Mean Value Analysis of Critical Attack Paths with Multiple Parameters

Graphical models like attack trees and attack graphs provide promising approaches to represent and analyze complex cyber infrastructures. One common analysis that graphical models are used for is to identify short, or other types of critical attack paths. In this paper, we consider attack graphs that are probabilistic, and the attack steps are characterized by multiple parameters, the probability of success, and the distribution of time to perform the attack step. We propose low-complexity solutions to find sets of critical paths according to flexible mean value-based utility functions. We demonstrate that the results are similar to the ones from Monte-Carlo simulations. Consequently, the utility function-based approach can substitute time-consuming simulations and can be a valuable component of dynamic defense strategies.