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Open Problems on Binary Bent Functions

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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.

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Notes

  1. 1.

    In public-key cryptography, the only key which must be kept secret is the decryption key, but as far as we know, bent functions play no big role in such ciphers.

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Acknowledgments

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

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Authors and Affiliations

  1. LAGA, Universities of Paris 8 and Paris 13, CNRS, UMR 7539, Paris, France

    Claude Carlet

  2. Department of Mathematics, University of Paris 8, 2 rue de la liberté, 93526, Saint-Denis cedex 02, France

    Claude Carlet

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  1. Claude Carlet
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Correspondence to Claude Carlet .

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Editors and Affiliations

  1. Dept. of Computer Science, University of California, Santa Barbara, Santa Barbara, California, USA

    Çetin Kaya Koç

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Carlet, C. (2014). Open Problems on Binary Bent Functions. In: Koç, Ç. (eds) Open Problems in Mathematics and Computational Science. Springer, Cham. https://doi.org/10.1007/978-3-319-10683-0_10

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  • DOI: https://doi.org/10.1007/978-3-319-10683-0_10

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