public override ECPoint Twice()
{
if (this.IsInfinity)
return this;
ECCurve curve = this.Curve;
SecP256K1FieldElement Y1 = (SecP256K1FieldElement)this.RawYCoord;
if (Y1.IsZero)
return curve.Infinity;
SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Z1 = (SecP256K1FieldElement)this.RawZCoords[0];
uint c;
uint[] Y1Squared = Nat256.Create();
SecP256K1Field.Square(Y1.x, Y1Squared);
uint[] T = Nat256.Create();
SecP256K1Field.Square(Y1Squared, T);
uint[] M = Nat256.Create();
SecP256K1Field.Square(X1.x, M);
c = Nat256.AddBothTo(M, M, M);
SecP256K1Field.Reduce32(c, M);
uint[] S = Y1Squared;
SecP256K1Field.Multiply(Y1Squared, X1.x, S);
c = Nat.ShiftUpBits(8, S, 2, 0);
SecP256K1Field.Reduce32(c, S);
uint[] t1 = Nat256.Create();
c = Nat.ShiftUpBits(8, T, 3, 0, t1);
SecP256K1Field.Reduce32(c, t1);
SecP256K1FieldElement X3 = new SecP256K1FieldElement(T);
SecP256K1Field.Square(M, X3.x);
SecP256K1Field.Subtract(X3.x, S, X3.x);
SecP256K1Field.Subtract(X3.x, S, X3.x);
SecP256K1FieldElement Y3 = new SecP256K1FieldElement(S);
SecP256K1Field.Subtract(S, X3.x, Y3.x);
SecP256K1Field.Multiply(Y3.x, M, Y3.x);
SecP256K1Field.Subtract(Y3.x, t1, Y3.x);
SecP256K1FieldElement Z3 = new SecP256K1FieldElement(M);
SecP256K1Field.Twice(Y1.x, Z3.x);
if (!Z1.IsOne)
{
SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
return new SecP256K1Point(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;
SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Y1 = (SecP256K1FieldElement)this.RawYCoord;
SecP256K1FieldElement X2 = (SecP256K1FieldElement)b.RawXCoord, Y2 = (SecP256K1FieldElement)b.RawYCoord;
SecP256K1FieldElement Z1 = (SecP256K1FieldElement)this.RawZCoords[0];
SecP256K1FieldElement Z2 = (SecP256K1FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat256.CreateExt();
uint[] t2 = Nat256.Create();
uint[] t3 = Nat256.Create();
uint[] t4 = Nat256.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
SecP256K1Field.Square(Z1.x, S2);
U2 = t2;
SecP256K1Field.Multiply(S2, X2.x, U2);
SecP256K1Field.Multiply(S2, Z1.x, S2);
SecP256K1Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
SecP256K1Field.Square(Z2.x, S1);
U1 = tt1;
SecP256K1Field.Multiply(S1, X1.x, U1);
SecP256K1Field.Multiply(S1, Z2.x, S1);
SecP256K1Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat256.Create();
SecP256K1Field.Subtract(U1, U2, H);
uint[] R = t2;
SecP256K1Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat256.IsZero(H))
{
if (Nat256.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;
SecP256K1Field.Square(H, HSquared);
uint[] G = Nat256.Create();
SecP256K1Field.Multiply(HSquared, H, G);
uint[] V = t3;
SecP256K1Field.Multiply(HSquared, U1, V);
SecP256K1Field.Negate(G, G);
Nat256.Mul(S1, G, tt1);
c = Nat256.AddBothTo(V, V, G);
SecP256K1Field.Reduce32(c, G);
SecP256K1FieldElement X3 = new SecP256K1FieldElement(t4);
SecP256K1Field.Square(R, X3.x);
SecP256K1Field.Subtract(X3.x, G, X3.x);
SecP256K1FieldElement Y3 = new SecP256K1FieldElement(G);
SecP256K1Field.Subtract(V, X3.x, Y3.x);
SecP256K1Field.MultiplyAddToExt(Y3.x, R, tt1);
SecP256K1Field.Reduce(tt1, Y3.x);
SecP256K1FieldElement Z3 = new SecP256K1FieldElement(H);
if (!Z1IsOne)
{
SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
SecP256K1Field.Multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[] { Z3 };
return new SecP256K1Point(curve, X3, Y3, zs, IsCompressed);
}
public virtual bool Equals(SecP256K1FieldElement other)
{
if (this == other)
return true;
if (null == other)
return false;
return Nat256.Eq(x, other.x);
}