public override ECPoint Twice() { if (base.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP160R1FieldElement rawYCoord = (SecP160R1FieldElement)base.RawYCoord; if (rawYCoord.IsZero) { return(curve.Infinity); } SecP160R1FieldElement rawXCoord = (SecP160R1FieldElement)base.RawXCoord; SecP160R1FieldElement element3 = (SecP160R1FieldElement)base.RawZCoords[0]; uint[] z = Nat160.Create(); uint[] numArray2 = Nat160.Create(); uint[] numArray3 = Nat160.Create(); SecP160R1Field.Square(rawYCoord.x, numArray3); uint[] numArray4 = Nat160.Create(); SecP160R1Field.Square(numArray3, numArray4); bool isOne = element3.IsOne; uint[] x = element3.x; if (!isOne) { x = numArray2; SecP160R1Field.Square(element3.x, x); } SecP160R1Field.Subtract(rawXCoord.x, x, z); uint[] numArray6 = numArray2; SecP160R1Field.Add(rawXCoord.x, x, numArray6); SecP160R1Field.Multiply(numArray6, z, numArray6); SecP160R1Field.Reduce32(Nat160.AddBothTo(numArray6, numArray6, numArray6), numArray6); uint[] numArray7 = numArray3; SecP160R1Field.Multiply(numArray3, rawXCoord.x, numArray7); SecP160R1Field.Reduce32(Nat.ShiftUpBits(5, numArray7, 2, 0), numArray7); SecP160R1Field.Reduce32(Nat.ShiftUpBits(5, numArray4, 3, 0, z), z); SecP160R1FieldElement element4 = new SecP160R1FieldElement(numArray4); SecP160R1Field.Square(numArray6, element4.x); SecP160R1Field.Subtract(element4.x, numArray7, element4.x); SecP160R1Field.Subtract(element4.x, numArray7, element4.x); SecP160R1FieldElement y = new SecP160R1FieldElement(numArray7); SecP160R1Field.Subtract(numArray7, element4.x, y.x); SecP160R1Field.Multiply(y.x, numArray6, y.x); SecP160R1Field.Subtract(y.x, z, y.x); SecP160R1FieldElement element6 = new SecP160R1FieldElement(numArray6); SecP160R1Field.Twice(rawYCoord.x, element6.x); if (!isOne) { SecP160R1Field.Multiply(element6.x, element3.x, element6.x); } return(new SecP160R1Point(curve, element4, y, new ECFieldElement[] { element6 }, base.IsCompressed)); }
public override ECPoint Twice() { if (base.IsInfinity) { return(this); } ECCurve curve = Curve; SecP160R2FieldElement secP160R2FieldElement = (SecP160R2FieldElement)base.RawYCoord; if (secP160R2FieldElement.IsZero) { return(curve.Infinity); } SecP160R2FieldElement secP160R2FieldElement2 = (SecP160R2FieldElement)base.RawXCoord; SecP160R2FieldElement secP160R2FieldElement3 = (SecP160R2FieldElement)base.RawZCoords[0]; uint[] array = Nat160.Create(); SecP160R2Field.Square(secP160R2FieldElement.x, array); uint[] array2 = Nat160.Create(); SecP160R2Field.Square(array, array2); uint[] array3 = Nat160.Create(); SecP160R2Field.Square(secP160R2FieldElement2.x, array3); uint x = Nat160.AddBothTo(array3, array3, array3); SecP160R2Field.Reduce32(x, array3); uint[] array4 = array; SecP160R2Field.Multiply(array, secP160R2FieldElement2.x, array4); x = Nat.ShiftUpBits(5, array4, 2, 0u); SecP160R2Field.Reduce32(x, array4); uint[] array5 = Nat160.Create(); x = Nat.ShiftUpBits(5, array2, 