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Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity

Authors:
Senshan Pan
Xiaotong Fu
Weiguo Zhang
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URL: http://eprint.iacr.org/2010/243
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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
}