Assuming a bit string is deemed cryptographically secure, e.g. PRNG using AES in counter mode, can we equally assume any permutation of said bit string is also cryptographically secure?
In a more practical sense, using a PRNG with AES in counter mode again (for instance), assume it turns out that AES can be more efficiently computed by permutating the input data and rearranging the implementation of the algorithm accordingly. Does the resulting pseudorandom bit string need to be permutated back to the correct order or can I use it directly as a cryptographically secure bitstring? (this is from a purely theoretical pov.)
PS: I used AES as an example, it could be any secure block cipher.
PS2: sorry about the sloppy use of technical terms, but I hope you will understand what I mean.