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Results on permutation symmetric Boolean functions

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Abstract

This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions. The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties. The proposed method is algebraic in nature. As a by-product, the authors correct and generalize the corresponding results of Stănică and Maitra (2008). Further, the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li (2006), and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky (1994).

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Author information

Authors and Affiliations

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

    Yanjuan Zhang & Yingpu Deng

Authors
  1. Yanjuan Zhang
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  2. Yingpu Deng
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Corresponding author

Correspondence to Yanjuan Zhang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11071285 and 61121062, 973 Project under Grant No. 2011CB302401, and the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences.

This paper was recommended for publication by Editor HU Lei.

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Zhang, Y., Deng, Y. Results on permutation symmetric Boolean functions. J Syst Sci Complex 26, 302–312 (2013). https://doi.org/10.1007/s11424-013-1125-6

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  • DOI: https://doi.org/10.1007/s11424-013-1125-6

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