Effective risk management in cybersecurity requires a thorough understanding of the interplay between attacker capabilities and defense strategies. Attack-Defense Trees (ADTs) are a commonly used methodology for representing this interplay; however, previous work in this domain has only focused on analyzing metrics such as cost, damage, or time from the perspective of the attacker. This approach provides an incomplete view of the system, as it neglects to model defender attributes: in real-world scenarios, defenders have finite resources for countermeasures and are similarly constrained. In this paper, we propose a novel framework that incorporates defense metrics into ADTs, and we present efficient algorithms for computing the Pareto front between defense and attack metrics. Our methods encode both attacker and defender metrics as semirings, allowing our methods to be used for many metrics such as cost, damage, and skill. We analyze tree-structured ADTs using a bottom-up approach and general ADTs by translating them into binary decision diagrams. Experiments on randomly generated ADTS demonstrate that both approaches effectively handle ADTs with several hundred nodes.

Abstract Systematic spare management is important to optimize the twin goals of high reliability and low costs. However, existing approaches to spare management do not incorporate a detailed analysis of the effect on the absence of spares on the system’s reliability. In this work, we combine fault tree analysis with statistical model checking to model spare part management as a stochastic priced timed game automaton (SPTGA). We use Uppaal Stratego to find the number of spares that minimizes the total costs due to downtime and spare purchasing. The resulting SPTGA model can then additionally be analyzed according to a wide range of other metrics, including expected availability. We apply these techniques to the emergency shutdown system of a research nuclear reactor. In this case study, the failure probability is low, so we change the settings of Uppaal Stratego setting to obtain reliable results about rare events. We consider both a single subsystem and the combination of two subsystems. In both situations, our methods find the optimal number of spares, minimizing cost while ensuring an expected availability of 99.96% and 99.93%, respectively.