using System; using System.Diagnostics; using Org.BouncyCastle.Crypto; using Org.BouncyCastle.Crypto.Digests; using Org.BouncyCastle.Math.EC.Rfc7748; using Org.BouncyCastle.Math.Raw; using Org.BouncyCastle.Security; using Org.BouncyCastle.Utilities; namespace Org.BouncyCastle.Math.EC.Rfc8032 { public static class Ed448 { // x^2 + y^2 == 1 - 39081 * x^2 * y^2 public enum Algorithm { Ed448 = 0, Ed448ph = 1, } private class F : X448Field {}; private const ulong M26UL = 0x03FFFFFFUL; private const ulong M28UL = 0x0FFFFFFFUL; private const int CoordUints = 14; private const int PointBytes = CoordUints * 4 + 1; private const int ScalarUints = 14; private const int ScalarBytes = ScalarUints * 4 + 1; public static readonly int PrehashSize = 64; public static readonly int PublicKeySize = PointBytes; public static readonly int SecretKeySize = 57; public static readonly int SignatureSize = PointBytes + ScalarBytes; // "SigEd448" private static readonly byte[] Dom4Prefix = new byte[]{ 0x53, 0x69, 0x67, 0x45, 0x64, 0x34, 0x34, 0x38 }; 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 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; // ScalarMultBase supports varying blocks, teeth, spacing so long as their product is in range [449, 479] private const int PrecompBlocks = 5; private const int PrecompTeeth = 5; private const int PrecompSpacing = 18; private const int PrecompRange = PrecompBlocks * PrecompTeeth * PrecompSpacing; // 448 < range < 480 private const int PrecompPoints = 1 << (PrecompTeeth - 1); private const int PrecompMask = PrecompPoints - 1; private static readonly object PrecompLock = new object(); private static PointAffine[] PrecompBaseWnaf = null; private static uint[] PrecompBaseComb = null; private struct PointAffine { internal uint[] x, y; } private struct PointExtended { internal uint[] x, y, z; } 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(ScalarUints, 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 int CheckPoint(uint[] x, uint[] y) { uint[] t = F.Create(); uint[] u = F.Create(); uint[] v = F.Create(); F.Sqr(x, u); F.Sqr(y, v); F.Mul(u, v, t); F.Add(u, v, u); F.Mul(t, -C_d, t); F.SubOne(t); F.Add(t, u, t); F.Normalize(t); return F.IsZero(t); } private static int CheckPoint(uint[] x, uint[] y, uint[] z) { uint[] t = F.Create(); uint[] u = F.Create(); uint[] v = F.Create(); uint[] w = F.Create(); F.Sqr(x, u); F.Sqr(y, v); F.Sqr(z, w); F.Mul(u, v, t); F.Add(u, v, u); F.Mul(u, w, u); F.Sqr(w, w); F.Mul(t, -C_d, t); F.Sub(t, w, t); F.Add(t, u, t); F.Normalize(t); return F.IsZero(t); } private static bool CheckPointVar(byte[] p) { if ((p[PointBytes - 1] & 0x7F) != 0x00) return false; uint[] t = new uint[CoordUints]; Decode32(p, 0, t, 0, CoordUints); return !Nat.Gte(CoordUints, t, P); } private static bool CheckScalarVar(byte[] s, uint[] n) { if (s[ScalarBytes - 1] != 0x00) return false; DecodeScalar(s, 0, n); return !Nat.Gte(ScalarUints, n, L); } private static byte[] Copy(byte[] buf, int off, int len) { byte[] result = new byte[len]; Array.Copy(buf, off, result, 0, len); return result; } public static