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IMA International Conference on Cryptography and Coding

IMACC 2011: Cryptography and Coding pp 61–78Cite as

Binary Kloosterman Sums with Value 4

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7089))

Abstract

Kloosterman sums have recently become the focus of much research, most notably due to their applications in cryptography and their relations to coding theory.

Very recently Mesnager has showed that the value 4 of binary Kloosterman sums gives rise to several infinite classes of bent functions, hyper-bent functions and semi-bent functions in even dimension.

In this paper we analyze the different strategies used to find zeros of binary Kloosterman sums to develop and implement an algorithm to find the value 4 of such sums. We then present experimental results showing that the value 4 of binary Kloosterman sums gives rise to bent functions for small dimensions, a case with no mathematical solution so far.

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Author information

Authors and Affiliations

  1. UMR 7539, CNRS LTCI, Institut Télécom, Télécom ParisTech, 46 rue Barrault, Cedex 13, F-75634, Paris, France

    Jean-Pierre Flori & Gérard Cohen

  2. LAGA (Laboratoire Analyse, Géometrie et Applications), UMR 7539, CNRS, Department of Mathematics, University of Paris XIII and University of Paris VIII, 2 rue de la liberté, 93526, Saint-Denis Cedex, France

    Sihem Mesnager

Authors
  1. Jean-Pierre Flori
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  2. Sihem Mesnager
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  3. Gérard Cohen
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Editor information

Editors and Affiliations

  1. Hewlett-Packard Laboratories, UK

    Liqun Chen

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Flori, JP., Mesnager, S., Cohen, G. (2011). Binary Kloosterman Sums with Value 4. In: Chen, L. (eds) Cryptography and Coding. IMACC 2011. Lecture Notes in Computer Science, vol 7089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25516-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-25516-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25515-1

  • Online ISBN: 978-3-642-25516-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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