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A note on two classes of Boolean functions with optimal algebraic immunity

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Abstract

Tu and Deng proposed a class of bent functions which are of optimal algebraic immunity under the assumption of a combinatorial conjecture. In this paper, the authors compute the dual of the Tu-Deng functions and then show that they are still of optimal algebraic immunity under the assumption of the same conjecture. For another class of Boolean functions constructed by Tang, et al. which are of optimal algebraic immunity with similar forms to Tu-Deng functions, the authors show that they are not bent functions by using some basic properties of binary complete Kloosterman sums.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Baofeng Wu

  2. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Baofeng Wu, Zhuojun Liu, Qingfang Jin & Xiaoming Zhang

Authors
  1. Baofeng Wu
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  2. Zhuojun Liu
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  3. Qingfang Jin
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  4. Xiaoming Zhang
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Corresponding author

Correspondence to Baofeng Wu.

Additional information

This research was supported by National Basic Research Program of China under Grant No. 2011CB302400.

This paper was recommended for publication by Editor LI Ziming.

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Wu, B., Liu, Z., Jin, Q. et al. A note on two classes of Boolean functions with optimal algebraic immunity. J Syst Sci Complex 27, 785–794 (2014). https://doi.org/10.1007/s11424-014-2132-y

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  • DOI: https://doi.org/10.1007/s11424-014-2132-y

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