Paper:

# A New Hyperchaotic System Generated by an External Periodic Excitation and its Image Encryption Application

## Jianping Cai^{*,**} and Jianbin He^{*,**,†}

^{*}School of Mathematics and Statistics, Minnan Nornal University

Zhangzhou 363000, China

^{**}Institute of Meteorological Big Data-Digital Fujian, Minnan Normal University

Zhangzhou 363000, China

^{†}Corresponding author

By using a controller of uniformly bounded sine function, the problem of chaos anti-control for continuous linear systems is studied, and the dynamic characteristics of the controlled system are analyzed via the Lyapunov exponent spectrum and bifurcation diagram. The controlled system can be at a state of periodic motion, chaos or hyperchaos with multiple positive Lyapunov exponents when the parameters of controller belong to different intervals. Based on the hyperchaotic system, a new scheme of chaotic image encryption is proposed and it is given in the following aspects: (1) five chaotic sequences are generated from the hyperchaotic system, and the preprocessed pseudo-random sequences are used in the scrambling of the pixel positions; (2) the pixel values of image are encrypted by the combination of multiple pseudo-random sequences; (3) though the double chaotic encryption, the security of the chaotic stream cipher is analyzed by means of key sensitivity analysis, histogram analysis and information entropy analysis, etc. Finally, the experimental results show the scheme is effective and feasible in image encryption, and it can resist some attacks, such as the differential attacks, chosen-plain-text attacks, and clipping attacks.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.26, No.3, pp. 418-430, 2022.

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