Biblio

We consider a two-player zero-sum network routing game in which a router wants to maximize the amount of legitimate traffic that flows from a given source node to a destination node and an attacker wants to block as much legitimate traffic as possible by flooding the network with malicious traffic. We address scenarios with asymmetric information, in which the router must reveal its policy before the attacker decides how to distribute the malicious traffic among the network links, which is naturally modeled by the notion of Stackelberg equilibria. The paper focuses on parallel networks, and includes three main contributions: we show that computing the optimal attack policy against a given routing policy is an NP-hard problem; we establish conditions under which the Stackelberg equilibria lead to no regret; and we provide a metric that can be used to quantify how uncertainty about the attacker's capabilities limits the router's performance.

We introduce a scalable observer architecture to estimate the states of a discrete-time linear-time-invariant (LTI) system whose sensors can be manipulated by an attacker. Given the maximum number of attacked sensors, we build on previous results on necessary and sufficient conditions for state estimation, and propose a novel multi-modal Luenberger (MML) observer based on efficient Satisfiability Modulo Theory (SMT) solving. We present two techniques to reduce the complexity of the estimation problem. As a first strategy, instead of a bank of distinct observers, we use a family of filters sharing a single dynamical equation for the states, but different output equations, to generate estimates corresponding to different subsets of sensors. Such an architecture can reduce the memory usage of the observer from an exponential to a linear function of the number of sensors. We then develop an efficient SMT-based decision procedure that is able to reason about the estimates of the MML observer to detect at runtime which sets of sensors are attack-free, and use them to obtain a correct state estimate. We provide proofs of convergence for our algorithm and report simulation results to compare its runtime performance with alternative techniques. Our algorithm scales well for large systems (including up to 5000 sensors) for which many previously proposed algorithms are not implementable due to excessive memory and time requirements. Finally, we illustrate the effectiveness of our algorithm on the design of resilient power distribution systems.