A Control-Theoretical Zero-Knowledge Proof Scheme for Networked Control Systems

Networked Control Systems (NCS) are pivotal for sectors like industrial automation, autonomous vehicles, and smart grids. However, merging communication networks with control loops brings complexities and security vulnerabilities, necessitating strong protection and authentication measures. This paper introduces an innovative Zero-Knowledge Proof (ZKP) scheme tailored for NCSs, enabling a networked controller to prove its knowledge of the dynamical model and its ability to control a discrete-time linear time-invariant (LTI) system to a sensor, without revealing the model. This verification is done through the controller's capacity to produce suitable control signals in response to the sensor's output demands. The completeness, soundness, and zero-knowledge properties of the proposed approach are demonstrated. The scheme is subsequently extended by considering the presence of delays and output noise. Additionally, a dual scenario where the sensor proves its model knowledge to the controller is explored, enhancing the method's versatility. Effectiveness is shown through numerical simulations and a case study on distributed agreement in multi-agent systems.