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The authors propose a novel small-domain pseudo-random permutation, also referred to as a small-domain cipher or small-domain (deterministic) encryption. They prove that their 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, their construction is 1,000 to 8,000 times faster in most realistic scenarios, in comparison with the best known construction (also achieving strong security). Their implementation leverages the extended instruction sets of modern processors; and they also introduce a smart caching strategy to freely tune the tradeoff between time and space.
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