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

Sihem Mesnager; Jean-Pierre Flori

Paper 2012/033

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.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Keywords: Boolean functions hyper-bent functions Walsh–Hadamard transform exponential sums Kloosterman sums Dickson polynomial finite field permutations Dillon exponent.
Contact author(s): flori @ enst fr
History: 2012-01-29: received
Short URL: https://ia.cr/2012/033
License: 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},
      url = {https://eprint.iacr.org/2012/033}
}