How to Encipher Messages on a Small Domain

Authors:
Ben Morris;Phillip Rogaway;Till Stegers
Affiliations:
Dept. of Mathematics, University of California, Davis, USA 95616;Dept. of Computer Science, University of California, Davis, USA 95616;Dept. of Computer Science, University of California, Davis, USA 95616
Venue:
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Year:
2009

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Abstract

We analyze the security of the Thorp shuffle, or, equivalently, a maximally unbalanced Feistel network. Roughly said, the Thorp shuffle on N cards mixes any N 1 驴 1/r of them in $O(r\lg N)$ steps. Correspondingly, making O(r) passes of maximally unbalanced Feistel over an n-bit string ensures CCA-security to 2 n(1 驴 1/r) queries. Our results, which employ Markov-chain techniques, enable the construction of a practical and provably-secure blockcipher-based scheme for deterministically enciphering credit card numbers and the like using a conventional blockcipher.