public static void SquareN(uint[] x, int n, uint[] z)
{
Debug.Assert(n > 0);
uint[] tt = Nat192.CreateExt();
Nat192.Square(x, tt);
Reduce(tt, z);
while (--n > 0)
{
Nat192.Square(z, tt);
Reduce(tt, z);
}
}
public static void Mul(uint[] x, uint[] y, uint[] zz)
{
Nat192.Mul(x, y, zz);
Nat192.Mul(x, 6, y, 6, zz, 12);
uint c18 = Nat192.AddToEachOther(zz, 6, zz, 12);
uint c12 = c18 + Nat192.AddTo(zz, 0, zz, 6, 0);
c18 += Nat192.AddTo(zz, 18, zz, 12, c12);
uint[] dx = Nat192.Create(), dy = Nat192.Create();
bool neg = Nat192.Diff(x, 6, x, 0, dx, 0) != Nat192.Diff(y, 6, y, 0, dy, 0);
uint[] tt = Nat192.CreateExt();
Nat192.Mul(dx, dy, tt);
c18 += neg ? Nat.AddTo(12, tt, 0, zz, 6) : (uint)Nat.SubFrom(12, tt, 0, zz, 6);
Nat.AddWordAt(24, c18, zz, 18);
}
public static void Square(uint[] x, uint[] zz)
{
Nat192.Square(x, zz);
Nat192.Square(x, 6, zz, 12);
uint c18 = Nat192.AddToEachOther(zz, 6, zz, 12);
uint c12 = c18 + Nat192.AddTo(zz, 0, zz, 6, 0);
c18 += Nat192.AddTo(zz, 18, zz, 12, c12);
uint[] dx = Nat192.Create();
Nat192.Diff(x, 6, x, 0, dx, 0);
uint[] m = Nat192.CreateExt();
Nat192.Square(dx, m);
c18 += (uint)Nat.SubFrom(12, m, 0, zz, 6);
Nat.AddWordAt(24, c18, zz, 18);
}
public static void Multiply(uint[] x, uint[] y, uint[] z)
{
uint[] tt = Nat192.CreateExt();
Nat192.Mul(x, y, tt);
Reduce(tt, z);
}
public static void Square(uint[] x, uint[] z)
{
uint[] tt = Nat192.CreateExt();
Nat192.Square(x, tt);
Reduce(tt, z);
}
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;
SecP192K1FieldElement X1 = (SecP192K1FieldElement)this.RawXCoord, Y1 = (SecP192K1FieldElement)this.RawYCoord;
SecP192K1FieldElement X2 = (SecP192K1FieldElement)b.RawXCoord, Y2 = (SecP192K1FieldElement)b.RawYCoord;
SecP192K1FieldElement Z1 = (SecP192K1FieldElement)this.RawZCoords[0];
SecP192K1FieldElement Z2 = (SecP192K1FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat192.CreateExt();
uint[] t2 = Nat192.Create();
uint[] t3 = Nat192.Create();
uint[] t4 = Nat192.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
SecP192K1Field.Square(Z1.x, S2);
U2 = t2;
SecP192K1Field.Multiply(S2, X2.x, U2);
SecP192K1Field.Multiply(S2, Z1.x, S2);
SecP192K1Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
SecP192K1Field.Square(Z2.x, S1);
U1 = tt1;
SecP192K1Field.Multiply(S1, X1.x, U1);
SecP192K1Field.Multiply(S1, Z2.x, S1);
SecP192K1Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat192.Create();
SecP192K1Field.Subtract(U1, U2, H);
uint[] R = t2;
SecP192K1Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat192.IsZero(H))
{
if (Nat192.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;
SecP192K1Field.Square(H, HSquared);
uint[] G = Nat192.Create();
SecP192K1Field.Multiply(HSquared, H, G);
uint[] V = t3;
SecP192K1Field.Multiply(HSquared, U1, V);
SecP192K1Field.Negate(G, G);
Nat192.Mul(S1, G, tt1);
c = Nat192.AddBothTo(V, V, G);
SecP192K1Field.Reduce32(c, G);
SecP192K1FieldElement X3 = new SecP192K1FieldElement(t4);
SecP192K1Field.Square(R, X3.x);
SecP192K1Field.Subtract(X3.x, G, X3.x);
SecP192K1FieldElement Y3 = new SecP192K1FieldElement(G);
SecP192K1Field.Subtract(V, X3.x, Y3.x);
SecP192K1Field.MultiplyAddToExt(Y3.x, R, tt1);
SecP192K1Field.Reduce(tt1, Y3.x);
SecP192K1FieldElement Z3 = new SecP192K1FieldElement(H);
if (!Z1IsOne)
{
SecP192K1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
SecP192K1Field.Multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[] { Z3 };
return(new SecP192K1Point(curve, X3, Y3, zs, IsCompressed));
}