On o-Equivalence of Niho Bent Functions

  • Lilya BudaghyanEmail author
  • Claude Carlet
  • Tor Helleseth
  • Alexander Kholosha
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9061)


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.


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



We are very grateful to Bill Cherowitzo for useful discussions. This research was supported by Norwegian Research Council. The research of the first author was also supported by Fondation Sciences Mathématiques de Paris.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Lilya Budaghyan
    • 1
    Email author
  • 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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