Stochastic Event-Based Physical Watermarks Against Replay Attacks in Cyber Physical Systems

In this paper, an event-based physical watermark is proposed and analyzed. It is well known that adding physical watermarks into Cyber-Physical Systems (CPSs) is an effective way to combat malicious attacks. However, the classical ways to adding physical watermarks are based on time, which leads to great decreases in Linear Quadratic Gaussian (LQG) performances while increasing detection rates. To deal with the performance loss after adding physical watermarks, an event-based physical watermark is designed to detect replay attacks. A stochastic event scheduler based on the innovation sequence is constructed to indicate adding physical watermarks or not. It is shown that the probability of adding physical watermarks will rise up if the system is under attacks. Based on the frequency of adding watermarks, a Count Detector is proposed, which provides lower memory and computation cost. LQG performance and detection rates of a $\chi ^{2}$ detector are further characterized. Herein, it is formally proved that the event-based independent identical distributed (i.i.d.) watermark is more efficient than the time-based i.i.d. watermark. Furthermore, we investigate the optimal parameters to enlarge detection performance in certain conditions. Finally, some simulations are given to show the superiority of our proposed event-based physical watermark.