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A method for obtaining cryptographically strong 8/spl times/8 S-boxes is presented. The method is based on the "mini version" of a new block cipher with block size of 8 bits and can be easily and efficiently performed on a computer. The cryptographic strength of some 8/spl times/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 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; and (5) their inverse S-boxes also possess the former four properties.