An easy way to access a large number of different permutations is to use a cipher and select a particular permutation with the key. In this sense the AES provi

An easy way to access a large number of different permutations is to use a cipher and select a particular permutation with the key. In this sense the AES provides a much larger number of reversible operations than all those listed :) For 32 bit permutations my go-to is skipfish. It's not a great cipher but it produces permutations (for e.g. producing a random permutation of all IPv4 addresses) perfectly well.