New constructions of balanced Boolean functions with high nonlinearity and optimal algebraic degree

In this paper, we propose a technique for constructing balanced Boolean functions on even numbers of variables. The main technique is to utilize a set of disjoint spectra functions and a special Boolean permutation to derive a balanced Boolean function with high nonlinearity and optimal algebraic degree. It is shown that the functions we construct are different from both Maiorana-McFarland's (M-M) super-class functions introduced by Carlet and modified M-M super-class functions presented by Zeng and Hu. Furthermore, we show that they have no nonzero linear structures.