Zero-dynamics attack on homomorphically encrypted control system

Against recent cyber-attack strategies on networked control systems which commonly utilize information of control data, the notion of encrypted control system has been introduced, to protect private data in the network layer by encryption. However, even though the adversary cannot learn the information from the encrypted control signals or parameters, it is known that their values can be manipulated by the adversaries, based on homomorphic property of the cryptosystem. In this paper, we demonstrate that the injection of zero-dynamics attack is possible even for encrypted control systems. By injecting an attack signal, generated with knowledge of the plant model, directly on the encrypted controller output being transmitted to the actuator, we show that it disrupts the plant state while it is undetectable from the input and output of the controller. Simulation results are presented to demonstrate the effectiveness of the proposed attack.