Estimating the Impact of Cyber-Attack Strategies for Stochastic Control Systems

Risk assessment is an inevitable step in implementation of a cyber-defense strategy. An important part of this assessment is to reason about the impact of possible attacks. In this paper, we propose a framework for estimating the impact of cyber-attacks in stochastic linear control systems. The framework can be used to estimate the impact of denial of service, rerouting, sign alternation, replay, false data injection, and bias injection attacks. For the stealthiness constraint, we adopt the Kullback-Leibler divergence between residual sequences during the attack. Two impact metrics are considered: (1) The probability that some of the critical states leave a safety region; and (2) The expected value of the infinity norm of the critical states. For the first metric, we prove that the impact estimation problem can be reduced to a set of convex optimization problems. Thus, the exact solution can be found efficiently. For the second metric, we derive an efficient to calculate lower bound. Finally, we demonstrate how the framework can be used for risk assessment on an example.