3, 0u, array5); SecP160R2Field.Reduce32(x, array5); SecP160R2FieldElement secP160R2FieldElement4 = new SecP160R2FieldElement(array2); SecP160R2Field.Square(array3, secP160R2FieldElement4.x); SecP160R2Field.Subtract(secP160R2FieldElement4.x, array4, secP160R2FieldElement4.x); SecP160R2Field.Subtract(secP160R2FieldElement4.x, array4, secP160R2FieldElement4.x); SecP160R2FieldElement secP160R2FieldElement5 = new SecP160R2FieldElement(array4); SecP160R2Field.Subtract(array4, secP160R2FieldElement4.x, secP160R2FieldElement5.x); SecP160R2Field.Multiply(secP160R2FieldElement5.x, array3, secP160R2FieldElement5.x); SecP160R2Field.Subtract(secP160R2FieldElement5.x, array5, secP160R2FieldElement5.x); SecP160R2FieldElement secP160R2FieldElement6 = new SecP160R2FieldElement(array3); SecP160R2Field.Twice(secP160R2FieldElement.x, secP160R2FieldElement6.x); if (!secP160R2FieldElement3.IsOne) { SecP160R2Field.Multiply(secP160R2FieldElement6.x, secP160R2FieldElement3.x, secP160R2FieldElement6.x); } return(new SecP160K1Point(curve, secP160R2FieldElement4, secP160R2FieldElement5, new ECFieldElement[1] { secP160R2FieldElement6 }, base.IsCompressed)); }
// B.3 pg 62 public override ECPoint Twice() { if (this.IsInfinity) return this; ECCurve curve = this.Curve; SecP160R2FieldElement Y1 = (SecP160R2FieldElement)this.RawYCoord; if (Y1.IsZero) return curve.Infinity; SecP160R2FieldElement X1 = (SecP160R2FieldElement)this.RawXCoord, Z1 = (SecP160R2FieldElement)this.RawZCoords[0]; uint c; uint[] Y1Squared = Nat160.Create(); SecP160R2Field.Square(Y1.x, Y1Squared); uint[] T = Nat160.Create(); SecP160R2Field.Square(Y1Squared, T); uint[] M = Nat160.Create(); SecP160R2Field.Square(X1.x, M); c = Nat160.AddBothTo(M, M, M); SecP160R2Field.Reduce32(c, M); uint[] S = Y1Squared; SecP160R2Field.Multiply(Y1Squared, X1.x, S); c = Nat.ShiftUpBits(5, S, 2, 0); SecP160R2Field.Reduce32(c, S); uint[] t1 = Nat160.Create(); c = Nat.ShiftUpBits(5, T, 3, 0, t1); SecP160R2Field.Reduce32(c, t1); SecP160R2FieldElement X3 = new SecP160R2FieldElement(T); SecP160R2Field.Square(M, X3.x); SecP160R2Field.Subtract(X3.x, S, X3.x); SecP160R2Field.Subtract(X3.x, S, X3.x); SecP160R2FieldElement Y3 = new SecP160R2FieldElement(S); SecP160R2Field.Subtract(S, X3.x, Y3.x); SecP160R2Field.Multiply(Y3.x, M, Y3.x); SecP160R2Field.Subtract(Y3.x, t1, Y3.x); SecP160R2FieldElement Z3 = new SecP160R2FieldElement(M); SecP160R2Field.Twice(Y1.x, Z3.x); if (!Z1.IsOne) { SecP160R2Field.Multiply(Z3.x, Z1.x, Z3.x); } return new SecP160K1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed); }
