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Results on the nonexistence of bent-negabent rotation symmetric Boolean functions

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Abstract

In this paper, we study the conjecture that there doesn’t exist bent-negabent rotation symmetric Boolean functions. We prove that the conjecture is true for almost all the cases based on the properties of autocorrelation spectra and the enumeration formulas of orbits.

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Acknowledgements

The authors are grateful to the Associate Editor and the anonymous reviewers for their valuable comments which have highly improved the manuscript.

Funding

This research is supported by the National Natural Science Foundation of China (Grant Nos. 61902107, 61902276 and 61971243), the Natural Science Foundation of Hebei Province (Grant Nos. F2019207112 and A2021205027), the Scientific Research and Development Program of Hebei University of Economics and Business (Grant No. 2021ZD02) and the Science Foundation of Hebei Normal University (Grant No. L2021B04).

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Authors and Affiliations

  1. College of Information Technology, Hebei University of Economics and Business, Shijiazhuang, 050061, China

    Lei Sun

  2. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, China

    Zexia Shi

  3. College of Intelligence and Computing, Tianjin University, Tianjin, 300350, China

    Jian Liu

  4. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China

    Fang-Wei Fu

Authors
  1. Lei Sun
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  2. Zexia Shi
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  3. Jian Liu
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  4. Fang-Wei Fu
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Contributions

Lei Sun and Zexia Shi contributed the central idea and wrote the paper; Jian Liu and Fang-wei Fu revised the manuscript; all authors discussed the results and determined the final version of this manuscript.

Corresponding author

Correspondence to Zexia Shi.

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Sun, L., Shi, Z., Liu, J. et al. Results on the nonexistence of bent-negabent rotation symmetric Boolean functions. Cryptogr. Commun. 14, 999–1008 (2022). https://doi.org/10.1007/s12095-022-00575-6

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  • DOI: https://doi.org/10.1007/s12095-022-00575-6

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