public override ECPoint Twice() { if (this.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP384R1FieldElement Y1 = (SecP384R1FieldElement)this.RawYCoord; if (Y1.IsZero) { return(curve.Infinity); } SecP384R1FieldElement X1 = (SecP384R1FieldElement)this.RawXCoord, Z1 = (SecP384R1FieldElement)this.RawZCoords[0]; uint c; uint[] t1 = Nat.Create(12); uint[] t2 = Nat.Create(12); uint[] Y1Squared = Nat.Create(12); SecP384R1Field.Square(Y1.x, Y1Squared); uint[] T = Nat.Create(12); SecP384R1Field.Square(Y1Squared, T); bool Z1IsOne = Z1.IsOne; uint[] Z1Squared = Z1.x; if (!Z1IsOne) { Z1Squared = t2; SecP384R1Field.Square(Z1.x, Z1Squared); } SecP384R1Field.Subtract(X1.x, Z1Squared, t1); uint[] M = t2; SecP384R1Field.Add(X1.x, Z1Squared, M); SecP384R1Field.Multiply(M, t1, M); c = Nat.AddBothTo(12, M, M, M); SecP384R1Field.Reduce32(c, M); uint[] S = Y1Squared; SecP384R1Field.Multiply(Y1Squared, X1.x, S); c = Nat.ShiftUpBits(12, S, 2, 0); SecP384R1Field.Reduce32(c, S); c = Nat.ShiftUpBits(12, T, 3, 0, t1); SecP384R1Field.Reduce32(c, t1); SecP384R1FieldElement X3 = new SecP384R1FieldElement(T); SecP384R1Field.Square(M, X3.x); SecP384R1Field.Subtract(X3.x, S, X3.x); SecP384R1Field.Subtract(X3.x, S, X3.x); SecP384R1FieldElement Y3 = new SecP384R1FieldElement(S); SecP384R1Field.Subtract(S, X3.x, Y3.x); SecP384R1Field.Multiply(Y3.x, M, Y3.x); SecP384R1Field.Subtract(Y3.x, t1, Y3.x); SecP384R1FieldElement Z3 = new SecP384R1FieldElement(M); SecP384R1Field.Twice(Y1.x, Z3.x); if (!Z1IsOne) { SecP384R1Field.Multiply(Z3.x, Z1.x, Z3.x); } return(new SecP384R1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, 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; SecP384R1FieldElement X1 = (SecP384R1FieldElement)this.RawXCoord, Y1 = (SecP384R1FieldElement)this.RawYCoord; SecP384R1FieldElement X2 = (SecP384R1FieldElement)b.RawXCoord, Y2 = (SecP384R1FieldElement)b.RawYCoord; SecP384R1FieldElement Z1 = (SecP384R1FieldElement)this.RawZCoords[0]; SecP384R1FieldElement Z2 = (SecP384R1FieldElement)b.RawZCoords[0]; uint c; uint[] tt1 = Nat.Create(24); uint[] tt2 = Nat.Create(24); uint[] t3 = Nat.Create(12); uint[] t4 = Nat.Create(12); bool Z1IsOne = Z1.IsOne; uint[] U2, S2; if (Z1IsOne) { U2 = X2.x; S2 = Y2.x; } else { S2 = t3; SecP384R1Field.Square(Z1.x, S2); U2 = tt2; SecP384R1Field.Multiply(S2, X2.x, U2); SecP384R1Field.Multiply(S2, Z1.x, S2); SecP384R1Field.Multiply(S2, Y2.x, S2); } bool Z2IsOne = Z2.IsOne; uint[] U1, S1; if (Z2IsOne) { U1 = X1.x; S1 = Y1.x; } else { S1 = t4; SecP384R1Field.Square(Z2.x, S1); U1 = tt1; SecP384R1Field.Multiply(S1, X1.x, U1); SecP384R1Field.Multiply(S1, Z2.x, S1); SecP384R1Field.Multiply(S1, Y1.x, S1); } uint[] H = Nat.Create(12); SecP384R1Field.Subtract(U1, U2, H); uint[] R = Nat.Create(12); SecP384R1Field.Subtract(S1, S2, R); // Check if b == this or b == -this if (Nat.IsZero(12, H)) { if (Nat.IsZero(12, 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; SecP384R1Field.Square(H, HSquared); uint[] G = Nat.Create(12); SecP384R1Field.Multiply(HSquared, H, G); uint[] V = t3; SecP384R1Field.Multiply(HSquared, U1, V); SecP384R1Field.Negate(G, G); Nat384.Mul(S1, G, tt1); c = Nat.AddBothTo(12, V, V, G); SecP384R1Field.Reduce32(c, G); SecP384R1FieldElement X3 = new SecP384R1FieldElement(t4); SecP384R1Field.Square(R, X3.x); SecP384R1Field.Subtract(X3.x, G, X3.x); SecP384R1FieldElement Y3 = new SecP384R1FieldElement(G); SecP384R1Field.Subtract(V, X3.x, Y3.x); Nat384.Mul(Y3.x, R, tt2); SecP384R1Field.AddExt(tt1, tt2, tt1); SecP384R1Field.Reduce(tt1, Y3.x); SecP384R1FieldElement Z3 = new SecP384R1FieldElement(H); if (!Z1IsOne) { SecP384R1Field.Multiply(Z3.x, Z1.x, Z3.x); } if (!Z2IsOne) { SecP384R1Field.Multiply(Z3.x, Z2.x, Z3.x); } ECFieldElement[] zs = new ECFieldElement[] { Z3 }; return(new SecP384R1Point(curve, X3, Y3, zs, IsCompressed)); }
public override ECFieldElement Subtract(ECFieldElement b) { uint[] z = Nat.Create(12); SecP384R1Field.Subtract(x, ((SecP384R1FieldElement)b).x, z); return(new SecP384R1FieldElement(z)); }