public override ECPoint Twice() { if (base.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP160R2FieldElement rawYCoord = (SecP160R2FieldElement)base.RawYCoord; if (rawYCoord.IsZero) { return(curve.Infinity); } SecP160R2FieldElement rawXCoord = (SecP160R2FieldElement)base.RawXCoord; SecP160R2FieldElement element3 = (SecP160R2FieldElement)base.RawZCoords[0]; uint[] z = Nat160.Create(); SecP160R2Field.Square(rawYCoord.x, z); uint[] numArray2 = Nat160.Create(); SecP160R2Field.Square(z, numArray2); uint[] numArray3 = Nat160.Create(); SecP160R2Field.Square(rawXCoord.x, numArray3); SecP160R2Field.Reduce32(Nat160.AddBothTo(numArray3, numArray3, numArray3), numArray3); uint[] numArray4 = z; SecP160R2Field.Multiply(z, rawXCoord.x, numArray4); SecP160R2Field.Reduce32(Nat.ShiftUpBits(5, numArray4, 2, 0), numArray4); uint[] numArray5 = Nat160.Create(); SecP160R2Field.Reduce32(Nat.ShiftUpBits(5, numArray2, 3, 0, numArray5), numArray5); SecP160R2FieldElement x = new SecP160R2FieldElement(numArray2); SecP160R2Field.Square(numArray3, x.x); SecP160R2Field.Subtract(x.x, numArray4, x.x); SecP160R2Field.Subtract(x.x, numArray4, x.x); SecP160R2FieldElement y = new SecP160R2FieldElement(numArray4); SecP160R2Field.Subtract(numArray4, x.x, y.x); SecP160R2Field.Multiply(y.x, numArray3, y.x); SecP160R2Field.Subtract(y.x, numArray5, y.x); SecP160R2FieldElement element6 = new SecP160R2FieldElement(numArray3); SecP160R2Field.Twice(rawYCoord.x, element6.x); if (!element3.IsOne) { SecP160R2Field.Multiply(element6.x, element3.x, element6.x); } return(new SecP160K1Point(curve, x, y, new ECFieldElement[] { element6 }, base.IsCompressed)); }
public override ECPoint Add(ECPoint b) { if (this.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } if (this == b) { return(Twice()); } ECCurve curve = this.Curve; SecP160R2FieldElement X1 = (SecP160R2FieldElement)this.RawXCoord, Y1 = (SecP160R2FieldElement)this.RawYCoord; SecP160R2FieldElement X2 = (SecP160R2FieldElement)b.RawXCoord, Y2 = (SecP160R2FieldElement)b.RawYCoord; SecP160R2FieldElement Z1 = (SecP160R2FieldElement)this.RawZCoords[0]; SecP160R2FieldElement Z2 = (SecP160R2FieldElement)b.RawZCoords[0]; uint c; uint[] tt1 = Nat160.CreateExt(); uint[] t2 = Nat160.Create(); uint[] t3 = Nat160.Create(); uint[] t4 = Nat160.Create(); bool Z1IsOne = Z1.IsOne; uint[] U2, S2; if (Z1IsOne) { U2 = X2.x; S2 = Y2.x; } else { S2 = t3; SecP160R2Field.Square(Z1.x, S2); U2 = t2; SecP160R2Field.Multiply(S2, X2.x, U2); SecP160R2Field.Multiply(S2, Z1.x, S2); SecP160R2Field.Multiply(S2, Y2.x, S2); } bool Z2IsOne = Z2.IsOne; uint[] U1, S1; if (Z2IsOne) { U1 = X1.x; S1 = Y1.x; } else { S1 = t4; SecP160R2Field.Square(Z2.x, S1); U1 = tt1; SecP160R2Field.Multiply(S1, X1.x, U1); SecP160R2Field.Multiply(S1, Z2.x, S1); SecP160R2Field.Multiply(S1, Y1.x, S1); } uint[] H = Nat160.Create(); SecP160R2Field.Subtract(U1, U2, H); uint[] R = t2; SecP160R2Field.Subtract(S1, S2, R); // Check if b == this or b == -this if (Nat160.IsZero(H)) { if (Nat160.IsZero(R)) { // this == b, i.e. this must be doubled return(this.Twice()); } // this == -b, i.e. the result is the point at infinity return(curve.Infinity); } uint[] HSquared = t3; SecP160R2Field.Square(H, HSquared); uint[] G = Nat160.Create(); SecP160R2Field.Multiply(HSquared, H, G); uint[] V = t3; SecP160R2Field.Multiply(HSquared, U1, V); SecP160R2Field.Negate(G, G); Nat160.Mul(S1, G, tt1); c = Nat160.AddBothTo(V, V, G); SecP160R2Field.Reduce32(c, G); SecP160R2FieldElement X3 = new SecP160R2FieldElement(t4); SecP160R2Field.Square(R, X3.x); SecP160R2Field.Subtract(X3.x, G, X3.x); SecP160R2FieldElement Y3 = new SecP160R2FieldElement(G); SecP160R2Field.Subtract(V, X3.x, Y3.x); SecP160R2Field.MultiplyAddToExt(Y3.x, R, tt1); SecP160R2Field.Reduce(tt1, Y3.x); SecP160R2FieldElement Z3 = new SecP160R2FieldElement(H); if (!Z1IsOne) { SecP160R2Field.Multiply(Z3.x, Z1.x, Z3.x); } if (!Z2IsOne) { SecP160R2Field.Multiply(Z3.x, Z2.x, Z3.x); } ECFieldElement[] zs = new ECFieldElement[] { Z3 }; return(new SecP160R2Point(curve, X3, Y3, zs, IsCompressed)); }
public override ECPoint Add(ECPoint b) { if (base.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } if (this == b) { return(this.Twice()); } ECCurve curve = this.Curve; SecP160R1FieldElement secP160R1FieldElement = (SecP160R1FieldElement)base.RawXCoord; SecP160R1FieldElement secP160R1FieldElement2 = (SecP160R1FieldElement)base.RawYCoord; SecP160R1FieldElement secP160R1FieldElement3 = (SecP160R1FieldElement)b.RawXCoord; SecP160R1FieldElement secP160R1FieldElement4 = (SecP160R1FieldElement)b.RawYCoord; SecP160R1FieldElement secP160R1FieldElement5 = (SecP160R1FieldElement)base.RawZCoords[0]; SecP160R1FieldElement secP160R1FieldElement6 = (SecP160R1FieldElement)b.RawZCoords[0]; uint[] array = Nat160.CreateExt(); uint[] array2 = Nat160.Create(); uint[] array3 = Nat160.Create(); uint[] array4 = Nat160.Create(); bool isOne = secP160R1FieldElement5.IsOne; uint[] array5; uint[] array6; if (isOne) { array5 = secP160R1FieldElement3.x; array6 = secP160R1FieldElement4.x; } else { array6 = array3; SecP160R1Field.Square(secP160R1FieldElement5.x, array6); array5 = array2; SecP160R1Field.Multiply(array6, secP160R1FieldElement3.x, array5); SecP160R1Field.Multiply(array6, secP160R1FieldElement5.x, array6); SecP160R1Field.Multiply(array6, secP160R1FieldElement4.x, array6); } bool isOne2 = secP160R1FieldElement6.IsOne; uint[] array7; uint[] array8; if (isOne2) { array7 = secP160R1FieldElement.x; array8 = secP160R1FieldElement2.x; } else { array8 = array4; SecP160R1Field.Square(secP160R1FieldElement6.x, array8); array7 = array; SecP160R1Field.Multiply(array8, secP160R1FieldElement.x, array7); SecP160R1Field.Multiply(array8, secP160R1FieldElement6.x, array8); SecP160R1Field.Multiply(array8, secP160R1FieldElement2.x, array8); } uint[] array9 = Nat160.Create(); SecP160R1Field.Subtract(array7, array5, array9); uint[] array10 = array2; SecP160R1Field.Subtract(array8, array6, array10); if (!Nat160.IsZero(array9)) { uint[] array11 = array3; SecP160R1Field.Square(array9, array11); uint[] array12 = Nat160.Create(); SecP160R1Field.Multiply(array11, array9, array12); uint[] array13 = array3; SecP160R1Field.Multiply(array11, array7, array13); SecP160R1Field.Negate(array12, array12); Nat160.Mul(array8, array12, array); uint