Re: On compressibility of random permutations



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.
.