Substitution boxes are important parts in many block and stream ciphers. The emergence of a range of crypto-attacks has led to the development of criteria for repelling such attacks. The non-linearity criterion provides some protection against well- known attacks, such as linear cryptanalysis and differential cryptanalysis. The open problem is constructed by generating methods which will be rapid and will generate S-boxes with the highest possible non-linearity. This paper deals with a new rapid method for generating regular 8x8 S-boxes with non-linearity up to a value of 104. The new method combines the special genetic algorithm with total tree searching
