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

  • Gaojun LuoEmail author
  • Xiwang Cao
  • Sihem Mesnager
Article
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Part of the following topical collections:
  1. Special Issue on Boolean Functions and Their Applications

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.

Keywords

Involution Bent function Permutation polynomial 

Mathematics Subject Classification (2014)

97N70 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.State Key Laboratory of Information SecurityInstitute of Information Engineering, Chinese Academy of SciencesBeijingChina
  3. 3.Department of MathematicsUniversity of Paris VIIISaint-DenisFrance
  4. 4.University of Paris XIII, CNRS, LAGA UMR 7539, Sorbonne Paris CitéVilletaneuseFrance
  5. 5.Telecom ParisTechParisFrance

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