A Scheme for Obtaining Secure S-Boxes Based on Chaotic Baker’s Map

In this paper, a method for obtaining cryptographically strong 8 × 8 substitution boxes (S-boxes) is presented. The method is based on chaotic baker’s map and a “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 × 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. The computational graph for the encryption process of the proposed S-box.