Paper 2012/020 Original: eprint.iacr.org/2012/020 ↗
Dickson polynomials, hyperelliptic curves and hyper-bent functions
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
- Preprint.
- History
- 2012-01-18: last updated
- 2012-01-18: published
- Short URL
- https://ia.cr/2012/020
- License
- https://creativecommons.org/licenses/by/4.0/
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},
url = {https://eprint.iacr.org/2012/020}
}