A study of differences between bent functions constructed using Rothaus method and randomly generated bent functions

Abstract

Bent functions, having the highest possible nonlinearity, are among the best candidates for construction of S-boxes. One problem with bent functions is the fact that they are hard to find among randomly generated set of Boolean functions already for 6 argument functions. There exist some algorithms that allow for easy generation of bent functions. The major drawback of these algorithms is the fact that they rely on deterministic dependencies and are only able to generate bent functions belonging to one specific class. In our paper we present an efficient generator of random bent functions of more than 4 arguments. Resulting functions are not bounded by constraints described above. The generator operates in algebraic normal form domain (ANF). We also present our result on comparing the performance of S-boxes build using our bent function generator versus a standard method of bent function construction. We also give some directions for further research.