#if !BESTHTTP_DISABLE_ALTERNATE_SSL && (!UNITY_WEBGL || UNITY_EDITOR) using System; using Org.BouncyCastle.Math.EC.Endo; using Org.BouncyCastle.Math.EC.Multiplier; using Org.BouncyCastle.Math.Field; namespace Org.BouncyCastle.Math.EC { public class ECAlgorithms { public static bool IsF2mCurve(ECCurve c) { return IsF2mField(c.Field); } public static bool IsF2mField(IFiniteField field) { return field.Dimension > 1 && field.Characteristic.Equals(BigInteger.Two) && field is IPolynomialExtensionField; } public static bool IsFpCurve(ECCurve c) { return IsFpField(c.Field); } public static bool IsFpField(IFiniteField field) { return field.Dimension == 1; } public static ECPoint SumOfMultiplies(ECPoint[] ps, BigInteger[] ks) { if (ps == null || ks == null || ps.Length != ks.Length || ps.Length < 1) throw new ArgumentException("point and scalar arrays should be non-null, and of equal, non-zero, length"); int count = ps.Length; switch (count) { case 1: return ps[0].Multiply(ks[0]); case 2: return SumOfTwoMultiplies(ps[0], ks[0], ps[1], ks[1]); default: break; } ECPoint p = ps[0]; ECCurve c = p.Curve; ECPoint[] imported = new ECPoint[count]; imported[0] = p; for (int i = 1; i < count; ++i) { imported[i] = ImportPoint(c, ps[i]); } GlvEndomorphism glvEndomorphism = c.GetEndomorphism() as GlvEndomorphism; if (glvEndomorphism != null) { return ValidatePoint(ImplSumOfMultipliesGlv(imported, ks, glvEndomorphism)); } return ValidatePoint(ImplSumOfMultiplies(imported, ks)); } public static ECPoint SumOfTwoMultiplies(ECPoint P, BigInteger a, ECPoint Q, BigInteger b) { ECCurve cp = P.Curve; Q = ImportPoint(cp, Q); // Point multiplication for Koblitz curves (using WTNAF) beats Shamir's trick { AbstractF2mCurve f2mCurve = cp as AbstractF2mCurve; if (f2mCurve != null && f2mCurve.IsKoblitz) { return ValidatePoint(P.Multiply(a).Add(Q.Multiply(b))); } } GlvEndomorphism glvEndomorphism = cp.GetEndomorphism() as GlvEndomorphism; if (glvEndomorphism != null) { return ValidatePoint( ImplSumOfMultipliesGlv(new ECPoint[] { P, Q }, new BigInteger[] { a, b }, glvEndomorphism)); } return ValidatePoint(ImplShamirsTrickWNaf(P, a, Q, b)); } /* * "Shamir's Trick", originally due to E. G. Straus * (Addition chains of vectors. American Mathematical Monthly, * 71(7):806-808, Aug./Sept. 1964) * * Input: The points P, Q, scalar k = (km?, ... , k1, k0) * and scalar l = (lm?, ... , l1, l0). * Output: R = k * P + l * Q. * 1: Z <- P + Q * 2: R <- O * 3: for i from m-1 down to 0 do * 4: R <- R + R {point doubling} * 5: if (ki = 1) and (li = 0) then R <- R + P end if * 6: if (ki = 0) and (li = 1) then R <- R + Q end if * 7: if (ki = 1) and (li = 1) then R <- R + Z end if * 8: end for * 9: return R */ public static ECPoint ShamirsTrick(ECPoint P, BigInteger k, ECPoint Q, BigInteger l) { ECCurve cp = P.Curve; Q = ImportPoint(cp, Q); return ValidatePoint(ImplShamirsTrickJsf(P, k, Q, l)); } public