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
Abstract
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.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- Bent functionBoolean functionEA-equivalencemaximum nonlinearityMagic actionmodified Magic actionNiho bent functiono-equivalenceo-polynomialsovalshyperovalsWalsh transform.
- Contact author(s)
- diana davidova @ uib no
- History
- 2019-07-14: received
- Short URL
- https://ia.cr/2019/789
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2019/789,
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{https://eprint.iacr.org/2019/789}},
url = {https://eprint.iacr.org/2019/789}
}
