A new image encryption based on hybrid heterogeneous time-delay chaotic systems

Yuzhen Zhou; Erxi Zhu; Yuzhen Zhou; Erxi Zhu

doi:10.3934/math.2024270

AIMS Mathematics

2024, Volume 9, Issue 3: 5582-5608. doi: 10.3934/math.2024270

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A new image encryption based on hybrid heterogeneous time-delay chaotic systems

Yuzhen Zhou ¹,
Erxi Zhu ^{1,2
,
,}

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

Received: 09 October 2023 Revised: 20 January 2024 Accepted: 24 January 2024 Published: 30 January 2024
MSC : 26E70

Chaos theory has been widely utilized in password design, resulting in an encryption algorithm that exhibits strong security and high efficiency. However, rapid advancements in cryptanalysis technology have rendered single system generated sequences susceptible to tracking and simulation, compromising encryption algorithm security. To address this issue, we propose an image encryption algorithm based on hybrid heterogeneous time-delay chaotic systems. Our algorithm utilizes a collection of sequences generated by multiple heterogeneous time-delay chaotic systems, rather than sequences from a single chaotic system. Specifically, three sequences are randomly assigned to image pixel scrambling and diffusion operations. Furthermore, the time-delay chaotic system comprises multiple hyperchaotic systems with positive Lyapunov exponents, exhibiting a more complex dynamic behavior than non-delay chaotic systems. Our encryption algorithm is developed by a plurality of time-delay chaotic systems, thereby increasing the key space, enhancing security, and making the encrypted image more difficult to crack. Simulation experiment results verify that our algorithm exhibits superior encryption efficiency and security compared to other encryption algorithms.
- image encryption,
- chaotic encryption,
- heterogeneous time-delay chaotic system,
- hopf bifurcation,
- stability
Citation: Yuzhen Zhou, Erxi Zhu. A new image encryption based on hybrid heterogeneous time-delay chaotic systems[J]. AIMS Mathematics, 2024, 9(3): 5582-5608. doi: 10.3934/math.2024270

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Abstract

Chaos theory has been widely utilized in password design, resulting in an encryption algorithm that exhibits strong security and high efficiency. However, rapid advancements in cryptanalysis technology have rendered single system generated sequences susceptible to tracking and simulation, compromising encryption algorithm security. To address this issue, we propose an image encryption algorithm based on hybrid heterogeneous time-delay chaotic systems. Our algorithm utilizes a collection of sequences generated by multiple heterogeneous time-delay chaotic systems, rather than sequences from a single chaotic system. Specifically, three sequences are randomly assigned to image pixel scrambling and diffusion operations. Furthermore, the time-delay chaotic system comprises multiple hyperchaotic systems with positive Lyapunov exponents, exhibiting a more complex dynamic behavior than non-delay chaotic systems. Our encryption algorithm is developed by a plurality of time-delay chaotic systems, thereby increasing the key space, enhancing security, and making the encrypted image more difficult to crack. Simulation experiment results verify that our algorithm exhibits superior encryption efficiency and security compared to other encryption algorithms.

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