Efficient and Generic Algorithms for Quantitative Attack Tree Analysis

Numerous analysis methods for quantitative attack tree analysis have been proposed. These algorithms compute relevant security metrics, i.e., performance indicators that quantify how good the security of a system is; typical metrics being the most likely attack, the cheapest, or the most damaging one. However, existing methods are only geared towards specific metrics or do not work on general attack trees. This article classifies attack trees in two dimensions: proper trees versus directed acyclic graphs (i.e., with shared subtrees); and static versus dynamic gates. For three out of these four classes, we propose novel algorithms that work over a generic attribute domain, encompassing a large number of concrete security metrics defined on the attack tree semantics; dynamic attack trees with directed acyclic graph structure are left as an open problem. We also analyse the computational complexity of our methods.