NDLI: Enumerative encoding of correlation immune Boolean functions

Content Provider	IEEE Xplore Digital Library
Author	Carrasco, N. Le Bars, J.-M. Viola, A.
Copyright Year	2011
Description	Author affiliation: CNRS UMR 6072, GREYC, Université de Caen, France (Le Bars, J.-M.) \|\| Universidad de la República, Uruguay (Carrasco, N.) \|\| Universidad de la República, Uruguay, Associate member of LIPN UMR 7030, Université Paris, 13 - CNRS, France (Viola, A.)
Abstract	Boolean functions are very important cryptographic primitives in stream or block ciphers. In order to be useful for cryptographic applications, these functions should satisfy some properties like high algebraic degree, high non linearity or being correlation immune. Since for most of the cryptographic criteria presented in the literature there is no complete characterization of the set of functions that optimally satisfy any of them, the possibility of finding an enumerative encoding of any such class of functions is extremely hard. In a recent paper Le Bars and Viola have presented an innovative recursive decomposition of the first order correlation immune Boolean functions. It is not a trivial task, however, to derive from this characterization an enumerative encoding. This paper presents an enumerative encoding for first order correlation immune functions. It provides the first enumerative encoding of a class of Boolean functions with cryptographic applications. The encoding naturally leads to efficient random generation algorithms. For example, we may construct, with uniform probability, any 1-resilient function (balanced first order correlation immune function) with 8 variables in less than 30 seconds, from a universe of around $10^{68}$ functions
Starting Page	643
Ending Page	647
File Size	330394
Page Count	5
File Format	PDF
ISBN	9781457704383
e-ISBN	9781457704376
DOI	10.1109/ITW.2011.6089576
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-10-16
Publisher Place	Brazil
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Boolean functions Correlation Encoding Cryptography Indexes Dictionaries Explosions 1-resilient functions Enumerative encoding uniform random generation decomposable structures
Content Type	Text
Resource Type	Article

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