public static void Invert(ulong[] x, ulong[] z)
{
if (Nat576.IsZero64(x))
{
throw new InvalidOperationException();
}
// Itoh-Tsujii inversion with bases { 2, 3, 5 }
ulong[] t0 = Nat576.Create64();
ulong[] t1 = Nat576.Create64();
ulong[] t2 = Nat576.Create64();
Square(x, t2);
// 5 | 570
Square(t2, t0);
Square(t0, t1);
Multiply(t0, t1, t0);
SquareN(t0, 2, t1);
Multiply(t0, t1, t0);
Multiply(t0, t2, t0);
// 3 | 114
SquareN(t0, 5, t1);
Multiply(t0, t1, t0);
SquareN(t1, 5, t1);
Multiply(t0, t1, t0);
// 2 | 38
SquareN(t0, 15, t1);
Multiply(t0, t1, t2);
// ! {2,3,5} | 19
SquareN(t2, 30, t0);
SquareN(t0, 30, t1);
Multiply(t0, t1, t0);
// 3 | 9
SquareN(t0, 60, t1);
Multiply(t0, t1, t0);
SquareN(t1, 60, t1);
Multiply(t0, t1, t0);
// 3 | 3
SquareN(t0, 180, t1);
Multiply(t0, t1, t0);
SquareN(t1, 180, t1);
Multiply(t0, t1, t0);
Multiply(t0, t2, z);
}
public static void Invert(ulong[] x, ulong[] z)
{
//IL_0008: Unknown result type (might be due to invalid IL or missing references)
if (Nat576.IsZero64(x))
{
throw new InvalidOperationException();
}
ulong[] array = Nat576.Create64();
ulong[] array2 = Nat576.Create64();
ulong[] array3 = Nat576.Create64();
Square(x, array3);
Square(array3, array);
Square(array, array2);
Multiply(array, array2, array);
SquareN(array, 2, array2);
Multiply(array, array2, array);
Multiply(array, array3, array);
SquareN(array, 5, array2);
Multiply(array, array2, array);
SquareN(array2, 5, array2);
Multiply(array, array2, array);
SquareN(array, 15, array2);
Multiply(array, array2, array3);
SquareN(array3, 30, array);
SquareN(array, 30, array2);
Multiply(array, array2, array);
SquareN(array, 60, array2);
Multiply(array, array2, array);
SquareN(array2, 60, array2);
Multiply(array, array2, array);
SquareN(array, 180, array2);
Multiply(array, array2, array);
SquareN(array2, 180, array2);
Multiply(array, array2, array);
Multiply(array, array3, z);
}
public override ECPoint Add(ECPoint b)
{
if (this.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
SecT571FieldElement X1 = (SecT571FieldElement)this.RawXCoord;
SecT571FieldElement X2 = (SecT571FieldElement)b.RawXCoord;
if (X1.IsZero)
{
if (X2.IsZero)
{
return(curve.Infinity);
}
return(b.Add(this));
}
SecT571FieldElement L1 = (SecT571FieldElement)this.RawYCoord, Z1 = (SecT571FieldElement)this.RawZCoords[0];
SecT571FieldElement L2 = (SecT571FieldElement)b.RawYCoord, Z2 = (SecT571FieldElement)b.RawZCoords[0];
ulong[] t1 = Nat576.Create64();
ulong[] t2 = Nat576.Create64();
ulong[] t3 = Nat576.Create64();
ulong[] t4 = Nat576.Create64();
ulong[] Z1Precomp = Z1.IsOne ? null : SecT571Field.PrecompMultiplicand(Z1.x);
ulong[] U2, S2;
if (Z1Precomp == null)
{
U2 = X2.x;
S2 = L2.x;
}
else
{
SecT571Field.MultiplyPrecomp(X2.x, Z1Precomp, U2 = t2);
SecT571Field.MultiplyPrecomp(L2.x, Z1Precomp, S2 = t4);
}
ulong[] Z2Precomp = Z2.IsOne ? null : SecT571Field.PrecompMultiplicand(Z2.x);
ulong[] U1, S1;
if (Z2Precomp == null)
{
U1 = X1.x;
S1 = L1.x;
}
else
{
SecT571Field.MultiplyPrecomp(X1.x, Z2Precomp, U1 = t1);
SecT571Field.MultiplyPrecomp(L1.x, Z2Precomp, S1 = t3);
}
ulong[] A = t3;
SecT571Field.Add(S1, S2, A);
ulong[] B = t4;
SecT571Field.Add(U1, U2, B);
if (Nat576.IsZero64(B))
{
if (Nat576.IsZero64(A))
{
