diff options
Diffstat (limited to 'crypto/src/math/ec/rfc8032/Ed25519.cs')
| -rw-r--r-- | crypto/src/math/ec/rfc8032/Ed25519.cs | 937 |
1 files changed, 937 insertions, 0 deletions
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); + } + } +} |