Abstract. Attack trees have found their way to practice because they have proved to be an intuitive aid in threat analysis. Despite, or perhaps thanks to, their apparent simplicity, they have not yet been provided with an unambiguous semantics. We argue that such a formal interpretation is indispensable to precisely understand how attack trees can be manipulated during construction and analysis. We provide a denotational semantics, based on a mapping to attack suites, which abstracts from the internal structure of an attack tree, we study transformations between attack trees, and we study the attribution and projection of an attack tree.

Abstract. We introduce and give formal definitions of attack-defense trees. We argue that these trees are a simple, yet powerful tool to analyze complex security and privacy problems. Our formalization is generic in the sense that it supports different semantical approaches. We present several semantics for attack-defense trees along with usage scenarios, and we show how to evaluate attributes.

Attack-defense trees are a novel methodology for graphical security modeling and assessment. They extend the well known formalism of attack trees by allowing nodes that represent defensive measures to appear at any level of the tree. This enlarges the modeling capabilities of attack trees and makes the new formalism suitable for representing interactions between an attacker and a defender. Our formalization supports different semantical approaches for which we provide usage scenarios. We also formalize how to quantitatively analyze attack and defense scenarios using attributes.

Abstract. We provide the first formal foundation of SAND attack trees which are a popular extension of the well-known attack trees. The SAND attack tree formalism increases the expressivity of attack trees by introducing the sequential conjunctive operator SAND. This operator enables the modeling of ordered events. We give a semantics to SAND attack trees by interpreting them as sets of series-parallel graphs and propose a complete axiomatization of this semantics. We define normal forms for SAND attack trees and a term rewriting system which allows identification of semantically equivalent trees. Finally, we formalize how to quantitatively analyze SAND attack trees using attributes.

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