static ECPoint ImportPoint(ECCurve c, ECPoint p) { ECCurve cp = p.Curve; if (!c.Equals(cp)) throw new ArgumentException("Point must be on the same curve"); return c.ImportPoint(p); } public static void MontgomeryTrick(ECFieldElement[] zs, int off, int len) { MontgomeryTrick(zs, off, len, null); } public static void MontgomeryTrick(ECFieldElement[] zs, int off, int len, ECFieldElement scale) { /* * Uses the "Montgomery Trick" to invert many field elements, with only a single actual * field inversion. See e.g. the paper: * "Fast Multi-scalar Multiplication Methods on Elliptic Curves with Precomputation Strategy Using Montgomery Trick" * by Katsuyuki Okeya, Kouichi Sakurai. */ ECFieldElement[] c = new ECFieldElement[len]; c[0] = zs[off]; int i = 0; while (++i < len) { c[i] = c[i - 1].Multiply(zs[off + i]); } --i; if (scale != null) { c[i] = c[i].Multiply(scale); } ECFieldElement u = c[i].Invert(); while (i > 0) { int j = off + i--; ECFieldElement tmp = zs[j]; zs[j] = c[i].Multiply(u); u = u.Multiply(tmp); } zs[off] = u; } /** * Simple shift-and-add multiplication. Serves as reference implementation * to verify (possibly faster) implementations, and for very small scalars. * * @param p * The point to multiply. * @param k * The multiplier. * @return The result of the point multiplication kP. */ public static ECPoint ReferenceMultiply(ECPoint p, BigInteger k) { BigInteger x = k.Abs(); ECPoint q = p.Curve.Infinity; int t = x.BitLength; if (t > 0) { if (x.TestBit(0)) { q = p; } for (int i = 1; i < t; i++) { p = p.Twice(); if (x.TestBit(i)) { q = q.Add(p); } } } return k.SignValue < 0 ? q.Negate() : q; } public static ECPoint ValidatePoint(ECPoint p) { if (!p.IsValid()) throw new ArgumentException("Invalid point", "p"); return p; } internal static ECPoint ImplShamirsTrickJsf(ECPoint P, BigInteger k, ECPoint Q, BigInteger l) { ECCurve curve = P.Curve; ECPoint infinity = curve.Infinity; // TODO conjugate co-Z addition (ZADDC) can return both of these ECPoint PaddQ = P.Add(Q); ECPoint PsubQ = P.Subtract(Q); ECPoint[] points = new ECPoint[] { Q, PsubQ, P, PaddQ }; curve.NormalizeAll(points); ECPoint[] table = new ECPoint[] { points[3].Negate(), points[2].Negate(), points[1].Negate(), points[0].Negate(), infinity, points[0], points[1], points[2], points[3] }; byte[] jsf = WNafUtilities.GenerateJsf(k, l); ECPoint R = infinity; int i = jsf.Length; while (--i >= 0) { int jsfi = jsf[i]; // NOTE: The shifting ensures the sign is extended correctly int kDigit = ((jsfi << 24) >> 28), lDigit = ((jsfi << 28) >> 28); int index = 4 + (kDigit * 3) + lDigit; R = R.TwicePlus(table[index]); } return R; } internal static ECPoint ImplShamirsTrickWNaf(ECPoint P, BigInteger k, ECPoint Q, BigInteger l) { bool negK = k.SignValue < 0, negL = l.SignValue < 0; k = k.Abs(); l = l.Abs(); int widthP = System.Math.Max(2, System.Math.Min(16, WNafUtilities.GetWindowSize(k.BitLength))); int