Discovering Rotation Symmetric Self-dual Bent Functions with Evolutionary Algorithms

Bent Boolean functions are interesting mathematical objects with diverse real-world applications. Besides looking at the whole class of bent functions, one could also consider subclasses like rotation symmetric bent functions or (anti)-self-dual bent functions. Such classes are naturally smaller, making it (potentially) easier to enumerate functions inside the class with a computer investigation. This work considers a novel problem of evolving rotation symmetric (anti)-self-dual bent functions. We consider two solution encodings and a number of evolutionary algorithms. We successfully find rotation symmetric (anti)-self-dual functions for several Boolean function sizes, which are the first known examples of such functions. We hope this work will open a new research direction that will result in finding more such functions for larger dimensions, as well as algebraic constructions that will be valid for infinite Boolean function sizes.