Is there a simple algorithm to encrypt integers? That is, a function E(i,k) that accepts an n-bit integer and a key (of any type) and produces another, unrelated n-bit integer that, when fed into a second function D(i,k) (along with the key) produces the original integer?

Obviously there are some simple reversible operations you can perform, but they all seem to produce clearly related outputs (e.g. consecutive inputs lead to consecutive outputs). Also, of course, there are cryptographically strong standard algorithms, but they don't produce small enough outputs (e.g. 32-bit). I know any 32-bit cryptography can be brute-forced, but I'm not looking for something cryptographically strong, just something that looks random. Theoretically speaking it should be possible; after all, I could just create a dictionary by randomly pairing every integer. But I was hoping for something a little less memory-intensive.