Sometimes-Recurse Shuffle: Almost-Random Permutations in Logarithmic Expected Time

Ben Morris; Phillip Rogaway

Paper 2013/560

Sometimes-Recurse Shuffle: Almost-Random Permutations in Logarithmic Expected Time

Ben Morris and Phillip Rogaway

Abstract

We describe a security-preserving construction of a random permutation of domain size~ $N$ from a random function, the construction tolerating adversaries asking all~ $N$ plaintexts, yet employing just $Θ (\lg N)$ calls, on average, to the one-bit-output random function. The approach is based on card shuffling. The basic idea is to use the \textit{sometimes-recurse} transformation: lightly shuffle the deck (with some other shuffle), cut the deck, and then recursively shuffle one of the two halves. Our work builds on a recent paper of Ristenpart and Yilek.

Note: Minor revisions and clarifications.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published by the IACR in EUROCRYPT 2014
Keywords: Card shuffling format-preserving encryption PRF-to-PRP conversion mix-and-cut shuffle pseudorandom permutations sometimes-recurse shuffle swap-or-not shuffle
Contact author(s): rogaway @ cs ucdavis edu
morris @ math ucdavis edu
History: 2014-04-02: revised; 2013-09-04: received; See all versions
Short URL: https://ia.cr/2013/560
License: CC BY

BibTeX

@misc{cryptoeprint:2013/560,
      author = {Ben Morris and Phillip Rogaway},
      title = {Sometimes-Recurse Shuffle: Almost-Random Permutations in Logarithmic Expected Time},
      howpublished = {Cryptology {ePrint} Archive, Paper 2013/560},
      year = {2013},
      url = {https://eprint.iacr.org/2013/560}
}