Modeling cyber-physical attacks based on stochastic game and Markov processes

Security of cyber-physical systems (CPS) has been a prime concern due to the ever-increasing integration of communication networks with physical devices. In this paper, we propose a zero - sum stochastic game model to capture the system dynamics resulting from the attacker - defender interactions in an attacked CPS. In addition to predicting the attacker behavior in terms of optimal strategies, the best strategies for counteracting the malicious activities are also determined. The lifetime of the attacked CPS is characterized based on a continuous time Markov chain (CTMC) and consequently, mean time to failure of the system is derived. Further, we address dependability issues of the system by formulating a semi-Markov model and obtaining different dependability measures such as reliability, availability and confidentiality. The studies identify critical states of the system with respect to its dependability. Theoretical results are also validated via simulation. The results of the studies are expected to be helpful in developing efficient and robust defense mechanisms.