def _test(self):
from sage.all import GF, PolynomialRing, proof
k = GF(4, 'u')
u = k.gen()
R = PolynomialRing(k, 'v')
v = R.gen()
l = R.quo(v**3 + v + 1)
v = l.gen()
R = PolynomialRing(l, 'x,y')
x, y = R.gens()
f = y**3 + x**3 + (u + 1) * x
with proof.WithProof('polynomial', False):
f.factor()
def test_enumerate_ea():
N = 8
F = GF(2**N, name="a")
# generating the Kim mapping
kim = []
for x_i in xrange(0, 2**N):
x = F.fetch_int(x_i)
y = x**3 + x**10 + F.gen()*x**24
kim.append(y.integer_representation())
classes = enumerate_ea_classes(kim)
for f in classes:
print algebraic_degree(f), pretty_spectrum(thickness_spectrum(f))
print "total: ", len(classes)
def _test(self):
from sage.all import GF, FunctionField, PolynomialRing
k = GF(4)
a = k.gen()
R = PolynomialRing(k, 'b')
b = R.gen()
l = k.extension(b**2 + b + a, 'b')
K = FunctionField(l, 'x')
x = K.gen()
R = PolynomialRing(K, 't')
t = R.gen()
F = t * x
F.factor(proof=False)
def test_ccz_permutations(number="all permutations"):
N = 6
F = GF(2**N, name="a")
# generating the Kim mapping
kim = []
for x_i in xrange(0, 2**N):
x = F.fetch_int(x_i)
y = x**3 + x**10 + F.gen() * x**24
kim.append(y.integer_representation())
permutations = ccz_equivalent_permutations(kim, number=number)
for i, p in enumerate(permutations):
print("{:2d} {} {} {}".format(
i, is_permutation(p), pretty_spectrum(differential_spectrum(p)),
pretty_vector(p)))
print("total: {}".format(len(permutations)))
def test_ea_classes():
N = 8
F = GF(2**N, name="a")
# generating the Kim mapping
kim = []
for x_i in xrange(0, 2**N):
x = F.fetch_int(x_i)
y = x**3 + x**10 + F.gen()*x**24
kim.append(y.integer_representation())
total = 0
for f in ea_classes_in_the_ccz_class_of(kim):
print algebraic_degree(f), pretty_spectrum(thickness_spectrum(f))
total += 1
print "total: ", total
"""Contains many 8-bit APN functions"""
from sage.all import GF, PolynomialRing
# global variables of the module
N = 8
F = GF(2**N, name="a")
g = F.gen()
POLY_RING = PolynomialRing(F, "X")
X = POLY_RING.gen()
def poly_to_lut(p):
s = []
for x_i in xrange(0, 2**N):
y = (p(F.fetch_int(x_i))).integer_representation()
s.append(y)
return s
def all_quadratic_polynomials():
"""All the functions in Table 9 of
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.215.5432&rep=rep1&type=pdf
"""
return [
poly_to_lut(X**3),
poly_to_lut(X**9),
poly_to_lut(X**3 + sum(X**(9 * 2**i) for i in xrange(0, N))),
poly_to_lut(X**9 + sum(X**(3 * 2**i) for i in xrange(0, N))),
poly_to_lut(X**3 + g**245 * X**33 + g**183 * X**66 + g**21 * X**144),