return(Twice());
}
return(curve.Infinity);
}
SecT571FieldElement X3, L3, Z3;
if (X2.IsZero)
{
// TODO This can probably be optimized quite a bit
ECPoint p = this.Normalize();
X1 = (SecT571FieldElement)p.XCoord;
ECFieldElement Y1 = p.YCoord;
ECFieldElement Y2 = L2;
ECFieldElement L = Y1.Add(Y2).Divide(X1);
X3 = (SecT571FieldElement)L.Square().Add(L).Add(X1).AddOne();
if (X3.IsZero)
{
return(new SecT571R1Point(curve, X3, SecT571R1Curve.SecT571R1_B_SQRT, IsCompressed));
}
ECFieldElement Y3 = L.Multiply(X1.Add(X3)).Add(X3).Add(Y1);
L3 = (SecT571FieldElement)Y3.Divide(X3).Add(X3);
Z3 = (SecT571FieldElement)curve.FromBigInteger(BigInteger.One);
}
else
{
SecT571Field.Square(B, B);
ulong[] APrecomp = SecT571Field.PrecompMultiplicand(A);
ulong[] AU1 = t1;
ulong[] AU2 = t2;
SecT571Field.MultiplyPrecomp(U1, APrecomp, AU1);
SecT571Field.MultiplyPrecomp(U2, APrecomp, AU2);
X3 = new SecT571FieldElement(t1);
SecT571Field.Multiply(AU1, AU2, X3.x);
if (X3.IsZero)
{
return(new SecT571R1Point(curve, X3, SecT571R1Curve.SecT571R1_B_SQRT, IsCompressed));
}
Z3 = new SecT571FieldElement(t3);
SecT571Field.MultiplyPrecomp(B, APrecomp, Z3.x);
if (Z2Precomp != null)
{
SecT571Field.MultiplyPrecomp(Z3.x, Z2Precomp, Z3.x);
}
ulong[] tt = Nat576.CreateExt64();
SecT571Field.Add(AU2, B, t4);
SecT571Field.SquareAddToExt(t4, tt);
SecT571Field.Add(L1.x, Z1.x, t4);
SecT571Field.MultiplyAddToExt(t4, Z3.x, tt);
L3 = new SecT571FieldElement(t4);
SecT571Field.Reduce(tt, L3.x);
if (Z1Precomp != null)
{
SecT571Field.MultiplyPrecomp(Z3.x, Z1Precomp, Z3.x);
}
}
return(new SecT571R1Point(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed));
}
public override ECPoint Twice()
{
if (this.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
SecT571FieldElement X1 = (SecT571FieldElement)this.RawXCoord;
if (X1.IsZero)
{
// A point with X == 0 is its own additive inverse
return(curve.Infinity);
}
SecT571FieldElement L1 = (SecT571FieldElement)this.RawYCoord, Z1 = (SecT571FieldElement)this.RawZCoords[0];
ulong[] t1 = Nat576.Create64();
ulong[] t2 = Nat576.Create64();
ulong[] Z1Precomp = Z1.IsOne ? null : SecT571Field.PrecompMultiplicand(Z1.x);
ulong[] L1Z1, Z1Sq;
if (Z1Precomp == null)
{
L1Z1 = L1.x;
Z1Sq = Z1.x;
}
else
{
SecT571Field.MultiplyPrecomp(L1.x, Z1Precomp, L1Z1 = t1);
SecT571Field.Square(Z1.x, Z1Sq = t2);
}
ulong[] T = Nat576.Create64();
SecT571Field.Square(L1.x, T);
SecT571Field.AddBothTo(L1Z1, Z1Sq, T);
if (Nat576.IsZero64(T))
{
return(new SecT571R1Point(curve, new SecT571FieldElement(T), SecT571R1Curve.SecT571R1_B_SQRT, IsCompressed));
}
ulong[] tt = Nat576.CreateExt64();
SecT571Field.MultiplyAddToExt(T, L1Z1, tt);
SecT571FieldElement X3 = new SecT571FieldElement(t1);
SecT571Field.Square(T, X3.x);
SecT571FieldElement Z3 = new SecT571FieldElement(T);
if (Z1Precomp != null)
{
SecT571Field.Multiply(Z3.x, Z1Sq, Z3.x);
}
ulong[] X1Z1;
if (Z1Precomp == null)
{
X1Z1 = X1.x;
}
else
{
SecT571Field.MultiplyPrecomp(X1.x, Z1Precomp, X1Z1 = t2);
}
SecT571Field.SquareAddToExt(X1Z1, tt);
SecT571Field.Reduce(tt, t2);
SecT571Field.AddBothTo(X3.x, Z3.x, t2);
SecT571FieldElement L3 = new SecT571FieldElement(t2);
return(new SecT571R1Point(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed));
}