Affiliations: in Mathematical and Computing Science, Department of Mathematical and Computing Science, School of Computing, Tokyo Institute of Technology, Tokyo, Japan
Abstract: Today, it is indispensable for us to know our IT infrastructure’s security level to make rational decisions to protect it from malicious attacks. However, the ever-growing scale and complexity of our infrastructures make it difficult. One available approach is attack-graph analysis, a model-based algorithm that generates a directed graph called an attack graph composed of possible attack actions and their AND/OR combinations. An attack graph allows us to identify the logical possibility of cyber-attacks. Unfortunately, attack graphs lack quantitative information, such as the likelihood of a successful attack – the reachability. Meanwhile, some advanced approaches, such as the Bayesian attack-graph, compute reachabilities with an attack graph. Still, those methods have problems in the scalability and the handling of cycles contained in attack graphs. This study proposes and examines another approach named reachability-graph analysis. A reachability graph is a directed graph obtained from an attack graph by which we can compute the reachabilities. It is extremely fast to generate, thus applicable to large-scale network analysis. Furthermore, this method allows cycles in attack graphs. Such a scalable algorithm has been awaited for over a decade; it generates probabilistic security metrics and is guaranteed applicable to any cyclic AND/OR graphs. We compare our approach’s computational efficiency with the Bayesian attack-graph. Also, we apply our approach to large-scale, cyclic attack graphs. Several theoretical properties with proofs and the computational complexity of our approach are examined too.
