Check if crc32 and md5 are affine

affine.py

"""Affinity test."""
from hashlib import md5
from binascii import crc32
from hypothesis import given
from hypothesis.strategies import integers, lists, tuples

# In practice, CRC operations are often started with a nonzero state. Because
# of this, the actual equation is usually of the form:

# crc(a)⊕crc(b)=crc(a⊕b)⊕c

# for some constant c (which depends on the length of a, b).

# An alternative way of expressing this is, for three any equal-length
# bitstrings a,b,ca,b,c, we have:

# crc(a)⊕crc(b)⊕crc(c)=crc(a⊕b⊕c)

# The technical term for this relationship is affine; in cryptography, we treat
# it as linear because, for attacks that assume linearity, affine works just as
# well.

_bin32 = integers(min_value=0, max_value=2**32 - 1)


def crc32i(a):
    """crc32 an integer."""
    return crc32(a.to_bytes(4, "big"))


def md532i(a):
    """md5 corresponding to the crc32i, to prove it is not affine."""
    d = md5(a.to_bytes(4, "big")).digest()
    return int.from_bytes(d[:4], "big", signed=True)


@given(lists(tuples(_bin32, _bin32), min_size=10))
def test_crc_not_affine(data):
    """If crc32 is affine as described above this should fail."""
    cl = map(lambda v: crc32i(v[0]) ^ crc32i(v[1]) ^ crc32i(v[0] ^ v[1]), data)
    # Check if c is constant
    x = next(cl)
    assert all(c == x for c in cl)


@given(lists(tuples(_bin32, _bin32), min_size=10))
def test_md5_not_affine(data):
    """If crc32 is affine as described above this should fail."""
    cl = map(lambda v: md532i(v[0]) ^ md532i(v[1]) ^ md532i(v[0] ^ v[1]), data)
    # Check if c is constant
    x = next(cl)
    assert all(c == x for c in cl)