A conservative chaotic system with coexisting chaotic-like attractors and its application in image encryption

Abstract

Unlike dissipative systems, conservative systems do not have attractors and no attractor reconstruction occurs. Therefore, these systems are more suitable for application in image encryption. On the basis of above appoints, here we develop and propose a conservative system with infinite chaotic-like attractors. The conservative and chaotic characteristics and coexistence chaotic-like attractors are studied using Lyapunov exponents, Poincare maps, and numerical simulation. The results show that the coexistence of chaotic-like attractors has a more complex structure and dynamic behaviour than traditional ones. Additionally, the developed system is further used to design an encryption system for a digital image. Using the coexistence chaotic-like attractor sequence to scramble and diffuse the image can destroy the correlation of adjacent pixels and hide the information of all pixels. The feasibility and security of the encryption scheme are demonstrated through the analysis of key space, histogram, information entropy, key sensitivity and pixel correlation.

Keywords:

• Conservative chaos system
• coexisting chaotic-like attractors
• digital image encryption
• safety analysis

Acknowledgements

China Macedonia intergovernmental scientific and technological cooperation project (Grant No. [2019] 22:6-8).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the china Macedonia Intergovernmental Scientific and Technological Cooperation Project [grant number [2019]22: 6-8].

Notes on contributors

Minxiu Yan

Minxiu Yan received her Ph.D. degree in Control Theory and Applications from the College of Information Science and Engineering, Northeastern University, China, in 2009. She is currently an associate professor at the College of Information Engineering, Shenyang University of Chemical Technology. Her research interests include modelling and optimal control of complex systems and optimal control of green renewable energy.

Junhong Xie

Junhong Xie was born on 26 June 1996. She is currently pursuing the MS degree in control engineering with the Shenyang University of Chemical Technology. Her research interests include modelling and optimal control of complex systems and image encryption.