Image Encryption Based on Hyperchaotic System and Improved Zigzag Diffusion Method

Classical two-dimensional chaotic systems are not safe enough due to few control parameters and limited chaotic range. To cope with this problem, a new wide-range 2D-Logistic-Sine hyperchaotic map (2D-LSHM) is proposed in this paper. By analyzing the bifurcation map and Lyapunov exponent of 2D-LSHM, the results prove that the map has good ergodicity and unpredictability. In addition, this paper proposes a 2D-LSHM-based image encryption scheme, LSHM-IES, to solve the problem that the dislocation diffusion algorithm based on specific rules is vulnerable to attacks. The scheme uses a 3 x 3 convolutional kernel to replace the pixel values in the dislocation process. An improved Zigzag transform is developed in the diffusion phase to make the algorithm more secure and the key space larger. Experimental results from a variety of performance tests on different images indicate that the LSHM-IES encryption scheme possesses favorable encryption performance, low time cost, and high robustness against data missing attacks and noise effects.