Efficient Discovery of Bent Function Using Reed-Muller Subsets

Bent functions are functions that have the biggest distance from all linear binary functions. Attacks against cryptosystems can be defeated when these systems use bent functions. Generalisation of bent functions is still unknown and when they have many variables, it is very difficult to find them. Therefore, the construction of bent functions is done by using discovery of them within a subset of functions. Thus, this paper describes a method for creating groups of functions in Reed-Muller (RM) domain within which efficient detection of bent functions is performed. As follows, the search space for discovery is limited, and it can be defined for various subsets of Boolean functions. Experimental results confirm that the time required for discovery of bent function when using RM subsets are smaller than when using general random discovery.