Cryptology ePrint Archive: Report 2015/982

A note on constructions of bent functions from involutions

Sihem Mesnager

Abstract: Bent functions are maximally nonlinear Boolean functions. They are important functions introduced by Rothaus and studied rstly by Dillon and next by many researchers for four decades. Since the complete classi cation of bent functions seems elusive, many researchers turn to design constructions of bent functions. In this note, we show that linear involutions (which are an important class of permutations) over nite elds give rise to bent functions in bivariate representations. In particular, we exhibit new constructions of bent functions involving binomial linear involutions whose dual functions are directly obtained without computation.

Category / Keywords: Bent functions, maximally nonlinear Boolean functions, Boolean functions, Permutations, Involutions.

Date: received 11 Oct 2015, last revised 13 Oct 2015

Contact author: smesnager at univ-paris8 fr

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Version: 20151013:110857 (All versions of this report)

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