[Cryptography] Security of a permute-only system?

[Henry Baker]

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.

This random permutation is used essentially as (part of) a symmetric session key.

Let's assume neither CPA nor CCA: this scheme might be part of a larger system.

Q: does such a random permutation provide any additional security, or is it merely a waste of time?

(Let's assume that we can efficiently perform the permutation w/o any side channels -- e.g., perhaps an oblivious Batcher-type sorting network.)