Data Encryption Based on Multi-granularity Reversible Cellular Automata

Traditional reversible cellular automata (RCA) is fit for cryptography for its rules being an affine function, i.e. one reversible CA\´s rule can be applied in encryption process while another counterpart rule can be applied in decryption process. However, there is few number of traditional RCA; for example, there are only six reversible rules in elementary CA. This property caused it cannot meet large key-space of cryptography. In this paper, an extended RCA is proposed aimed to be applied in cryptography. Analysis indicates that the extended RCA can be obtained by a pair of complementary traditional rule. Furthermore, in order to improve the complexity of CA\´s dynamics, which is a crux in cryptography, traditional CA model is replaced by multi-granularity cellular automata (MGCA). In MGCA, different granularity cells have their own rules. Based on MGCA and RCA a cryptography algorithm that is proposed which called MGRCA. In MGRCA, cells have different granularity and can adjust their granularity dynamically by "split-recombination" behavior during the process of encryption and decryption. Unlike DES, the length of block in MGRCA can be adjusted by user. The analysis results show that the cryptosystem can resist brute attack and differential attack, and also has high security. The hardware that shared by encryption and decryption caused the cryptosystem has a strong practicability.