### A note on hyper-bent functions via Dillon-like exponents

Sihem Mesnager and Jean-Pierre Flori

##### Abstract

This note is devoted to hyper-bent functions with multiple trace terms (including binomial functions) via Dillon-like exponents. We show how the approach developed by Mesnager to extend the Charpin–Gong family and subsequently extended by Wang et al. fits in a much more general setting. To this end, we first explain how the original restriction for Charpin–Gong criterion can be weakened before generalizing the Mesnager approach to arbitrary Dillon-like exponents. Afterward, we tackle the problem of devising infinite families of extension degrees for which a given exponent is valid and apply these results not only to reprove straightforwardly the results of Mesnager and Wang et al., but also to characterize the hyper-bentness of new infinite classes of Boolean functions.

Available format(s)
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
Boolean functionshyper-bent functionsWalsh–Hadamard transformexponential sumsKloosterman sumsDickson polynomialfinite field permutationsDillon exponent.
Contact author(s)
flori @ enst fr
History
Short URL
https://ia.cr/2012/033

CC BY

BibTeX

@misc{cryptoeprint:2012/033,
author = {Sihem Mesnager and Jean-Pierre Flori},
title = {A note on hyper-bent functions via Dillon-like exponents},
howpublished = {Cryptology ePrint Archive, Paper 2012/033},
year = {2012},
note = {\url{https://eprint.iacr.org/2012/033}},
url = {https://eprint.iacr.org/2012/033}
}

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