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 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.