[Cryptography] Security of a permute-only system?

[Henry Baker]

At 09:49 PM 11/29/2015, Ray Dillinger wrote:
>On 11/25/2015 03:34 PM, Henry Baker wrote:
>> Given a message source that's already "whitened", but otherwise unencrypted, how much security can be achieved strictly through an unknown, but random permutation?
>> 
>> I.e., if n=171, then a random permutation of size n would appear to require 1026 bits to specify it.
>> 
>> Suppose we simply applied our random permutation to each block of 171 pre-whitened bits.
>
>I forgot to mention this, because at first glance I thought
>it was obvious.  However, on reflection it may not be.
>
>You must not apply the SAME permutation to each block;
>if you do, then you win absolutely nothing w/r/t security
>because your opponent can then undo your permutation
>via parallel anagramming.
>
>Like a stream cipher means XORing with a random string of
>bits but you NEVER repeat that random string, any security
>gained from permutations only holds as long as you don't
>repeat the same permutation.

Could you provide just a tad more info?

Remember, I said no CPA, no CCA; pre-whitened bits prior to permutation.

W/o whitening, any non-uniform statistics will eventually reveal the permutation.

If you can compare input to output, you can eventually reveal the permutation, even if you can't choose the input.

But if you can't compare the bits coming in to the bits going out, how do you recover the permutation?