Construction of subsets of bent functions satisfying restrictions in the Reed-Muller domain

Abstract

Bent functions are Boolean functions with highest nonlinearity which makes them interesting for cryptography. Determination of bent functions is an important but hard problem, since the general structure of bent functions is still unknown. Various constructions methods for bent functions are based on certain deterministic procedures, which might result in some regularity that is a feature undesired for applications in cryptography. Random generation of bent functions is an alternative, however, the search space is very large and the related procedures are time consuming. A solution is to restrict the search space by imposing some conditions that should be satisfied by the produced bent functions. In this paper, we propose three ways of imposing such restrictions to construct subsets of Boolean functions within which the bent functions are searched. We estimate experimentally the number of bent functions in the corresponding subsets of Boolean functions.