# Re: On compressibility of random permutations

*From*: WTShaw <lurens1@xxxxxxxxx>*Date*: Fri, 29 Jan 2010 01:35:38 -0800 (PST)

On Jan 21, 6:28 am, "Joseph Ashwood" <ashw...@xxxxxxx> wrote:

"Peter Fairbrother" <zenadsl6...@xxxxxxxxx> wrote in message

news:4b576ab4$0$2532$da0feed9@xxxxxxxxxxxxxxxxx

In general there is the idea that random permutations, or sequences, are

not compressible.

Actually permutations are compressible. Labeling each permutation with an

integer, significantly abbreviated the permutation. As an example take AES,

the key can be trivially converted to an integer, and serves as such an

index.

If you index a permutation as an integer in another base, all you have

done is just that and such is useless without a conversion table

assigning values to the elements in the permutation. Consider that

permutations can be floating and reassigned convenient to a specific

algorithm in use and the specific elements in them would have no

ranking or absolute value at all. This fact is most useful when

properly harnessed using nonlinear algorithms.

Permutations need not be simply used as linear strings as they could

be but as endless wheels of N characters. The number of permutations

would be somewhat less since there would be not true ends to each

different string. Again, many permutations can be used in linear

manner or best utilized in other ways. Its easier to implement logical

programmed manipulations that simulate real world models than try to

tackle them as anything line linear functions, which they are not.

Randomness in circular permutations distributed differently in each

wheel and available to encrypt random value added to the system as

might be necessary in encryption and be automatically recovered in

decryption. The problem that the attacker faces should be in never

seeing a linear or comprehensive use all segments of permutation keys.

This does meet Shannon's requirement for relative strength without the

linear pitfalls of the OTP.

Although not truly esoteric,if this process is still a mystery to many

of you, remember it has not been beyond more than several others and

have implemented these ideas with some novel differences.

.

**References**:**On compressibility of random permutations***From:*Peter Fairbrother

**Re: On compressibility of random permutations***From:*Joseph Ashwood

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