Coprime Factorization-Based Encryption and Attack Detection for Nonlinear Cyber-Physical Systems Using Deep Learning Approach

This paper presents a data-driven framework for integrating encryption transmission and attack detection in cyber-physical systems (CPS) with nonlinear physical plants. The main focus of this research is to use deep neural networks to realize the coprime factorization (CF) of nonlinear systems. The definition of the CF guides the network training and designing process, and the model’s topology is designed in the state-space form, which improves the interpretability of the data-driven CF. Based on the CF-aided neural networks, an encrypted transmission module is designed that projects information related to system dynamics into a perpendicular data space, which complements existing encryption methods from a control theory perspective. Subsequently, an anomaly detector are designed using the same CF pairs. This detector not only provides high-accuracy detection of attacks but also distinguishes between attacks and faults, thereby reducing the false positive rate and enhancing the reliability of the attack detection. The proposed method has been validated in a real CPS using a mecanum-wheeled vehicle as the physical plant, demonstrating its effectiveness and applicability. Note to Practitioners—Given new security challenges posed by eavesdropping and stealthy attacks in CPS, this paper presents a data-driven framework that integrates encrypted transmission and attack detection for nonlinear CPS based solely on input and output data. The CF-aided neural networks enable an encrypted transmission module that maintains accuracy while projecting system dynamics into a perpendicular data space, which enhances existing encryption from a control theory perspective. Furthermore, the framework includes an attack detection mechanism that effectively differentiates between attacks and system faults, which is rarely considered in existing work. The framework has been validated in a real-world CPS application using a mecanum-wheeled vehicle, showcasing its practical applicability. Its data-driven and model-agnostic design makes it adaptable to various critical CPS applications. For instance, the proposed deep learning-based method shows promise in smart grid systems, effectively addressing complex sensor signal processing challenges. Additionally, the experimental validation provides a foundational reference for extending this methodology to other unmanned vehicle systems. However, implementation may require specific computational resources and deep learning expertise, which could hinder immediate adoption. Further research is needed to explore its scalability across different CPS applications, focusing on optimizing computational efficiency and adapting to domain-specific requirements.