On Hyperbent Functions and Semibent Functions with Dillon-Like Exponents

Abstract

The main contribution of this paper is to characterize the hyperbentness of two infinite classes of Boolean functions via Dillon-like exponents, and give new classes of semibent functions with Dillon-like exponents and Niho exponents. In this paper, the approaches of Mesnager and Wang et al. are generalized to Charpin-Gong like functions with two additional trace terms. By using the partial exponential sums and Dickson polynomials, it also gives the necessary and sufficient conditions of the hyperbent properties for their subclasses of Boolean functions, and gives two corresponding examples on F_2³⁰. Thanks to the result of Carlet et al., new classes of semibent functions are obtained by using new hyperbent functions and the known Niho bent functions. Finally, this paper extends the Works of Lisonek and Flori and Mesnager, and gives different characterizations of new hyperbent functions and new semibent functions with some restrictions in terms of the number of points on hyperelliptic curves. These results provide more nonlinear functions for designing the filter generators of stream ciphers.