Evolving Algebraic Constructions for Designing Bent Boolean Functions

Stjepan Picek, Domagoj Jakobovic

Abstract: The evolution of Boolean functions that can be used in cryptography is a topic well studied in the last decades. Previous research, however, has focused on evolving Boolean functions directly, and not on general methods that are capable of generating the desired functions. The former approach has the advantage of being able to produce a large number of functions in a relatively short time, but it directly depends on the size of the search space. In this paper, we present a method to evolve algebraic constructions for generation of bent Boolean functions. To strengthen our approach, we define three types of constructions and give experimental results for them. Our results show that this approach is able to produce a large number of constructions, which could in turn enable the construction of many more Boolean functions with a larger number of variables.