# Re: commutative property of algorithms

*From*: "J.D." <degolyer181@xxxxxxxxx>*Date*: Mon, 15 Mar 2010 15:24:09 -0700 (PDT)

@Scott Fluhrer

WTShaw might not have intended to ask about permutation cycles; however,You appear to be correct about whether WTShaw was talking about

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".

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 parity...do you have any suggestions?

.

**Follow-Ups**:**Re: commutative property of algorithms***From:*Scott Fluhrer

**References**:**Re: commutative property of algorithms***From:*unruh

**Re: commutative property of algorithms***From:*WTShaw

**Re: commutative property of algorithms***From:*Scott Fluhrer

**Re: commutative property of algorithms***From:*J.D.

**Re: commutative property of algorithms***From:*Scott Fluhrer

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