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; SecP521R1FieldElement X1 = (SecP521R1FieldElement)this.RawXCoord, Y1 = (SecP521R1FieldElement)this.RawYCoord; SecP521R1FieldElement X2 = (SecP521R1FieldElement)b.RawXCoord, Y2 = (SecP521R1FieldElement)b.RawYCoord; SecP521R1FieldElement Z1 = (SecP521R1FieldElement)this.RawZCoords[0]; SecP521R1FieldElement Z2 = (SecP521R1FieldElement)b.RawZCoords[0]; uint[] t1 = Nat.Create(17); uint[] t2 = Nat.Create(17); uint[] t3 = Nat.Create(17); uint[] t4 = Nat.Create(17); bool Z1IsOne = Z1.IsOne; uint[] U2, S2; if (Z1IsOne) { U2 = X2.x; S2 = Y2.x; } else { S2 = t3; SecP521R1Field.Square(Z1.x, S2); U2 = t2; SecP521R1Field.Multiply(S2, X2.x, U2); SecP521R1Field.Multiply(S2, Z1.x, S2); SecP521R1Field.Multiply(S2, Y2.x, S2); } bool Z2IsOne = Z2.IsOne; uint[] U1, S1; if (Z2IsOne) { U1 = X1.x; S1 = Y1.x; } else { S1 = t4; SecP521R1Field.Square(Z2.x, S1); U1 = t1; SecP521R1Field.Multiply(S1, X1.x, U1); SecP521R1Field.Multiply(S1, Z2.x, S1); SecP521R1Field.Multiply(S1, Y1.x, S1); } uint[] H = Nat.Create(17); SecP521R1Field.Subtract(U1, U2, H); uint[] R = t2; SecP521R1Field.Subtract(S1, S2, R); // Check if b == this or b == -this if (Nat.IsZero(17, H)) { if (Nat.IsZero(17, 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; SecP521R1Field.Square(H, HSquared); uint[] G = Nat.Create(17); SecP521R1Field.Multiply(HSquared, H, G); uint[] V = t3; SecP521R1Field.Multiply(HSquared, U1, V); SecP521R1Field.Multiply(S1, G, t1); SecP521R1FieldElement X3 = new SecP521R1FieldElement(t4); SecP521R1Field.Square(R, X3.x); SecP521R1Field.Add(X3.x, G, X3.x); SecP521R1Field.Subtract(X3.x, V, X3.x); SecP521R1Field.Subtract(X3.x, V, X3.x); SecP521R1FieldElement Y3 = new SecP521R1FieldElement(G); SecP521R1Field.Subtract(V, X3.x, Y3.x); SecP521R1Field.Multiply(Y3.x, R, t2); SecP521R1Field.Subtract(t2, t1, Y3.x); SecP521R1FieldElement Z3 = new SecP521R1FieldElement(H); if (!Z1IsOne) { SecP521R1Field.Multiply(Z3.x, Z1.x, Z3.x); } if (!Z2IsOne) { SecP521R1Field.Multiply(Z3.x, Z2.x, Z3.x); } ECFieldElement[] zs = new ECFieldElement[] { Z3 }; return(new SecP521R1Point(curve, X3, Y3, zs)); }
public override ECFieldElement Negate() { uint[] z = Nat.Create(17); SecP521R1Field.Negate(x, z); return(new SecP521R1FieldElement(z)); }
public override ECFieldElement Multiply(ECFieldElement b) { uint[] z = Nat.Create(17); SecP521R1Field.Multiply(x, ((SecP521R1FieldElement)b).x, z); return(new SecP521R1FieldElement(z)); }
public override ECPoint Twice() { if (this.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP521R1FieldElement Y1 = (SecP521R1FieldElement)this.RawYCoord; if (Y1.IsZero) { return(curve.Infinity); } SecP521R1FieldElement X1 = (SecP521R1FieldElement)this.RawXCoord, Z1 = (SecP521R1FieldElement)this.RawZCoords[0]; uint[] t1 = Nat.Create(17); uint[] t2 = Nat.Create(17); uint[] Y1Squared = Nat.Create(17); SecP521R1Field.Square(Y1.x, Y1Squared); uint[] T = Nat.Create(17); SecP521R1Field.Square(Y1Squared, T); bool Z1IsOne = Z1.IsOne; uint[] Z1Squared = Z1.x; if (!Z1IsOne) { Z1Squared = t2; SecP521R1Field.Square(Z1.x, Z1Squared); } SecP521R1Field.Subtract(X1.x, Z1Squared, t1); uint[] M = t2; SecP521R1Field.Add(X1.x, Z1Squared, M); SecP521R1Field.Multiply(M, t1, M); Nat.AddBothTo(17, M, M, M); SecP521R1Field.Reduce23(M); uint[] S = Y1Squared; SecP521R1Field.Multiply(Y1Squared, X1.x, S); Nat.ShiftUpBits(17, S, 2, 0); SecP521R1Field.Reduce23(S); Nat.ShiftUpBits(17, T, 3, 0, t1); SecP521R1Field.Reduce23(t1); SecP521R1FieldElement X3 = new SecP521R1FieldElement(T); SecP521R1Field.Square(M, X3.x); SecP521R1Field.Subtract(X3.x, S, X3.x); SecP521R1Field.Subtract(X3.x, S, X3.x); SecP521R1FieldElement Y3 = new SecP521R1FieldElement(S); SecP521R1Field.Subtract(S, X3.x, Y3.x); SecP521R1Field.Multiply(Y3.x, M, Y3.x); SecP521R1Field.Subtract(Y3.x, t1, Y3.x); SecP521R1FieldElement Z3 = new SecP521R1FieldElement(M); SecP521R1Field.Twice(Y1.x, Z3.x); if (!Z1IsOne) { SecP521R1Field.Multiply(Z3.x, Z1.x, Z3.x); } return(new SecP521R1Point(curve, X3, Y3, new ECFieldElement[] { Z3 })); }
