Expected cost analysis of attack-defense trees

Attack-defense trees () are an established formalism for assessing system security. We extend with costs and success probabilities of basic events. We design a framework to analyze the probability of a successful attack/defense, its expected cost, and its probability for a given maximum cost. On the conceptual level, we show that a proper analysis requires to model the problem using sequential decision making and non-tree structures, in contrast to classical analysis. On the technical level, we provide three algorithms: (i) reduction to PRISM-games, (ii) dedicated game solution utilizing the structure of the problem, and (iii) direct analysis of for certain settings. We demonstrate the framework and compare the solutions on several examples.