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Recent advances in block-cipher theory deliver security analyses in models where one or more underlying components e.g., a function or a permutation are ideal i.e., randomly chosen. This paper addresses the question of finding new constructions achieving the highest possible security level under minimal assumptions in such ideal models. We present a new block-cipher construction, derived from the Swap-or-Not construction by Hoang et al. CRYPTO '12. With n-bit block length, our construction is a secure pseudorandom permutation PRP against attackers making $$2^{n - O\\log n}$$ block-cipher queries, and $$2^{n - O1}$$ queries to the underlying component which has itself domain size roughly n. This security level is nearly optimal. So far, only key-alternating ciphers have been known to achieve comparable security using On independent random permutations. In contrast, we only use a singlefunction or permutation, and still achieve similar efficiency. Our second contribution is a generic method to enhance a block cipher, initially only secure as a PRP, to additionally withstand related-key attacks without substantial loss in terms of concrete security.

Optimally Secure Block Ciphers from Ideal Primitives