Attack trees are a popular way to represent and evaluate potential security threats on systems or infrastructures. The goal of this work is to provide a framework allowing to express and check whether an attack tree is consistent with the analyzed system. We model real systems using transition systems and introduce attack trees with formally specified node labels. We formulate the correctness properties of an attack tree with respect to a system and study the complexity of the corresponding decision problems. The proposed framework can be used in practice to assist security experts in manual creation of attack trees and enhance development of tools for automated generation of attack trees. This is an extended version of the work published at ESORICS 2017 [4].

Attack trees are a well established and commonly used framework for security modeling. They provide a readable and structured representation of possible attacks against a system to protect. Their hierarchical structure reveals common features of the attacks and enables quantitative evaluation of security, thus highlighting the most severe vulnerabilities to focus on while implementing countermeasures. Since in real-life studies attack trees have a large number of nodes, their manual creation is a tedious and error-prone process, and their analysis is a computationally challenging task. During the last half decade, the attack tree community witnessed a growing interest in employing formal methods to deal with the aforementioned difficulties. We survey recent advances in graphical security modeling with focus on the application of formal methods to the interpretation, (semi-)automated creation, and quantitative analysis of attack trees and their extensions. We provide a unified description of existing frameworks, compare their features, and outline interesting open questions.

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