Design of hyperchaotic system based on multi-scroll and its encryption algorithm in color image

Abstract

Chaotic systems are suitable for image encryption due to their numerous intrinsic properties. However, the low-dimensional chaotic systems used in many existing chaos-based image encryption algorithms suffer from various drawbacks. To overcome such problems, a new four-dimensional multi-scroll hyperchaotic system is constructed in this paper. By studying the stability of equilibrium point, dissipation attractors, Lyapunov exponent spectrum, and bifurcation diagram of the system, these are proved that the system has rich dynamical behaviors. Then, based on the system, a new color image encryption algorithm is designed by using the classical structure of the ‘scrambling-diffusion-scrambling’ algorithm. In this image encryption algorithm, an optimized Arnold transform is used and the plaintext pixel sum is applied to the scrambling parameters so that different plaintext image pixels correspond to different scrambling parameters and are fully resistant to plaintext attacks. Then for the three Red, Green, Blue (RGB) channels, three different diffusion directions are adopted. Finally, the correlation between the pixels is further broken by an ascending permutation scrambling operation to get the final encrypted image. The experimental results show that the key space is up to 2207, the information entropy is up to 7.9998, the Number of Pixels Change Rate (NPCR) and the Unified Average Changing Intensity (UACI) values are close to the ideal values, the scheme can resist exhaustive and differential attacks, and the scheme has good robustness through noise attacks and crop attacks.