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 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 a LSMCL-based image encryption algorithm (LSMCL-IEA) with two rounds of permutation and diffusion operation. Firstly, 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, respectively. Finally, we provide some theoretical analyses and simulations to confirm the security and the validity of the proposed algorithm.

The composite discrete chaotic system (CDCS) is a complex chaotic system that combines two or more discrete chaotic systems. This system holds the chaotic characteristics of different chaotic systems in a random way and has more complex chaotic behaviors. In this paper, we aim to provide a novel image encryption algorithm based on a new two-dimensional (2D) CDCS. The proposed scheme consists of two parts: firstly, we propose a new 2D CDCS and analysis the chaotic behaviors, then, we introduce the bit-level permutation and pixel-level diffusion encryption architecture with the new CDCS to form the full proposed algorithm. Random values and the total information of the plain image are added into the diffusion procedure to enhance the security of the proposed algorithm. Both the theoretical analysis and simulations confirm the security of the proposed algorithm.