Dickson Polynomials, Hyperelliptic Curves and Hyper-bent Functions

  • Jean-Pierre Flori
  • Sihem Mesnager
Conference paper

DOI: 10.1007/978-3-642-30615-0_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7280)
Cite this paper as:
Flori JP., Mesnager S. (2012) Dickson Polynomials, Hyperelliptic Curves and Hyper-bent Functions. In: Helleseth T., Jedwab J. (eds) Sequences and Their Applications – SETA 2012. SETA 2012. Lecture Notes in Computer Science, vol 7280. Springer, Berlin, Heidelberg

Abstract

In this paper, we study the action of Dickson polynomials on subsets of finite fields of even characteristic related to the trace of the inverse of an element and provide an alternate proof of a not so well-known result. Such properties are then applied to the study of a family of Boolean functions and a characterization of their hyper-bentness in terms of exponential sums recently proposed by Wang et al.Finally, we extend previous works of Lisoněk and Flori and Mesnager to reformulate this characterization in terms of the number of points on hyperelliptic curves and present some numerical results leading to an interesting problem.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jean-Pierre Flori
    • 1
  • Sihem Mesnager
    • 2
  1. 1.ANSSI (Agence nationale de la sécurité des sytèmes d’information)ParisFrance
  2. 2.LAGA (Laboratoire Analyse, Géometrie et Applications), UMR 7539, CNRS, Department of MathematicsUniversity of Paris XIII and University of Paris VIIISaint-Denis CedexFrance

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