Open Problems on Binary Bent Functions

Chapter

Abstract

This chapter gives a survey of the recent results on Boolean bent functions and lists some open problems in this domain. It includes also new results. We recall the definitions and basic results, including known and new characterizations of bent functions; we describe the constructions (primary and secondary; known and new) and give the known infinite classes, in multivariate representation and in trace representation (univariate and bivariate). We also focus on the particular class of rotation symmetric (RS) bent functions and on the related notion of bent idempotent: we give the known infinite classes and secondary constructions of such functions, and we describe the properties of a recently introduced transformation of RS functions into idempotents.

Notes

Acknowledgments

We thank Thomas Cusick, Guangpu Gao, and Sihem Mesnager for useful information.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.LAGAUniversities of Paris 8 and Paris 13, CNRS, UMR 7539ParisFrance
  2. 2.Department of MathematicsUniversity of Paris 8Saint-Denis cedex 02France

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