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Results on Characterizations of Plateaued Functions in Arbitrary Characteristic

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Cryptography and Information Security in the Balkans (BalkanCryptSec 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9540))

Abstract

Bent and plateaued functions play a significant role in cryptography since they can have various desirable cryptographic properties. In this work, we first provide the characterizations of plateaued functions in terms of the moments of their Walsh transforms. Next, we generalize the characterizations of Boolean bent and plateaued functions in terms of their second-order derivatives to arbitrary characteristic. Moreover, we present a new characterization of plateaued functions in terms of fourth power moments of their Walsh transforms. Furthermore, we give a new proof of the characterization of vectorial bent functions. Finally, we present the characterizations of vectorial s-plateaued functions in terms of moments of their Walsh transforms and the zeros of their second-order derivatives.

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Acknowledgment

The third author is partially supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK)-BİDEB 2211 program.

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

  3. Telecom ParisTech, Paris, France

    Sihem Mesnager

  4. Department of Mathematics, Middle East Technical University, Ankara, Turkey

    Ferruh Özbudak

  5. Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Ferruh Özbudak & Ahmet Sınak

  6. Department of Mathematics and Computer Sciences, Necmettin Erbakan University, Konya, Turkey

    Ahmet Sınak

Authors
  1. Sihem Mesnager
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  2. Ferruh Özbudak
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  3. Ahmet Sınak
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Corresponding author

Correspondence to Ahmet Sınak .

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Editors and Affiliations

  1. University of Primorska, Koper, Slovenia

    Enes Pasalic

  2. Technical University of Denmark, Kgs. Lyngby, Denmark

    Lars R. Knudsen

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Mesnager, S., Özbudak, F., Sınak, A. (2016). Results on Characterizations of Plateaued Functions in Arbitrary Characteristic. In: Pasalic, E., Knudsen, L. (eds) Cryptography and Information Security in the Balkans. BalkanCryptSec 2015. Lecture Notes in Computer Science(), vol 9540. Springer, Cham. https://doi.org/10.1007/978-3-319-29172-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-29172-7_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29171-0

  • Online ISBN: 978-3-319-29172-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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