An image encryption algorithm based on the double time-delay Lorenz system

Yuzhen Zhou; Erxi Zhu; Shan Li; Yuzhen Zhou; Erxi Zhu; Shan Li

doi:10.3934/mbe.2023821

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18491-18522. doi: 10.3934/mbe.2023821

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An image encryption algorithm based on the double time-delay Lorenz system

1.
College of Internet of Things Engineering, Jiangsu Vocational College of Information Technology, No.1 qianou Road, Huishan District, Jiangsu Wuxi, 214153, China
2.
College of Computer science and technology, Nanjing University of Aeronautics & Astronautics, No 29 Jiangjun Avenue, Jiangning District, Nanjing, 211106, China
3.
Zhejiang Cainiao Supply Chain Management Co. LTD, Zhejinag Hangzhou, 310000, China

Received: 16 July 2023 Revised: 07 September 2023 Accepted: 13 September 2023 Published: 27 September 2023

The traditional image encryption technology has the disadvantages of low encryption efficiency and low security. According to the characteristics of image information, an image encryption algorithm based on double time-delay chaos is proposed by combining the delay chaotic system with traditional encryption technology. Because of the infinite dimension and complex dynamic behavior of the delayed chaotic system, it is difficult to be simulated by AI technology. Furthermore time delay and time delay position have also become elements to be considered in the key space. The proposed encryption algorithm has good quality. The stability and the existence condition of Hopf bifurcation of Lorenz system with double delay at the equilibrium point are studied by nonlinear dynamics theory, and the critical delay value of Hopf bifurcation is obtained. The system intercepts the pseudo-random sequence in chaotic state and encrypts the image by means of scrambling operation and diffusion operation. The algorithm is simulated and analyzed from key space size, key sensitivity, plaintext image sensitivity and plaintext histogram. The results show that the algorithm can produce satisfactory scrambling effect and can effectively encrypt and decrypt images without distortion. Moreover, the scheme is not only robust to statistical attacks, selective plaintext attacks and noise, but also has high stability.
- image encryption,
- chaotic encryption,
- double time-delay Lorenz system,
- Hopf bifurcation
Citation: Yuzhen Zhou, Erxi Zhu, Shan Li. An image encryption algorithm based on the double time-delay Lorenz system[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18491-18522. doi: 10.3934/mbe.2023821

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Abstract

The traditional image encryption technology has the disadvantages of low encryption efficiency and low security. According to the characteristics of image information, an image encryption algorithm based on double time-delay chaos is proposed by combining the delay chaotic system with traditional encryption technology. Because of the infinite dimension and complex dynamic behavior of the delayed chaotic system, it is difficult to be simulated by AI technology. Furthermore time delay and time delay position have also become elements to be considered in the key space. The proposed encryption algorithm has good quality. The stability and the existence condition of Hopf bifurcation of Lorenz system with double delay at the equilibrium point are studied by nonlinear dynamics theory, and the critical delay value of Hopf bifurcation is obtained. The system intercepts the pseudo-random sequence in chaotic state and encrypts the image by means of scrambling operation and diffusion operation. The algorithm is simulated and analyzed from key space size, key sensitivity, plaintext image sensitivity and plaintext histogram. The results show that the algorithm can produce satisfactory scrambling effect and can effectively encrypt and decrypt images without distortion. Moreover, the scheme is not only robust to statistical attacks, selective plaintext attacks and noise, but also has high stability.

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