A Kolmogorov Complexity Approach for Measuring Attack Path Complexity

The difficulty associated with breaching an enterprise network is commensurate with the security of that network. A security breach, or a security policy violation, occurs as a result of an attacker successfully executing some attack path. The difficulty associated with this attack path, then, is critical to understanding how secure a given network is. Currently, however, there are no consistent methods for measuring attack path complexity that make the assumptions of a modeler explicit while providing flexibility in how the modeler models the attack path. To provide these desirable attributes, we propose a regular-expressions-inspired language whose rationale for attack path complexity measurement is based on Kolmogorov Complexity. After detailing our Kolmogorov Complexity-based method, we demonstrate how it can be applied to a novel security metric: the K-step Capability Accumulation metric–a metric that defines the security of a network in terms of the network assets attainable for attack effort exerted.