[Resource Topic] 2015/868: Optimally Secure Block Ciphers from Ideal Primitives

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Title:
Optimally Secure Block Ciphers from Ideal Primitives

Authors: Stefano Tessaro

Abstract:

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 {\em ideal} (i.e., randomly chosen). This paper addresses the question of finding {\em 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 - O(1)} 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 levels using O(n) independent random permutations. In contrast, here we only assume that a {\em single} {\em function} or {\em permutation} is available, while achieving similar efficiency. Our second contribution is a generic method to enhance a block cipher, initially only secure as a PRP, to achieve related-key security with comparable quantitative security.

ePrint: https://eprint.iacr.org/2015/868

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