Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity |
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| Authors: | Sen-Shan Pan Xiao-Tong Fu Wei-Guo Zhang |
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| Affiliation: | (1) State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, 710071, China;(2) State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China |
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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. |
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