Galois Field (GF) is a field contains a finite number of elements. There are 2 types of Galois Field:
- Prime Field (m = 1)
- Extension Field (m != 1)
In prime field, elements are integer within [0, p-1] range. Prime field have a prime p that limits our value so it will always be within the field.
In extension field, elements can be polynomials with maximum degree of (m-1). Extension field have a prime p and prime polynomial (irreducible) that limits our polynomial and its values so it will always be within the field.
pip install GaloisField
- Python 3
from galois_field.GF import GF, FFElement
from galois_field.fast_polynom import FastPolynom
irr_poly = FastPolynom({0: 1, 1: 1, 3: 1})
ff = GF(2, 3, irr_poly)
e1 = FFElement(ff, FastPolynom({0: 1, 1: 1}))
e2 = FFElement(ff, FastPolynom({0: 1, 1: 1}))
e_res = e1 * e2
assert (e2 == e_res / e1)