public override ECPoint Add(ECPoint b) { if (base.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } if (this == b) { return(Twice()); } ECCurve curve = Curve; SecP521R1FieldElement secP521R1FieldElement = (SecP521R1FieldElement)base.RawXCoord; SecP521R1FieldElement secP521R1FieldElement2 = (SecP521R1FieldElement)base.RawYCoord; SecP521R1FieldElement secP521R1FieldElement3 = (SecP521R1FieldElement)b.RawXCoord; SecP521R1FieldElement secP521R1FieldElement4 = (SecP521R1FieldElement)b.RawYCoord; SecP521R1FieldElement secP521R1FieldElement5 = (SecP521R1FieldElement)base.RawZCoords[0]; SecP521R1FieldElement secP521R1FieldElement6 = (SecP521R1FieldElement)b.RawZCoords[0]; uint[] array = Nat.Create(17); uint[] array2 = Nat.Create(17); uint[] array3 = Nat.Create(17); uint[] array4 = Nat.Create(17); bool isOne = secP521R1FieldElement5.IsOne; uint[] array5; uint[] array6; if (isOne) { array5 = secP521R1FieldElement3.x; array6 = secP521R1FieldElement4.x; } else { array6 = array3; SecP521R1Field.Square(secP521R1FieldElement5.x, array6); array5 = array2; SecP521R1Field.Multiply(array6, secP521R1FieldElement3.x, array5); SecP521R1Field.Multiply(array6, secP521R1FieldElement5.x, array6); SecP521R1Field.Multiply(array6, secP521R1FieldElement4.x, array6); } bool isOne2 = secP521R1FieldElement6.IsOne; uint[] array7; uint[] array8; if (isOne2) { array7 = secP521R1FieldElement.x; array8 = secP521R1FieldElement2.x; } else { array8 = array4; SecP521R1Field.Square(secP521R1FieldElement6.x, array8); array7 = array; SecP521R1Field.Multiply(array8, secP521R1FieldElement.x, array7); SecP521R1Field.Multiply(array8, secP521R1FieldElement6.x, array8); SecP521R1Field.Multiply(array8, secP521R1FieldElement2.x, array8); } uint[] array9 = Nat.Create(17); SecP521R1Field.Subtract(array7, array5, array9); uint[] array10 = array2; SecP521R1Field.Subtract(array8, array6, array10); if (Nat.IsZero(17, array9)) { if (Nat.IsZero(17, array10)) { return(Twice()); } return(curve.Infinity); } uint[] array11 = array3; SecP521R1Field.Square(array9, array11); uint[] array12 = Nat.Create(17); SecP521R1Field.Multiply(array11, array9, array12); uint[] array13 = array3; SecP521R1Field.Multiply(array11, array7, array13); SecP521R1Field.Multiply(array8, array12, array); SecP521R1FieldElement secP521R1FieldElement7 = new SecP521R1FieldElement(array4); SecP521R1Field.Square(array10, secP521R1FieldElement7.x); SecP521R1Field.Add(secP521R1FieldElement7.x, array12, secP521R1FieldElement7.x); SecP521R1Field.Subtract(secP521R1FieldElement7.x, array13, secP521R1FieldElement7.x); SecP521R1Field.Subtract(secP521R1FieldElement7.x, array13, secP521R1FieldElement7.x); SecP521R1FieldElement secP521R1FieldElement8 = new SecP521R1FieldElement(array12); SecP521R1Field.Subtract(array13, secP521R1FieldElement7.x, secP521R1FieldElement8.x); SecP521R1Field.Multiply(secP521R1FieldElement8.x, array10, array2); SecP521R1Field.Subtract(array2, array, secP521R1FieldElement8.x); SecP521R1FieldElement secP521R1FieldElement9 = new SecP521R1FieldElement(array9); if (!isOne) { SecP521R1Field.Multiply(secP521R1FieldElement9.x, secP521R1FieldElement5.x, secP521R1FieldElement9.x); } if (!isOne2) { SecP521R1Field.Multiply(secP521R1FieldElement9.x, secP521R1FieldElement6.x, secP521R1FieldElement9.x); } ECFieldElement[] zs = new ECFieldElement[1] { secP521R1FieldElement9 }; return(new SecP521R1Point(curve, secP521R1FieldElement7, secP521R1FieldElement8, zs, base.IsCompressed)); }
