[Cryptography] Conjecture on mathematically evaluating the ideal cipher model

[Ryan Carboni]

It is unknown how far the distance is between full avalanche and an ideal
cipher is. I do not believe this has been publicly noted, but every cipher
round generates a polynomial. In the most simple case:
(a + 1)(b + 1) vs. (a + 1)(b)
ab + a + b + 1 vs. ab + b

Normal ciphers are algebraically more complex, but the above example shows
a 2-bit cipher with a 1-bit key, as a xor is simply bitwise addition. A
cipher that is secure has enough rounds for algebraic terms to cancel out,
dependent on the key.

It is likely that ciphers do not become secure until they have enough
rounds for the generated polynomial to become a randomly selected
polynomial from all possible polynomials that generate secure permutations
for the given width, or indistinguishability. This may be why some ciphers
are vulnerable to slide attacks, or rotational cryptanalysis, as many
output bits are similar terms at the point of full avalanche.
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