#if !BESTHTTP_DISABLE_ALTERNATE_SSL && (!UNITY_WEBGL || UNITY_EDITOR) using System; namespace Org.BouncyCastle.Math.EC.Multiplier { public abstract class WNafUtilities { public static readonly string PRECOMP_NAME = "bc_wnaf"; private static readonly int[] DEFAULT_WINDOW_SIZE_CUTOFFS = new int[]{ 13, 41, 121, 337, 897, 2305 }; private static readonly byte[] EMPTY_BYTES = new byte[0]; private static readonly int[] EMPTY_INTS = new int[0]; private static readonly ECPoint[] EMPTY_POINTS = new ECPoint[0]; public static int[] GenerateCompactNaf(BigInteger k) { if ((k.BitLength >> 16) != 0) throw new ArgumentException("must have bitlength < 2^16", "k"); if (k.SignValue == 0) return EMPTY_INTS; BigInteger _3k = k.ShiftLeft(1).Add(k); int bits = _3k.BitLength; int[] naf = new int[bits >> 1]; BigInteger diff = _3k.Xor(k); int highBit = bits - 1, length = 0, zeroes = 0; for (int i = 1; i < highBit; ++i) { if (!diff.TestBit(i)) { ++zeroes; continue; } int digit = k.TestBit(i) ? -1 : 1; naf[length++] = (digit << 16) | zeroes; zeroes = 1; ++i; } naf[length++] = (1 << 16) | zeroes; if (naf.Length > length) { naf = Trim(naf, length); } return naf; } public static int[] GenerateCompactWindowNaf(int width, BigInteger k) { if (width == 2) { return GenerateCompactNaf(k); } if (width < 2 || width > 16) throw new ArgumentException("must be in the range [2, 16]", "width"); if ((k.BitLength >> 16) != 0) throw new ArgumentException("must have bitlength < 2^16", "k"); if (k.SignValue == 0) return EMPTY_INTS; int[] wnaf = new int[k.BitLength / width + 1]; // 2^width and a mask and sign bit set accordingly int pow2 = 1 << width; int mask = pow2 - 1; int sign = pow2 >> 1; bool carry = false; int length = 0, pos = 0; while (pos <= k.BitLength) { if (k.TestBit(pos) == carry) { ++pos; continue; } k = k.ShiftRight(pos); int digit = k.IntValue & mask; if (carry) { ++digit; } carry = (digit & sign) != 0; if (carry) { digit -= pow2; } int zeroes = length > 0 ? pos - 1 : pos; wnaf[length++] = (digit << 16) | zeroes; pos = width; } // Reduce the WNAF array to its actual length if (wnaf.Length > length) { wnaf = Trim(wnaf, length); } return wnaf; } public static byte[] GenerateJsf(BigInteger g, BigInteger h) { int digits = System.Math.Max(g.BitLength, h.BitLength) + 1; byte[] jsf = new byte[digits]; BigInteger k0 = g, k1 = h; int j = 0, d0 = 0, d1 = 0; int offset = 0; while ((d0 | d1) != 0 || k0.BitLength > offset || k1.BitLength > offset) { int n0 = ((int)((uint)k0.IntValue >> offset) + d0) & 7; int n1 = ((int)((uint)k1.IntValue >> offset) + d1) & 7; int u0 = n0 & 1; if (u0 != 0) { u0 -= (n0 & 2); if ((n0 + u0) == 4 && (n1 & 3) == 2) { u0 = -u0; } } int u1 = n1 & 1; if (u1 != 0) { u1 -= (n1 & 2); if ((n1 + u1) == 4 && (n0 & 3) == 2) { u1 = -u1; } } if ((d0 << 1) == 1 + u0) { d0 ^= 1; } if ((d1 << 1) == 1 + u1) { d1 ^= 1; } if (++offset == 30) { offset = 0; k0 = k0.ShiftRight(30); k1 = k1.ShiftRight(30); } jsf[j++] = (byte)((u0 << 4) | (u1 & 0xF)); } // Reduce the JSF array to its actual length if (jsf.Length > j) { jsf = Trim(jsf, j); } return jsf; } public static byte[] GenerateNaf(BigInteger k) { if (k.SignValue == 0) return EMPTY_BYTES; BigInteger _3k = k.ShiftLeft(1).Add(k); int digits = _3k.BitLength - 1; byte[] naf = new byte[digits]; BigInteger diff = _3k.Xor(k); for (int i = 1; i < digits; ++i) { if (diff.TestBit(i)) { naf[i - 1] = (byte)(k.TestBit(i) ? -1 : 