Mul(t, x222, z); + } + private static void Reduce(uint[] z, int c) { uint z15 = z[15]; @@ -836,6 +893,38 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 } } + public static bool SqrtRatioVar(uint[] u, uint[] v, uint[] z) + { + uint[] u3v = Create(); + uint[] u5v3 = Create(); + + Sqr(u, u3v); + Mul(u3v, v, u3v); + Sqr(u3v, u5v3); + Mul(u3v, u, u3v); + Mul(u5v3, u, u5v3); + Mul(u5v3, v, u5v3); + + uint[] x = Create(); + PowPm3d4(u5v3, x); + Mul(x, u3v, x); + + uint[] t = Create(); + Sqr(x, t); + Mul(t, v, t); + + Sub(u, t, t); + Normalize(t); + + if (IsZeroVar(t)) + { + Copy(x, 0, z, 0); + return true; + } + + return false; + } + public static void Sub(uint[] x, uint[] y, uint[] z) { uint x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4], x5 = x[5], x6 = x[6], x7 = x[7]; @@ -900,5 +989,13 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748 z[14] = z14; z[15] = z15; } + + public static void Zero(uint[] z) + { + for (int i = 0; i < Size; ++i) + { + z[i] = 0; + } + } } } diff --git a/crypto/src/math/ec/rfc8032/Ed25519.cs b/crypto/src/math/ec/rfc8032/Ed25519.cs new file mode 100644 index 000000000..ff4587cb2 --- /dev/null +++ b/crypto/src/math/ec/rfc8032/Ed25519.cs @@ -0,0 +1,937 @@ +using System; +using System.Diagnostics; +using System.Runtime.CompilerServices; + +using Org.BouncyCastle.Crypto.Digests; +using Org.BouncyCastle.Math.EC.Rfc7748; +using Org.BouncyCastle.Math.Raw; +using Org.BouncyCastle.Utilities; + +namespace Org.BouncyCastle.Math.EC.Rfc8032 +{ + public abstract class Ed25519 + { + private const long M28L = 0x0FFFFFFFL; + private const long M32L = 0xFFFFFFFFL; + + private const int PointBytes = 32; + private const int ScalarUints = 8; + private const int ScalarBytes = ScalarUints * 4; + + public static readonly int PublicKeySize = PointBytes; + public static readonly int SecretKeySize = 32; + public static readonly int SignatureSize = PointBytes + ScalarBytes; + + //private static readonly byte[] Dom2Prefix = Strings.ToByteArray("SigEd25519 no Ed25519 collisions"); + + private static readonly uint[] P = { 0xFFFFFFEDU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0x7FFFFFFFU }; + private static readonly uint[] L = { 0x5CF5D3EDU, 0x5812631AU, 0xA2F79CD6U, 0x14DEF9DEU, 0x00000000U, 0x00000000U, 0x00000000U, 0x10000000U }; + + private const int L0 = unchecked((int)0xFCF5D3ED); // L0:26/-- + private const int L1 = 0x012631A6; // L1:24/22 + private const int L2 = 0x079CD658; // L2:27/-- + private const int L3 = unchecked((int)0xFF9DEA2F); // L3:23/-- + private const int L4 = 0x000014DF; // L4:12/11 + + private static readonly int[] B_x = { 0x0325D51A, 0x018B5823, 0x007B2C95, 0x0304A92D, 0x00D2598E, 0x01D6DC5C, + 0x01388C7F, 0x013FEC0A, 0x029E6B72, 0x0042D26D }; + private static readonly int[] B_y = { 0x02666658, 0x01999999, 0x00666666, 0x03333333, 0x00CCCCCC, 0x02666666, + 0x01999999, 0x00666666, 0x03333333, 0x00CCCCCC, }; + private static readonly int[] C_d = { 0x035978A3, 0x02D37284, 0x018AB75E, 0x026A0A0E, 0x0000E014, 0x0379E898, + 0x01D01E5D, 0x01E738CC, 0x03715B7F, 0x00A406D9 }; + private static readonly int[] C_d2 = { 0x02B2F159, 0x01A6E509, 0x01156EBD, 0x00D4141D, 0x0001C029, 0x02F3D130, + 0x03A03CBB, 0x01CE7198, 0x02E2B6FF, 0x00480DB3 }; + private static readonly int[] C_d4 = { 0x0165E2B2, 0x034DCA13, 0x002ADD7A, 0x01A8283B, 0x00038052, 0x01E7A260, + 0x03407977, 0x019CE331, 0x01C56DFF, 0x00901B67 }; + + private const int WnafWidthBase = 7; + + private const int PrecompBlocks = 8; + private const int PrecompTeeth = 4; + private const int PrecompSpacing = 8; + private const int PrecompPoints = 1 << (PrecompTeeth - 1); + private const int PrecompMask = PrecompPoints - 1; + + // TODO[ed25519] Convert to PointPrecomp + private static PointExt[] precompBaseTable = null; + private static int[] precompBase = null; + + private class PointAccum + { + internal int[] x = X25519Field.Create(); + internal int[] y = X25519Field.Create(); + internal int[] z = X25519Field.Create(); + internal int[] u = X25519Field.Create(); + internal int[] v = X25519Field.Create(); + } + + private class PointExt + { + internal int[] x = X25519Field.Create(); + internal int[] y = X25519Field.Create(); + internal int[] z = X25519Field.Create(); + internal int[] t = X25519Field.Create(); + } + + private class PointPrecomp + { + internal int[] ypx_h = X25519Field.Create(); + internal int[] ymx_h = X25519Field.Create(); + internal int[] xyd = X25519Field.Create(); + } + + private static byte[] CalculateS(byte[] r, byte[] k, byte[] s) + { + uint[] t = new uint[ScalarUints * 2]; DecodeScalar(r, 0, t); + uint[] u = new uint[ScalarUints]; DecodeScalar(k, 0, u); + uint[] v = new uint[ScalarUints]; DecodeScalar(s, 0, v); + + Nat256.MulAddTo(u, v, t); + + byte[] result = new byte[ScalarBytes * 2]; + for (int i = 0; i < t.Length; ++i) + { + Encode32(t[i], result, i * 4); + } + return ReduceScalar(result); + } + + private static bool CheckPointVar(byte[] p) + { + uint[] t = new uint[8]; + Decode32(p, 0, t, 0, 8); + t[7] &= 0x7FFFFFFFU; + return !Nat256.Gte(t, P); + } + + private static bool CheckScalarVar(byte[] s) + { + uint[] n = new uint[ScalarUints]; + DecodeScalar(s, 0, n); + return !Nat256.Gte(n, L); + } + + private static uint Decode24(byte[] bs, int off) + { + uint n = bs[off]; + n |= (uint)bs[++off] << 8; + n |= (uint)bs[++off] << 16; + return n; + } + + private static uint Decode32(byte[] bs, int off) + { + uint n = bs[off]; + n |= (uint)bs[++off] << 8; + n |= (uint)bs[++off] << 16; + n |= (uint)bs[++off] << 24; + return n; + } + + private static void Decode32(byte[] bs, int bsOff, uint[] n, int nOff, int nLen) + { + for (int i = 0; i < nLen; ++i) + { + n[nOff + i] = Decode32(bs, bsOff + i * 4); + } + } + + private static bool DecodePointVar(byte[] p, int pOff, bool negate, PointExt r) + { + byte[] py = Arrays.CopyOfRange(p, pOff, pOff + PointBytes); + if (!CheckPointVar(py)) + { + return false; + } + + int x_0 = (py[PointBytes - 1] & 0x80) >> 7; + py[PointBytes - 1] &= 0x7F; + + X25519Field.Decode(py, 0, r.y); + + int[] u = X25519Field.Create(); + int[] v = X25519Field.Create(); + + X25519Field.Sqr(r.y, u); + X25519Field.Mul(C_d, u, v); + X25519Field.SubOne(u); + X25519Field.AddOne(v); + + if (!X25519Field.SqrtRatioVar(u, v, r.x)) + { + return false; + } + + X25519Field.Normalize(r.x); + if (x_0 == 1 && X25519Field.IsZeroVar(r.x)) + { + return false; + } + + if (negate ^ (x_0 != (r.x[0] & 1))) + { + X25519Field.Negate(r.x, r.x); + } + + PointExtendXY(r); + return true; + } + + private static void DecodeScalar(byte[] k, int kOff, uint[] n) + { + Decode32(k, kOff, n, 0, ScalarUints); + } + + private static void Encode24(uint n, byte[] bs, int