galois.is_irreducible(poly) seems to return some false negatives in large odd exponent GFs

Hi Matt, hope all is well.

Even though it works fine for other groups (e.g. even groups likes GF(2^256) work well), still I 've been getting the following false negative result when using the galois.is_irreducible(poly) over odd groups tο produce irreducible polynomials over GF(2^233).

For example, we know from previous publications and research that x^233+x^74+1 is irreducible over GF(2) for creating the quotient ring of GF(2^233) but the following code returns Null for every polynomial (including the aforementioned one):

def loop_init_trinomial():
    #initial detection loop
    for k in range(1, 233):
        poly = galois.Poly.Degrees([233, k, 0])
        if galois.is_irreducible(poly):
            print("Found one: ", k, poly, poly.string)

Care to share some thoughts?

[mhostetter]

And to be clear, I was incorrect about prime exponents. That wasn’t the issue. The issue was large exponents (that were secretly np.int64). I believe this bug was introduced after the refactor and major speed-ups from v0.0.26.

Again, I appreciate the bug report! 🙏

[geostergiop]

Yep sorry, bad reference!