IXof CreatePrehash() { return CreateXof(); } private static IXof CreateXof() { return new ShakeDigest(256); } 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, ref PointExtended r) { byte[] py = Copy(p, pOff, PointBytes); if (!CheckPointVar(py)) return false; int x_0 = (py[PointBytes - 1] & 0x80) >> 7; py[PointBytes - 1] &= 0x7F; F.Decode(py, 0, r.y); uint[] u = F.Create(); uint[] v = F.Create(); F.Sqr(r.y, u); F.Mul(u, (uint)-C_d, v); F.Negate(u, u); F.AddOne(u); F.AddOne(v); if (!F.SqrtRatioVar(u, v, r.x)) return false; F.Normalize(r.x); if (x_0 == 1 && F.IsZeroVar(r.x)) return false; if (negate ^ (x_0 != (r.x[0] & 1))) { F.Negate(r.x, r.x); } PointExtendXY(ref 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(IXof d, byte phflag, byte[] ctx) { int n = Dom4Prefix.Length; byte[] t = new byte[n + 2 + ctx.Length]; Dom4Prefix.CopyTo(t, 0); t[n] = phflag; t[n + 1] = (byte)ctx.Length; ctx.CopyTo(t, n + 2); d.BlockUpdate(t, 0, t.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 int EncodePoint(ref PointExtended p, byte[] r, int rOff) { uint[] x = F.Create(); uint[] y = F.Create(); F.Inv(p.z, y); F.Mul(p.x, y, x); F.Mul(p.y, y, y); F.Normalize(x); F.Normalize(y); int result = CheckPoint(x, y); F.Encode(y, r, rOff); r[rOff + PointBytes - 1] = (byte)((x[0] & 1) << 7); return result; } public static void GeneratePrivateKey(SecureRandom random, byte[] k) { random.NextBytes(k); } public static void GeneratePublicKey(byte[] sk, int skOff, byte[] pk, int pkOff) { IXof d = CreateXof(); 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 uint GetWindow4(uint[] x, int n) { int w = (int)((uint)n >> 3), b = (n & 7) << 2; return (x[w] >> b) & 15U; } private static sbyte[] GetWnafVar(uint[] n, int width) { Debug.Assert(n[ScalarUints - 1] <= L[ScalarUints - 1]); Debug.Assert(2 <= width && width <= 8); 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[447]; int lead = 32 - width; 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 | 1U) << lead; carry = digit >> 31; ws[(i << 4) + j] = (sbyte)((int)digit >> lead); j += width; } } Debug.Assert(carry == 0); return ws; } private static void ImplSign(IXof d, byte[] h, byte[] s, byte[] pk, int pkOff, byte[] ctx, byte phflag, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) { 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 ImplSign(byte[] sk, int skOff, byte[] ctx, byte phflag, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) { if (!CheckContextVar(ctx)) throw new ArgumentException("ctx"); IXof d = CreateXof(); 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, phflag, m, mOff, mLen, sig, sigOff); } private static void ImplSign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte phflag, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) { if (!CheckContextVar(ctx)) throw new ArgumentException("ctx"); IXof d = CreateXof(); 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, phflag, m, mOff, mLen, sig, sigOff); } private static bool ImplVerify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte phflag, byte[] m, int mOff, int mLen) { if (!CheckContextVar(ctx)) throw