public override ECPoint Add(ECPoint b) { if (base.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } ECCurve curve = Curve; ECFieldElement rawXCoord = base.RawXCoord; ECFieldElement rawXCoord2 = b.RawXCoord; if (rawXCoord.IsZero) { if (rawXCoord2.IsZero) { return(curve.Infinity); } return(b.Add(this)); } ECFieldElement rawYCoord = base.RawYCoord; ECFieldElement eCFieldElement = base.RawZCoords[0]; ECFieldElement rawYCoord2 = b.RawYCoord; ECFieldElement eCFieldElement2 = b.RawZCoords[0]; bool isOne = eCFieldElement.IsOne; ECFieldElement eCFieldElement3 = rawXCoord2; ECFieldElement eCFieldElement4 = rawYCoord2; if (!isOne) { eCFieldElement3 = eCFieldElement3.Multiply(eCFieldElement); eCFieldElement4 = eCFieldElement4.Multiply(eCFieldElement); } bool isOne2 = eCFieldElement2.IsOne; ECFieldElement eCFieldElement5 = rawXCoord; ECFieldElement eCFieldElement6 = rawYCoord; if (!isOne2) { eCFieldElement5 = eCFieldElement5.Multiply(eCFieldElement2); eCFieldElement6 = eCFieldElement6.Multiply(eCFieldElement2); } ECFieldElement eCFieldElement7 = eCFieldElement6.Add(eCFieldElement4); ECFieldElement eCFieldElement8 = eCFieldElement5.Add(eCFieldElement3); if (eCFieldElement8.IsZero) { if (eCFieldElement7.IsZero) { return(Twice()); } return(curve.Infinity); } ECFieldElement eCFieldElement10; ECFieldElement y; ECFieldElement eCFieldElement12; if (rawXCoord2.IsZero) { ECPoint eCPoint = Normalize(); rawXCoord = eCPoint.XCoord; ECFieldElement yCoord = eCPoint.YCoord; ECFieldElement b2 = rawYCoord2; ECFieldElement eCFieldElement9 = yCoord.Add(b2).Divide(rawXCoord); eCFieldElement10 = eCFieldElement9.Square().Add(eCFieldElement9).Add(rawXCoord); if (eCFieldElement10.IsZero) { return(new SecT409K1Point(curve, eCFieldElement10, curve.B, base.IsCompressed)); } ECFieldElement eCFieldElement11 = eCFieldElement9.Multiply(rawXCoord.Add(eCFieldElement10)).Add(eCFieldElement10).Add(yCoord); y = eCFieldElement11.Divide(eCFieldElement10).Add(eCFieldElement10); eCFieldElement12 = curve.FromBigInteger(BigInteger.One); } else { eCFieldElement8 = eCFieldElement8.Square(); ECFieldElement eCFieldElement13 = eCFieldElement7.Multiply(eCFieldElement5); ECFieldElement eCFieldElement14 = eCFieldElement7.Multiply(eCFieldElement3); eCFieldElement10 = eCFieldElement13.Multiply(eCFieldElement14); if (eCFieldElement10.IsZero) { return(new SecT409K1Point(curve, eCFieldElement10, curve.B, base.IsCompressed)); } ECFieldElement eCFieldElement15 = eCFieldElement7.Multiply(eCFieldElement8); if (!isOne2) { eCFieldElement15 = eCFieldElement15.Multiply(eCFieldElement2); } y = eCFieldElement14.Add(eCFieldElement8).SquarePlusProduct(eCFieldElement15, rawYCoord.Add(eCFieldElement)); eCFieldElement12 = eCFieldElement15; if (!isOne) { eCFieldElement12 = eCFieldElement12.Multiply(eCFieldElement); } } return(new SecT409K1Point(curve, eCFieldElement10, y, new ECFieldElement[1] { eCFieldElement12 }, base.IsCompressed)); }
