Hyper-bent Multiple-Valued Functions

Hyper-bent functions constitute a subset of bent functions and are harder to approximate than bent functions, making them particularly attractive for cryptographic applications. In the multiple-valued world, up to now, characterization and generation of hyper-bent functions represent an interesting challenging mathematical problem. We show that multiple-valued hyper-bent functions constitute a reduced subset of the multiple-valued bent functions and give a simple characterization lemma. Finally we introduce a new concept, that of strict hyper-bent functions, and study some of the properties of these functions. The only mathematical requirements of the paper are college algebra and a basic knowledge of Galois fields.