A method for obtaining cryptographically strong 8x8 S-boxes

In this paper, a method for obtaining cryptographically strong 8x8 S-boxes is presented. The method is based on the ''mini version'' of a new block cipher with block size 8 bits and can be easily and efficiently performed on a computer. The cryptographic strength of some 8 x 8 S-boxes randomly produced by the method is analyzed. The results show (1) All of them are bijective; (2) The nonlinearity of each output bit of them is usually about 100; (3) All of them approximately satisfy the strict avalanche criterion and output bits independence criterion; (4) They all have an almost equiprobable input/output XOR distribution; (5) Their inverse S-boxes also possess the former four properties.