Design of Higher-Dimensional Hyperchaotic System based on Combined Control and its Encryption Application

According to the anti-control principle of chaos, a combined control method is proposed based on a class of asymptotically stable linear systems with multiple controllers. A higher-dimensional hyperchaotic system is investigated by the Lyapunov exponents method and equilibrium points analysis, and it exists the largest number of positive Lyapunov exponents. The chaotic pseudo-random sequences of the higher-dimensional hyperchaotic system can pass all NIST tests after preprocessing, and behave better chaotic characteristics. Meanwhile, a new encryption algorithm of image information with position scrambling, sequential diffusion and reverse diffusion is designed based on the chaotic pseudo-random sequences. The experiments of image information are given to verify the effectiveness and feasibility of the encryption algorithm. Finally, the security analyses are also discussed by the key sensitivity, differential attack and statistical analysis. It is shown that the encryption algorithm has large enough key space and can be applied to secure communication.

Automated summary

This article proposes a combined control method based on the anti-control principle of chaos for a class of asymptotically stable linear systems with multiple controllers. The Lyapunov exponents method and equilibrium points analysis are used to investigate a higher-dimensional hyperchaotic system, which exhibits the largest number of positive Lyapunov exponents. The chaotic pseudo-random sequences of the system pass all NIST tests after preprocessing and demonstrate improved chaotic characteristics. An encryption algorithm for image information is designed based on these chaotic pseudo-random sequences, utilizing position scrambling, sequential diffusion, and reverse diffusion. Experimental results confirm the effectiveness and feasibility of the encryption algorithm. Moreover, security analyses including key sensitivity, differential attack, and statistical analysis are discussed, showing that the encryption algorithm has a sufficiently large key space and can be applied to secure communication.