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.

Attack trees (ATs) are a popular formalism for security analysis, and numerous variations and tools have been developed around them. These were mostly developed independently, and offer little interoperability or ability to combine various AT features. We present ATTop, a software bridging tool that enables automated analysis of ATs using a model-driven engineering approach. ATTop fulfills two purposes: 1. It facilitates interoperation between several AT analysis methodologies and resulting tools (e.g., ATE, ATCalc, ADTool 2.0), 2. it can perform a comprehensive analysis of attack trees by translating them into timed automata and analyzing them using the popular model checker Uppaal, and translating the analysis results back to the original ATs. Technically, our approach uses various metamodels to provide a unified description of AT variants. Based on these metamodels, we perform model transformations that allow to apply various analysis methods to an AT and trace the results back to the AT domain. We illustrate our approach on the basis of a case study from the AT literature.

We employ uncertain parametric CTMCs with parametric transition rates and a prior on the parameter values. The prior encodes uncertainty about the actual transition rates, while the parameters allow dependencies between transition rates. Sampling the parameter values from the prior distribution then yields a standard CTMC, for which we may compute relevant reachability probabilities. We provide a principled solution, based on a technique called scenario-optimization, to the following problem: From a finite set of parameter samples and a user-specified confidence level, compute prediction regions on the reachability probabilities. The prediction regions should (with high probability) contain the reachability probabilities of a CTMC induced by any additional sample. To boost the scalability of the approach, we employ standard abstraction techniques and adapt our methodology to support approximate reachability probabilities. Experiments with various well-known benchmarks show the applicability of the approach.

Numerous analysis methods for quantitative attack tree analysis have been proposed. These algorithms compute relevant security metrics, i.e. performance indicators that quantity 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.