Paper 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 classication 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.

Note: a reference was completed

Metadata
Available format(s)
PDF
Publication info
Preprint. MINOR revision.
Keywords
Bent functionsmaximally nonlinear Boolean functionsBoolean functionsPermutationsInvolutions.
Contact author(s)
smesnager @ univ-paris8 fr
History
2015-10-13: last of 2 revisions
2015-10-12: received
See all versions
Short URL
https://ia.cr/2015/982
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/982,
      author = {Sihem Mesnager},
      title = {A note on constructions of bent functions from involutions},
      howpublished = {Cryptology ePrint Archive, Paper 2015/982},
      year = {2015},
      note = {\url{https://eprint.iacr.org/2015/982}},
      url = {https://eprint.iacr.org/2015/982}
}
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