Attack graphs provide compact representations of the attack paths that an
attacker can follow to compromise network resources by analysing network
vulnerabilities and topology. These representations are a powerful tool for
security risk assessment. Bayesian inference on attack graphs enables the
estimation of the risk of compromise to the system's components given their
vulnerabilities and interconnections, and accounts for multi-step attacks
spreading through the system. Whilst static analysis considers the risk posture
at rest, dynamic analysis also accounts for evidence of compromise, e.g. from
SIEM software or forensic investigation. However, in this context, exact
Bayesian inference techniques do not scale well. In this paper we show how
Loopy Belief Propagation - an approximate inference technique - can be applied
to attack graphs, and that it scales linearly in the number of nodes for both
static and dynamic analysis, making such analyses viable for larger networks.
We experiment with different topologies and network clustering on synthetic
Bayesian attack graphs with thousands of nodes to show that the algorithm's
accuracy is acceptable and converge to a stable solution. We compare sequential
and parallel versions of Loopy Belief Propagation with exact inference
techniques for both static and dynamic analysis, showing the advantages of
approximate inference techniques to scale to larger attack graphs.Comment: 30 pages, 14 figure