/**
* 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 2^519
uint[] x1 = this.x;
if (Nat.IsZero(17, x1) || Nat.IsOne(17, x1))
{
return(this);
}
uint[] t1 = Nat.Create(17);
uint[] t2 = Nat.Create(17);
SecP521R1Field.SquareN(x1, 519, t1);
SecP521R1Field.Square(t1, t2);
return(Nat.Eq(17, x1, t2) ? new SecP521R1FieldElement(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;
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, IsCompressed));
}
public override ECFieldElement Square()
{
uint[] z = Nat.Create(17);
SecP521R1Field.Square(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 }, IsCompressed));
}