Stochastic Simulation Techniques for Inference and Sensitivity Analysis of Bayesian Attack Graphs

Abstract

A vulnerability scan combined with information about a computer network can be used to create an attack graph, a model of how the elements of a network could be used in an attack to reach specific states or goals in the network. These graphs can be understood probabilistically by turning them into Bayesian attack graphs (BAGs), making it possible to quantitatively analyse the security of large networks. In the event of an attack, probabilities on the graph change depending on the evidence discovered (e.g., by an intrusion detection system or knowledge of a host’s activity). Since such scenarios are difficult to solve through direct computation, we discuss three stochastic simulation techniques for updating the probabilities dynamically based on the evidence and compare their speed and accuracy. From our experiments we conclude that likelihood weighting is most efficient for most uses. We also consider sensitivity analysis of BAGs, to identify the most critical nodes for protection of the network and solve the uncertainty problem for the assignment of priors to nodes. Since sensitivity analysis can easily become computationally expensive, we present and demonstrate an efficient sensitivity analysis approach that exploits a quantitative relation with stochastic inference.