FastPRP: Fast Pseudo-Random Permutations for Small Domains

We propose a novel small-domain pseudo-random permutation, also referred to as a small-domain cipher or smalldomain (deterministic) encryption. We prove that our construction achieves “strong security”, i.e., is indistinguishable from a random permutation even when an adversary has observed all possible input-output pairs. More importantly, our construction is 1,000 to 8,000 times faster in most realistic scenarios, in comparison with the best known construction (also achieving strong security). Our implementation leverages the extended instruction sets of modern processors; and we also introduce a smart caching strategy to freely tune the tradeoff between time and space.