new ArgumentException("ctx"); byte[] R = Copy(sig, sigOff, PointBytes); byte[] S = Copy(sig, sigOff + PointBytes, ScalarBytes); if (!CheckPointVar(R)) return false; uint[] nS = new uint[ScalarUints]; if (!CheckScalarVar(S, nS)) return false; PointExtended pA; Init(out pA); if (!DecodePointVar(pk, pkOff, true, ref pA)) return false; IXof d = CreateXof(); 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[] nA = new uint[ScalarUints]; DecodeScalar(k, 0, nA); PointExtended pR; Init(out pR); ScalarMultStrausVar(nS, nA, ref pA, ref pR); byte[] check = new byte[PointBytes]; return 0 != EncodePoint(ref pR, check, 0) && Arrays.AreEqual(check, R); } private static void Init(out PointAffine r) { r.x = F.Create(); r.y = F.Create(); } private static void Init(out PointExtended r) { r.x = F.Create(); r.y = F.Create(); r.z = F.Create(); } private static void InvertZs(PointExtended[] points) { int count = points.Length; uint[] cs = F.CreateTable(count); uint[] u = F.Create(); F.Copy(points[0].z, 0, u, 0); F.Copy(u, 0, cs, 0); int i = 0; while (++i < count) { F.Mul(u, points[i].z, u); F.Copy(u, 0, cs, i * F.Size); } F.InvVar(u, u); --i; uint[] t = F.Create(); while (i > 0) { int j = i--; F.Copy(cs, i * F.Size, t, 0); F.Mul(t, u, t); F.Mul(u, points[j].z, u); F.Copy(t, 0, points[j].z, 0); } F.Copy(u, 0, points[0].z, 0); } private static bool IsNeutralElementVar(uint[] x, uint[] y) { return F.IsZeroVar(x) && F.IsOneVar(y); } private static bool IsNeutralElementVar(uint[] x, uint[] y, uint[] z) { return F.IsZeroVar(x) && F.AreEqualVar(y, z); } private static void PointAddAffine(ref PointAffine p, ref PointExtended r) { uint[] b = F.Create(); uint[] c = F.Create(); uint[] d = F.Create(); uint[] e = F.Create(); uint[] f = F.Create(); uint[] g = F.Create(); uint[] h = F.Create(); F.Sqr(r.z, b); F.Mul(p.x, r.x, c); F.Mul(p.y, r.y, d); F.Mul(c, d, e); F.Mul(e, -C_d, e); //F.Apm(b, e, f, g); F.Add(b, e, f); F.Sub(b, e, g); F.Add(p.x, p.y, b); F.Add(r.x, r.y, e); F.Mul(b, e, h); //F.Apm(d, c, b, e); F.Add(d, c, b); F.Sub(d, c, e); F.Carry(b); F.Sub(h, b, h); F.Mul(h, r.z, h); F.Mul(e, r.z, e); F.Mul(f, h, r.x); F.Mul(e, g, r.y); F.Mul(f, g, r.z); } private static void PointAddAffineVar(bool negate, ref PointAffine p, ref PointExtended r) { uint[] b = F.Create(); uint[] c = F.Create(); uint[] d = F.Create(); uint[] e = F.Create(); uint[] f = F.Create(); uint[] g = F.Create(); uint[] h = F.Create(); uint[] px = F.Create(); if (negate) { F.Negate(p.x, px); } else { F.Copy(p.x, 0, px, 0); } F.Sqr(r.z, b); F.Mul(px, r.x, c); F.Mul(p.y, r.y, d); F.Mul(c, d, e); F.Mul(e, -C_d, e); //F.Apm(b, e, f, g); F.Add(b, e, f); F.Sub(b, e, g); F.Add(px, p.y, b); F.Add(r.x, r.y, e); F.Mul(b, e, h); //F.Apm(d, c, b, e); F.Add(d, c, b); F.Sub(d, c, e); F.Carry(b); F.Sub(h, b, h); F.Mul(h, r.z, h); F.Mul(e, r.z, e); F.Mul(f, h, r.x); F.Mul(e, g, r.y); F.Mul(f, g, r.z); } private static void PointAddExtended(ref PointExtended p, ref PointExtended r) { uint[] a = F.Create(); uint[] b = F.Create(); uint[] c = F.Create(); uint[] d = F.Create(); uint[] e = F.Create(); uint[] f = F.Create(); uint[] g = F.Create(); uint[] h = F.Create(); F.Mul(p.z, r.z, a); F.Sqr(a, b); F.Mul(p.x, r.x, c); F.Mul(p.y, r.y, d); F.Mul(c, d, e); F.Mul(e, -C_d, e); //F.Apm(b, e, f, g); F.Add(b, e, f); F.Sub(b, e, g); F.Add(p.x, p.y, b); F.Add(r.x, r.y, e); F.Mul(b, e, h); //F.Apm(d, c, b, e); F.Add(d, c, b); F.Sub(d, c, e); F.Carry(b); F.Sub(h, b, h); F.Mul(h, a, h); F.Mul(e, a, e); F.Mul(f, h, r.x); F.Mul(e, g, r.y); F.Mul(f, g, r.z); } private static void PointAddExtendedVar(bool negate, ref PointExtended p, ref PointExtended r) { uint[] a = F.Create(); uint[] b = F.Create(); uint[] c = F.Create(); uint[] d = F.Create(); uint[] e = F.Create(); uint[] f = F.Create(); uint[] g = F.Create(); uint[] h = F.Create(); uint[] px = F.Create(); if (negate) { F.Negate(p.x, px); } else { F.Copy(p.x, 0, px, 0); } F.Mul(p.z, r.z, a); F.Sqr(a, b); F.Mul(px, r.x, c); F.Mul(p.y, r.y, d); F.Mul(c, d, e); F.Mul(e, -C_d, e); //F.Apm(b, e, f, g); F.Add(b, e, f); F.Sub(b, e, g); F.Add(px, p.y, b); F.Add(r.x, r.y, e); F.Mul(b, e, h); //F.Apm(d, c, b, e); F.Add(d, c, b); F.Sub(d, c, e); F.Carry(b); F.Sub(h, b, h); F.Mul(h, a, h); F.Mul(e, a, e); F.Mul(f, h, r.x); F.Mul(e, g, r.y); F.Mul(f, g, r.z); } private static void PointCopy(ref PointExtended p, ref PointExtended r) { F.Copy(p.x, 0, r.x, 0); F.Copy(p.y, 0, r.y, 0); F.Copy(p.z, 0, r.z, 0); } private static void PointDouble(ref PointExtended r) { uint[] b = F.Create(); uint[] c = F.Create(); uint[] d = F.Create(); uint[] e = F.Create(); uint[] h = F.Create(); uint[] j = F.Create(); F.Add(r.x, r.y, b); F.Sqr(b, b); F.Sqr(r.x, c); F.Sqr(r.y, d); F.Add(c, d, e); F.Carry(e); F.Sqr(r.z, h); F.Add(h, h, h); F.Carry(h); F.Sub(e, h, j); F.Sub(b, e, b); F.Sub(c, d, c); F.Mul(b, j, r.x); F.Mul(e, c, r.y); F.Mul(e, j, r.z); } private static void PointExtendXY(ref PointExtended p) { F.One(p.z); } private static void PointLookup(int block, int index, ref PointAffine p) { Debug.Assert(0 <= block && block < PrecompBlocks); Debug.Assert(0 <= index && index < PrecompPoints); int off = block * PrecompPoints * 2 * F.Size; for (int i = 0; i < PrecompPoints; ++i) { int cond = ((i ^ index) - 1) >> 31; F.CMov(cond, PrecompBaseComb, off, p.x, 0); off += F.Size; F.CMov(cond, PrecompBaseComb, off, p.y, 0); off += F.Size; } } private static void PointLookup(uint[] x, int n, uint[] table, ref PointExtended r) { // TODO This method is currently hardcoded to 4-bit windows and 8 precomputed points uint w = GetWindow4(x, n); int sign = (int)(w >> (4 - 1)) ^ 1; int abs = ((int)w ^ -sign) & 7; Debug.Assert(sign == 0 || sign == 1); Debug.Assert(0 <= abs && abs < 8); for (int i = 0, off = 0; i < 8; ++i) { int cond = ((i ^ abs) - 1) >> 31; F.CMov(cond, table, off, r.x, 0); off += F.Size; F.CMov(cond, table, off, r.y, 0); off += F.Size; F.CMov(cond, table, off, r.z, 0); off += F.Size; } F.CNegate(sign, r.x); } private static void PointLookup15(uint[] table, ref PointExtended r) { int off = F.Size * 3 * 7; F.Copy(table, off, r.x, 0); off += F.Size; F.Copy(table, off, r.y, 0); off += F.Size; F.Copy(table, off, r.z, 