public override ECPoint Add(ECPoint b) { if (this.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } ECCurve curve = this.Curve; ECFieldElement X1 = this.RawXCoord; ECFieldElement X2 = b.RawXCoord; if (X1.IsZero) { if (X2.IsZero) { return(curve.Infinity); } return(b.Add(this)); } ECFieldElement L1 = this.RawYCoord, Z1 = this.RawZCoords[0]; ECFieldElement L2 = b.RawYCoord, Z2 = b.RawZCoords[0]; bool Z1IsOne = Z1.IsOne; ECFieldElement U2 = X2, S2 = L2; if (!Z1IsOne) { U2 = U2.Multiply(Z1); S2 = S2.Multiply(Z1); } bool Z2IsOne = Z2.IsOne; ECFieldElement U1 = X1, S1 = L1; if (!Z2IsOne) { U1 = U1.Multiply(Z2); S1 = S1.Multiply(Z2); } ECFieldElement A = S1.Add(S2); ECFieldElement B = U1.Add(U2); if (B.IsZero) { if (A.IsZero) { return(Twice()); } return(curve.Infinity); } ECFieldElement X3, L3, Z3; if (X2.IsZero) { // TODO This can probably be optimized quite a bit ECPoint p = this.Normalize(); X1 = p.XCoord; ECFieldElement Y1 = p.YCoord; ECFieldElement Y2 = L2; ECFieldElement L = Y1.Add(Y2).Divide(X1); //X3 = L.Square().Add(L).Add(X1).Add(curve.A); X3 = L.Square().Add(L).Add(X1).AddOne(); if (X3.IsZero) { return(new SecT163R2Point(curve, X3, curve.B.Sqrt(), IsCompressed)); } ECFieldElement Y3 = L.Multiply(X1.Add(X3)).Add(X3).Add(Y1); L3 = Y3.Divide(X3).Add(X3); Z3 = curve.FromBigInteger(BigInteger.One); } else { B = B.Square(); ECFieldElement AU1 = A.Multiply(U1); ECFieldElement AU2 = A.Multiply(U2); X3 = AU1.Multiply(AU2); if (X3.IsZero) { return(new SecT163R2Point(curve, X3, curve.B.Sqrt(), IsCompressed)); } ECFieldElement ABZ2 = A.Multiply(B); if (!Z2IsOne) { ABZ2 = ABZ2.Multiply(Z2); } L3 = AU2.Add(B).SquarePlusProduct(ABZ2, L1.Add(Z1)); Z3 = ABZ2; if (!Z1IsOne) { Z3 = Z3.Multiply(Z1); } } return(new SecT163R2Point(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed)); }
public override ECPoint TwicePlus(ECPoint b) { if (this.IsInfinity) { return(b); } if (b.IsInfinity) { return(Twice()); } ECCurve curve = this.Curve; ECFieldElement X1 = this.RawXCoord; if (X1.IsZero) { // A point with X == 0 is it's own Additive inverse return(b); } ECFieldElement X2 = b.RawXCoord, Z2 = b.RawZCoords[0]; if (X2.IsZero || !Z2.IsOne) { return(Twice().Add(b)); } ECFieldElement L1 = this.RawYCoord, Z1 = this.RawZCoords[0]; ECFieldElement L2 = b.RawYCoord; ECFieldElement X1Sq = X1.Square(); ECFieldElement L1Sq = L1.Square(); ECFieldElement Z1Sq = Z1.Square(); ECFieldElement L1Z1 = L1.Multiply(Z1); //ECFieldElement T = curve.A.Multiply(Z1Sq).Add(L1Sq).Add(L1Z1); ECFieldElement T = Z1Sq.Add(L1Sq).Add(L1Z1); ECFieldElement L2plus1 = L2.AddOne(); //ECFieldElement A = curve.A.Add(L2plus1).Multiply(Z1Sq).Add(L1Sq).MultiplyPlusProduct(T, X1Sq, Z1Sq); ECFieldElement A = L2.Multiply(Z1Sq).Add(L1Sq).MultiplyPlusProduct(T, X1Sq, Z1Sq); ECFieldElement X2Z1Sq = X2.Multiply(Z1Sq); ECFieldElement B = X2Z1Sq.Add(T).Square(); if (B.IsZero) { if (A.IsZero) { return(b.Twice()); } return(curve.Infinity); } if (A.IsZero) { return(new SecT163R2Point(curve, A, curve.B.Sqrt(), IsCompressed)); } ECFieldElement X3 = A.Square().Multiply(X2Z1Sq); ECFieldElement Z3 = A.Multiply(B).Multiply(Z1Sq); ECFieldElement L3 = A.Add(B).Square().MultiplyPlusProduct(T, L2plus1, Z3); return(new SecT163R2Point(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed)); }
