In this talk, we consider secondary construction methods of bent and plateaued functions.

The first part of this talk focuses on plateaued functions, where we analyse the concept of its dual. In contrary to bent functions, for which the dual is well established, the dual of a plateaued functions never received enough attention. Using suitable ordering(s) in combination with signs of non-zero entries of the Walsh spectra of a plateaued function, we show that new characterization of plateaued functions can be derived. In addition, these results will lead to completely new approach (so-called Spectral method) for construction of cryptographically significant Boolean functions. 

The second part of the talk focuses on secondary constructions of bent and plateaued functions. As we noticed that almost all secondary constructions deduced in the last four decades can be generalized using the composition of one Boolean (usually plateaued) and one vectorial function, we show how one can generalize almost all known secondary construction methods of bent and plateaued functions, by applying the concept of the dual developed for plateaued functions. The so-called “composite representation” of Boolean functions gives a better understanding of the existing secondary constructions and it also allows us to provide a general construction framework of these objects.