Ability to check if an element is a square

[Rexicon226]

Hello!

I'm wondering if adding an API to check if a field element is a valid square would be possible.
Currently, the sqrt() function hangs if the input isn't a square, making it a bit difficult to work with when the input comes from some user-facing process.

The two best options I can see would be to either make the sqrt() function return an error if m is equal to the two-adicity of the field, and then another check below to see that x.square() == value.

libff/libff/algebra/field_utils/algorithms.tcc

Lines 136 to 146 in 674e437

	while (b != one)
	{
	size_t m = 0;
	FieldT b2m = b;
	while (b2m != one)
	{
	/* invariant: b2m = b^(2^m) after entering this loop */
	b2m = b2m.squared();
	m += 1;
	}

or adding a standalone function that checks via the legendre symbol, or maybe some more efficient way I'm not aware of (still pretty new to cryptography!);

I need this functionality for both Fp and Fp2.

Thanks!