An efficient characterization of a family of hyper-bent functions with multiple trace terms

Lisoněk recently reformulated the characterization of Charpin and Gong of a large class of hyper-bent functions in terms of cardinalities of hyperelliptic curves following previous ideas of Lachaud and Wolfmann, and Katz and Livné. In this paper, we present a generic approach of such ideas and show that it applies naturally to a distinct family of functions proposed by Mesnager. Doing so, a polynomial time and space test for the hyper-bentness of functions in this family is obtained. We then show how this reformulation can be transformed to obtain a more efficient test leading to a substantial practical gain. We finally elaborate on an open problem about hyperelliptic curves related to a family of Boolean functions studied by charpin and Gong.