Modeling Attacks in Computer Networks Using Boolean Constraint Propagation

Abstract

We propose a new approach to modeling the processes of the development of attacks in computer networks. This approach is based on the idea that it is possible to associate with a considered computer network a Discrete Dynamical System (DDS) of automaton type. Under the standard assumptions, employed in computer security, such DDS has a single stationary point and cannot have cycles of length greater than one. With each DDS of such kind one can naturally link an effectively computed discrete function. As a result of propositional encoding of an algorithm, defining this function a Boolean formula in a Conjunctive Normal Form, is constructed. By applying to it the state-of-the-art SAT solvers it is possible to make conclusions, regarding different properties of a considered DDS. In the present paper we use the formulas of such kind to effectively construct the attack graphs for computer networks. We show that for this purpose it is sufficient to employ the simple algorithm known as the Unit Propagation rule. We compare the effectiveness of the proposed method for constructing the attack graphs with the well-known MulVAlsoftware system and show that our method outperforms MulVAlby a number of criteria.