Biblio

A cyber-physical system (CPS) is expected to be resilient to more than one type of adversary. In this paper, we consider a CPS that has to satisfy a linear temporal logic (LTL) objective in the presence of two kinds of adversaries. The first adversary has the ability to tamper with inputs to the CPS to influence satisfaction of the LTL objective. The interaction of the CPS with this adversary is modeled as a stochastic game. We synthesize a controller for the CPS to maximize the probability of satisfying the LTL objective under any policy of this adversary. The second adversary is an eavesdropper who can observe labeled trajectories of the CPS generated from the previous step. It could then use this information to launch other kinds of attacks. A labeled trajectory is a sequence of labels, where a label is associated to a state and is linked to the satisfaction of the LTL objective at that state. We use differential privacy to quantify the indistinguishability between states that are related to each other when the eavesdropper sees a labeled trajectory. Two trajectories of equal length will be differentially private if they are differentially private at each state along the respective trajectories. We use a skewed Kantorovich metric to compute distances between probability distributions over states resulting from actions chosen according to policies from related states in order to quantify differential privacy. Moreover, we do this in a manner that does not affect the satisfaction probability of the LTL objective. We validate our approach on a simulation of a UAV that has to satisfy an LTL objective in an adversarial environment.

In this paper, we study system security against Advanced Persistent Threats (APTs). APTs are stealthy and persistent but APTs interact with system and introduce information flows in the system as data-flow and control-flow commands. Dynamic Information Flow Tracking (DIFT) is a promising detection mechanism against APTs which taints suspicious input sources in the system and performs online security analysis when a tainted information is used in unauthorized manner. Our objective in this paper is to model DIFT that handle data-flow and conditional branches in the program that arise from control-flow commands. We use game theoretic framework and provide the first analytical model of DIFT with data-flow and conditional-branch tracking. Our game model which is an undiscounted infinite-horizon stochastic game captures the interaction between APTs and DIFT and the notion of conditional branching. We prove that the best response of the APT is a maximal reachability probability problem and provide a polynomial-time algorithm to find the best response by solving a linear optimization problem. We formulate the best response of the defense as a linear optimization problem and show that an optimal solution to the linear program returns a deterministic optimal policy for the defense. Since finding Nash equilibrium for infinite-horizon undiscounted stochastic games is computationally difficult, we present a nonlinear programming based polynomial-time algorithm to find an E-Nash equilibrium. Finally, we perform experimental analysis of our algorithm on real-world data for NetRecon attack augmented with conditional branching.