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

  • Claude Carlet
  • Sihem Mesnager
  • Ferruh Özbudak
  • Ahmet Sınak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Vectorial functions p-ary functions Bent functions Plateaued functions 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Claude Carlet
    • 1
    • 3
  • Sihem Mesnager
    • 1
    • 3
    • 4
  • Ferruh Özbudak
    • 5
    • 6
  • Ahmet Sınak
    • 2
    • 6
    • 7
  1. 1.Department of MathematicsUniversity of Paris VIIISaint-DenisFrance
  2. 2.LAGA, UMR 7539, CNRS, University of Paris VIIISaint-DenisFrance
  3. 3.LAGA, UMR 7539, CNRS, University of Paris XIIIVilletaneuseFrance
  4. 4.Telecom ParisTechParisFrance
  5. 5.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey
  6. 6.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  7. 7.Department of Mathematics and Computer SciencesNecmettin Erbakan UniversityKonyaTurkey

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