Boolean Function Design Using Hill Climbing Methods

This paper outlines a general approach to the iterative incremental improvement of the cryptographic properties of arbitrary Boolean functions. These methods, which are known as hill climbing, offer a fast way to obtain Boolean functions that have properties superior to those of randomly generated functions. They provide a means to improve the attainable compromise between conflicting cryptographic criteria. We give an overview of the different options available, concentrating on reducing the maximum value of the Walsh-Hadamard transform and autocorrelation function. A user selected heuristic allows the methods to be flexible. Thus we obtain Boolean functions that are locally optimal with regard to one or more important cryptographic properties such as nonlinearity and global autocorrelation.