A Code-Driven Tutorial on Encrypted Control: From Pioneering Realizations to Modern Implementations

The growing interconnectivity in control systems due to robust wireless communication and cloud usage paves the way for exciting new opportunities such as data-driven control and service-based decision-making. At the same time, connected systems are susceptible to cyberattacks and data leakages. Against this background, encrypted control aims to increase the security and safety of cyber- physical systems. A central goal is to ensure confidentiality of process data during networked controller evaluations, which is enabled by, e.g., homomorphic encryption. However, the integration of advanced cryptographic systems renders the design of encrypted controllers an inter-disciplinary challenge. This code-driven tutorial paper aims to facilitate the access to encrypted control by providing exemplary realizations based on popular homomorphic cryptosystems. In particular, we discuss the encrypted implementation of state feedback and PI controllers using the Paillier, GSW, and CKKS cryptosystem.