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A combinatorial condition and Boolean functions with optimal algebraic immunity

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Abstract

This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal algebraic degree and high nonlinearity. Both classes have optimal algebraic immunity based on a general combinatorial conjecture.

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Author information

Authors and Affiliations

  1. Key Laboratory of System and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Qingfang Jin

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

    Zhuojun Liu & Xiaoming Zhang

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

    Baofeng Wu

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

Correspondence to Qingfang Jin.

Additional information

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

This paper was recommended for publication by Editor LI Ziming.

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Jin, Q., Liu, Z., Wu, B. et al. A combinatorial condition and Boolean functions with optimal algebraic immunity. J Syst Sci Complex 28, 725–742 (2015). https://doi.org/10.1007/s11424-014-2133-x

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  • DOI: https://doi.org/10.1007/s11424-014-2133-x

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