Characteristic Analysis of 2D Lag-Complex Logistic Map and Its Application in Image Encryption

In this study, we propose a novel 2D lag-complex logistic map (LCLM). The 2D-LCLM is derived from the conventional 2D logistic map by extending its variables from real numbers to complex field. The bifurcation diagrams, Lyapunov exponents, and the evolution of chaotic attractors have been exploited for evaluating the chaotic behavior. Results show that the 2D-LCLM has extensive chaotic intervals, good ergodicity, and unpredictable trajectories. For further studying its practical significance, we then construct a color image cryptosystem based on 2D-LCLM. Bit-level permutation and one-time keys are used for speeding up the computational speed and defending chosen plaintext attack. Simulation results and corresponding analysis reveal that the cryptosystem has large key-space and good key sensitivity, and its information entropy approaches to the ideal value. Hence, the cryptosystem based on 2D-LCLM can strongly resist traditional cipher attacks.