On the evolution of bent (n, m) functions

Abstract

Boolean functions and their generalizations, vectorial Boolean functions, are extremely active areas of research. Their applications can be found in domains such as error correcting codes, communication, and cryptography. Accordingly, various methods of obtaining Boolean functions are explored where one group belongs to heuristic techniques and, more precisely, evolutionary algorithms. In this paper we explore how to evolve (vectorial) Boolean functions with specific properties by utilizing several different algorithms and encodings. As far as we are aware, we are the first to explore the topic of evolution of vectorial Boolean functions where the output dimension is strictly smaller than the input dimension. Our results show that evolutionary algorithms can represent a valuable option to produce vectorial Boolean functions where good results are obtained for various sizes. On the other hand, as the number of outputs grows, we can observe that evolutionary algorithms are still able to obtain high quality results but with increasing difficulty.