/// <summary>
/// Calculates y from y^2 = x^3 + ax + b (mod p) by having x and the first byte indicating whether y is odd or even.
/// Return value indicates success.
/// </summary>
/// <param name="x">X coordinate</param>
/// <param name="firstByte">The first byte indicating whether y is odd or even (must be 2 or 3)</param>
/// <param name="y">Calculated y (0 if fails to calculate)</param>
/// <returns>True if y was found, otherwise false.</returns>
public bool TryFindY(BigInteger x, byte firstByte, out BigInteger y)
{
if (firstByte != 2 && firstByte != 3)
{
return(false);
}
if (x.Sign < 1)
{
return(false);
}
// Curve.A is zero
BigInteger right = (BigInteger.Pow(x, 3) + curve.B) % curve.P;
if (SquareRoot.TryFind(right, curve.P, out y))
{
if (firstByte == 2 && !y.IsEven)
{
// We know point is already on curve
y = PointNegChecked(new EllipticCurvePoint(x, y)).Y;
}
else if (firstByte == 3 && y.IsEven)
{
y = PointNegChecked(new EllipticCurvePoint(x, y)).Y;
}
return(true);
}
else
{
return(false);
}
}
/// <summary>
/// Calculates y from y^2 = x^3 + ax + b (mod p) by having x for Schnorr encoding.
/// Return value indicates success.
/// </summary>
/// <param name="x">X coordinate</param>
/// <param name="y">Calculated y (0 if fails to calculate)</param>
/// <returns>True if y was found, otherwise false.</returns>
public bool TryFindYSchnorr(BigInteger x, out BigInteger y)
{
if (x.Sign < 1 || x > curve.P)
{
return(false);
}
// Curve.A is zero
BigInteger right = (BigInteger.Pow(x, 3) + curve.B) % curve.P;
return(SquareRoot.TryFind(right, curve.P, out y));
}