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Characterizations of Plateaued and Bent Functions in Characteristic \(p\)

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Sequences and Their Applications - SETA 2014 (SETA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8865))

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Abstract

We characterize bent functions and plateaued functions in terms of moments of their Walsh transforms. We introduce in any characteristic the notion of directional difference and establish a link between the fourth moment and that notion. We show that this link allows to identify bent elements of particular families. Notably, we characterize bent functions of algebraic degree \(3\).

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Author information

Authors and Affiliations

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

    Sihem Mesnager

  2. LAGA, UMR 7539, CNRS, University of Paris XIII, Villetaneuse, France

    Sihem Mesnager

Authors
  1. Sihem Mesnager
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Correspondence to Sihem Mesnager .

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Editors and Affiliations

  1. Otto-von-Guericke University, Magdeburg, Germany

    Kai-Uwe Schmidt

  2. Austrian Academy of Sciences, Linz, Austria

    Arne Winterhof

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Mesnager, S. (2014). Characterizations of Plateaued and Bent Functions in Characteristic \(p\) . In: Schmidt, KU., Winterhof, A. (eds) Sequences and Their Applications - SETA 2014. SETA 2014. Lecture Notes in Computer Science(), vol 8865. Springer, Cham. https://doi.org/10.1007/978-3-319-12325-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-12325-7_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12324-0

  • Online ISBN: 978-3-319-12325-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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