Encrypted control systems have attracted much attention in the control community in recent years. Homomorphic encryption (HE) schemes can not only encrypt the signals transmitted over the communication network but also carry out the calculations needed in dynamic feedback controllers in an encrypted environment. Therefore, both the confidentiality of the signals but also the confidentiality of controller parameters can be protected. In this paper, we focus on several important practical aspects of homomorphic encryption schemes such as computational complexity, network load and storage space. For this purpose, two representative homomorphic encryption schemes, namely, the learning with errors (LWE) scheme and the resilient homomorphic encryption (RHE) scheme will be employed in the investigation with the help of well-established quadruple-tank benchmark process.

Encrypted control systems have received much attention recently to improve the cyber security of industrial control systems. In this paper, an approach is given to reduce network communication load significantly in encrypted control systems. For this purpose, the resilient homomorphic encryption (RHE) scheme proposed in [1] is further developed to explore the Chinese remainder theorem (CRT) so that multiple plaintexts can be encrypted into a single ciphertext. As a result, the amount of ciphertexts transferred over the network is decreased and thus the network communication load is significantly reduced. It is proven that the resulting multi-slot resilient homomorphic encryption (MS-RHE) scheme still keeps the ability of resilience and additive attacks injected into the ciphertexts can still be neutralized. A simulation example of the well-established quadruple-tank benchmark process is used to demonstrate the proposed MS-RHE scheme for encrypted control systems.