Measure Large Scale Network Security Using Adjacency Matrix Attack Graphs

An Attack Graph capable of disclosing causal relationships between multiple vulnerabilities has become a desirable tool for administrators to analyze and locate potential risks to protect critical networked resources against internal or external multi-step attacks. However, probabilistic security metric computations, using currently applied attack graphs, have complexity problems due to their scale. It is hard or even impossible for current attack graphs to be applied to large scale networks. This paper proposes a novel approach that combines the advantages of exploit-dependency attack graphs and adjacency matrices, which results in quadratic complexity. We first give a motivating example to introduce the approach. We then define the adjacency matrix attack graphs. We show that computing probabilistic cumulative scores by means of adjacency matrix attack graphs is efficient and readily scalable.