On linear logic, functional programming, and attack trees

Abstract

This paper has two main contributions. The first is a new linear logical semantics of causal attack trees in four-valued truth tables. Our semantics is very simple and expressive, supporting specializations, and supports the ideal semantics of causal attack trees, and partially supporting the filter semantics of causal attack trees. Our second contribution is Lina, a new embedded, in Haskell, domain specific functional programming language for conducting threat analysis using attack trees. Lina has many benefits over existing tools; for example, Lina allows one to specify attack trees very abstractly, which provides the ability to develop libraries of attack trees, furthermore, Lina is compositional, allowing one to break down complex attack trees into smaller ones that can be reasoned about and analyzed incrementally. Furthermore, Lina supports automatically proving properties of attack trees, such as equivalences and specializations, using Maude and the semantics introduced in this paper.