Dickson Polynomials, Hyperelliptic Curves and Hyper-Bent Functions

In this paper, the authors 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, they extend previous works of Lisonek 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.

Provided by: University of Paris Topic: Security Date Added: Jan 2012 Format: PDF

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