Paper 2012/020

Dickson polynomials, hyperelliptic curves and hyper-bent functions

Jean-Pierre Flori and Sihem Mesnager

Abstract

In this paper, we study the action of Dickson polynomials on subsets of finite fields of even characteristic related to the trace of the inverse of an element and provide an alternate proof of a not so well-known result. Such properties are then applied to the study of a family of Boolean functions and a characterization of their hyper-bentness in terms of exponential sums recently proposed by Wang et al. Finally, we extend previous works of Lisoněk and Flori and Mesnager to reformulate this characterization in terms of the number of points on hyperelliptic curves and present some numerical results leading to an interesting problem.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
Boolean functionshyper-bent functionsnonlinearityhyperelliptic curvesDickson polynomials
Contact author(s)
flori @ enst fr
History
2012-01-18: received
Short URL
https://ia.cr/2012/020
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2012/020,
      author = {Jean-Pierre Flori and Sihem Mesnager},
      title = {Dickson polynomials, hyperelliptic curves and hyper-bent functions},
      howpublished = {Cryptology ePrint Archive, Paper 2012/020},
      year = {2012},
      note = {\url{https://eprint.iacr.org/2012/020}},
      url = {https://eprint.iacr.org/2012/020}
}
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