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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2016/767}},
      url = {https://eprint.iacr.org/2016/767}
}
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