The Mix-and-Cut Shuffle: Small-Domain Encryption Secure against N Queries.

We provide a new shuffling algorithm, called Mix-and-Cut, that provides a provably-secure block cipher even for adversaries that can observe the encryption of all N = 2(n) domain points. Such fully secure ciphers are useful for format-preserving encryption, where small domains (e.g., n = 30) are common and databases may well include examples of almost all ciphertexts. Mix-and-Cut derives from a general framework for building fully secure pseudorandom permutations (PRPs) from fully secure pseudorandom separators (PRSs). The latter is a new primitive that we treat for the first time. Our framework was inspired by, and uses ideas from, a particular cipher due to Granboulin and Pornin. To achieve full security for Mix-and-Cut using this framework, we give a simple proof that a PRP secure for (1 - epsilon) N queries (recently achieved efficiently by Hoang, Morris, and Rogaway's Swap-or-Not cipher) yields a PRS secure for N queries.