Key-Alternating Ciphers in a Provable Setting: Encryption Using a Small Number of Public Permutations (Extended Abstract)

Andrey Bogdanov, L.R. Knudsen, Gregor Leander, Francois-Xavier Standaert, John Steinberger, E. Tischhauser

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    Abstract

    This paper considers—for the first time—the concept of key-alternating ciphers in a provable security setting. Key-alternating ciphers can be seen as a generalization of a construction proposed by Even and Mansour in 1991. This construction builds a block cipher PX from an n-bit permutation P and two n-bit keys k 0 and k 1, setting PXk0,k1(x)=k1⊕P(x⊕k0) . Here we consider a (natural) extension of the Even-Mansour construction with t permutations P 1,…,P t and t + 1 keys, k 0,…, k t . We demonstrate in a formal model that such a cipher is secure in the sense that an attacker needs to make at least 22n/3 queries to the underlying permutations to be able to distinguish the construction from random. We argue further that the bound is tight for t = 2 but there is a gap in the bounds for t > 2, which is left as an open and interesting problem. Additionally, in terms of statistical attacks, we show that the distribution of Fourier coefficients for the cipher over all keys is close to ideal. Lastly, we define a practical instance of the construction with t = 2 using AES referred to as AES2. Any attack on AES2 with complexity below 285 will have to make use of AES with a fixed known key in a non-black box manner. However, we conjecture its security is 2128.
    Original languageEnglish
    Title of host publicationAdvances in Cryptology – CRYPTO 2012 : 32nd Annual Cryptology Conference, Santa Barbara, CA, USA, August 19-23, 2012. Proceedings
    Volume7417
    PublisherSpringer
    Publication date2012
    Pages45-62
    ISBN (Print)978-3-642-32008-8
    ISBN (Electronic)978-3-642-32009-5
    Publication statusPublished - 2012
    Event32nd Annual Cryptology Conference - CRYPTO 2012 - Santa Barbara, CA, United States
    Duration: 19 Aug 201223 Dec 2012

    Conference

    Conference32nd Annual Cryptology Conference - CRYPTO 2012
    CountryUnited States
    CitySanta Barbara, CA
    Period19/08/201223/12/2012
    SeriesLecture Notes in Computer Science
    Volume7417

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