public override ECFieldElement Sqrt()
{
uint[] y = x;
if (Nat256.IsZero(y) || Nat256.IsOne(y))
{
return(this);
}
uint[] array = Nat256.Create();
uint[] array2 = Nat256.Create();
SecP256R1Field.Square(y, array);
SecP256R1Field.Multiply(array, y, array);
SecP256R1Field.SquareN(array, 2, array2);
SecP256R1Field.Multiply(array2, array, array2);
SecP256R1Field.SquareN(array2, 4, array);
SecP256R1Field.Multiply(array, array2, array);
SecP256R1Field.SquareN(array, 8, array2);
SecP256R1Field.Multiply(array2, array, array2);
SecP256R1Field.SquareN(array2, 16, array);
SecP256R1Field.Multiply(array, array2, array);
SecP256R1Field.SquareN(array, 32, array);
SecP256R1Field.Multiply(array, y, array);
SecP256R1Field.SquareN(array, 96, array);
SecP256R1Field.Multiply(array, y, array);
SecP256R1Field.SquareN(array, 94, array);
SecP256R1Field.Multiply(array, array, array2);
return((!Nat256.Eq(y, array2)) ? null : new SecP256R1FieldElement(array));
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat256.IsZero(x) || Nat256.IsOne(x))
{
return(this);
}
uint[] z = Nat256.Create();
uint[] numArray3 = Nat256.Create();
SecP256R1Field.Square(x, z);
SecP256R1Field.Multiply(z, x, z);
SecP256R1Field.SquareN(z, 2, numArray3);
SecP256R1Field.Multiply(numArray3, z, numArray3);
SecP256R1Field.SquareN(numArray3, 4, z);
SecP256R1Field.Multiply(z, numArray3, z);
SecP256R1Field.SquareN(z, 8, numArray3);
SecP256R1Field.Multiply(numArray3, z, numArray3);
SecP256R1Field.SquareN(numArray3, 0x10, z);
SecP256R1Field.Multiply(z, numArray3, z);
SecP256R1Field.SquareN(z, 0x20, z);
SecP256R1Field.Multiply(z, x, z);
SecP256R1Field.SquareN(z, 0x60, z);
SecP256R1Field.Multiply(z, x, z);
SecP256R1Field.SquareN(z, 0x5e, z);
SecP256R1Field.Multiply(z, z, numArray3);
return(!Nat256.Eq(x, numArray3) ? null : new SecP256R1FieldElement(z));
}
/**
* 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 2^254 - 2^222 + 2^190 + 2^94
uint[] x1 = this.x;
if (Nat256.IsZero(x1) || Nat256.IsOne(x1))
{
return(this);
}
uint[] t1 = Nat256.Create();
uint[] t2 = Nat256.Create();
SecP256R1Field.Square(x1, t1);
SecP256R1Field.Multiply(t1, x1, t1);
SecP256R1Field.SquareN(t1, 2, t2);
SecP256R1Field.Multiply(t2, t1, t2);
SecP256R1Field.SquareN(t2, 4, t1);
SecP256R1Field.Multiply(t1, t2, t1);
SecP256R1Field.SquareN(t1, 8, t2);
SecP256R1Field.Multiply(t2, t1, t2);
SecP256R1Field.SquareN(t2, 16, t1);
SecP256R1Field.Multiply(t1, t2, t1);
SecP256R1Field.SquareN(t1, 32, t1);
SecP256R1Field.Multiply(t1, x1, t1);
SecP256R1Field.SquareN(t1, 96, t1);
SecP256R1Field.Multiply(t1, x1, t1);
SecP256R1Field.SquareN(t1, 94, t1);
SecP256R1Field.Multiply(t1, t1, t2);
return(Nat256.Eq(x1, t2) ? new SecP256R1FieldElement(t1) : null);
}