protected override ECPoint DecompressPoint(int yTilde, BigInteger X1) { ECFieldElement eCFieldElement = FromBigInteger(X1); ECFieldElement eCFieldElement2 = null; if (eCFieldElement.IsZero) { eCFieldElement2 = B.Sqrt(); } else { ECFieldElement beta = eCFieldElement.Square().Invert().Multiply(B) .Add(A) .Add(eCFieldElement); ECFieldElement eCFieldElement3 = SolveQuadraticEquation(beta); if (eCFieldElement3 != null) { if (eCFieldElement3.TestBitZero() != (yTilde == 1)) { eCFieldElement3 = eCFieldElement3.AddOne(); } int coordinateSystem = CoordinateSystem; eCFieldElement2 = ((coordinateSystem != 5 && coordinateSystem != 6) ? eCFieldElement3.Multiply(eCFieldElement) : eCFieldElement3.Add(eCFieldElement)); } } if (eCFieldElement2 == null) { throw new ArgumentException("Invalid point compression"); } return(CreateRawPoint(eCFieldElement, eCFieldElement2, withCompression: true)); }
public override ECPoint Add(ECPoint b) { ECFieldElement element13; ECFieldElement element14; ECFieldElement element15; if (base.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } ECCurve curve = this.Curve; ECFieldElement rawXCoord = base.RawXCoord; ECFieldElement element2 = b.RawXCoord; if (rawXCoord.IsZero) { if (element2.IsZero) { return(curve.Infinity); } return(b.Add(this)); } ECFieldElement rawYCoord = base.RawYCoord; ECFieldElement element4 = base.RawZCoords[0]; ECFieldElement element5 = b.RawYCoord; ECFieldElement element6 = b.RawZCoords[0]; bool isOne = element4.IsOne; ECFieldElement element7 = element2; ECFieldElement element8 = element5; if (!isOne) { element7 = element7.Multiply(element4); element8 = element8.Multiply(element4); } bool flag2 = element6.IsOne; ECFieldElement element9 = rawXCoord; ECFieldElement element10 = rawYCoord; if (!flag2) { element9 = element9.Multiply(element6); element10 = element10.Multiply(element6); } ECFieldElement element11 = element10.Add(element8); ECFieldElement element12 = element9.Add(element7); if (element12.IsZero) { if (element11.IsZero) { return(this.Twice()); } return(curve.Infinity); } if (element2.IsZero) { ECPoint point = this.Normalize(); rawXCoord = point.XCoord; ECFieldElement yCoord = point.YCoord; ECFieldElement element17 = element5; ECFieldElement element18 = yCoord.Add(element17).Divide(rawXCoord); element13 = element18.Square().Add(element18).Add(rawXCoord).Add(curve.A); if (element13.IsZero) { return(new SecT113R2Point(curve, element13, curve.B.Sqrt(), base.IsCompressed)); } element14 = element18.Multiply(rawXCoord.Add(element13)).Add(element13).Add(yCoord).Divide(element13).Add(element13); element15 = curve.FromBigInteger(BigInteger.One); } else { element12 = element12.Square(); ECFieldElement element20 = element11.Multiply(element9); ECFieldElement element21 = element11.Multiply(element7); element13 = element20.Multiply(element21); if (element13.IsZero) { return(new SecT113R2Point(curve, element13, curve.B.Sqrt(), base.IsCompressed)); } ECFieldElement x = element11.Multiply(element12); if (!flag2) { x = x.Multiply(element6); } element14 = element21.Add(element12).SquarePlusProduct(x, rawYCoord.Add(element4)); element15 = x; if (!isOne) { element15 = element15.Multiply(element4); } } return(new SecT113R2Point(curve, element13, element14, new ECFieldElement[] { element15 }, base.IsCompressed)); }
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); }