1); ++i; } } naf[digits - 1] = 1; return naf; } /** * Computes the Window NAF (non-adjacent Form) of an integer. * @param width The width w of the Window NAF. The width is * defined as the minimal number w, such that for any * w consecutive digits in the resulting representation, at * most one is non-zero. * @param k The integer of which the Window NAF is computed. * @return The Window NAF of the given width, such that the following holds: * k = &sum;i=0l-1 ki2i * , where the ki denote the elements of the * returned byte[]. */ public static byte[] GenerateWindowNaf(int width, BigInteger k) { if (width == 2) { return GenerateNaf(k); } if (width < 2 || width > 8) throw new ArgumentException("must be in the range [2, 8]", "width"); if (k.SignValue == 0) return EMPTY_BYTES; byte[] wnaf = new byte[k.BitLength + 1]; // 2^width and a mask and sign bit set accordingly int pow2 = 1 << width; int mask = pow2 - 1; int sign = pow2 >> 1; bool carry = false; int length = 0, pos = 0; while (pos <= k.BitLength) { if (k.TestBit(pos) == carry) { ++pos; continue; } k = k.ShiftRight(pos); int digit = k.IntValue & mask; if (carry) { ++digit; } carry = (digit & sign) != 0; if (carry) { digit -= pow2; } length += (length > 0) ? pos - 1 : pos; wnaf[length++] = (byte)digit; pos = width; } // Reduce the WNAF array to its actual length if (wnaf.Length > length) { wnaf = Trim(wnaf, length); } return wnaf; } public static int GetNafWeight(BigInteger k) { if (k.SignValue == 0) return 0; BigInteger _3k = k.ShiftLeft(1).Add(k); BigInteger diff = _3k.Xor(k); return diff.BitCount; } public static WNafPreCompInfo GetWNafPreCompInfo(ECPoint p) { return GetWNafPreCompInfo(p.Curve.GetPreCompInfo(p, PRECOMP_NAME)); } public static WNafPreCompInfo GetWNafPreCompInfo(PreCompInfo preCompInfo) { if ((preCompInfo != null) && (preCompInfo is WNafPreCompInfo)) { return (WNafPreCompInfo)preCompInfo; } return new WNafPreCompInfo(); } /** * Determine window width to use for a scalar multiplication of the given size. * * @param bits the bit-length of the scalar to multiply by * @return the window size to use */ public static int GetWindowSize(int bits) { return GetWindowSize(bits, DEFAULT_WINDOW_SIZE_CUTOFFS); } /** * Determine window width to use for a scalar multiplication of the given size. * * @param bits the bit-length of the scalar to multiply by * @param windowSizeCutoffs a monotonically increasing list of bit sizes at which to increment the window width * @return the window size to use */ public static int GetWindowSize(int bits, int[] windowSizeCutoffs) { int w = 0; for (; w < windowSizeCutoffs.Length; ++w) { if (bits < windowSizeCutoffs[w]) { break; } } return w + 2; } public static ECPoint MapPointWithPrecomp(ECPoint p, int width, bool includeNegated, ECPointMap pointMap) { ECCurve c = p.Curve; WNafPreCompInfo wnafPreCompP = Precompute(p, width, includeNegated); ECPoint q = pointMap.Map(p); WNafPreCompInfo wnafPreCompQ = GetWNafPreCompInfo(c.GetPreCompInfo(q, PRECOMP_NAME)); ECPoint twiceP = wnafPreCompP.Twice; if (twiceP != null) { ECPoint twiceQ = pointMap.Map(twiceP); wnafPreCompQ.Twice = twiceQ; } ECPoint[] preCompP = wnafPreCompP.PreComp; ECPoint[] preCompQ = new ECPoint[preCompP.Length]; for (int i = 0; i < preCompP.Length; ++i) { preCompQ[i] = pointMap.Map(preCompP[i]); } wnafPreCompQ.PreComp = preCompQ; if (includeNegated) { ECPoint[] preCompNegQ = new ECPoint[preCompQ.Length]; for (int i = 0; i < preCompNegQ.Length; ++i) { preCompNegQ[i] = preCompQ[i].Negate(); } wnafPreCompQ.PreCompNeg = preCompNegQ; } c.SetPreCompInfo(q, PRECOMP_NAME, wnafPreCompQ); return q; } public static WNafPreCompInfo Precompute(ECPoint p, int width, bool includeNegated) { ECCurve c = p.Curve; WNafPreCompInfo wnafPreCompInfo = GetWNafPreCompInfo(c.GetPreCompInfo(p, PRECOMP_NAME)); int iniPreCompLen = 0, reqPreCompLen = 1 << System.Math.Max(0, width - 2); ECPoint[] preComp = wnafPreCompInfo.PreComp; if (preComp == null) { preComp = EMPTY_POINTS; } else { iniPreCompLen = preComp.Length; } if (iniPreCompLen < reqPreCompLen) { preComp = ResizeTable(preComp, reqPreCompLen); if (reqPreCompLen == 1) { preComp[0] = p.Normalize(); } else { int curPreCompLen = iniPreCompLen; if (curPreCompLen == 0) { preComp[0] = p; curPreCompLen = 1; } ECFieldElement iso = null; if (reqPreCompLen == 2) { preComp[1] = p.ThreeTimes(); } else { ECPoint twiceP = wnafPreCompInfo.Twice, last = preComp[curPreCompLen - 1]; if (twiceP == null) { twiceP = preComp[0].Twice(); wnafPreCompInfo.Twice = twiceP; /* * For Fp curves with Jacobian projective coordinates, use a (quasi-)isomorphism * where 'twiceP' is "affine", so that the subsequent additions are cheaper. This * also requires scaling the initial point's X, Y coordinates, and reversing the * isomorphism as part of the subsequent normalization. * * NOTE: The correctness of this optimization depends on: * 1) additions do not use the curve's A, B coefficients. * 2) no special cases (i.e. Q +/- Q) when calculating 1P, 3P, 5P, ... */ if (ECAlgorithms.IsFpCurve(c) && c.FieldSize >= 64) { switch (c.CoordinateSystem) { case ECCurve.COORD_JACOBIAN: case ECCurve.COORD_JACOBIAN_CHUDNOVSKY: case ECCurve.COORD_JACOBIAN_MODIFIED: { iso = twiceP.GetZCoord(0); twiceP = c.CreatePoint(twiceP.XCoord.ToBigInteger(), twiceP.YCoord.ToBigInteger()); ECFieldElement iso2 = iso.Square(), iso3 = iso2.Multiply(iso); last = last.ScaleX(iso2).ScaleY(iso3); if (iniPreCompLen == 0) { preComp[0] = last; } break; } } } } while (curPreCompLen < reqPreCompLen) { /* * Compute the new ECPoints for the precomputation array. The values 1, 3, * 5, ..., 2^(width-1)-1 times p are computed */ preComp[curPreCompLen++] = last = last.Add(twiceP); } } /* * Having oft-used operands in affine form makes operations faster. */ c.NormalizeAll(preComp, iniPreCompLen, reqPreCompLen - iniPreCompLen, iso); } } wnafPreCompInfo.PreComp = preComp; if (includeNegated) { ECPoint[] preCompNeg = wnafPreCompInfo.PreCompNeg; int pos; if (preCompNeg == null) { pos = 0; preCompNeg = new ECPoint[reqPreCompLen]; } else { pos = preCompNeg.Length; if (pos < reqPreCompLen) { preCompNeg = ResizeTable(preCompNeg, reqPreCompLen); } } while (pos < reqPreCompLen) { preCompNeg[pos] = preComp[pos].Negate(); ++pos; } wnafPreCompInfo.PreCompNeg = preCompNeg; } c.SetPreCompInfo(p, PRECOMP_NAME, wnafPreCompInfo); return wnafPreCompInfo; } private static byte[] Trim(byte[] a, int length) { byte[] result = new byte[length]; Array.Copy(a, 0, result, 0, result.Length); return result; } private static int[] Trim(int[] a, int length) { int[] result = new int[length]; Array.Copy(a, 0, result, 0, result.Length); return result; } private static ECPoint[] ResizeTable(ECPoint[] a, int length) { ECPoint[] result = new ECPoint[length]; Array.Copy(a, 0, result, 0, a.Length); return result; } } } #endif