Study on the Application of Graph Theory Algorithms and Attack Graphs in Cybersecurity Assessment

Postulating the behavior of attackers is important in the design of cybersecurity protection measures. Attack graph is a technique employed for this purpose, which aids in identifying and modeling the potential attack paths an attacker could take to gain unauthorized access to a cyber network, exploit vulnerabilities, and compromise the system's confidentiality, integrity, and availability. In this study, we propose a framework aimed at identifying potential attack paths and determining the shortest path with the highest probability of a successful attack. Meanwhile, based on the attack graph determine the minimum patch sets with the most severity to protect the network security. Common Vulnerability Scoring System (CVSS) is utilized to quantify the exploitability and severity of each vulnerability. The Dijkstra algorithm is utilized to calculate the shortest path with the highest probability, and the Stoer-Wagner algorithm is utilized to calculate the minimum patch sets with the most severity. To demonstrate the proposed framework, we apply it to a simplified SCADA system within a corporate network susceptible to cyber attacks.