On o-Equivalence of Niho Bent Functions

  • Lilya Budaghyan
  • Claude Carlet
  • Tor Helleseth
  • Alexander Kholosha
Conference paper

DOI: 10.1007/978-3-319-16277-5_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9061)
Cite this paper as:
Budaghyan L., Carlet C., Helleseth T., Kholosha A. (2015) On o-Equivalence of Niho Bent Functions. In: Koç Ç., Mesnager S., Savaş E. (eds) Arithmetic of Finite Fields. WAIFI 2014. Lecture Notes in Computer Science, vol 9061. Springer, Cham

Abstract

As observed recently by the second author and S. Mesnager, the projective equivalence of o-polynomials defines, for Niho bent functions, an equivalence relation called o-equivalence. These authors also observe that, in general, the two o-equivalent Niho bent functions defined from an o-polynomial \(F\) and its inverse \(F^{-1}\) are EA-inequivalent. In this paper we continue the study of o-equivalence. We study a group of order 24 of transformations preserving o-polynomials which has been studied by Cherowitzo 25 years ago. We point out that three of the transformations he included in the group are not correct. We also deduce two more transformations preserving o-equivalence but providing potentially EA-inequivalent bent functions. We exhibit examples of infinite classes of o-polynomials for which at least three EA-inequivalent Niho bent functions can be derived.

Keywords

Bent function Boolean function Maximum nonlinearity Niho bent function o-polynomials Walsh transform 

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Lilya Budaghyan
    • 1
  • Claude Carlet
    • 2
  • Tor Helleseth
    • 1
  • Alexander Kholosha
    • 1
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.LAGA, UMR 7539, CNRS, Department of MathematicsUniversity of Paris 8 and University of Paris 13Saint-Denis CedexFrance

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