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

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 2 k variables by a suitable choice of 2 k -dimension subspace of F 2 2 2 k − 1 − 2 k − 1 . Further, we extend our results to the so-called hyper-bent functions. [ABSTRACT FROM AUTHOR]