# 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.

This talk will cover two topics, namely, modeling and design of Moving Target Defense (MTD), and DIFT games for modeling Advanced Persistent Threats (APTs). We will first present a game-theoretic approach to characterizing the trade-off between resource efficiency and defense effectiveness in decoy- and randomization-based MTD. We will then address the game formulation for APTs. APTs are mounted by intelligent and resourceful adversaries who gain access to a targeted system and gather information over an extended period of time. APTs consist of multiple stages, including initial system compromise, privilege escalation, and data exfiltration, each of which involves strategic interaction between the APT and the targeted system. While this interaction can be viewed as a game, the stealthiness, adaptiveness, and unpredictability of APTs imply that the information structure of the game and the strategies of the APT are not readily available. Our approach to modeling APTs is based on the insight that the persistent nature of APTs creates information flows in the system that can be monitored. One monitoring mechanism is Dynamic Information Flow Tracking (DIFT), which taints and tracks malicious information flows through a system and inspects the flows at designated traps. Since tainting all flows in the system will incur significant memory and storage overhead, efficient tagging policies are needed to maximize the probability of detecting the APT while minimizing resource costs. In this work, we develop a multi-stage stochastic game framework for modeling the interaction between an APT and a DIFT, as well as designing an efficient DIFT-based defense. Our model is grounded on APT data gathered using the Refinable Attack Investigation (RAIN) flow-tracking framework. We present the current state of our formulation, insights that it provides on designing effective defenses against APTs, and directions for future work.