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Finding balanced S-boxes with high nonlinearity and low transparency order is a difficult problem. The property of transparency order is important since it specifies the resilience of an S-box against differential power analysis. Better values for transparency order and hence improved sidechannel security often imply less in terms of nonlinearity. Therefore, it is impossible to find an S-box with all optimal values. Currently, there are no algebraic procedures that can give the preferred and complete set of properties for an S-box. In this paper, we employ evolutionary algorithms to find S-boxes with desired cryptographic properties. Specifically, we conduct experiments for the 8×8 S-box case as used in the AES standard. The results of our experiments proved the feasibility of finding S-boxes with the desired properties in the case of AES. In addition, we show preliminary results of side-channel experiments on different versions of "improved" S-boxes.

Crossover is the most important operator in realcoded genetic algorithms. However, the choice of the best operator for a specific problem can be a difficult task. In this paper we compare 16 crossover operators on a set of 24 benchmark functions. A detailed statistical analysis is performed in an effort to find the best performing operators. The results show that there are significant differences in efficiency of different crossover operators, and that the efficiency may also depend on the distinctive properties of the fitness function. Additionally, the results point out that the combination of crossover operators yields the best results.