Evolutionary Methods for the Construction of Cryptographic Boolean Functions

Boolean functions represent an important primitive when constructing many stream ciphers. Since they are often the only nonlinear element of such ciphers, without them the algorithm would be trivial to break. Therefore, it is not surprising there exist a substantial body of work on the methods of constructing Boolean functions. Among those methods, evolutionary computation (EC) techniques play a significant role. Previous works show it is possible to use EC methods to generate high-quality Boolean functions that even surpass those built by algebraic constructions. However, up to now, there was no work investigating the use of Cartesian Genetic Programming (CGP) for producing Boolean functions suitable for cryptography. In this paper we compare Genetic Programming (GP) and CGP algorithms in order to reach the conclusion which algorithm is better suited to evolve Boolean functions suitable for cryptographic usage. Our experiments show that CGP performs much better than the GP when the goal is obtaining as high as possible nonlinearity. Our results indicate that CGP should be further tested with different fitness objectives in order to check the boundaries of its performance.