Cryptology ePrint Archive: Report 2019/789

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

Diana Davidova and Lilya Budaghyan and Claude Carlet and Tor Helleseth and 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.

Category / Keywords: foundations / Bent function, Boolean function, EA-equivalence, maximum nonlinearity, Magic action, modified Magic action, Niho bent function, o-equivalence, o-polynomials, ovals, hyperovals, Walsh transform.

Date: received 6 Jul 2019

Contact author: diana davidova at uib no

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Version: 20190714:153144 (All versions of this report)

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