x = Nat160.AddBothTo(array13, array13, array12); SecP160R1Field.Reduce32(x, array12); SecP160R1FieldElement secP160R1FieldElement7 = new SecP160R1FieldElement(array4); SecP160R1Field.Square(array10, secP160R1FieldElement7.x); SecP160R1Field.Subtract(secP160R1FieldElement7.x, array12, secP160R1FieldElement7.x); SecP160R1FieldElement secP160R1FieldElement8 = new SecP160R1FieldElement(array12); SecP160R1Field.Subtract(array13, secP160R1FieldElement7.x, secP160R1FieldElement8.x); SecP160R1Field.MultiplyAddToExt(secP160R1FieldElement8.x, array10, array); SecP160R1Field.Reduce(array, secP160R1FieldElement8.x); SecP160R1FieldElement secP160R1FieldElement9 = new SecP160R1FieldElement(array9); if (!isOne) { SecP160R1Field.Multiply(secP160R1FieldElement9.x, secP160R1FieldElement5.x, secP160R1FieldElement9.x); } if (!isOne2) { SecP160R1Field.Multiply(secP160R1FieldElement9.x, secP160R1FieldElement6.x, secP160R1FieldElement9.x); } ECFieldElement[] zs = new ECFieldElement[] { secP160R1FieldElement9 }; return(new SecP160R1Point(curve, secP160R1FieldElement7, secP160R1FieldElement8, zs, base.IsCompressed)); } if (Nat160.IsZero(array10)) { return(this.Twice()); } return(curve.Infinity); }
public override ECPoint Add(ECPoint b) { uint[] numArray5; uint[] numArray6; uint[] numArray7; uint[] numArray8; if (base.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } if (this == b) { return(this.Twice()); } ECCurve curve = this.Curve; SecP160R1FieldElement rawXCoord = (SecP160R1FieldElement)base.RawXCoord; SecP160R1FieldElement rawYCoord = (SecP160R1FieldElement)base.RawYCoord; SecP160R1FieldElement element3 = (SecP160R1FieldElement)b.RawXCoord; SecP160R1FieldElement element4 = (SecP160R1FieldElement)b.RawYCoord; SecP160R1FieldElement element5 = (SecP160R1FieldElement)base.RawZCoords[0]; SecP160R1FieldElement element6 = (SecP160R1FieldElement)b.RawZCoords[0]; uint[] zz = Nat160.CreateExt(); uint[] numArray2 = Nat160.Create(); uint[] numArray3 = Nat160.Create(); uint[] x = Nat160.Create(); bool isOne = element5.IsOne; if (isOne) { numArray5 = element3.x; numArray6 = element4.x; } else { numArray6 = numArray3; SecP160R1Field.Square(element5.x, numArray6); numArray5 = numArray2; SecP160R1Field.Multiply(numArray6, element3.x, numArray5); SecP160R1Field.Multiply(numArray6, element5.x, numArray6); SecP160R1Field.Multiply(numArray6, element4.x, numArray6); } bool flag2 = element6.IsOne; if (flag2) { numArray7 = rawXCoord.x; numArray8 = rawYCoord.x; } else { numArray8 = x; SecP160R1Field.Square(element6.x, numArray8); numArray7 = zz; SecP160R1Field.Multiply(numArray8, rawXCoord.x, numArray7); SecP160R1Field.Multiply(numArray8, element6.x, numArray8); SecP160R1Field.Multiply(numArray8, rawYCoord.x, numArray8); } uint[] z = Nat160.Create(); SecP160R1Field.Subtract(numArray7, numArray5, z); uint[] numArray10 = numArray2; SecP160R1Field.Subtract(numArray8, numArray6, numArray10); if (Nat160.IsZero(z)) { if (Nat160.IsZero(numArray10)) { return(this.Twice()); } return(curve.Infinity); } uint[] numArray11 = numArray3; SecP160R1Field.Square(z, numArray11); uint[] numArray12 = Nat160.Create(); SecP160R1Field.Multiply(numArray11, z, numArray12); uint[] numArray13 = numArray3; SecP160R1Field.Multiply(numArray11, numArray7, numArray13); SecP160R1Field.Negate(numArray12, numArray12); Nat160.Mul(numArray8, numArray12, zz); SecP160R1Field.Reduce32(Nat160.AddBothTo(numArray13, numArray13, numArray12), numArray12); SecP160R1FieldElement element7 = new SecP160R1FieldElement(x); SecP160R1Field.Square(numArray10, element7.x); SecP160R1Field.Subtract(element7.x, numArray12, element7.x); SecP160R1FieldElement y = new SecP160R1FieldElement(numArray12); SecP160R1Field.Subtract(numArray13, element7.x, y.x); SecP160R1Field.MultiplyAddToExt(y.x, numArray10, zz); SecP160R1Field.Reduce(zz, y.x); SecP160R1FieldElement element9 = new SecP160R1FieldElement(z); if (!isOne) { SecP160R1Field.Multiply(element9.x, element5.x, element9.x); } if (!flag2) { SecP160R1Field.Multiply(element9.x, element6.x, element9.x); } ECFieldElement[] zs = new ECFieldElement[] { element9 }; return(new SecP160R1Point(curve, element7, y, zs, base.IsCompressed)); }
public override ECPoint Twice() { if (this.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP160R2FieldElement Y1 = (SecP160R2FieldElement)this.RawYCoord; if (Y1.IsZero) { return(curve.Infinity); } SecP160R2FieldElement X1 = (SecP160R2FieldElement)this.RawXCoord, Z1 = (SecP160R2FieldElement)this.RawZCoords[0]; uint c; uint[] t1 = Nat160.Create(); uint[] t2 = Nat160.Create(); uint[] Y1Squared = Nat160.Create(); SecP160R2Field.Square(Y1.x, Y1Squared); uint[] T = Nat160.Create(); SecP160R2Field.Square(Y1Squared, T); bool Z1IsOne = Z1.IsOne; uint[] Z1Squared = Z1.x; if (!Z1IsOne) { Z1Squared = t2; SecP160R2Field.Square(Z1.x, Z1Squared); } SecP160R2Field.Subtract(X1.x, Z1Squared, t1); uint[] M = t2; SecP160R2Field.Add(X1.x, Z1Squared, M); SecP160R2Field.Multiply(M, t1, M); c = Nat160.AddBothTo(M, M, M); SecP160R2Field.Reduce32(c, M); uint[] S = Y1Squared; SecP160R2Field.Multiply(Y1Squared, X1.x, S); c = Nat.ShiftUpBits(5, S, 2, 0); SecP160R2Field.Reduce32(c, S); c = Nat.ShiftUpBits(5, T, 3, 0, t1); SecP160R2Field.Reduce32(c, t1); SecP160R2FieldElement X3 = new SecP160R2FieldElement(T); SecP160R2Field.Square(M, X3.x); SecP160R2Field.Subtract(X3.x, S, X3.x); SecP160R2Field.Subtract(X3.x, S, X3.x); SecP160R2FieldElement Y3 = new SecP160R2FieldElement(S); SecP160R2Field.Subtract(S, X3.x, Y3.x); SecP160R2Field.Multiply(Y3.x, M, Y3.x); SecP160R2Field.Subtract(Y3.x, t1, Y3.x); SecP160R2FieldElement Z3 = new SecP160R2FieldElement(M); SecP160R2Field.Twice(Y1.x, Z3.x); if (!Z1IsOne) { SecP160R2Field.Multiply(Z3.x, Z1.x, Z3.x); } return(new SecP160R2Point(curve, X3, Y3, new ECFieldElement[] { Z3 })); }