  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, such as the most
likely attack, the cheapest, or the most damaging one. This paper classifies
attack trees in two dimensions: proper trees vs. directed acyclic graphs (i.e.
with shared subtrees); and static vs. dynamic gates. For each class, 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.
We also analyse the computational complexity of our methods.
