Dynamic and implicit latin square doubly stochastic S-boxes with reversibility

S-Boxes play a vital role in cipher designs and have been researched for years. In this article a new way of dynamically designing S-boxes using Latin Square doubly stochastic matrix is proposed. And it is demonstrated that the enciphering/deciphering process is a mimic of a Markov chain Monte Carlo simulation. Unlike conventional dynamic S-boxes, the proposed S-boxes are not directly defined by keys, but contained in the key dependent doubly stochastic matrix. The created matrix has desired properties including: (1) it implicitly contains S-boxes and thus complicates the internal structure of S-boxes; (2) it naturally defines S-boxes with reversibility and thus any S-boxes used for encryption can be directly used for decryption; (3) it satisfies the Strict Avalanche Criterion (SAC) for S-Boxes and thus it has good resistance to differential or linear cryptanalysis; (4) it guarantees the independence of the ciphertext distribution from plaintext one; and (5) it ensures that the expected ciphertext distribution is uniform and thus attains excellent confusion properties when use these S-Boxes iteratively. Theoretical and experimental results show that the proposed S-box has a high security level and is suitable to design cryptosystem for data encryption. We also extend our S-boxes to a simple image cipher. Experimental results show that the proposed dynamical flexible structure S-boxes has cryptographic properties comparable or better than some existing image encryption methods.