A Novel Approach to Construct 1-D Discrete Complex Variable Chaotic Systems and Its Application

Conventional real-valued 1-D chaotic models are constrained by three fundamental limitations: Restricted chaotic regimes, susceptibility to dynamic degradation in finite-precision implementations, and inherent tradeoffs between security assurance and computational efficiency. These constraints signi...

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Vydáno v:IEEE transactions on industrial informatics Ročník 21; číslo 12; s. 9655 - 9665
Hlavní autoři: Sun, Xiangguang, Zheng, Jun, Xie, Yulai, He, Peisong
Médium: Journal Article
Jazyk:angličtina
Vydáno: Piscataway IEEE 01.12.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Chaos theory
Chaotic communication
Chaotic systems
complex variable function
Complex variables
Complexity theory
Computational efficiency
Degradation
Efficiency
Encryption
Field programmable gate arrays
field-programmable gate array (FPGA) implementation
Hardware
image encryption (IE)
Informatics
Liapunov exponents
Resistance
Security
security analysis
Systems design
Zinc
ISSN:1551-3203, 1941-0050
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Shrnutí:Conventional real-valued 1-D chaotic models are constrained by three fundamental limitations: Restricted chaotic regimes, susceptibility to dynamic degradation in finite-precision implementations, and inherent tradeoffs between security assurance and computational efficiency. These constraints significantly limit the applicability of chaos-based systems. This article presents a novel approach for constructing 1-D discrete complex-variable chaotic systems (1D-DCVCS). The proposed methodology establishes a flexible architecture that enables the derivation of 1D-DCVCS with guaranteed positive Lyapunov exponents. Extensive numerical experiments confirm that the constructed systems exhibit rich dynamical properties, while retaining strong chaotic behavior even in low-precision implementations. Hardware validation via field-programmable gate array implementation confirms the practical viability of the proposed approach. To address existing challenges in chaos-based image encryption (IE), particularly inadequate chaotic behavior, vulnerable key structures, and suboptimal operational efficiency, a lightweight IE scheme is developed by leveraging the advantages of 1D-DCVCS. The cryptographic system achieves enhanced security while maintaining computational efficiency, with quantitative security analysis demonstrating superior performance. This work provides a comprehensive solution that simultaneously addresses theoretical limitations in chaotic system design and practical requirements in secure communication applications.
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ISSN:1551-3203
1941-0050
DOI:10.1109/TII.2025.3600762