A Game Theoretic Approach for Dynamic Information Flow Tracking with Conditional Branching

Abstract

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.