Julian Miller

The role of Boolean functions is prominent in several areas like cryptography, sequences, and coding theory. Therefore, various methods for the construction of Boolean functions with desired properties are of direct interest. New motivations on the role of Boolean functions in cryptography with attendant new properties have emerged during the years. There are still many combinations of design criteria left unexplored and in this matter evolutionary computation can play a distinct role. This paper concentrates on two scenarios for use of Boolean functions in cryptography. The first uses Boolean functions as the source of the nonlinearity in filter and combiner generators. Although relatively well explored using evolutionary algorithms, it still presents an interesting goal in terms of the practical sizes of Boolean functions. The second scenario appeared rather recently where the objective is to find Boolean functions that have various orders of the correlation immunity and minimal Hamming weight. In both those scenarios we see that evolutionary algorithms are able to find high quality solutions where genetic programming performs the best.