# Can we use merely permutation to hide a message?

This question is related to this:

I think the below question is a simplified version of that.

Assume we have a 40-bit message $m$ (or 40-bit string). The message is picked from a universe of size one; so $m \in U$, where $|U|=1$.

We permute the bits in $m$. So we would have a 40-bit string, $m'$

Question: Given the message $m'$ can the adversary learn the original message, $m$, with a non-negligible probability?

• Surely |U| is 2^40, if U is the set of all 40-bit binary numbers? – r3mainer Jan 28 '16 at 19:35
• @squeamishossifrage It depends how to look at it. For simplicity I defined the message domain as $U$. consider $U$ as a small domain of valid English name. So not all $2^{40}$ are valid names. Here I assumed that there exists only one valid name. – user153465 Jan 28 '16 at 20:37
• "Non-negligible" is meaningless if the key size is fixed, as is the case here (the key is a permutation of a finite set). – fkraiem Jan 29 '16 at 4:09
• @fkraiem What if I mix the message original bit with some random bits (e.g. 40-bit) and then shuffle all? – user153465 Jan 29 '16 at 10:03