  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 paper classifies attack trees in two dimensions:
proper trees vs. directed acyclic graphs (i.e. with shared subtrees); and
static vs. 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.
