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

Senshan Pan; Xiaotong Fu; Weiguo Zhang

Paper 2010/243

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

Senshan Pan, Xiaotong Fu, and Weiguo Zhang

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.

Note: We revise some details for clear statementwe, and we find a good example by computer searching.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: boolean functions
Contact author(s): pansenshan @ gmail com
History: 2010-05-09: revised; 2010-05-02: received; See all versions
Short URL: https://ia.cr/2010/243
License: CC BY

BibTeX

@misc{cryptoeprint:2010/243,
      author = {Senshan Pan and Xiaotong Fu and Weiguo Zhang},
      title = {Construction of  1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/243},
      year = {2010},
      url = {https://eprint.iacr.org/2010/243}
}