public static IPolynomial SquareRoot(IPolynomial startPolynomial, IPolynomial f, BigInteger p, int degree, BigInteger m)
{
BigInteger q = BigInteger.Pow(p, degree);
BigInteger s = q - 1;
int r = 0;
while (s.Mod(2) == 0)
{
s /= 2;
r++;
}
BigInteger halfS = ((s + 1) / 2);
if (r == 1 && q.Mod(4) == 3)
{
halfS = ((q + 1) / 4);
}
BigInteger quadraticNonResidue = Legendre.SymbolSearch(m + 1, q, -1);
BigInteger theta = quadraticNonResidue;
BigInteger minusOne = BigInteger.ModPow(theta, ((q - 1) / 2), p);
IPolynomial omegaPoly = Polynomial.Field.ExponentiateMod(startPolynomial, halfS, f, p);
BigInteger lambda = minusOne;
BigInteger zeta = 0;
int i = 0;
do
{
i++;
zeta = BigInteger.ModPow(theta, (i * s), p);
lambda = (lambda * BigInteger.Pow(zeta, (int)Math.Pow(2, (r - i)))).Mod(p);
omegaPoly = Polynomial.Field.Multiply(omegaPoly, BigInteger.Pow(zeta, (int)Math.Pow(2, ((r - i) - 1))), p);
}while (!((lambda == 1) || (i > (r))));
return(omegaPoly);
}
