Biblio

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.

It is well known that superposition coding, namely separately encoding the independent sources, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). However, the characterization of the coding rate region therein involves uncountably many linear inequalities and the constant term (i.e., the lower bound) in each inequality is given in terms of the solution of a linear optimization problem. Thus this implicit characterization of the coding rate region does not enable the determination of the achievability of a given rate tuple. In this paper, we first obtain closed-form expressions of these uncountably many inequalities. Then we identify a finite subset of inequalities that is sufficient for characterizing the coding rate region. This gives an explicit characterization of the coding rate region. We further show by the symmetry of the problem that only a much smaller subset of this finite set of inequalities needs to be verified in determining the achievability of a given rate tuple. Yet, the cardinality of this smaller set grows at least exponentially fast with L.