The Complexity of Estimating Systematic Risk in Networks

ABSTRACT. This risk of catastrophe from an attack is a consequence of a network's structure formed by the connected individuals, businesses and computer systems. Understanding the likelihood of extreme events, or, more generally, the probability distribution of the number of compromised nodes is an essential requirement to provide risk-mitigation or cyber-insurance. However, previous network security research has not considered the higher moments of this distribution, while previous cyber-insurance research has not considered the effect of topologies on the supply side.

We provide a mathematical basis for bridging this gap: we study the complexity of computing these loss-number distributions, both generally and for special cases of common real-world networks. In the case of scale-free networks, we demonstrate that expected loss alone cannot determine the riskiness of a network, and that this riskiness cannot be naively estimated from smaller samples, which highlights the lack/importance of topological data in security incident reporting.