off) + { + bs[off] = (byte)(n); + bs[++off] = (byte)(n >> 8); + bs[++off] = (byte)(n >> 16); + } + + private static void Encode32(uint n, byte[] bs, int off) + { + bs[off] = (byte)(n); + bs[++off] = (byte)(n >> 8); + bs[++off] = (byte)(n >> 16); + bs[++off] = (byte)(n >> 24); + } + + private static void Encode56(ulong n, byte[] bs, int off) + { + Encode32((uint)n, bs, off); + Encode24((uint)(n >> 32), bs, off + 4); + } + + private static void EncodePoint(PointAccum p, byte[] r, int rOff) + { + int[] x = X25519Field.Create(); + int[] y = X25519Field.Create(); + + X25519Field.Inv(p.z, y); + X25519Field.Mul(p.x, y, x); + X25519Field.Mul(p.y, y, y); + X25519Field.Normalize(x); + X25519Field.Normalize(y); + + X25519Field.Encode(y, r, rOff); + r[rOff + PointBytes - 1] |= (byte)((x[0] & 1) << 7); + } + + public static void GeneratePublicKey(byte[] sk, int skOff, byte[] pk, int pkOff) + { + Sha512Digest d = new Sha512Digest(); + byte[] h = new byte[d.GetDigestSize()]; + + d.BlockUpdate(sk, skOff, SecretKeySize); + d.DoFinal(h, 0); + + byte[] s = new byte[ScalarBytes]; + PruneScalar(h, 0, s); + + ScalarMultBaseEncoded(s, pk, pkOff); + } + + private static sbyte[] GetWnaf(uint[] n, int width) + { + Debug.Assert(n[ScalarUints - 1] >> 31 == 0); + + uint[] t = new uint[ScalarUints * 2]; + { + uint c = 0; + int tPos = t.Length, i = ScalarUints; + while (--i >= 0) + { + uint next = n[i]; + t[--tPos] = (next >> 16) | (c << 16); + t[--tPos] = c = next; + } + } + + sbyte[] ws = new sbyte[256]; + + uint pow2 = 1U << width; + uint mask = pow2 - 1U; + uint sign = pow2 >> 1; + + uint carry = 0U; + int j = 0; + for (int i = 0; i < t.Length; ++i, j -= 16) + { + uint word = t[i]; + while (j < 16) + { + uint word16 = word >> j; + uint bit = word16 & 1U; + + if (bit == carry) + { + ++j; + continue; + } + + uint digit = (word16 & mask) + carry; + carry = digit & sign; + digit -= (carry << 1); + carry >>= (width - 1); + + ws[(i << 4) + j] = (sbyte)digit; + + j += width; + } + } + + Debug.Assert(carry == 0); + + return ws; + } + + private static void ImplSign(Sha512Digest d, byte[] h, byte[] s, byte[] pk, int pkOff, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) + { + d.BlockUpdate(h, ScalarBytes, ScalarBytes); + d.BlockUpdate(m, mOff, mLen); + d.DoFinal(h, 0); + + byte[] r = ReduceScalar(h); + byte[] R = new byte[PointBytes]; + ScalarMultBaseEncoded(r, R, 0); + + d.BlockUpdate(R, 0, PointBytes); + d.BlockUpdate(pk, 0, PointBytes); + d.BlockUpdate(m, mOff, mLen); + d.DoFinal(h, 0); + + byte[] k = ReduceScalar(h); + byte[] S = CalculateS(r, k, s); + + Array.Copy(R, 0, sig, sigOff, PointBytes); + Array.Copy(S, 0, sig, sigOff + PointBytes, ScalarBytes); + } + + private static void PointAddVar(bool negate, PointExt p, PointAccum r) + { + int[] A = X25519Field.Create(); + int[] B = X25519Field.Create(); + int[] C = X25519Field.Create(); + int[] D = X25519Field.Create(); + int[] E = r.u; + int[] F = X25519Field.Create(); + int[] G = X25519Field.Create(); + int[] H = r.v; + + int[] c, d, f, g; + if (negate) + { + c = D; d = C; f = G; g = F; + } + else + { + c = C; d = D; f = F; g = G; + } + + X25519Field.Apm(r.y, r.x, B, A); + X25519Field.Apm(p.y, p.x, d, c); + X25519Field.Mul(A, C, A); + X25519Field.Mul(B, D, B); + X25519Field.Mul(r.u, r.v, C); + X25519Field.Mul(C, p.t, C); + X25519Field.Mul(C, C_d2, C); + X25519Field.Mul(r.z, p.z, D); + X25519Field.Add(D, D, D); + X25519Field.Apm(B, A, H, E); + X25519Field.Apm(D, C, g, f); + X25519Field.Carry(g); + X25519Field.Mul(E, F, r.x); + X25519Field.Mul(G, H, r.y); + X25519Field.Mul(F, G, r.z); + } + + private static void PointAddVar(bool negate, PointExt p, PointExt q, PointExt r) + { + int[] A = X25519Field.Create(); + int[] B = X25519Field.Create(); + int[] C = X25519Field.Create(); + int[] D = X25519Field.Create(); + int[] E = X25519Field.Create(); + int[] F = X25519Field.Create(); + int[] G = X25519Field.Create(); + int[] H = X25519Field.Create(); + + int[] c, d, f, g; + if (negate) + { + c = D; d = C; f = G; g = F; + } + else + { + c = C; d = D; f = F; g = G; + } + + X25519Field.Apm(p.y, p.x, B, A); + X25519Field.Apm(q.y, q.x, d, c); + X25519Field.Mul(A, C, A); + X25519Field.Mul(B, D, B); + X25519Field.Mul(p.t, q.t, C); + X25519Field.Mul(C, C_d2, C); + X25519Field.Mul(p.z, q.z, D); + X25519Field.Add(D, D, D); + X25519Field.Apm(B, A, H, E); + X25519Field.Apm(D, C, g, f); + X25519Field.Carry(g); + X25519Field.Mul(E, F, r.x); + X25519Field.Mul(G, H, r.y); + X25519Field.Mul(F, G, r.z); + X25519Field.Mul(E, H, r.t); + } + + private static void PointAddPrecomp(PointPrecomp p, PointAccum r) + { + int[] A = X25519Field.Create(); + int[] B = X25519Field.Create(); + int[] C = X25519Field.Create(); + int[] E = r.u; + int[] F = X25519Field.Create(); + int[] G = X25519Field.Create(); + int[] H = r.v; + + X25519Field.Apm(r.y, r.x, B, A); + X25519Field.Mul(A, p.ymx_h, A); + X25519Field.Mul(B, p.ypx_h, B); + X25519Field.Mul(r.u, r.v, C); + X25519Field.Mul(C, p.xyd, C); + X25519Field.Apm(B, A, H, E); + X25519Field.Apm(r.z, C, G, F); + X25519Field.Carry(G); + X25519Field.Mul(E, F, r.x); + X25519Field.Mul(G, H, r.y); + X25519Field.Mul(F, G, r.z); + } + + private static PointExt PointCopy(PointAccum p) + { + PointExt r = new PointExt(); + X25519Field.Copy(p.x, 0, r.x, 0); + X25519Field.Copy(p.y, 0, r.y, 0); + X25519Field.Copy(p.z, 0, r.z, 0); + X25519Field.Mul(p.u, p.v, r.t); + return r; + } + + private static PointExt PointCopy(PointExt p) + { + PointExt r = new PointExt(); + X25519Field.Copy(p.x, 0, r.x, 0); + X25519Field.Copy(p.y, 0, r.y, 0); + X25519Field.Copy(p.z, 0, r.z, 0); + X25519Field.Copy(p.t, 0, r.t, 0); + return r; + } + + private static void PointDouble(PointAccum r) + { + int[] A = X25519Field.Create(); + int[] B = X25519Field.Create(); + int[] C = X25519Field.Create(); + int[] E = r.u; + int[] F = X25519Field.Create(); + int[] G = X25519Field.Create(); + int[] H = r.v; + + X25519Field.Sqr(r.x, A); + X25519Field.Sqr(r.y, B); + X25519Field.Sqr(r.z, C); + X25519Field.Add(C, C, C); + X25519Field.Apm(A, B, H, G); + X25519Field.Add(r.x, r.y, E); + X25519Field.Sqr(E, E); + X25519Field.Sub(H, E, E); + X25519Field.Add(C, G, F); + X25519Field.Carry(F); + X25519Field.Mul(E, F, r.x); + X25519Field.Mul(G, H, r.y); + X25519Field.Mul(F, G, r.z); + } + + private static void PointExtendXY(PointAccum p) + { + X25519Field.One(p.z); + X25519Field.Copy(p.x, 0, p.u, 0); + X25519Field.Copy(p.y, 0, p.v, 0); + } + + private static void PointExtendXY(PointExt p) + { + X25519Field.One(p.z); + X25519Field.Mul(p.x, p.y, p.t); + } + + private static void PointLookup(int block, int index, PointPrecomp p) + { + Debug.Assert(0 <= block && block < PrecompBlocks); + Debug.Assert(0 <= index && index < PrecompPoints); + + int off = block * PrecompPoints * 3 * X25519Field.Size; + + for (int i = 0; i < PrecompPoints; ++i) + { + int mask = ((i ^ index) - 1) >> 31; + Nat.CMov(X25519Field.Size, mask, precompBase, off, p.ypx_h, 0); off += X25519Field.Size; + Nat.CMov(X25519Field.Size, mask, precompBase, off, p.ymx_h, 0); off += X25519Field.Size; + Nat.CMov(X25519Field.Size, mask, precompBase, off, p.xyd, 0); off += X25519Field.Size; + } + } + + private static PointExt[] PointPrecompVar(PointExt p, int count) + { + Debug.Assert(count > 0); + + PointExt d = new PointExt(); + PointAddVar(false, p, p, d); + + PointExt[] table = new PointExt[count]; + table[0] = PointCopy(p); + for (int i = 1; i < count; ++i) + { + PointAddVar(false, table[i - 1], d, table[i] = new PointExt()); + } + return table; + } + + private static void PointSetNeutral(PointAccum p) + { + X25519Field.Zero(p.x); + X25519Field.One(p.y); + X25519Field.One(p.z); + X25519Field.Zero(p.u); + X25519Field.One(p.v); + } + + private static void PointSetNeutral(PointExt p) + { + X25519Field.Zero(p.x); + X25519Field.One(p.y); + X25519Field.One(p.z); + X25519Field.Zero(p.t); + } + + [MethodImpl(MethodImplOptions.Synchronized)] + public static void Precompute() + { + if (precompBase != null) + { + return; + } + + // Precomputed table for the base point in verification ladder + { + PointExt b = new PointExt(); + X25519Field.Copy(B_x, 0, b.x, 0); + X25519Field.Copy(B_y, 0, b.y, 0); + PointExtendXY(b); + + precompBaseTable = PointPrecompVar(b, 1 << (WnafWidthBase - 2)); + } + + PointAccum p = new PointAccum(); + X25519Field.Copy(B_x, 0, p.x, 0); + X25519Field.Copy(B_y, 0, p.y, 0); + PointExtendXY(p); + + precompBase = new int[PrecompBlocks * PrecompPoints * 3 * X25519Field.Size]; + + int off = 0; + for (int b = 0; b < PrecompBlocks; ++b) + { + PointExt[] ds = new PointExt[PrecompTeeth]; + + PointExt sum = new PointExt(); + PointSetNeutral(sum); + + for (int t = 0; t < PrecompTeeth; ++t) + { + PointExt q = PointCopy(p); + PointAddVar(true, sum, q, sum); + PointDouble(p); + + ds[t] = PointCopy(p); + + for (int s = 1; s < PrecompSpacing; ++s) + { + PointDouble(p); + } + } + + PointExt[] points = new PointExt[PrecompPoints]; + int k = 0; + points[k++] = sum; + + for (int t = 0; t < (PrecompTeeth - 1); ++t) + { + int size = 1 << t; + for (int j = 0; j < size; ++j, ++k) + { + PointAddVar(false, points[k - size], ds[t], points[k] = new PointExt()); + } + } + + Debug.Assert(k == PrecompPoints); + + for (int i = 0; i < PrecompPoints; ++i) + { + PointExt q = points[i]; + + int[] x = X25519Field.Create(); + int[] y = X25519Field.Create(); + + X25519Field.Add(q.z, q.z, x); + // TODO[ed25519] Batch inversion + X25519Field.Inv(x, y); + X25519Field.Mul(q.x, y, x); + X25519Field.Mul(q.y, y, y); + + PointPrecomp r = new PointPrecomp(); + X25519Field.Apm(y, x, r.ypx_h, r.ymx_h); + X25519Field.Mul(x, y, r.xyd); + X25519Field.Mul(r.xyd, C_d4, r.xyd); + + X25519Field.Normalize(r.ypx_h); + X25519Field.Normalize(r.ymx_h); + //X25519Field.Normalize(r.xyd); + + X25519Field.Copy(r.ypx_h, 0, precompBase, off); off += X25519Field.Size; + X25519Field.Copy(r.ymx_h, 0, precompBase, off); off += X25519Field.Size; + X25519Field.Copy(r.xyd, 0, precompBase, off); off += X25519Field.Size; + } + } + + Debug.Assert(off == precompBase.Length); + } + + private static void PruneScalar(byte[] n, int nOff, byte[] r) + { + Array.Copy(n, nOff, r, 0, ScalarBytes); + + r[0] &= 0xF8; + r[ScalarBytes - 1] &= 0x7F; + r[ScalarBytes - 1] |= 0x40; + } + + private static byte[] ReduceScalar(byte[] n) + { + long x00 = Decode32(n, 0) & M32L; // x00:32/-- + long x01 = (Decode24(n, 4) << 4) & M32L; // x01:28/-- + long x02 = Decode32(n, 7) & M32L; // x02:32/-- + long x03 = (Decode24(n, 11) << 4) & M32L; // x03:28/-- + long x04 = Decode32(n, 14) & M32L; // x04:32/-- + long x05 = (Decode24(n, 18) << 4) & M32L; // x05:28/-- + long x06 = Decode32(n, 21) & M32L; // x06:32/-- + long x07 = (Decode24(n, 25) << 4) & M32L; // x07:28/-- + long x08 = Decode32(n, 28) & M32L; // x08:32/-- + long x09 = (Decode24(n, 32) << 4) & M32L; // x09:28/-- + long x10 = Decode32(n, 35) & M32L; // x10:32/-- + long x11 = (Decode24(n, 39) << 4) & M32L; // x11:28/-- + long x12 = Decode32(n, 42) & M32L; // x12:32/-- + long x13 = (Decode24(n, 46) << 4) & M32L; // x13:28/-- + long x14 = Decode32(n, 49) & M32L; // x14:32/-- + long x15 = (Decode24(n, 53) << 4) & M32L; // x15:28/-- + long x16 = Decode32(n, 56) & M32L; // x16:32/-- + long x17 = (Decode24(n, 60) << 4) & M32L; // x17:28/-- + long x18 = n[63] & 0xFFL; // x18:08/-- + long t; + + //x18 += (x17 >> 28); x17 &= M28L; + x09 -= x18 * L0; // x09:34/28 + x10 -= x18 * L1; // x10:33/30 + x11 -= x18 * L2; // x11:35/28 + x12 -= x18 * L3; // x12:32/31 + x13 -= x18 * L4; // x13:28/21 + + x17 += (x16 >> 28); x16 &= M28L; // x17:28/--, x16:28/-- + x08 -= x17 * L0; // x08:54/32 + x09 -= x17 * L1; // x09:52/51 + x10 -= x17 * L2; // x10:55/34 + x11 -= x17 * L3; // x11:51/36 + x12 -= x17 * L4; // x12:41/-- + + //x16 += (x15 >> 28); x15 &= M28L; + x07 -= x16 * L0; // x07:54/28 + x08 -= x16 * L1; // x08:54/53 + x09 -= x16 * L2; // x09:55/53 + x10 -= x16 * L3; // x10:55/52 + x11 -= x16 * L4; // x11:51/41 + + x15 += (x14 >> 28); x14 &= M28L; // x15:28/--, x14:28/-- + x06 -= x15 * L0; // x06:54/32 + x07 -= x15 * L1; // x07:54/53 + x08 -= x15 * L2; // x08:56/-- + x09 -= x15 * L3; // x09:55/54 + x10 -= x15 * L4; // x10:55/53 + + //x14 += (x13 >> 28); x13 &= M28L; + x05 -= x14 * L0; // x05:54/28 + x06 -= x14 * L1; // x06:54/53 + x07 -= x14 * L2; // x07:56/-- + x08 -= x14 * L3; // x08:56/51 + x09 -= x14 * L4; // x09:56/-- + + x13 += (x12 >> 28); x12 &= M28L; // x13:28/22, x12:28/-- + x04 -= x13 * L0; // x04:54/49 + x05 -= x13 * L1; // x05:54/53 + x06 -= x13 * L2; // x06:56/-- + x07 -= x13 * L3; // x07:56/52 + x08 -= x13 * L4; // x08:56/52 + + x12 += (x11 >> 28); x11 &= M28L; // x12:28/24, x11:28/-- + x03 -= x12 * L0; // x03:54/49 + x04 -= x12 * L1; // x04:54/51 + x05 -= x12 * L2; // x05:56/-- + x06 -= x12 * L3; // x06:56/52 + x07 -= x12 * L4; // x07:56/53 + + x11 += (x10 >> 28); x10 &= M28L; // x11:29/--, x10:28/-- + x02 -= x11 * L0; // x02:55/32 + x03 -= x11 * L1; // x03:55/-- + x04 -= x11 * L2; // x04:56/55 + x05 -= x11 * L3; // x05:56/52 + x06 -= x11 * L4; // x06:56/53 + + x10 += (x09 >> 28); x09 &= M28L; // x10:29/--, x09:28/-- + x01 -= x10 * L0; // x01:55/28 + x02 -= x10 * L1; // x02:55/54 + x03 -= x10 * L2; // x03:56/55 + x04 -= x10 * L3; // x04:57/-- + x05 -= x10 * L4; // x05:56/53 + + x08 += (x07 >> 28); x07 &= M28L; // x08:56/53, x07:28/-- + x09 += (x08 >> 28); x08 &= M28L; // x09:29/25, x08:28/-- + + t = (x08 >> 27) & 1L; + x09 += t; // x09:29/26 + + x00 -= x09 * L0; // x00:55/53 + x01 -= x09 * L1; // x01:55/54 + x02 -= x09 * L2; // x02:57/-- + x03 -= x09 * L3; // x03:57/-- + x04 -= x09 * L4; // x04:57/42 + + x01 += (x00 >> 28); x00 &= M28L; + x02 += (x01 >> 28); x01 &= M28L; + x03 += (x02 >> 28); x02 &= M28L; + x04 += (x03 >> 28); x03 &= M28L; + x05 += (x04 >> 28); x04 &= M28L; + x06 += (x05 >> 28); x05 &= M28L; + x07 += (x06 >> 28); x06 &= M28L; + x08 += (x07 >> 28); x07 &= M28L; + x09 = (x08 >> 28); x08 &= M28L; + + x09 -= t; + + Debug.Assert(x09 == 0L || x09 == -1L); + + x00 += x09 & L0; + x01 += x09 & L1; + x02 += x09 & L2; + x03 += x09 & L3; + x04 += x09 & L4; + + x01 += (x00 >> 28); x00 &= M28L; + x02 += (x01 >> 28); x01 &= M28L; + x03 += (x02 >> 28); x02 &= M28L; + x04 += (x03 >> 28); x03 &= M28L; + x05 += (x04 >> 28); x04 &= M28L; + x06 += (x05 >> 28); x05 &= M28L; + x07 += (x06 >> 28); x06 &= M28L; + x08 += (x07 >> 28); x07 &= M28L; + + byte[] r = new byte[ScalarBytes]; + Encode56((ulong)(x00 | (x01 << 28)), r, 0); + Encode56((ulong)(x02 | (x03 << 28)), r, 7); + Encode56((ulong)(x04 | (x05 << 28)), r, 14); + Encode56((ulong)(x06 | (x07 << 28)), r, 21); + Encode32((uint)x08, r, 28); + return r; + } + + private static void ScalarMultBase(byte[] k, PointAccum r) + { + Precompute(); + + PointSetNeutral(r); + + uint[] n = new uint[ScalarUints]; + DecodeScalar(k, 0, n); + + // Recode the scalar into signed-digit form, then group comb bits in each block + { + uint c1 = Nat.CAdd(ScalarUints, ~(int)n[0] & 1, n, L, n); Debug.Assert(c1 == 0); + uint c2 = Nat.ShiftDownBit(ScalarUints, n, 1U); Debug.Assert(c2 == (1U << 31)); + + for (int i = 0; i < ScalarUints; ++i) + { + n[i] = Interleave.Shuffle2(n[i]); + } + } + + PointPrecomp p = new PointPrecomp(); + + int cOff = (PrecompSpacing - 1) * PrecompTeeth; + for (; ; ) + { + for (int b = 0; b < PrecompBlocks; ++b) + { + uint w = n[b] >> cOff; + int sign = (int)(w >> (PrecompTeeth - 1)) & 1; + int abs = ((int)w ^ -sign) & PrecompMask; + + Debug.Assert(sign == 0 || sign == 1); + Debug.Assert(0 <= abs && abs < PrecompPoints); + + PointLookup(b, abs, p); + + X25519Field.CSwap(sign, p.ypx_h, p.ymx_h); + X25519Field.CNegate(sign, p.xyd); + + PointAddPrecomp(p, r); + } + + if ((cOff -= PrecompTeeth) < 0) + { + break; + } + + PointDouble(r); + } + } + + private static void ScalarMultBaseEncoded(byte[] k, byte[] r, int rOff) + { + PointAccum p = new PointAccum(); + ScalarMultBase(k, p); + EncodePoint(p, r, rOff); + } + + private static void ScalarMultStraussVar(uint[] nb, uint[] np, PointExt p, PointAccum r) + { + Precompute(); + + int width = 5; + + sbyte[] ws_b = GetWnaf(nb, WnafWidthBase); + sbyte[] ws_p = GetWnaf(np, width); + + PointExt[] tp = PointPrecompVar(p, 1 << (width - 2)); + + PointSetNeutral(r); + + int bit = 255; + while (bit > 0 && (ws_b[bit] | ws_p[bit]) == 0) + { + --bit; + } + + for (; ; ) + { + int wb = ws_b[bit]; + if (wb != 0) + { + int sign = wb >> 31; + int index = (wb ^ sign) >> 1; + + PointAddVar((sign != 0), precompBaseTable[index], r); + } + + int wp = ws_p[bit]; + if (wp != 0) + { + int sign = wp >> 31; + int index = (wp ^ sign) >> 1; + + PointAddVar((sign != 0), tp[index], r); + } + + if (--bit < 0) + { + break; + } + + PointDouble(r); + } + } + + public static void Sign(byte[] sk, int skOff, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) + { + Sha512Digest d = new Sha512Digest(); + byte[] h = new byte[d.GetDigestSize()]; + + d.BlockUpdate(sk, skOff, SecretKeySize); + d.DoFinal(h, 0); + + byte[] s = new byte[ScalarBytes]; + PruneScalar(h, 0, s); + + byte[] pk = new byte[PointBytes]; + ScalarMultBaseEncoded(s, pk, 0); + + ImplSign(d, h, s, pk, 0, m, mOff, mLen, sig, sigOff); + } + + public static void Sign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) + { + Sha512Digest d = new Sha512Digest(); + byte[] h = new byte[d.GetDigestSize()]; + + d.BlockUpdate(sk, skOff, SecretKeySize); + d.DoFinal(h, 0); + + byte[] s = new byte[ScalarBytes]; + PruneScalar(h, 0, s); + + ImplSign(d, h, s, pk, pkOff, m, mOff, mLen, sig, sigOff); + } + + public static bool Verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] m, int mOff, int mLen) + { + byte[] R = Arrays.CopyOfRange(sig, sigOff, sigOff + PointBytes); + byte[] S = Arrays.CopyOfRange(sig, sigOff + PointBytes, sigOff + SignatureSize); + + if (!CheckPointVar(R)) + { + return false; + } + if (!CheckScalarVar(S)) + { + return false; + } + + PointExt pA = new PointExt(); + if (!DecodePointVar(pk, pkOff, true, pA)) + { + return false; + } + + Sha512Digest d = new Sha512Digest(); + byte[] h = new byte[d.GetDigestSize()]; + + d.BlockUpdate(R, 0, PointBytes); + d.BlockUpdate(pk, pkOff, PointBytes); + d.BlockUpdate(m, mOff, mLen); + d.DoFinal(h, 0); + + byte[] k = ReduceScalar(h); + + uint[] nS = new uint[ScalarUints]; + DecodeScalar(S, 0, nS); + + uint[] nA = new uint[ScalarUints]; + DecodeScalar(k, 0, nA); + + PointAccum pR = new PointAccum(); + ScalarMultStraussVar(nS, nA, pA, pR); + + byte[] check = new byte[PointBytes]; + EncodePoint(pR, check, 0); + + return Arrays.AreEqual(check, R); + } + } +} diff --git a/crypto/src/math/ec/rfc8032/Ed448.cs b/crypto/src/math/ec/rfc8032/Ed448.cs new file mode 100644 index 000000000..52c215160 --- /dev/null +++ b/crypto/src/math/ec/rfc8032/Ed448.cs @@ -0,0 +1,1067 @@ +using System; +using System.Diagnostics; +using System.Runtime.CompilerServices; + +using Org.BouncyCastle.Crypto.Digests; +using Org.BouncyCastle.Math.EC.Rfc7748; +using Org.BouncyCastle.Math.Raw; +using Org.BouncyCastle.Utilities; + +namespace Org.BouncyCastle.Math.EC.Rfc8032 +{ + public abstract class Ed448 + { + private const ulong M26UL = 0x03FFFFFFUL; + private const ulong M28UL = 0x0FFFFFFFUL; + + private const int PointBytes = 57; + private const int ScalarUints = 14; + private const int ScalarBytes = ScalarUints * 4 + 1; + + public static readonly int PublicKeySize = PointBytes; + public static readonly int SecretKeySize = 57; + public static readonly int SignatureSize = PointBytes + ScalarBytes; + + private static readonly byte[] Dom4Prefix = Strings.ToByteArray("SigEd448"); + + private static readonly uint[] P = { 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, + 0xFFFFFFFEU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU }; + private static readonly uint[] L = { 0xAB5844F3U, 0x2378C292U, 0x8DC58F55U, 0x216CC272U, 0xAED63690U, 0xC44EDB49U, 0x7CCA23E9U, + 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0x3FFFFFFFU }; + private static readonly BigInteger N = Nat.ToBigInteger(L.Length, L); + + private const int L_0 = 0x04A7BB0D; // L_0:26/24 + private const int L_1 = 