An Enciphering Scheme Based on a Card Shuffle
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.
Cite
@article{arxiv.1208.1176,
title = {An Enciphering Scheme Based on a Card Shuffle},
author = {Viet Tung Hoang and Ben Morris and Phillip Rogaway},
journal= {arXiv preprint arXiv:1208.1176},
year = {2014}
}