Uniform non-degeneracy discrete chaotic system and its application in image encryption

It is a challenging topic to design an image encryption algorithm based on chaotic systems with expected cryptographic properties. In view of this problem, we first propose a chaotic system generation algorithm to construct the non-degeneracy discrete chaotic system with uniformly distributed trajectories. The generated chaotic systems can exhibit strong chaotic behaviors and generate the chaotic sequences with ideal pseudo-randomness. Then, a chaotic S-box generation algorithm supporting multi-objective optimization is designed based on the non-domination sorting genetic algorithm and a novel gene modification method we designed. The proposed chaotic S-box generation algorithm can effectively construct the S-boxes with high nonlinearity and strong resistances to linear and differential attacks. Finally, we design a color image encryption algorithm by applying our chaotic S-box. The experimental results indicate that the cipher images encrypted by our algorithm have good cryptographic properties in terms of key sensitivity, plaintext sensitivity, robustness, correlation, and information entropy.