0x0873D6D5; // L_1:27/23 + private const int L_2 = 0x0A70AADC; // L_2:27/26 + private const int L_3 = 0x03D8D723; // L_3:26/-- + private const int L_4 = 0x096FDE93; // L_4:27/25 + private const int L_5 = 0x0B65129C; // L_5:27/26 + private const int L_6 = 0x063BB124; // L_6:27/-- + private const int L_7 = 0x08335DC1; // L_7:27/22 + + private const int L4_0 = 0x029EEC34; // L4_0:25/24 + private const int L4_1 = 0x01CF5B55; // L4_1:25/-- + private const int L4_2 = 0x09C2AB72; // L4_2:27/25 + private const int L4_3 = 0x0F635C8E; // L4_3:28/-- + private const int L4_4 = 0x05BF7A4C; // L4_4:26/25 + private const int L4_5 = 0x0D944A72; // L4_5:28/-- + private const int L4_6 = 0x08EEC492; // L4_6:27/24 + private const int L4_7 = 0x20CD7705; // L4_7:29/24 + + private static readonly uint[] B_x = { 0x070CC05EU, 0x026A82BCU, 0x00938E26U, 0x080E18B0U, 0x0511433BU, 0x0F72AB66U, 0x0412AE1AU, + 0x0A3D3A46U, 0x0A6DE324U, 0x00F1767EU, 0x04657047U, 0x036DA9E1U, 0x05A622BFU, 0x0ED221D1U, 0x066BED0DU, 0x04F1970CU }; + private static readonly uint[] B_y = { 0x0230FA14U, 0x008795BFU, 0x07C8AD98U, 0x0132C4EDU, 0x09C4FDBDU, 0x01CE67C3U, 0x073AD3FFU, + 0x005A0C2DU, 0x07789C1EU, 0x0A398408U, 0x0A73736CU, 0x0C7624BEU, 0x003756C9U, 0x02488762U, 0x016EB6BCU, 0x0693F467U }; + private const int C_d = -39081; + + private const int WnafWidthBase = 7; + + private const int PrecompBlocks = 5; + private const int PrecompTeeth = 5; + private const int PrecompSpacing = 18; + private const int PrecompPoints = 1 << (PrecompTeeth - 1); + private const int PrecompMask = PrecompPoints - 1; + + // TODO[ed448] Convert to PointPrecomp + private static PointExt[] precompBaseTable = null; + private static uint[] precompBase = null; + + private class PointExt + { + internal uint[] x = X448Field.Create(); + internal uint[] y = X448Field.Create(); + internal uint[] z = X448Field.Create(); + } + + private class PointPrecomp + { + internal uint[] x = X448Field.Create(); + internal uint[] y = X448Field.Create(); + } + + private static byte[] CalculateS(byte[] r, byte[] k, byte[] s) + { + uint[] t = new uint[ScalarUints * 2]; DecodeScalar(r, 0, t); + uint[] u = new uint[ScalarUints]; DecodeScalar(k, 0, u); + uint[] v = new uint[ScalarUints]; DecodeScalar(s, 0, v); + + Nat.MulAddTo(14, u, v, t); + + byte[] result = new byte[ScalarBytes * 2]; + for (int i = 0; i < t.Length; ++i) + { + Encode32(t[i], result, i * 4); + } + return ReduceScalar(result); + } + + private static bool CheckContextVar(byte[] ctx) + { + return ctx != null && ctx.Length < 256; + } + + private static bool CheckPointVar(byte[] p) + { + if ((p[PointBytes - 1] & 0x7F) != 0x00) + { + return false; + } + + uint[] t = new uint[14]; + Decode32(p, 0, t, 0, 14); + return !Nat.Gte(14, t, P); + } + + private static bool CheckScalarVar(byte[] s) + { + if (s[ScalarBytes - 1] != 0x00) + { + return false; + } + + uint[] n = new uint[ScalarUints]; + DecodeScalar(s, 0, n); + return !Nat.Gte(ScalarUints, n, L); + } + + private static uint Decode16(byte[] bs, int off) + { + uint n = bs[off]; + n |= (uint)bs[++off] << 8; + return n; + } + + private static uint Decode24(byte[] bs, int off) + { + uint n = bs[off]; + n |= (uint)bs[++off] << 8; + n |= (uint)bs[++off] << 16; + return n; + } + + private static uint Decode32(byte[] bs, int off) + { + uint n = bs[off]; + n |= (uint)bs[++off] << 8; + n |= (uint)bs[++off] << 16; + n |= (uint)bs[++off] << 24; + return n; + } + + private static void Decode32(byte[] bs, int bsOff, uint[] n, int nOff, int nLen) + { + for (int i = 0; i < nLen; ++i) + { + n[nOff + i] = Decode32(bs, bsOff + i * 4); + } + } + + private static bool DecodePointVar(byte[] p, int pOff, bool negate, PointExt r) + { + byte[] py = Arrays.CopyOfRange(p, pOff, pOff + PointBytes); + if (!CheckPointVar(py)) + { + return false; + } + + int x_0 = (py[PointBytes - 1] & 0x80) >> 7; + py[PointBytes - 1] &= 0x7F; + + X448Field.Decode(py, 0, r.y); + + uint[] u = X448Field.Create(); + uint[] v = X448Field.Create(); + + X448Field.Sqr(r.y, u); + X448Field.Mul(u, (uint)-C_d, v); + X448Field.Negate(u, u); + X448Field.AddOne(u); + X448Field.AddOne(v); + + if (!X448Field.SqrtRatioVar(u, v, r.x)) + { + return false; + } + + X448Field.Normalize(r.x); + if (x_0 == 1 && X448Field.IsZeroVar(r.x)) + { + return false; + } + + if (negate ^ (x_0 != (r.x[0] & 1))) + { + X448Field.Negate(r.x, r.x); + } + + PointExtendXY(r); + return true; + } + + private static void DecodeScalar(byte[] k, int kOff, uint[] n) + { + Debug.Assert(k[kOff + ScalarBytes - 1] == 0x00); + + Decode32(k, kOff, n, 0, ScalarUints); + } + + private static void Dom4(ShakeDigest d, byte x, byte[] y) + { + d.BlockUpdate(Dom4Prefix, 0, Dom4Prefix.Length); + d.Update(x); + d.Update((byte)y.Length); + d.BlockUpdate(y, 0, y.Length); + } + + private static void Encode24(uint n, byte[] bs, int off) + { + bs[off] = (byte)(n); + bs[++off] = (byte)(n >> 8); + bs[++off] = (byte)(n >> 16); + } + + private static void Encode32(uint n, byte[] bs, int off) + { + bs[off] = (byte)(n); + bs[++off] = (byte)(n >> 8); + bs[++off] = (byte)(n >> 16); + bs[++off] = (byte)(n >> 24); + } + + private static void Encode56(ulong n, byte[] bs, int off) + { + Encode32((uint)n, bs, off); + Encode24((uint)(n >> 32), bs, off + 4); + } + + private static void EncodePoint(PointExt p, byte[] r, int rOff) + { + uint[] x = X448Field.Create(); + uint[] y = X448Field.Create(); + + X448Field.Inv(p.z, y); + X448Field.Mul(p.x, y, x); + X448Field.Mul(p.y, y, y); + X448Field.Normalize(x); + X448Field.Normalize(y); + + X448Field.Encode(y, r, rOff); + r[rOff + PointBytes - 1] = (byte)((x[0] & 1) << 7); + } + + public static void GeneratePublicKey(byte[] sk, int skOff, byte[] pk, int pkOff) + { + ShakeDigest d = new ShakeDigest(256); + byte[] h = new byte[ScalarBytes * 2]; + + d.BlockUpdate(sk, skOff, SecretKeySize); + d.DoFinal(h, 0, h.Length); + + byte[] s = new byte[ScalarBytes]; + PruneScalar(h, 0, s); + + ScalarMultBaseEncoded(s, pk, pkOff); + } + + private static sbyte[] GetWnaf(uint[] n, int width) + { + Debug.Assert(n[ScalarUints - 1] >> 31 == 0U); + + uint[] t = new uint[ScalarUints * 2]; + { + uint c = 0; + int tPos = t.Length, i = ScalarUints; + while (--i >= 0) + { + uint next = n[i]; + t[--tPos] = (next >> 16) | (c << 16); + t[--tPos] = c = next; + } + } + + sbyte[] ws = new sbyte[448]; + + uint pow2 = 1U << width; + uint mask = pow2 - 1U; + uint sign = pow2 >> 1; + + uint carry = 0U; + int j = 0; + for (int i = 0; i < t.Length; ++i, j -= 16) + { + uint word = t[i]; + while (j < 16) + { + uint word16 = word >> j; + uint bit = word16 & 1U; + + if (bit == carry) + { + ++j; + continue; + } + + uint digit = (word16 & mask) + carry; + carry = digit & sign; + digit -= (carry << 1); + carry >>= (width - 1); + + ws[(i << 4) + j] = (sbyte)digit; + + j += width; + } + } + + Debug.Assert(carry == 0); + + return ws; + } + + private static void ImplSign(ShakeDigest d, byte[] h, byte[] s, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) + { + byte phflag = 0x00; + + Dom4(d, phflag, ctx); + d.BlockUpdate(h, ScalarBytes, ScalarBytes); + d.BlockUpdate(m, mOff, mLen); + d.DoFinal(h, 0, h.Length); + + byte[] r = ReduceScalar(h); + byte[] R = new byte[PointBytes]; + ScalarMultBaseEncoded(r, R, 0); + + Dom4(d, phflag, ctx); + d.BlockUpdate(R, 0, PointBytes); + d.BlockUpdate(pk, pkOff, PointBytes); + d.BlockUpdate(m, mOff, mLen); + d.DoFinal(h, 0, h.Length); + + byte[] k = ReduceScalar(h); + byte[] S = CalculateS(r, k, s); + + Array.Copy(R, 0, sig, sigOff, PointBytes); + Array.Copy(S, 0, sig, sigOff + PointBytes, ScalarBytes); + } + + private static void PointAddVar(bool negate, PointExt p, PointExt r) + { + uint[] A = X448Field.Create(); + uint[] B = X448Field.Create(); + uint[] C = X448Field.Create(); + uint[] D = X448Field.Create(); + uint[] E = X448Field.Create(); + uint[] F = X448Field.Create(); + uint[] G = X448Field.Create(); + uint[] H = X448Field.Create(); + + uint[] b, e, f, g; + if (negate) + { + b = E; e = B; f = G; g = F; + X448Field.Sub(p.y, p.x, H); + } + else + { + b = B; e = E; f = F; g = G; + X448Field.Add(p.y, p.x, H); + } + + X448Field.Mul(p.z, r.z, A); + X448Field.Sqr(A, B); + X448Field.Mul(p.x, r.x, C); + X448Field.Mul(p.y, r.y, D); + X448Field.Mul(C, D, E); + X448Field.Mul(E, -C_d, E); + // X448Field.Apm(B, E, F, G); + X448Field.Add(B, E, f); + X448Field.Sub(B, E, g); + X448Field.Add(r.x, r.y, E); + X448Field.Mul(H, E, H); + // X448Field.Apm(D, C, B, E); + X448Field.Add(D, C, b); + X448Field.Sub(D, C, e); + X448Field.Carry(b); + X448Field.Sub(H, B, H); + X448Field.Mul(H, A, H); + X448Field.Mul(E, A, E); + X448Field.Mul(F, H, r.x); + X448Field.Mul(E, G, r.y); + X448Field.Mul(F, G, r.z); + } + + private static void PointAddPrecomp(PointPrecomp p, PointExt r) + { + uint[] B = X448Field.Create(); + uint[] C = X448Field.Create(); + uint[] D = X448Field.Create(); + uint[] E = X448Field.Create(); + uint[] F = X448Field.Create(); + uint[] G = X448Field.Create(); + uint[] H = X448Field.Create(); + + X448Field.Sqr(r.z, B); + X448Field.Mul(p.x, r.x, C); + X448Field.Mul(p.y, r.y, D); + X448Field.Mul(C, D, E); + X448Field.Mul(E, -C_d, E); + // X448Field.Apm(B, E, F, G); + X448Field.Add(B, E, F); + X448Field.Sub(B, E, G); + X448Field.Add(p.x, p.y, B); + X448Field.Add(r.x, r.y, E); + X448Field.Mul(B, E, H); + // X448Field.Apm(D, C, B, E); + X448Field.Add(D, C, B); + X448Field.Sub(D, C, E); + X448Field.Carry(B); + X448Field.Sub(H, B, H); + X448Field.Mul(H, r.z, H); + X448Field.Mul(E, r.z, E); + X448Field.Mul(F, H, r.x); + X448Field.Mul(E, G, r.y); + X448Field.Mul(F, G, r.z); + } + + private static PointExt PointCopy(PointExt p) + { + PointExt r = new PointExt(); + X448Field.Copy(p.x, 0, r.x, 0); + X448Field.Copy(p.y, 0, r.y, 0); + X448Field.Copy(p.z, 0, r.z, 0); + return r; + } + + private static void PointDouble(PointExt r) + { + uint[] B = X448Field.Create(); + uint[] C = X448Field.Create(); + uint[] D = X448Field.Create(); + uint[] E = X448Field.Create(); + uint[] H = X448Field.Create(); + uint[] J = X448Field.Create(); + + X448Field.Add(r.x, r.y, B); + X448Field.Sqr(B, B); + X448Field.Sqr(r.x, C); + X448Field.Sqr(r.y, D); + X448Field.Add(C, D, E); + X448Field.Carry(E); + X448Field.Sqr(r.z, H); + X448Field.Add(H, H, H); + X448Field.Carry(H); + X448Field.Sub(E, H, J); + X448Field.Sub(B, E, B); + X448Field.Sub(C, D, C); + X448Field.Mul(B, J, r.x); + X448Field.Mul(E, C, r.y); + X448Field.Mul(E, J, r.z); + } + + private static void PointExtendXY(PointExt p) + { + X448Field.One(p.z); + } + + private static void PointLookup(int block, int index, PointPrecomp p) + { + Debug.Assert(0 <= block && block < PrecompBlocks); + Debug.Assert(0 <= index && index < PrecompPoints); + + int off = block * PrecompPoints * 2 * X448Field.Size; + + for (int i = 0; i < PrecompPoints; ++i) + { + int mask = ((i ^ index) - 1) >> 31; + Nat.CMov(X448Field.Size, mask, precompBase, off, p.x, 0); off += X448Field.Size; + Nat.CMov(X448Field.Size, mask, precompBase, off, p.y, 0); off += X448Field.Size; + } + } + + private static PointExt[] PointPrecompVar(PointExt p, int count) + { + Debug.Assert(count > 0); + + PointExt d = PointCopy(p); + PointDouble(d); + + PointExt[] table = new PointExt[count]; + table[0] = PointCopy(p); + for (int i = 1; i < count; ++i) + { + table[i] = PointCopy(table[i - 1]); + PointAddVar(false, d, table[i]); + } + return table; + } + + private static void PointSetNeutral(PointExt p) + { + X448Field.Zero(p.x); + X448Field.One(p.y); + X448Field.One(p.z); + } + + [MethodImpl(MethodImplOptions.Synchronized)] + public static void Precompute() + { + if (precompBase != null) + { + return; + } + + PointExt p = new PointExt(); + X448Field.Copy(B_x, 0, p.x, 0); + X448Field.Copy(B_y, 0, p.y, 0); + PointExtendXY(p); + + precompBaseTable = PointPrecompVar(p, 1 << (WnafWidthBase - 2)); + + precompBase = new uint[PrecompBlocks * PrecompPoints * 2 * X448Field.Size]; + + int off = 0; + for (int b = 0; b < PrecompBlocks; ++b) + { + PointExt[] ds = new PointExt[PrecompTeeth]; + + PointExt sum = new PointExt(); + PointSetNeutral(sum); + + for (int t = 0; t < PrecompTeeth; ++t) + { + PointAddVar(true, p, sum); + PointDouble(p); + + ds[t] = PointCopy(p); + + for (int s = 1; s < PrecompSpacing; ++s) + { + PointDouble(p); + } + } + + PointExt[] points = new PointExt[PrecompPoints]; + int k = 0; + points[k++] = sum; + + for (int t = 0; t < (PrecompTeeth - 1); ++t) + { + int size = 1 << t; + for (int j = 0; j < size; ++j, ++k) + { + points[k] = PointCopy(points[k - size]); + PointAddVar(false, ds[t], points[k]); + } + } + + Debug.Assert(k == PrecompPoints); + + for (int i = 0; i < PrecompPoints; ++i) + { + PointExt q = points[i]; + // TODO[ed448] Batch inversion + X448Field.Inv(q.z, q.z); + X448Field.Mul(q.x, q.z, q.x); + X448Field.Mul(q.y, q.z, q.y); + + // X448Field.Normalize(q.x); + // X448Field.Normalize(q.y); + + X448Field.Copy(q.x, 0, precompBase, off); off += X448Field.Size; + X448Field.Copy(q.y, 0, precompBase, off); off += X448Field.Size; + } + } + + Debug.Assert(off == precompBase.Length); + } + + private static void PruneScalar(byte[] n, int nOff, byte[] r) + { + Array.Copy(n, nOff, r, 0, ScalarBytes); + + r[0] &= 0xFC; + r[ScalarBytes - 2] |= 0x80; + r[ScalarBytes - 1] &= 0x00; + } + + private static byte[] ReduceScalar(byte[] n) + { + ulong x00 = Decode32(n, 0); // x00:32/-- + ulong x01 = (Decode24(n, 4) << 4); // x01:28/-- + ulong x02 = Decode32(n, 7); // x02:32/-- + ulong x03 = (Decode24(n, 11) << 4); // x03:28/-- + ulong x04 = Decode32(n, 14); // x04:32/-- + ulong x05 = (Decode24(n, 18) << 4); // x05:28/-- + ulong x06 = Decode32(n, 21); // x06:32/-- + ulong x07 = (Decode24(n, 25) << 4); // x07:28/-- + ulong x08 = Decode32(n, 28); // x08:32/-- + ulong x09 = (Decode24(n, 32) << 4); // x09:28/-- + ulong x10 = Decode32(n, 35); // x10:32/-- + ulong x11 = (Decode24(n, 39) << 4); // x11:28/-- + ulong x12 = Decode32(n, 42); // x12:32/-- + ulong x13 = (Decode24(n, 46) << 4); // x13:28/-- + ulong x14 = Decode32(n, 49); // x14:32/-- + ulong x15 = (Decode24(n, 53) << 4); // x15:28/-- + ulong x16 = Decode32(n, 56); // x16:32/-- + ulong x17 = (Decode24(n, 60) << 4); // x17:28/-- + ulong x18 = Decode32(n, 63); // x18:32/-- + ulong x19 = (Decode24(n, 67) << 4); // x19:28/-- + ulong x20 = Decode32(n, 70); // x20:32/-- + ulong x21 = (Decode24(n, 74) << 4); // x21:28/-- + ulong x22 = Decode32(n, 77); // x22:32/-- + ulong x23 = (Decode24(n, 81) << 4); // x23:28/-- + ulong x24 = Decode32(n, 84); // x24:32/-- + ulong x25 = (Decode24(n, 88) << 4); // x25:28/-- + ulong x26 = Decode32(n, 91); // x26:32/-- + ulong x27 = (Decode24(n, 95) << 4); // x27:28/-- + ulong x28 = Decode32(n, 98); // x28:32/-- + ulong x29 = (Decode24(n, 102) << 4); // x29:28/-- + ulong x30 = Decode32(n, 105); // x30:32/-- + ulong x31 = (Decode24(n, 109) << 4); // x31:28/-- + ulong x32 = Decode16(n, 112); // x32:16/-- + + // x32 += (x31 >> 28); x31 &= M28UL; + x16 += x32 * L4_0; // x16:42/-- + x17 += x32 * L4_1; // x17:41/28 + x18 += x32 * L4_2; // x18:43/42 + x19 += x32 * L4_3; // x19:44/28 + x20 += x32 * L4_4; // x20:43/-- + x21 += x32 * L4_5; // x21:44/28 + x22 += x32 * L4_6; // x22:43/41 + x23 += x32 * L4_7; // x23:45/41 + + x31 += (x30 >> 28); x30 &= M28UL; // x31:28/--, x30:28/-- + x15 += x31 * L4_0; // x15:54/-- + x16 += x31 * L4_1; // x16:53/42 + x17 += x31 * L4_2; // x17:55/54 + x18 += x31 * L4_3; // x18:56/44 + x19 += x31 * L4_4; // x19:55/-- + x20 += x31 * L4_5; // x20:56/43 + x21 += x31 * L4_6; // x21:55/53 + x22 += x31 * L4_7; // x22:57/53 + + // x30 += (x29 >> 28); x29 &= M28UL; + x14 += x30 * L4_0; // x14:54/-- + x15 += x30 * L4_1; // x15:54/53 + x16 += x30 * L4_2; // x16:56/-- + x17 += x30 * L4_3; // x17:57/-- + x18 += x30 * L4_4; // x18:56/55 + x19 += x30 * L4_5; // x19:56/55 + x20 += x30 * L4_6; // x20:57/-- + x21 += x30 * L4_7; // x21:57/56 + + x29 += (x28 >> 28); x28 &= M28UL; // x29:28/--, x28:28/-- + x13 += x29 * L4_0; // x13:54/-- + x14 += x29 * L4_1; // x14:54/53 + x15 += x29 * L4_2; // x15:56/-- + x16 += x29 * L4_3; // x16:57/-- + x17 += x29 * L4_4; // x17:57/55 + x18 += x29 * L4_5; // x18:57/55 + x19 += x29 * L4_6; // x19:57/52 + x20 += x29 * L4_7; // x20:58/52 + + // x28 += (x27 >> 28); x27 &= M28UL; + x12 += x28 * L4_0; // x12:54/-- + x13 += x28 * L4_1; // x13:54/53 + x14 += x28 * L4_2; // x14:56/-- + x15 += x28 * L4_3; // x15:57/-- + x16 += x28 * L4_4; // x16:57/55 + x17 += x28 * L4_5; // x17:58/-- + x18 += x28 * L4_6; // x18:58/-- + x19 += x28 * L4_7; // x19:58/53 + + x27 += (x26 >> 28); x26 &= M28UL; // x27:28/--, x26:28/-- + x11 += x27 * L4_0; // x11:54/-- + x12 += x27 * L4_1; // x12:54/53 + x13 += x27 * L4_2; // x13:56/-- + x14 += x27 * L4_3; // x14:57/-- + x15 += x27 * L4_4; // x15:57/55 + x16 += x27 * L4_5; // x16:58/-- + x17 += x27 * L4_6; // x17:58/56 + x18 += x27 * L4_7; // x18:59/-- + + // x26 += (x25 >> 28); x25 &= M28UL; + x10 += x26 * L4_0; // x10:54/-- + x11 += x26 * L4_1; // x11:54/53 + x12 += x26 * L4_2; // x12:56/-- + x13 += x26 * L4_3; // x13:57/-- + x14 += x26 * L4_4; // x14:57/55 + x15 += x26 * L4_5; // x15:58/-- + x16 += x26 * L4_6; // x16:58/56 + x17 += x26 * L4_7; // x17:59/-- + + x25 += (x24 >> 28); x24 &= M28UL; // x25:28/--, x24:28/-- + x09 += x25 * L4_0; // x09:54/-- + x10 += x25 * L4_1; // x10:54/53 + x11 += x25 * L4_2; // x11:56/-- + x12 += x25 * L4_3; // x12:57/-- + x13 += x25 * L4_4; // x13:57/55 + x14 += x25 * L4_5; // x14:58/-- + x15 += x25 * L4_6; // x15:58/56 + x16 += x25 * L4_7; // x16:59/-- + + x21 += (x20 >> 28); x20 &= M28UL; // x21:58/--, x20:28/-- + x22 += (x21 >> 28); x21 &= M28UL; // x22:57/54, x21:28/-- + x23 += (x22 >> 28); x22 &= M28UL; // x23:45/42, x22:28/-- + x24 += (x23 >> 28); x23 &= M28UL; // x24:28/18, x23:28/-- + + x08 += x24 * L4_0; // x08:54/-- + x09 += x24 * L4_1; // x09:55/-- + x10 += x24 * L4_2; // x10:56/46 + x11 += x24 * L4_3; // x11:57/46 + x12 += x24 * L4_4; // x12:57/55 + x13 += x24 * L4_5; // x13:58/-- + x14 += x24 * L4_6; // x14:58/56 + x15 += x24 * L4_7; // x15:59/-- + + x07 += x23 * L4_0; // x07:54/-- + x08 += x23 * L4_1; // x08:54/53 + x09 += x23 * L4_2; // x09:56/53 + x10 += x23 * L4_3; // x10:57/46 + x11 += x23 * L4_4; // x11:57/55 + x12 += x23 * L4_5; // x12:58/-- + x13 += x23 * L4_6; // x13:58/56 + x14 += x23 * L4_7; // x14:59/-- + + x06 += x22 * L4_0; // x06:54/-- + x07 += x22 * L4_1; // x07:54/53 + x08 += x22 * L4_2; // x08:56/-- + x09 += x22 * L4_3; // x09:57/53 + x10 += x22 * L4_4; // x10:57/55 + x11 += x22 * L4_5; // x11:58/-- + x12 += x22 * L4_6; // x12:58/56 + x13 += x22 * L4_7; // x13:59/-- + + x18 += (x17 >> 28); x17 &= M28UL; // x18:59/31, x17:28/-- + x19 += (x18 >> 28); x18 &= M28UL; // x19:58/54, x18:28/-- + x20 += (x19 >> 28); x19 &= M28UL; // x20:30/29, x19:28/-- + x21 += (x20 >> 28); x20 &= M28UL; // x21:28/03, x20:28/-- + + x05 += x21 * L4_0; // x05:54/-- + x06 += x21 * L4_1; // x06:55/-- + x07 += x21 * L4_2; // x07:56/31 + x08 += x21 * L4_3; // x08:57/31 + x09 += x21 * L4_4; // x09:57/56 + x10 += x21 * L4_5; // x10:58/-- + x11 += x21 * L4_6; // x11:58/56 + x12 += x21 * L4_7; // x12:59/-- + + x04 += x20 * L4_0; // x04:54/-- + x05 += x20 * L4_1; // x05:54/53 + x06 += x20 * L4_2; // x06:56/53 + x07 += x20 * L4_3; // x07:57/31 + x08 += x20 * L4_4; // x08:57/55 + x09 += x20 * L4_5; // x09:58/-- + x10 += x20 * L4_6; // x10:58/56 + x11 += x20 * L4_7; // x11:59/-- + + x03 += x19 * L4_0; // x03:54/-- + x04 += x19 * L4_1; // x04:54/53 + x05 += x19 * L4_2; // x05:56/-- + x06 += x19 * L4_3; // x06:57/53 + x07 += x19 * L4_4; // x07:57/55 + x08 += x19 * L4_5; // x08:58/-- + x09 += x19 * L4_6; // x09:58/56 + x10 += x19 * L4_7; // x10:59/-- + + x15 += (x14 >> 28); x14 &= M28UL; // x15:59/31, x14:28/-- + x16 += (x15 >> 28); x15 &= M28UL; // x16:59/32, x15:28/-- + x17 += (x16 >> 28); x16 &= M28UL; // x17:31/29, x16:28/-- + x18 += (x17 >> 28); x17 &= M28UL; // x18:28/04, x17:28/-- + + x02 += x18 * L4_0; // x02:54/-- + x03 += x18 * L4_1; // x03:55/-- + x04 += x18 * L4_2; // x04:56/32 + x05 += x18 * L4_3; // x05:57/32 + x06 += x18 * L4_4; // x06:57/56 + x07 += x18 * L4_5; // x07:58/-- + x08 += x18 * L4_6; // x08:58/56 + x09 += x18 * L4_7; // x09:59/-- + + x01 += x17 * L4_0; // x01:54/-- + x02 += x17 * L4_1; // x02:54/53 + x03 += x17 * L4_2; // x03:56/53 + x04 += x17 * L4_3; // x04:57/32 + x05 += x17 * L4_4; // x05:57/55 + x06 += x17 * L4_5; // x06:58/-- + x07 += x17 * L4_6; // x07:58/56 + x08 += x17 * L4_7; // x08:59/-- + + x16 *= 4; + x16 += (x15 >> 26); x15 &= M26UL; + x16 += 1; // x16:30/01 + + x00 += x16 * L_0; + x01 += x16 * L_1; + x02 += x16 * L_2; + x03 += x16 * L_3; + x04 += x16 * L_4; + x05 += x16 * L_5; + x06 += x16 * L_6; + x07 += x16 * L_7; + + x01 += (x00 >> 28); x00 &= M28UL; + x02 += (x01 >> 28); x01 &= M28UL; + x03 += (x02 >> 28); x02 &= M28UL; + x04 += (x03 >> 28); x03 &= M28UL; + x05 += (x04 >> 28); x04 &= M28UL; + x06 += (x05 >> 28); x05 &= M28UL; + x07 += (x06 >> 28); x06 &= M28UL; + x08 += (x07 >> 28); x07 &= M28UL; + x09 += (x08 >> 28); x08 &= M28UL; + x10 += (x09 >> 28); x09 &= M28UL; + x11 += (x10 >> 28); x10 &= M28UL; + x12 += (x11 >> 28); x11 &= M28UL; + x13 += (x12 >> 28); x12 &= M28UL; + x14 += (x13 >> 28); x13 &= M28UL; + x15 += (x14 >> 28); x14 &= M28UL; + x16 = (x15 >> 26); x15 &= M26UL; + + x16 -= 1; + + Debug.Assert(x16 == 0UL || x16 == ulong.MaxValue); + + x00 -= x16 & L_0; + x01 -= x16 & L_1; + x02 -= x16 & L_2; + x03 -= x16 & L_3; + x04 -= x16 & L_4; + x05 -= x16 & L_5; + x06 -= x16 & L_6; + x07 -= x16 & L_7; + + x01 += (ulong)((long)x00 >> 28); x00 &= M28UL; + x02 += (ulong)((long)x01 >> 28); x01 &= M28UL; + x03 += (ulong)((long)x02 >> 28); x02 &= M28UL; + x04 += (ulong)((long)x03 >> 28); x03 &= M28UL; + x05 += (ulong)((long)x04 >> 28); x04 &= M28UL; + x06 += (ulong)((long)x05 >> 28); x05 &= M28UL; + x07 += (ulong)((long)x06 >> 28); x06 &= M28UL; + x08 += (ulong)((long)x07 >> 28); x07 &= M28UL; + x09 += (ulong)((long)x08 >> 28); x08 &= M28UL; + x10 += (ulong)((long)x09 >> 28); x09 &= M28UL; + x11 += (ulong)((long)x10 >> 28); x10 &= M28UL; + x12 += (ulong)((long)x11 >> 28); x11 &= M28UL; + x13 += (ulong)((long)x12 >> 28); x12 &= M28UL; + x14 += (ulong)((long)x13 >> 28); x13 &= M28UL; + x15 += (ulong)((long)x14 >> 28); x14 &= M28UL; + + Debug.Assert(x15 >> 26 == 0UL); + + byte[] r = new byte[ScalarBytes]; + Encode56(x00 | (x01 << 28), r, 0); + Encode56(x02 | (x03 << 28), r, 7); + Encode56(x04 | (x05 << 28), r, 14); + Encode56(x06 | (x07 << 28), r, 21); + Encode56(x08 | (x09 << 28), r, 28); + Encode56(x10 | (x11 << 28), r, 35); + Encode56(x12 | (x13 << 28), r, 42); + Encode56(x14 | (x15 << 28), r, 49); + // r[ScalarBytes - 1] = 0; + return r; + } + + private static void ScalarMultBase(byte[] k, PointExt r) + { + Precompute(); + + PointSetNeutral(r); + + uint[] n = new uint[ScalarUints + 1]; + DecodeScalar(k, 0, n); + + // Recode the scalar into signed-digit form + { + n[ScalarUints] = 4U + Nat.CAdd(ScalarUints, ~(int)n[0] & 1, n, L, n); + uint c = Nat.ShiftDownBit(n.Length, n, 0); + Debug.Assert(c == (1U << 31)); + } + + PointPrecomp p = new PointPrecomp(); + + int cOff = PrecompSpacing - 1; + for (;;) + { + int tPos = cOff; + + for (int b = 0; b < PrecompBlocks; ++b) + { + uint w = 0; + for (int t = 0; t < PrecompTeeth; ++t) + { + uint tBit = (n[tPos >> 5] >> (tPos & 0x1F)) & 1U; + w |= tBit << t; + tPos += PrecompSpacing; + } + + int sign = (int)(w >> (PrecompTeeth - 1)) & 1; + int abs = ((int)w ^ -sign) & PrecompMask; + + Debug.Assert(sign == 0 || sign == 1); + Debug.Assert(0 <= abs && abs < PrecompPoints); + + PointLookup(b, abs, p); + + X448Field.CNegate(sign, p.x); + + PointAddPrecomp(p, r); + } + + if (--cOff < 0) + { + break; + } + + PointDouble(r); + } + } + + private static void ScalarMultBaseEncoded(byte[] k, byte[] r, int rOff) + { + PointExt p = new PointExt(); + ScalarMultBase(k, p); + EncodePoint(p, r, rOff); + } + + private static void ScalarMultStraussVar(uint[] nb, uint[] np, PointExt p, PointExt r) + { + Precompute(); + + int width = 5; + + sbyte[] ws_b = GetWnaf(nb, WnafWidthBase); + sbyte[] ws_p = GetWnaf(np, width); + + PointExt[] tp = PointPrecompVar(p, 1 << (width - 2)); + + PointSetNeutral(r); + + int bit = 447; + while (bit > 0 && (ws_b[bit] | ws_p[bit]) == 0) + { + --bit; + } + + for (;;) + { + int wb = ws_b[bit]; + if (wb != 0) + { + int sign = wb >> 31; + int index = (wb ^ sign) >> 1; + + PointAddVar((sign != 0), precompBaseTable[index], r); + } + + int wp = ws_p[bit]; + if (wp != 0) + { + int sign = wp >> 31; + int index = (wp ^ sign) >> 1; + + PointAddVar((sign != 0), tp[index], r); + } + + if (--bit < 0) + { + break; + } + + PointDouble(r); + } + } + + public static void Sign(byte[] sk, int skOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) + { + if (!CheckContextVar(ctx)) + { + throw new ArgumentException("ctx"); + } + + ShakeDigest d = new ShakeDigest(256); + byte[] h = new byte[ScalarBytes * 2]; + + d.BlockUpdate(sk, skOff, SecretKeySize); + d.DoFinal(h, 0, h.Length); + + byte[] s = new byte[ScalarBytes]; + PruneScalar(h, 0, s); + + byte[] pk = new byte[PointBytes]; + ScalarMultBaseEncoded(s, pk, 0); + + ImplSign(d, h, s, pk, 0, ctx, m, mOff, mLen, sig, sigOff); + } + + public static void Sign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) + { + if (!CheckContextVar(ctx)) + { + throw new ArgumentException("ctx"); + } + + ShakeDigest d = new ShakeDigest(256); + byte[] h = new byte[ScalarBytes * 2]; + + d.BlockUpdate(sk, skOff, SecretKeySize); + d.DoFinal(h, 0, h.Length); + + byte[] s = new byte[ScalarBytes]; + PruneScalar(h, 0, s); + + ImplSign(d, h, s, pk, pkOff, ctx, m, mOff, mLen, sig, sigOff); + } + + public static bool Verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen) + { + if (!CheckContextVar(ctx)) + { + throw new ArgumentException("ctx"); + } + + byte[] R = Arrays.CopyOfRange(sig, sigOff, sigOff + PointBytes); + byte[] S = Arrays.CopyOfRange(sig, sigOff + PointBytes, sigOff + SignatureSize); + + if (!CheckPointVar(R)) + { + return false; + } + if (!CheckScalarVar(S)) + { + return false; + } + + PointExt pA = new PointExt(); + if (!DecodePointVar(pk, pkOff, true, pA)) + { + return false; + } + + byte phflag = 0x00; + + ShakeDigest d = new ShakeDigest(256); + byte[] h = new byte[ScalarBytes * 2]; + + Dom4(d, phflag, ctx); + d.BlockUpdate(R, 0, PointBytes); + d.BlockUpdate(pk, pkOff, PointBytes); + d.BlockUpdate(m, mOff, mLen); + d.DoFinal(h, 0, h.Length); + + byte[] k = ReduceScalar(h); + + uint[] nS = new uint[ScalarUints]; + DecodeScalar(S, 0, nS); + + uint[] nA = new uint[ScalarUints]; + DecodeScalar(k, 0, nA); + + PointExt pR = new PointExt(); + ScalarMultStraussVar(nS, nA, pA, pR); + + byte[] check = new byte[PointBytes]; + EncodePoint(pR, check, 0); + + return Arrays.AreEqual(check, R); + } + } +} |