0); } private static uint[] PointPrecompute(ref PointExtended p, int count) { Debug.Assert(count > 0); PointExtended q; Init(out q); PointCopy(ref p, ref q); PointExtended d; Init(out d); PointCopy(ref q, ref d); PointDouble(ref d); uint[] table = F.CreateTable(count * 3); int off = 0; int i = 0; for (;;) { F.Copy(q.x, 0, table, off); off += F.Size; F.Copy(q.y, 0, table, off); off += F.Size; F.Copy(q.z, 0, table, off); off += F.Size; if (++i == count) break; PointAddExtended(ref d, ref q); } return table; } private static void PointPrecomputeVar(ref PointExtended p, PointExtended[] points, int count) { Debug.Assert(count > 0); PointExtended d; Init(out d); PointCopy(ref p, ref d); PointDouble(ref d); Init(out points[0]); PointCopy(ref p, ref points[0]); for (int i = 1; i < count; ++i) { Init(out points[i]); PointCopy(ref points[i - 1], ref points[i]); PointAddExtendedVar(false, ref d, ref points[i]); } } private static void PointSetNeutral(ref PointExtended p) { F.Zero(p.x); F.One(p.y); F.One(p.z); } public static void Precompute() { lock (PrecompLock) { if (PrecompBaseWnaf != null && PrecompBaseComb != null) return; Debug.Assert(PrecompRange > 448); Debug.Assert(PrecompRange < 480); int wnafPoints = 1 << (WnafWidthBase - 2); int combPoints = PrecompBlocks * PrecompPoints; int totalPoints = wnafPoints + combPoints; PointExtended[] points = new PointExtended[totalPoints]; PointExtended p; Init(out p); F.Copy(B_x, 0, p.x, 0); F.Copy(B_y, 0, p.y, 0); PointExtendXY(ref p); PointPrecomputeVar(ref p, points, wnafPoints); int pointsIndex = wnafPoints; PointExtended[] toothPowers = new PointExtended[PrecompTeeth]; for (int tooth = 0; tooth < PrecompTeeth; ++tooth) { Init(out toothPowers[tooth]); } for (int block = 0; block < PrecompBlocks; ++block) { ref PointExtended sum = ref points[pointsIndex++]; Init(out sum); PointSetNeutral(ref sum); for (int tooth = 0; tooth < PrecompTeeth; ++tooth) { PointAddExtendedVar(true, ref p, ref sum); PointDouble(ref p); PointCopy(ref p, ref toothPowers[tooth]); if (block + tooth != PrecompBlocks + PrecompTeeth - 2) { for (int s = 1; s < PrecompSpacing; ++s) { PointDouble(ref p); } } } for (int tooth = 0; tooth < (PrecompTeeth - 1); ++tooth) { int size = 1 << tooth; for (int j = 0; j < size; ++j, ++pointsIndex) { Init(out points[pointsIndex]); PointCopy(ref points[pointsIndex - size], ref points[pointsIndex]); PointAddExtendedVar(false, ref toothPowers[tooth], ref points[pointsIndex]); } } } Debug.Assert(pointsIndex == totalPoints); InvertZs(points); PrecompBaseWnaf = new PointAffine[wnafPoints]; for (int i = 0; i < wnafPoints; ++i) { ref PointExtended q = ref points[i]; ref PointAffine r = ref PrecompBaseWnaf[i]; Init(out r); F.Mul(q.x, q.z, r.x); F.Normalize(r.x); F.Mul(q.y, q.z, r.y); F.Normalize(r.y); } PrecompBaseComb = F.CreateTable(combPoints * 2); int off = 0; for (int i = wnafPoints; i < totalPoints; ++i) { ref PointExtended q = ref points[i]; F.Mul(q.x, q.z, q.x); F.Normalize(q.x); F.Mul(q.y, q.z, q.y); F.Normalize(q.y); F.Copy(q.x, 0, PrecompBaseComb, off); off += F.Size; F.Copy(q.y, 