Function ModularSquareRoot

src/cryptopp/nbtheory.cpp:574–621

}

Integer ModularSquareRoot(const Integer &a, const Integer &p)
{
	if (p%4 == 3)
		return a_exp_b_mod_c(a, (p+1)/4, p);

	Integer q=p-1;
	unsigned int r=0;
	while (q.IsEven())
	{
		r++;
		q >>= 1;
	}

	Integer n=2;
	while (Jacobi(n, p) != -1)
		++n;

	Integer y = a_exp_b_mod_c(n, q, p);
	Integer x = a_exp_b_mod_c(a, (q-1)/2, p);
	Integer b = (x.Squared()%p)*a%p;
	x = a*x%p;
	Integer tempb, t;

	while (b != 1)
	{
		unsigned m=0;
		tempb = b;
		do
		{
			m++;
			b = b.Squared()%p;
			if (m==r)
				return Integer::Zero();
		}
		while (b != 1);

		t = y;
		for (unsigned i=0; i<r-m-1; i++)
			t = t.Squared()%p;
		y = t.Squared()%p;
		r = m;
		x = x*t%p;
		b = tempb*y%p;
	}

	CRYPTOPP_ASSERT(x.Squared()%p == a);
	return x;
}

bool SolveModularQuadraticEquation(Integer &r1, Integer &r2, const Integer &a, const Integer &b, const Integer &c, const Integer &p)
{