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Explicit Characterizations for Plateaued-ness of p-ary (Vectorial) Functions

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Codes, Cryptology and Information Security (C2SI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10194))

Abstract

Plateaued (vectorial) functions have an important role in the sequence and cryptography frameworks. Given their importance, they have not been studied in detail in general framework. Several researchers found recently results on their characterizations and introduced new tools to understand their structure and to design such functions. In this work, we mainly extend some of the observations made in characteristic 2 and given in (Carlet, IEEE Trans. Inf. Theor. 61(11), 6272–6289, 2015) to arbitrary characteristic. We first extend to arbitrary characteristic the characterizations of plateaued (vectorial) Boolean functions by the autocorrelation functions, next their characterizations in terms of the second-order derivatives, and finally their characterizations via the moments of the Walsh transform.

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Acknowledgment

The fourth author is supported by the Scientific and Technological Research Council of Turkey (TÜBITAK)-BIDEB 2214-A program.

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Authors and Affiliations

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

    Claude Carlet & Sihem Mesnager

  2. LAGA, UMR 7539, CNRS, University of Paris VIII, Saint-Denis, France

    Ahmet Sınak

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

    Claude Carlet & Sihem Mesnager

  4. Telecom ParisTech, Paris, France

    Sihem Mesnager

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

    Ferruh Özbudak

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

    Ferruh Özbudak & Ahmet Sınak

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

    Ahmet Sınak

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

Correspondence to Sihem Mesnager .

Editor information

Editors and Affiliations

  1. University of Mohammed V, Rabat, Morocco

    Said El Hajji

  2. University of Caen, Caen, France

    Abderrahmane Nitaj

  3. University of Mohammed V, Rabat, Morocco

    El Mamoun Souidi

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Carlet, C., Mesnager, S., Özbudak, F., Sınak, A. (2017). Explicit Characterizations for Plateaued-ness of p-ary (Vectorial) Functions. In: El Hajji, S., Nitaj, A., Souidi, E. (eds) Codes, Cryptology and Information Security. C2SI 2017. Lecture Notes in Computer Science(), vol 10194. Springer, Cham. https://doi.org/10.1007/978-3-319-55589-8_22

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  • DOI: https://doi.org/10.1007/978-3-319-55589-8_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55588-1

  • Online ISBN: 978-3-319-55589-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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