Paper 2019/789

Relation between o-equivalence and EA-equivalence for Niho bent functions

Diana Davidova, Lilya Budaghyan, Claude Carlet, Tor Helleseth, Ferdinand Ihringer, and Tim Penttila


Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent functions, so-called Niho bent functions there is a more general equivalence relation called o-equivalence which is induced from the equivalence of o-polynomials. In the present work we study, for a given o-polynomial, a general construction which provides all possible o-equivalent Niho bent functions, and we considerably simplify it to a form which excludes EA-equivalent cases. That is, we identify all cases which can potentially lead to pairwise EA-inequivalent Niho bent functions derived from o-equivalence of any given Niho bent function. Furthermore, we determine all pairwise EA-inequivalent Niho bent functions arising from all known o-polynomials via o-equivalence.

Available format(s)
Publication info
Preprint. MINOR revision.
Bent functionBoolean functionEA-equivalencemaximum nonlinearityMagic actionmodified Magic actionNiho bent functiono-equivalenceo-polynomialsovalshyperovalsWalsh transform.
Contact author(s)
diana davidova @ uib no
2019-07-14: received
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Creative Commons Attribution


      author = {Diana Davidova and Lilya Budaghyan and Claude Carlet and Tor Helleseth and Ferdinand Ihringer and Tim Penttila},
      title = {Relation between o-equivalence and EA-equivalence for Niho bent functions},
      howpublished = {Cryptology ePrint Archive, Paper 2019/789},
      year = {2019},
      note = {\url{}},
      url = {}
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