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A Construction of 1-Resilient Boolean Functions with Good Cryptographic Properties

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Abstract

This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified functions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the “continuity” of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known 1-resilient functions modified by Tu-Deng and Tang-Carlet-Tang functions.

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Author information

Authors and Affiliations

  1. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Jinyong Shan, Lei Hu & Xiangyong Zeng

  2. DCS, Chinese Academy of Sciences, Beijing, 100093, China

    Jinyong Shan

  3. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, China

    Lei Hu

  4. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, 430062, China

    Xiangyong Zeng

  5. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    Chunlei Li

Authors
  1. Jinyong Shan
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  2. Lei Hu
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  3. Xiangyong Zeng
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  4. Chunlei Li
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Corresponding author

Correspondence to Lei Hu.

Additional information

This research was supported by the National Key Basic Research Program of China under Grant No. 2013CB834203, the National Natural Science Foundation of China under Grant Nos. 61472417 and 61472120, and the Research Council of Norway.

This paper was recommended for publication by Editor DENG Yingpu.

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Shan, J., Hu, L., Zeng, X. et al. A Construction of 1-Resilient Boolean Functions with Good Cryptographic Properties. J Syst Sci Complex 31, 1042–1064 (2018). https://doi.org/10.1007/s11424-017-6177-6

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  • DOI: https://doi.org/10.1007/s11424-017-6177-6

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