Constructions of Maiorana-McFarland's Bent Functions of Prescribed Degree

Abstract

A Boolean function with an even number $n=2k$ of variables is called Bent if it is maximally nonlinear. A technique on constructing Maiorana-McFarland's Bent functions of arbitrary degree is described. Based on the properties of Maiorana-McFarland's Bent functions, a Bent function with arbitrary degree can be constructed by changing the order of concatenating linear functions.