0, PrecompBaseComb, off); off += F.Size; } Debug.Assert(off == PrecompBaseComb.Length); } } private static void PruneScalar(byte[] n, int nOff, byte[] r) { Array.Copy(n, nOff, r, 0, ScalarBytes - 1); 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 ScalarMult(byte[] k, ref PointExtended p, ref PointExtended r) { uint[] n = new uint[ScalarUints]; DecodeScalar(k, 0, n); // Recode the scalar into signed-digit form { uint c1 = Nat.CAdd(ScalarUints, ~(int)n[0] & 1, n, L, n); uint c2 = Nat.ShiftDownBit(ScalarUints, n, c1); Debug.Assert(c2 == (1U << 31)); // NOTE: Bit 448 is implicitly set after the signed-digit recoding } uint[] table = PointPrecompute(ref p, 8); PointExtended q; Init(out q); // Replace first 4 doublings (2^4 * P) with 1 addition (P + 15 * P) PointLookup15(table, ref r); PointAddExtended(ref p, ref r); int w = 111; for (;;) { PointLookup(n, w, table, ref q); PointAddExtended(ref q, ref r); if (--w < 0) break; for (int i = 0; i < 4; ++i) { PointDouble(ref r); } } } private static void ScalarMultBase(byte[] k, ref PointExtended r) { // Equivalent (but much slower) //PointExtended p; InitExtended(out p); //F.Copy(B_x, 0, p.x, 0); //F.Copy(B_y, 0, p.y, 0); //PointExtendXY(ref p); //ScalarMult(k, ref p, ref r); Precompute(); uint[] n = new uint[ScalarUints + 1]; DecodeScalar(k, 0, n); // Recode the scalar into signed-digit form { n[ScalarUints] = (1U << (PrecompRange - 448)) + Nat.CAdd(ScalarUints, ~(int)n[0] & 1, n, L, n); uint c = Nat.ShiftDownBit(n.Length, n, 0); Debug.Assert(c == (1U << 31)); } PointAffine p; Init(out p); PointSetNeutral(ref r); 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); w &= ~(1U << t); 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, ref p); F.CNegate(sign, p.x); PointAddAffine(ref p, ref r); } if (--cOff < 0) break; PointDouble(ref r); } } private static void ScalarMultBaseEncoded(byte[] k, byte[] r, int rOff) { PointExtended p; Init(out p); ScalarMultBase(k, ref p); if (0 == EncodePoint(ref p, r, rOff)) throw new InvalidOperationException(); } internal static void ScalarMultBaseXY(byte[] k, int kOff, uint[] x, uint[] y) { byte[] n = new byte[ScalarBytes]; PruneScalar(k, kOff, n); PointExtended p; Init(out p); ScalarMultBase(n, ref p); if (0 == CheckPoint(p.x, p.y, p.z)) throw new InvalidOperationException(); F.Copy(p.x, 0, x, 0); F.Copy(p.y, 0, y, 0); } private static void ScalarMultOrderVar(ref PointExtended p, ref PointExtended r) { int width = 5; sbyte[] ws_p = GetWnafVar(L, width); int count = 1 << (width - 2); PointExtended[] tp = new PointExtended[count]; PointPrecomputeVar(ref p, tp, count); PointSetNeutral(ref r); for (int bit = 446;;) { int wp = ws_p[bit]; if (wp != 0) { int sign = wp >> 31; int index = (wp ^ sign) >> 1; PointAddExtendedVar(sign != 0, ref tp[index], ref r); } if (--bit < 0) break; PointDouble(ref r); } } private static void ScalarMultStrausVar(uint[] nb, uint[] np, ref PointExtended p, ref PointExtended r) { Precompute(); int width = 5; sbyte[] ws_b = GetWnafVar(nb, WnafWidthBase); sbyte[] ws_p = GetWnafVar(np, width); int count = 1 << (width - 