## Cryptology ePrint Archive: Report 2010/243

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

Senshan Pan and 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.

Category / Keywords: boolean functions

Date: received 29 Apr 2010, last revised 8 May 2010

Contact author: pansenshan at gmail com

Available format(s): PDF | BibTeX Citation

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

Short URL: ia.cr/2010/243

[ Cryptology ePrint archive ]