An Enciphering Scheme Based on a Card Shuffle

Viet Tung Hoang; Ben Morris; Phillip Rogaway

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arXiv · 1208.1176

An Enciphering Scheme Based on a Card Shuffle

Viet Tung Hoang·Ben Morris·Phillip Rogaway

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Abstract

We introduce the swap-or-not shuffle and show that the technique gives rise to a new method to convert a pseudorandom function (PRF) into a pseudorandom permutation (PRP) (or, alternatively, to directly build a confusion/diffusion blockcipher). We then prove that swap-or-not has excellent quantitative security bounds, giving a Luby-Rackoff type result that ensures security (assuming an ideal round function) to a number of adversarial queries that is nearly the size of the construction's domain. Swap-or-not provides a direct solution for building a small-domain cipher and achieving format-preserving encryption, yielding the best bounds known for a practical scheme for enciphering credit-card numbers. The analysis of swap-or-not is based on the theory of mixing times of Markov chains.

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Viet Tung Hoang, Ben Morris, Phillip Rogaway. 2012-08-06. An Enciphering Scheme Based on a Card Shuffle. https://arxiv.org/abs/1208.1176

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