Cryptology ePrint Archive: Report 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.

Category / Keywords: foundations / Boolean functions, hyper-bent functions, nonlinearity, hyperelliptic curves, Dickson polynomials

Date: received 13 Jan 2012

Contact author: flori at enst fr

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Version: 20120118:130520 (All versions of this report)

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