Construction of 1-resilient boolean functions with optimal algebraic immunity and good nonlinearity

Authors:
Sen-Shan Pan;Xiao-Tong Fu;Wei-Guo Zhang
Affiliations:
State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, China;State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, China and State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, ...;State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, China
Venue:
Journal of Computer Science and Technology
Year:
2011

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Abstract

This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler's upper bound of algebraic degree. Also a class of 1-resilient functions on any number n 2 of variables with at least sub-optimal algebraic immunity is provided.