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Boolean functions with four-valued Walsh spectra

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Abstract

Three classes of Boolean functions with four-valued Walsh spectra are presented and their Walsh spectrum distributions are determined. They are derived from Bent functions of the Maiorana-McFarland and Dillon PS ap types and of the monomial form \(Tr_1^{2m} (\lambda x^{r(2^m - 1)} )\) by complementing the values of the Bent functions at two points.

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Authors and Affiliations

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

    Zhiqiang Sun

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

    Lei Hu

  3. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, 100093, China

    Lei Hu

Authors
  1. Zhiqiang Sun
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  2. Lei Hu
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Corresponding author

Correspondence to Zhiqiang Sun.

Additional information

This research is supported by the National Key Basic Research Program of China under Grant No. 2013CB834203, the National Natural Science Foundation of China under Grant No. 61472417, the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No. XDA06010702, and the State Key Laboratory of Information Security, Chinese Academy of Sciences.

This paper was recommended for publication by Editor LI Ziming.

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Sun, Z., Hu, L. Boolean functions with four-valued Walsh spectra. J Syst Sci Complex 28, 743–754 (2015). https://doi.org/10.1007/s11424-014-2224-8

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  • DOI: https://doi.org/10.1007/s11424-014-2224-8

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