CryptoDB
Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity
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Abstract: | This paper presents a construction for a class of 1-resilient Boolean functions with optimal algebraic immunity on an even number of variables by dividing them into two correlation classes, i.e. equivalence classes. From which, a nontrivial pair of functions has been found by applying the generating matrix. For $n$ is small (e.g. $n=6$), a part of these functions achieve almost optimal nonlinearity. Apart from their good nonlinearity, the functions reach Siegenthaler's \cite{Siegenthaler} upper bound of algebraic degree. Furthermore, a class of 1-resilient functions on any number $n>2$ of variables with at least sub-optimal algebraic immunity is provided. |
BibTeX
@misc{eprint-2010-23144, title={Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity}, booktitle={IACR Eprint archive}, keywords={boolean functions}, url={http://eprint.iacr.org/2010/243}, note={ pansenshan@gmail.com 14738 received 29 Apr 2010, last revised 8 May 2010}, author={Senshan Pan and Xiaotong Fu and Weiguo Zhang}, year=2010 }