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Several new classes of self-dual bent functions derived from involutions

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Abstract

Bent functions are a kind of Boolean functions which have the maximum Hamming distance to linear and affine functions, they have some interesting applications in combinatorics, coding theory, cryptography and sequences. However, generally speaking, how to find new bent functions is a hard work and is a hot research project during the past decades. A subclass of bent functions that has received attention since Dillon’s seminal thesis (1974) is the subclass of those Boolean functions that are equal to their dual (or Fourier transform in Dillon’s terminology): the so-called self dual bent functions. In this paper, we propose a construction of involutions from linear translators, and provide two methods for constructing new involutions by utilizing some given involutions. With the involutions presented in this paper, several new classes of self-dual bent functions are produced.

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Acknowledgments

The authors thank the Associate Editor and the anonymous reviewers for their valuable comments which have highly improved then manuscript.

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Authors and Affiliations

  1. Department of Math, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, China

    Gaojun Luo & Xiwang Cao

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

    Xiwang Cao

  3. Department of Mathematics, University of Paris VIII, 93526, Saint-Denis, France

    Sihem Mesnager

  4. University of Paris XIII, CNRS, LAGA UMR 7539, Sorbonne Paris Cité, 93430, Villetaneuse, France

    Sihem Mesnager

  5. Telecom ParisTech, 75013, Paris, France

    Sihem Mesnager

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  1. Gaojun Luo
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  2. Xiwang Cao
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  3. Sihem Mesnager
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Correspondence to Gaojun Luo.

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This article is part of the Topical Collection on Special Issue on Boolean Functions and Their Applications

This work was supported by the National Natural Science Foundation of China (Grant No. 11771007 and 61572027).

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Luo, G., Cao, X. & Mesnager, S. Several new classes of self-dual bent functions derived from involutions. Cryptogr. Commun. 11, 1261–1273 (2019). https://doi.org/10.1007/s12095-019-00371-9

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  • DOI: https://doi.org/10.1007/s12095-019-00371-9

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