2); PointExtended[] tp = new PointExtended[count]; PointPrecomputeVar(ref p, tp, count); PointSetNeutral(ref r); for (int bit = 446;;) { int wb = ws_b[bit]; if (wb != 0) { int sign = wb >> 31; int index = (wb ^ sign) >> 1; PointAddAffineVar(sign != 0, ref PrecompBaseWnaf[index], ref r); } int wp = ws_p[bit]; if (wp != 0) { int sign = wp >> 31; int index = (wp ^ sign) >> 1; PointAddExtendedVar(sign != 0, ref tp[index], ref r); } if (--bit < 0) break; PointDouble(ref r); } } public static void Sign(byte[] sk, int skOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff) { byte phflag = 0x00; ImplSign(sk, skOff, ctx, phflag, 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) { byte phflag = 0x00; ImplSign(sk, skOff, pk, pkOff, ctx, phflag, m, mOff, mLen, sig, sigOff); } public static void SignPrehash(byte[] sk, int skOff, byte[] ctx, byte[] ph, int phOff, byte[] sig, int sigOff) { byte phflag = 0x01; ImplSign(sk, skOff, ctx, phflag, ph, phOff, PrehashSize, sig, sigOff); } public static void SignPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff, byte[] sig, int sigOff) { byte phflag = 0x01; ImplSign(sk, skOff, pk, pkOff, ctx, phflag, ph, phOff, PrehashSize, sig, sigOff); } public static void SignPrehash(byte[] sk, int skOff, byte[] ctx, IXof ph, byte[] sig, int sigOff) { byte[] m = new byte[PrehashSize]; if (PrehashSize != ph.DoFinal(m, 0, PrehashSize)) throw new ArgumentException("ph"); byte phflag = 0x01; ImplSign(sk, skOff, ctx, phflag, m, 0, m.Length, sig, sigOff); } public static void SignPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, IXof ph, byte[] sig, int sigOff) { byte[] m = new byte[PrehashSize]; if (PrehashSize != ph.DoFinal(m, 0, PrehashSize)) throw new ArgumentException("ph"); byte phflag = 0x01; ImplSign(sk, skOff, pk, pkOff, ctx, phflag, m, 0, m.Length, sig, sigOff); } public static bool ValidatePublicKeyFull(byte[] pk, int pkOff) { PointExtended p; Init(out p); if (!DecodePointVar(pk, pkOff, false, ref p)) return false; F.Normalize(p.x); F.Normalize(p.y); F.Normalize(p.z); if (IsNeutralElementVar(p.x, p.y, p.z)) return false; PointExtended r; Init(out r); ScalarMultOrderVar(ref p, ref r); F.Normalize(r.x); F.Normalize(r.y); F.Normalize(r.z); return IsNeutralElementVar(r.x, r.y, r.z); } public static bool ValidatePublicKeyPartial(byte[] pk, int pkOff) { PointExtended p; Init(out p); return DecodePointVar(pk, pkOff, false, ref p); } public static bool Verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen) { byte phflag = 0x00; return ImplVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, mOff, mLen); } public static bool VerifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff) { byte phflag = 0x01; return ImplVerify(sig, sigOff, pk, pkOff, ctx, phflag, ph, phOff, PrehashSize); } public static bool VerifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, IXof ph) { byte[] m = new byte[PrehashSize]; if (PrehashSize != ph.DoFinal(m, 0, PrehashSize)) throw new ArgumentException("ph"); byte phflag = 0x01; return ImplVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, 0, m.Length); } } }