Modeling cyber-physical attacks based on probabilistic colored Petri nets and mixed-strategy game theory

Cyber-physical attacks are posing great threats to the safety and security of cyber-physical systems. Modeling cyber-physical attacks reasonably and efficiently is the basis for defending cyber-physical systems effectively, which requires the development of quantitative analysis and modeling approaches for expressing threat propagation in cyber-physical systems. This paper extends the colored Petri net model by defining a probabilistic colored Petri net model that comprises basic models, rules, logical operators and transitions that describe threat propagation between nodes. Basic cyber-physical attack models based on probabilistic colored Petri nets are presented. Furthermore, a systematic modeling approach is presented for constructing a quantitative cyber-physical attack model for a cyber-physical system. The weights of the cyber-physical attack model connections are computed using a mixed-strategy attack-defense game model for each node and solving the Nash equilibrium. Additionally, a hierarchical method of division and integration is proposed to efficiently model complex, large-scale cyber-physical systems. Finally, the systematic cyber-physical attack modeling approach is applied to a case study involving a thermal power plant.