Efficient and Generic Algorithms for Quantitative Attack Tree Analysis

TL;DR

This paper introduces efficient, general algorithms for quantitative attack tree analysis, capable of computing various security metrics across different attack tree structures, with some limitations on dynamic DAGs.

Contribution

It proposes novel algorithms for three attack tree classes that operate over a broad attribute domain, advancing the analysis of security metrics.

Findings

Algorithms work on static trees and proper trees for multiple metrics.

Complexity analysis of the proposed algorithms.

Open problem remains for dynamic attack trees with DAG structure.

Abstract

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.