Two-dimensional-lag Complex Logistic Map with Complex Parameters and Its Encryption Application

With the rapid development of internet technology, security protection of information has become more and more prominent, especially information encryption. Considering the great advantages of chaotic encryption, we propose a 2D-lag complex logistic map with complex parameters (2D-LCLMCP) and corresponding encryption schemes. Firstly, we present the model of the 2D-LCLMCP and analyze its chaotic properties and system stability through fixed points, Lyapunov exponent, bifurcation diagram, phase diagram, etc. Secondly, a block cipher algorithm based on the 2D-LCLMCP is proposed, the plaintext data is preprocessed using a pseudorandom sequence generated by the 2D-LCLMCP. Based on the generalized Feistel cipher structure, a round function F is constructed using dynamic S-box and DNA encoding rules as the core of the block cipher algorithm. The generalized Feistel cipher structure consists of two F functions, four XOR operations, and one permutation operation per round. The symmetric dynamic round keys that change with the plaintext are generated by the 2D-LCLMCP. Finally, experimental simulation and performance analysis tests are conducted. The results show that the block cipher algorithm has low complexit, good diffusion and a large key space. When the block length is 64 bits, only six rounds of encryption are required to provide sufficient security and robustness against cryptographic attacks.