Constructing hyper-bent functions from Boolean functions with the Walsh spectrum taking the same value twice, by Chunming Tang and Yanfeng Qi

Hyper-bent functions as a subclass of bent functions attract much interest and it is elusive to completely characterize hyper-bent functions. Most of known hyper-bent functions are Boolean functions with Dillon exponents and they are often characterized by special values of Kloosterman sums. In this paper, we present a method for characterizing hyper-bent functions with Dillon exponents. A class of hyper-bent functions with Dillon exponents over $\mathbb{F}_{2^{2m}}$ can be characterized by a Boolean function over $\mathbb{F}_{2^m}$, whose Walsh spectrum takes the same value twice. Further, we show several classes of hyper-bent functions with Dillon exponents characterized by Kloosterman sum identities and the Walsh spectra of some common Boolean functions.