New characterizations and construction methods of bent and hyper-bent Boolean functions

Abstract

In this paper, we first derive a necessary and sufficient condition for a bent Boolean function by analyzing their support set. Next, using this condition and the Pless power moment identities, we propose a construction method of bent functions of 2k variables by a suitable choice of 2k-dimension subspace of F222k−1−2k−1. Further, we extend our results to the so-called hyper-bent functions.