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On the 2m-variable symmetric Boolean functions with maximum algebraic immunity

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Abstract

The properties of the 2m-variable symmetric Boolean functions with maximum algebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtained. At last, some necessary conditions for a symmetric Boolean function on even number variables to have maximum algebraic immunity are introduced.

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Authors and Affiliations

  1. Department of Mathematic and System Science, National University of Defense Technology, Changsha, 410073, China

    Qu LongJiang & Li Chao

  2. Key Lab of Network Security and Cryptology Technique, Fujian Normal University, Fuzhou, 350007, China

    Li Chao

Authors
  1. Qu LongJiang
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  2. Li Chao
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Corresponding author

Correspondence to Qu LongJiang.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 60573028), the Open Founds of Key Lab of Fujian Province University Network Security and Cryptology (Grant No. 07A003) and the Basic Research Foundation of National University of Defense Technology (Grant No. JC07-02-03)

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Qu, L., Li, C. On the 2m-variable symmetric Boolean functions with maximum algebraic immunity. Sci. China Ser. F-Inf. Sci. 51, 120–127 (2008). https://doi.org/10.1007/s11432-008-0010-8

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  • DOI: https://doi.org/10.1007/s11432-008-0010-8

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