def test_element_generation():
f = finite.Field(17)
el = f.element(10)
assert el.coeff == [10]
f = finite.Field(16)
el = f.element(10)
assert el.coeff == [0, 1, 0, 1]
f = finite.Field(9)
el = f.element(7)
assert el.coeff == [1, 2]
def test_characteristic(n):
f = finite.Field(n)
_sanity_run_check = False
for m in int_sampler(n, limit=int(MAX_ITER_N / f.prime) + 1):
_sanity_run_check = True
el = f.element(m)
assert sum(el for _ in range(f.prime)) == f.element(0)
assert _sanity_run_check
def test_mul_identity(n):
f = finite.Field(n)
multiplicitive_identity = f.element(1)
for m in range(n):
el = f.element(m)
x = el * multiplicitive_identity
print(x)
print(el.unreduced_mul(multiplicitive_identity))
assert el * multiplicitive_identity == el
def test_div_identity(n):
f = finite.Field(n)
multiplicitive_identity = f.element(1)
for m in range(n):
el = f.element(m)
quot = el / multiplicitive_identity
# repad quotient to same number of coefficients
quot = quot + [0] * (f.power - len(quot))
assert f.element(quot) == el
def test_aes_examples():
"""Examples from FIPS 197 (AES) section 4.2.1"""
f = finite.Field(2**8)
assert f.mod_poly == [1, 1, 0, 1, 1, 0, 0, 0, 1]
assert f.E(0x57) * f.E(0x01) == f.E(0x57)
assert f.E(0x57) * f.E(0x02) == f.E(0xAE)
assert f.E(0x57) * f.E(0x08) == f.E(0x8E)
assert f.E(0x57) * f.E(0x10) == f.E(0x07)
assert f.E(0x57) * f.E(0x13) == f.E(0xFE)
assert f.E(0x57) * (f.E(0x01) + f.E(0x02) + f.E(0x10)) == f.E(0xFE)
assert f.E(0x57) + f.E(0xAE) + f.E(0x07) == f.E(0xFE)
def test_associative(n, func):
f = finite.Field(n)
_op = "*" if func is operator.mul else "+"
for na, nb, nc in int_sampler([n, n, n], seed=n):
a = f.element(na)
b = f.element(nb)
c = f.element(nc)
if func(func(a, b), c) != func(a, func(b, c)):
print(na, nb, nc)
ab = func(a, b)
bc = func(b, c)
ab_c = func(ab, c)
a_bc = func(a, bc)
print(f)
print(f.mod_poly)
print(f"a: {na} -> {a}")
print(f"b: {nb} -> {b}")
print(f"c: {nc} -> {c}")
print(f"{ab=}, {ab_c=}")
print(f"{bc=}, {a_bc=}")
_note = f"in {f}: ({na} {_op} {nb}) {_op} {nc} != {na} {_op} ({nb} {_op} {nc})"
pytest.fail(_note)
def test_add_identity(n, func):
f = finite.Field(n)
additive_identity = f.element(0)
for m in int_sampler(n):
el = f.element(m)
assert func(el, additive_identity) == el
def test_element_roundtrip(n):
f = finite.Field(n)
for m in int_sampler(n):
el = f.element(m)
assert int(el) == m
def test_invalid_fields(n, factorization):
with pytest.raises(ValueError, match=re.escape(factorization)):
finite.Field(n)
def test_field_creation(n, ex_prime, ex_pow):
f = finite.Field(n)
assert f.prime == ex_prime
assert f.power == ex_pow
def test_unreduced_multiplication():
f = finite.Field(27)
assert f.element([2, 1,
2]).unreduced_mul(f.element([2, 1,
2])) == [1, 1, 0, 1, 1]
def test_sub(n):
f = finite.Field(n)
additive_identity = f.element(0)
for m in range(min(n, MAX_ITER_N)):
el = f.element(m)
assert el - el == additive_identity
def test_commutative(n, func):
f = finite.Field(n)
for na, nb in int_sampler([n, n]):
a = f.element(na)
b = f.element(nb)
assert func(a, b) == func(b, a), (a, b)
def test_add_inverse(n):
f = finite.Field(n)
additive_identity = f.element(0)
for m in int_sampler(n):
el = f.element(m)
assert el + (-el) == additive_identity
