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Constructing new APN functions and bent functions over finite fields of odd characteristic via the switching method

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Abstract

The switching method is a very powerful method to construct new APN functions and differentially 4-uniform permutations over finite fields of even characteristic. In this paper, using this method, we present several new constructions of infinite classes of nonpower APN functions and two new classes of bent functions in finite fields of odd characteristic.

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Acknowledgments

The authors would like to thank the two anonymous referees for their helpful comments which have improved the presentation and quality of this paper. This research is supported by the National Natural Science Foundation of China (Grants 11371011 and 61403157) and the Natural Science Foundation of Huainan Normal University (NO. 2013XJ67).

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Guangkui Xu, Xiwang Cao & Shanding Xu

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

    Xiwang Cao

  3. Department of Applied Mathematics, Huainan Normal University, Huainan, 232038, China

    Guangkui Xu

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  1. Guangkui Xu
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  2. Xiwang Cao
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  3. Shanding Xu
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Correspondence to Xiwang Cao.

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Xu, G., Cao, X. & Xu, S. Constructing new APN functions and bent functions over finite fields of odd characteristic via the switching method. Cryptogr. Commun. 8, 155–171 (2016). https://doi.org/10.1007/s12095-015-0145-6

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  • DOI: https://doi.org/10.1007/s12095-015-0145-6

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