public override ECFieldElement Divide(ECFieldElement b) { // return multiply(b.invert()); uint[] z = Nat160.Create(); Mod.Invert(SecP160R1Field.P, ((SecP160R1FieldElement)b).x, z); SecP160R1Field.Multiply(z, x, z); return(new SecP160R1FieldElement(z)); }
// D.1.4 91 /** * return a sqrt root - the routine verifies that the calculation returns the right value - if * none exists it returns null. */ public override ECFieldElement Sqrt() { /* * Raise this element to the exponent 2^158 - 2^29 * * Breaking up the exponent's binary representation into "repunits", we get: * { 129 1s } { 29 0s } * * Therefore we need an addition chain containing 129 (the length of the repunit) We use: * 1, 2, 4, 8, 16, 32, 64, 128, [129] */ uint[] x1 = this.x; if (Nat160.IsZero(x1) || Nat160.IsOne(x1)) { return(this); } uint[] x2 = Nat160.Create(); SecP160R1Field.Square(x1, x2); SecP160R1Field.Multiply(x2, x1, x2); uint[] x4 = Nat160.Create(); SecP160R1Field.SquareN(x2, 2, x4); SecP160R1Field.Multiply(x4, x2, x4); uint[] x8 = x2; SecP160R1Field.SquareN(x4, 4, x8); SecP160R1Field.Multiply(x8, x4, x8); uint[] x16 = x4; SecP160R1Field.SquareN(x8, 8, x16); SecP160R1Field.Multiply(x16, x8, x16); uint[] x32 = x8; SecP160R1Field.SquareN(x16, 16, x32); SecP160R1Field.Multiply(x32, x16, x32); uint[] x64 = x16; SecP160R1Field.SquareN(x32, 32, x64); SecP160R1Field.Multiply(x64, x32, x64); uint[] x128 = x32; SecP160R1Field.SquareN(x64, 64, x128); SecP160R1Field.Multiply(x128, x64, x128); uint[] x129 = x64; SecP160R1Field.Square(x128, x129); SecP160R1Field.Multiply(x129, x1, x129); uint[] t1 = x129; SecP160R1Field.SquareN(t1, 29, t1); uint[] t2 = x128; SecP160R1Field.Square(t1, t2); return(Nat160.Eq(x1, t2) ? new SecP160R1FieldElement(t1) : null); }
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; SecP160R1FieldElement X1 = (SecP160R1FieldElement)this.RawXCoord, Y1 = (SecP160R1FieldElement)this.RawYCoord; SecP160R1FieldElement X2 = (SecP160R1FieldElement)b.RawXCoord, Y2 = (SecP160R1FieldElement)b.RawYCoord; SecP160R1FieldElement Z1 = (SecP160R1FieldElement)this.RawZCoords[0]; SecP160R1FieldElement Z2 = (SecP160R1FieldElement)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; SecP160R1Field.Square(Z1.x, S2); U2 = t2; SecP160R1Field.Multiply(S2, X2.x, U2); SecP160R1Field.Multiply(S2, Z1.x, S2); SecP160R1Field.Multiply(S2, Y2.x, S2); } bool Z2IsOne = Z2.IsOne; uint[] U1, S1; if (Z2IsOne) { U1 = X1.x; S1 = Y1.x; } else { S1 = t4; SecP160R1Field.Square(Z2.x, S1); U1 = tt1; SecP160R1Field.Multiply(S1, X1.x, U1); SecP160R1Field.Multiply(S1, Z2.x, S1); SecP160R1Field.Multiply(S1, Y1.x, S1); } uint[] H = Nat160.Create(); SecP160R1Field.Subtract(U1, U2, H); uint[] R = t2; SecP160R1Field.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; SecP160R1Field.Square(H, HSquared); uint[] G = Nat160.Create(); SecP160R1Field.Multiply(HSquared, H, G); uint[] V = t3; SecP160R1Field.Multiply(HSquared, U1, V); SecP160R1Field.Negate(G, G); Nat160.Mul(S1, G, tt1); c = Nat160.AddBothTo(V, V, G); SecP160R1Field.Reduce32(c, G); SecP160R1FieldElement X3 = new SecP160R1FieldElement(t4); SecP160R1Field.Square(R, X3.x); SecP160R1Field.Subtract(X3.x, G, X3.x); SecP160R1FieldElement Y3 = new SecP160R1FieldElement(G); SecP160R1Field.Subtract(V, X3.x, Y3.x); SecP160R1Field.MultiplyAddToExt(Y3.x, R, tt1); SecP160R1Field.Reduce(tt1, Y3.x); SecP160R1FieldElement Z3 = new SecP160R1FieldElement(H); if (!Z1IsOne) { SecP160R1Field.Multiply(Z3.x, Z1.x, Z3.x); } if (!Z2IsOne) { SecP160R1Field.Multiply(Z3.x, Z2.x, Z3.x); } ECFieldElement[] zs = new ECFieldElement[] { Z3 }; return(new SecP160R1Point(curve, X3, Y3, zs, IsCompressed)); }
public override ECPoint Twice() { if (this.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP160R1FieldElement Y1 = (SecP160R1FieldElement)this.RawYCoord; if (Y1.IsZero) { return(curve.Infinity); } SecP160R1FieldElement X1 = (SecP160R1FieldElement)this.RawXCoord, Z1 = (SecP160R1FieldElement)this.RawZCoords[0]; uint c; uint[] t1 = Nat160.Create(); uint[] t2 = Nat160.Create(); uint[] Y1Squared = Nat160.Create(); SecP160R1Field.Square(Y1.x, Y1Squared); uint[] T = Nat160.Create(); SecP160R1Field.Square(Y1Squared, T); bool Z1IsOne = Z1.IsOne; uint[] Z1Squared = Z1.x; if (!Z1IsOne) { Z1Squared = t2; SecP160R1Field.Square(Z1.x, Z1Squared); } SecP160R1Field.Subtract(X1.x, Z1Squared, t1); uint[] M = t2; SecP160R1Field.Add(X1.x, Z1Squared, M); SecP160R1Field.Multiply(M, t1, M); c = Nat160.AddBothTo(M, M, M); SecP160R1Field.Reduce32(c, M); uint[] S = Y1Squared; SecP160R1Field.Multiply(Y1Squared, X1.x, S); c = Nat.ShiftUpBits(5, S, 2, 0); SecP160R1Field.Reduce32(c, S); c = Nat.ShiftUpBits(5, T, 3, 0, t1); SecP160R1Field.Reduce32(c, t1); SecP160R1FieldElement X3 = new SecP160R1FieldElement(T); SecP160R1Field.Square(M, X3.x); SecP160R1Field.Subtract(X3.x, S, X3.x); SecP160R1Field.Subtract(X3.x, S, X3.x); SecP160R1FieldElement Y3 = new SecP160R1FieldElement(S); SecP160R1Field.Subtract(S, X3.x, Y3.x); SecP160R1Field.Multiply(Y3.x, M, Y3.x); SecP160R1Field.Subtract(Y3.x, t1, Y3.x); SecP160R1FieldElement Z3 = new SecP160R1FieldElement(M); SecP160R1Field.Twice(Y1.x, Z3.x); if (!Z1IsOne) { SecP160R1Field.Multiply(Z3.x, Z1.x, Z3.x); } return(new SecP160R1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed)); }
public override ECFieldElement Multiply(ECFieldElement b) { uint[] z = Nat160.Create(); SecP160R1Field.Multiply(x, ((SecP160R1FieldElement)b).x, z); return(new SecP160R1FieldElement(z)); }