Characterizations of Partially Bent and Plateaued Functions over Finite Fields

  • Sihem Mesnager
  • Ferruh Özbudak
  • Ahmet SınakEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11321)


Partially bent and plateaued functions over finite fields have significant applications in cryptography, sequence theory, coding theory, design theory and combinatorics. They have been extensively studied due to their various desirable cryptographic properties. In this paper, we study on characterizations of partially bent and plateaued functions over finite fields, with the aim of clarifying their structure. We first redefine the notion of partially bent functions over any finite field \({\mathbb {F}}_q\), with q a prime power, and then provide a few characterizations of these functions in terms of their derivatives, Walsh power moments and autocorrelation functions. We next characterize partially bent (vectorial) functions over \({\mathbb {F}}_p\), with p a prime, by means of their derivatives and Walsh power moments. We finally characterize plateaued functions over \({\mathbb {F}}_p\) in terms of their Walsh power moments, derivatives and autocorrelation functions.


p-ary functions q-ary functions Partially bent Plateaued Additive character 



The authors would like to thank the anonymous reviewers of WAIFI-2018 for their valuable comments and suggestions. The third author is supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK), program no: BİDEB 2214/A.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sihem Mesnager
    • 1
    • 2
    • 3
    • 4
  • Ferruh Özbudak
    • 5
    • 6
  • Ahmet Sınak
    • 2
    • 3
    • 6
    • 7
    Email author
  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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