How to construct pseudorandom permutations from pseudorandom functions
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Given (deterministic) ciphers ε and E that can enciphermessages of l and n bits, respectively, we construct a cipher ε* = XLS[ε,E] that can encipher messages of l + s bits for any s . Enciphering such a string will take one call to E and two calls to E. We prove that ε is a strong pseudorandom permutation as long as ε and E are. Our construction works even in the tweakable and VIL (variable-input-length) settings. It makes use of a multipermutation (a pair of orthogonal Latin squares), a combinatorial object not previously used to get a provablesecurity result.