A conjecture about Gauss sums and bentness of binomial Boolean functions

Jean-Pierre Flori

Paper 2016/767

A conjecture about Gauss sums and bentness of binomial Boolean functions

Jean-Pierre Flori

Abstract

In this note, the polar decomposition of binary fields of even extension degree is used to reduce the evaluation of the Walsh transform of binomial Boolean functions to that of Gauss sums. In the case of extensions of degree four times an odd number, an explicit formula involving a Kloosterman sum is conjectured, proved with further restrictions, and supported by extensive experimental data in the general case. In particular, the validity of this formula is shown to be equivalent to a simple and efficient characterization for bentness previously conjectured by Mesnager.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Minor revision. WAIFI 2016
Keywords: boolean functions
Contact author(s): jean-pierre flori @ ssi gouv fr
History: 2016-08-12: received
Short URL: https://ia.cr/2016/767
License: CC BY

BibTeX

@misc{cryptoeprint:2016/767,
      author = {Jean-Pierre Flori},
      title = {A conjecture about Gauss sums and bentness of binomial Boolean functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2016/767},
      year = {2016},
      url = {https://eprint.iacr.org/2016/767}
}