widthQ = System.Math.Max(2, System.Math.Min(16, WNafUtilities.GetWindowSize(l.BitLength))); WNafPreCompInfo infoP = WNafUtilities.Precompute(P, widthP, true); WNafPreCompInfo infoQ = WNafUtilities.Precompute(Q, widthQ, true); ECPoint[] preCompP = negK ? infoP.PreCompNeg : infoP.PreComp; ECPoint[] preCompQ = negL ? infoQ.PreCompNeg : infoQ.PreComp; ECPoint[] preCompNegP = negK ? infoP.PreComp : infoP.PreCompNeg; ECPoint[] preCompNegQ = negL ? infoQ.PreComp : infoQ.PreCompNeg; byte[] wnafP = WNafUtilities.GenerateWindowNaf(widthP, k); byte[] wnafQ = WNafUtilities.GenerateWindowNaf(widthQ, l); return ImplShamirsTrickWNaf(preCompP, preCompNegP, wnafP, preCompQ, preCompNegQ, wnafQ); } internal static ECPoint ImplShamirsTrickWNaf(ECPoint P, BigInteger k, ECPointMap pointMapQ, BigInteger l) { bool negK = k.SignValue < 0, negL = l.SignValue < 0; k = k.Abs(); l = l.Abs(); int width = System.Math.Max(2, System.Math.Min(16, WNafUtilities.GetWindowSize(System.Math.Max(k.BitLength, l.BitLength)))); ECPoint Q = WNafUtilities.MapPointWithPrecomp(P, width, true, pointMapQ); WNafPreCompInfo infoP = WNafUtilities.GetWNafPreCompInfo(P); WNafPreCompInfo infoQ = WNafUtilities.GetWNafPreCompInfo(Q); ECPoint[] preCompP = negK ? infoP.PreCompNeg : infoP.PreComp; ECPoint[] preCompQ = negL ? infoQ.PreCompNeg : infoQ.PreComp; ECPoint[] preCompNegP = negK ? infoP.PreComp : infoP.PreCompNeg; ECPoint[] preCompNegQ = negL ? infoQ.PreComp : infoQ.PreCompNeg; byte[] wnafP = WNafUtilities.GenerateWindowNaf(width, k); byte[] wnafQ = WNafUtilities.GenerateWindowNaf(width, l); return ImplShamirsTrickWNaf(preCompP, preCompNegP, wnafP, preCompQ, preCompNegQ, wnafQ); } private static ECPoint ImplShamirsTrickWNaf(ECPoint[] preCompP, ECPoint[] preCompNegP, byte[] wnafP, ECPoint[] preCompQ, ECPoint[] preCompNegQ, byte[] wnafQ) { int len = System.Math.Max(wnafP.Length, wnafQ.Length); ECCurve curve = preCompP[0].Curve; ECPoint infinity = curve.Infinity; ECPoint R = infinity; int zeroes = 0; for (int i = len - 1; i >= 0; --i) { int wiP = i < wnafP.Length ? (int)(sbyte)wnafP[i] : 0; int wiQ = i < wnafQ.Length ? (int)(sbyte)wnafQ[i] : 0; if ((wiP | wiQ) == 0) { ++zeroes; continue; } ECPoint r = infinity; if (wiP != 0) { int nP = System.Math.Abs(wiP); ECPoint[] tableP = wiP < 0 ? preCompNegP : preCompP; r = r.Add(tableP[nP >> 1]); } if (wiQ != 0) { int nQ = System.Math.Abs(wiQ); ECPoint[] tableQ = wiQ < 0 ? preCompNegQ : preCompQ; r = r.Add(tableQ[nQ >> 1]); } if (zeroes > 0) { R = R.TimesPow2(zeroes); zeroes = 0; } R = R.TwicePlus(r); } if (zeroes > 0) { R = R.TimesPow2(zeroes); } return R; } internal static ECPoint ImplSumOfMultiplies(ECPoint[] ps, BigInteger[] ks) { int count = ps.Length; bool[] negs = new bool[count]; WNafPreCompInfo[] infos = new WNafPreCompInfo[count]; byte[][] wnafs = new byte[count][]; for (int i = 0; i < count; ++i) { BigInteger