Re: commutative property of algorithms

@Scott Fluhrer

WTShaw might not have intended to ask about permutation cycles; however,
that does appear to be the answer to his question.  When he says "repeatedly
encrypting with it while moving output bits to input bits", it sounds like
he is talking about the sequence X, E(X), E(E(X)), ..., E^n(X)

When he then ask whether "you pass through all combinations of data", it
sounds like whether, for a fixed key and X, whether all possible 2^128
values can be represented by E^n(X), for some n.  This is precisely the
single-cycle permuation criteria.

And, as AES is known not to be a single cycle permutation for any key, we
know that the answer to his question is "No".
You appear to be correct about whether WTShaw was talking about
permutation cycles. However I cannot understand your argument for why
AES can never be a single cycle for any key. I suppose I will have to
read more about permutation you have any suggestions?