Improved hill-climbing methods in the design of bijective S-boxes

Substitution boxes(S-boxes) are important components of many symmetric cipher algorithms. They must be designed very carefully to resist attack. Some of the methods known to generate S-boxes are based on evolutionary heuristics. In this paper, we propose a method to increase the nonlinearity on the basis of William Millan´s hill-climbing, which could improve the nonlinearity furtherly when hill-climbing algorithm could not.