ki = ks[i]; negs[i] = ki.SignValue < 0; ki = ki.Abs(); int width = System.Math.Max(2, System.Math.Min(16, WNafUtilities.GetWindowSize(ki.BitLength))); infos[i] = WNafUtilities.Precompute(ps[i], width, true); wnafs[i] = WNafUtilities.GenerateWindowNaf(width, ki); } return ImplSumOfMultiplies(negs, infos, wnafs); } internal static ECPoint ImplSumOfMultipliesGlv(ECPoint[] ps, BigInteger[] ks, GlvEndomorphism glvEndomorphism) { BigInteger n = ps[0].Curve.Order; int len = ps.Length; BigInteger[] abs = new BigInteger[len << 1]; for (int i = 0, j = 0; i < len; ++i) { BigInteger[] ab = glvEndomorphism.DecomposeScalar(ks[i].Mod(n)); abs[j++] = ab[0]; abs[j++] = ab[1]; } ECPointMap pointMap = glvEndomorphism.PointMap; if (glvEndomorphism.HasEfficientPointMap) { return ECAlgorithms.ImplSumOfMultiplies(ps, pointMap, abs); } ECPoint[] pqs = new ECPoint[len << 1]; for (int i = 0, j = 0; i < len; ++i) { ECPoint p = ps[i], q = pointMap.Map(p); pqs[j++] = p; pqs[j++] = q; } return ECAlgorithms.ImplSumOfMultiplies(pqs, abs); } internal static ECPoint ImplSumOfMultiplies(ECPoint[] ps, ECPointMap pointMap, BigInteger[] ks) { int halfCount = ps.Length, fullCount = halfCount << 1; bool[] negs = new bool[fullCount]; WNafPreCompInfo[] infos = new WNafPreCompInfo[fullCount]; byte[][] wnafs = new byte[fullCount][]; for (int i = 0; i < halfCount; ++i) { int j0 = i << 1, j1 = j0 + 1; BigInteger kj0 = ks[j0]; negs[j0] = kj0.SignValue < 0; kj0 = kj0.Abs(); BigInteger kj1 = ks[j1]; negs[j1] = kj1.SignValue < 0; kj1 = kj1.Abs(); int width = System.Math.Max(2, System.Math.Min(16, WNafUtilities.GetWindowSize(System.Math.Max(kj0.BitLength, kj1.BitLength)))); ECPoint P = ps[i], Q = WNafUtilities.MapPointWithPrecomp(P, width, true, pointMap); infos[j0] = WNafUtilities.GetWNafPreCompInfo(P); infos[j1] = WNafUtilities.GetWNafPreCompInfo(Q); wnafs[j0] = WNafUtilities.GenerateWindowNaf(width, kj0); wnafs[j1] = WNafUtilities.GenerateWindowNaf(width, kj1); } return ImplSumOfMultiplies(negs, infos, wnafs); } private static ECPoint ImplSumOfMultiplies(bool[] negs, WNafPreCompInfo[] infos, byte[][] wnafs) { int len = 0, count = wnafs.Length; for (int i = 0; i < count; ++i) { len = System.Math.Max(len, wnafs[i].Length); } ECCurve curve = infos[0].PreComp[0].Curve; ECPoint infinity = curve.Infinity; ECPoint R = infinity; int zeroes = 0; for (int i = len - 1; i >= 0; --i) { ECPoint r = infinity; for (int j = 0; j < count; ++j) { byte[] wnaf = wnafs[j]; int wi = i < wnaf.Length ? (int)(sbyte)wnaf[i] : 0; if (wi != 0) { int n = System.Math.Abs(wi); WNafPreCompInfo info = infos[j]; ECPoint[] table = (wi < 0 == negs[j]) ? info.PreComp : info.PreCompNeg; r = r.Add(table[n >> 1]); } } if (r == infinity) { ++zeroes; continue; } if (zeroes > 0) { R = R.TimesPow2(zeroes); zeroes = 0; } R = R.TwicePlus(r); } if (zeroes > 0) { R = R.TimesPow2(zeroes); } return R; } } } #endif