public override ECFieldElement Subtract(ECFieldElement b) { uint[] z = Nat.Create(17); SecP521R1Field.Subtract(x, ((SecP521R1FieldElement)b).x, z); return(new SecP521R1FieldElement(z)); }
public override ECPoint Twice() { if (base.IsInfinity) { return(this); } ECCurve curve = Curve; SecP521R1FieldElement secP521R1FieldElement = (SecP521R1FieldElement)base.RawYCoord; if (secP521R1FieldElement.IsZero) { return(curve.Infinity); } SecP521R1FieldElement secP521R1FieldElement2 = (SecP521R1FieldElement)base.RawXCoord; SecP521R1FieldElement secP521R1FieldElement3 = (SecP521R1FieldElement)base.RawZCoords[0]; uint[] array = Nat.Create(17); uint[] array2 = Nat.Create(17); uint[] array3 = Nat.Create(17); SecP521R1Field.Square(secP521R1FieldElement.x, array3); uint[] array4 = Nat.Create(17); SecP521R1Field.Square(array3, array4); bool isOne = secP521R1FieldElement3.IsOne; uint[] array5 = secP521R1FieldElement3.x; if (!isOne) { array5 = array2; SecP521R1Field.Square(secP521R1FieldElement3.x, array5); } SecP521R1Field.Subtract(secP521R1FieldElement2.x, array5, array); uint[] array6 = array2; SecP521R1Field.Add(secP521R1FieldElement2.x, array5, array6); SecP521R1Field.Multiply(array6, array, array6); Nat.AddBothTo(17, array6, array6, array6); SecP521R1Field.Reduce23(array6); uint[] array7 = array3; SecP521R1Field.Multiply(array3, secP521R1FieldElement2.x, array7); Nat.ShiftUpBits(17, array7, 2, 0u); SecP521R1Field.Reduce23(array7); Nat.ShiftUpBits(17, array4, 3, 0u, array); SecP521R1Field.Reduce23(array); SecP521R1FieldElement secP521R1FieldElement4 = new SecP521R1FieldElement(array4); SecP521R1Field.Square(array6, secP521R1FieldElement4.x); SecP521R1Field.Subtract(secP521R1FieldElement4.x, array7, secP521R1FieldElement4.x); SecP521R1Field.Subtract(secP521R1FieldElement4.x, array7, secP521R1FieldElement4.x); SecP521R1FieldElement secP521R1FieldElement5 = new SecP521R1FieldElement(array7); SecP521R1Field.Subtract(array7, secP521R1FieldElement4.x, secP521R1FieldElement5.x); SecP521R1Field.Multiply(secP521R1FieldElement5.x, array6, secP521R1FieldElement5.x); SecP521R1Field.Subtract(secP521R1FieldElement5.x, array, secP521R1FieldElement5.x); SecP521R1FieldElement secP521R1FieldElement6 = new SecP521R1FieldElement(array6); SecP521R1Field.Twice(secP521R1FieldElement.x, secP521R1FieldElement6.x); if (!isOne) { SecP521R1Field.Multiply(secP521R1FieldElement6.x, secP521R1FieldElement3.x, secP521R1FieldElement6.x); } return(new SecP521R1Point(curve, secP521R1FieldElement4, secP521R1FieldElement5, new ECFieldElement[1] { secP521R1FieldElement6 }, base.IsCompressed)); }
public static void Multiply(uint[] x, uint[] y, uint[] z) { uint[] array = Nat.Create(33); SecP521R1Field.ImplMultiply(x, y, array); SecP521R1Field.Reduce(array, z); }
public static void Square(uint[] x, uint[] z) { uint[] array = Nat.Create(33); SecP521R1Field.ImplSquare(x, array); SecP521R1Field.Reduce(array, z); }
public override ECFieldElement AddOne() { uint[] z = Nat.Create(0x11); SecP521R1Field.AddOne(this.x, z); return(new SecP521R1FieldElement(z)); }
public override ECFieldElement RandomFieldElement(SecureRandom r) { uint[] x = Nat.Create(17); SecP521R1Field.Random(r, x); return(new SecP521R1FieldElement(x)); }