Bounded Search of Cryptographically Strong Boolean Functions

Abstract

In this paper we consider methods for obtaining Boolean functions with desirable cryptographic properties based on search algorithms. We investigate the possibility of optimizing such algorithms, primarily due to a significant reduction in the search space. Here we use the general idea of partition of the set of Boolean functions into equivalence classes in accordance to some transformation group and the idea of exhaustive search among these classes as vertices of a specific graph called class graph. The P-equivalence proposed in this paper if considered on the set of balanced Boolean functions ensures the preservation of almost all cryptographically significant properties of functions within one equivalence class.