2D Logistic-Modulated-Sine-Coupling-Logistic Chaotic Map for Image Encryption

Due to the significant properties of unpredictability, ergodicity, and initial state sensitivity, chaotic system is widely used as a useful tool in image encryption. In this paper, we propose a 2-dimensional logistic-modulated-sine-coupling-logistic chaotic map (LSMCL), where we use the logistic map to modulate Sine map and couple the result of modulation and Sine map together. In terms of chaotic trajectory, Lyapunov exponent, and Kolmogorov entropy, comparing with other existing chaotic maps, we can observe that LSMCL has better chaotic performance. Furthermore, we propose an LSMCL-based image encryption algorithm with two rounds of permutation and diffusion operation. First, we provide a secret key generation procedure to generate the initial values and do permutation operation with the chaotic matrix by LSMCL. Furthermore, in diffusion procedure, we use two different chaotic matrices generated by LSMCL to change the pixel values in row and column. Finally, we provide some theoretical analyses and simulations to confirm the security and the validity of the proposed algorithm.