Visualising Attack Trees

Attack trees, as developed and used in the TREsPASS consortium, are a tool to capture all possible attacks to reach a specific goal, as described in the root node. To build such an attack tree, experts typically gather and, starting from the goal node, try to enumerate possible ways of attack to reach this goal. Each sub node can be iteratively refined as far as it seems fit. Individual intermediate nodes can thereby be either conjunctive or disjunctive. A conjunctive node requires that all of its children be fulfilled in order to proceed up the tree, whereas disjunctive nodes only require one child to be satisfied in order to proceed. A complete path of actions consists of any number of leaf and intermediate nodes leading to the root node. Within the project, each leaf node is considered to contain four parameters: difficulty, minimum cost, probability of success, and minimum time required to complete. Depending on the effort put into the creation, these attack trees can be very complex, comprising hundreds or thousands of nodes, especially when they are generated programmatically from an underlying model as is the aim of the project. When attempting to visualise these trees, such visualisations quickly become complex and unreadable.

 

tree_radial
Attack tree visualised in radial form where each node corresponds to an attack step. The root node, i.e., the goal, is placed in the center. The edges are coloured according to three parameters: difficulty is indicated as stroke width, time as stroke colour, and probability as stroke opacity.

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In their traditional form, attack trees present a wide variety of important and relevant information, but are not easily visualised, oftentimes shown as an arrangement of text in a directed graph. From a visualisation perspective, attack trees have several flaws; the tree structure gets very wide rapidly, repeating lots of elements to eventually become effectively unreadable even in a medium allowing arbitrary zooming. Also, because attack trees consist of conjunctive and disjunctive nodes, it needs to become visually clear that in the case of conjunctive nodes, all steps need to be fulfilled in order to proceed. We can counteract this complexity by improving the way the tree is laid out and labelled, as well as by testing alternative layouts that result in more compact trees, while maintaining readability. Next to that, exploring interactivity by allowing the user to zoom and pan, and to collapse sub-trees at any level, makes it easier to concentrate only on certain parts of the tree.

tree_radialwtime
Same attack tree as the attack tree above, using the TREsPASS unified colour scheme, including opacity to indicate probability.

A visual language can be developed based on this. It is important to keep in mind that attack trees can vary greatly in size, as their construction is largely dependent on the scenario and environment that they are trying to model. As a result, the language should be scaleable to any size tree. In initial explorations, user feedback revealed that when representing the graph with directed graphs, edges carry much more weight and information visually. Subsequently, most of the parameters were mapped to the edge leading to parent nodes. This allows focus to be placed on the path rather than on each individual step. The resulting legend was developed by parameterising the visual properties of a line and creating a mapping to the attack tree vocabulary.

tree_radial_notime-copy
Same attack tree as the attack tree above, using the TREsPASS unified colour scheme, showing only cost and time as parameters.

 

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