def polyring(self, n=None, names=None):
if isinstance(names, str):
assert n is None
names = names.replace(",", " ").split()
elif isinstance(names, (tuple, list)):
assert n is None
else:
if n is None:
n = 1
assert names is None
names = list("xyzwuv")[:n]
PR = PolynomialRing(Zmod(self.n), names=",".join(names))
return (PR, ) + tuple(PR.gens())
def power(e, n=None, field=None):
assert (n is not None) ^ (field is not None)
field = field or GF(2**n, name='a')
x = PolynomialRing(field, names='x').gen()
return SBox2(x**e)
def get_x(cls, n=None, field=None):
assert (n is not None) ^ (field is not None)
field = field or GF(2**n, name='a')
return PolynomialRing(field, names='x').gen()
def all_irreducible_polynomials(N, p=2):
FR = PolynomialRing(GF(p), names=("X", ))
for poly in FR.polynomials(of_degree=N):
if poly.is_irreducible():
yield poly