Stochastic Tools for Network Security: Anonymity Protocol Analysis and Network Intrusion Detection

With the rapid development of Internet and the sharp increase of network crime, network security has become very important and received a lot of attention. In this dissertation, we model security issues as stochastic systems. This allows us to find weaknesses in existing security systems and propose new solutions. Exploring the vulnerabilities of existing security tools can prevent cyber-attacks from taking advantages of the system weaknesses. We consider The Onion Router (Tor), which is one of the most popular anonymity systems in use today, and show how to detect a protocol tunnelled through Tor. A hidden Markov model (HMM) is used to represent the protocol. Hidden Markov models are statistical models of sequential data like network traffic, and are an effective tool for pattern analysis. New, flexible and adaptive security schemes are needed to cope with emerging security threats. We propose a hybrid network security scheme including intrusion detection systems (IDSs) and honeypots scattered throughout the network. This combines the advantages of two security technologies. A honeypot is an activity-based network security system, which could be the logical supplement of the passive detection policies used by IDSs. This integration forces us to balance security performance versus cost by scheduling device activities for the proposed system. By formulating the scheduling problem as a decentralized partially observable Markov decision process (DEC-POMDP), decisions are made in a distributed manner at each device without requiring centralized control. When using a HMM, it is important to ensure that it accurately represents both the data used to train the model and the underlying process. Current methods assume that observations used to construct a HMM completely represent the underlying process. It is often the case that the training data size is not large enough to adequately capture all statistical dependencies in the system. It is therefore important to know the statistical significance level that the constructed model ii represents the underlying process, not only the training set. We present a method to determine if the observation data and constructed model fully express the underlying process with a given level of statistical significance. We apply this approach to detecting the existence of protocols tunnelled through Tor. While HMMs are a powerful tool for representing patterns allowing for uncertainties, they cannot be used for system control. The partially observable Markov decision process (POMDP) is a useful choice for controlling stochastic systems. As a combination of two Markov models, POMDPs combine the strength of HMM (capturing dynamics that depend on unobserved states) and that of Markov decision process (MDP) (taking the decision aspect into account). Decision making under uncertainty is used in many parts of business and science. We use here for security tools. We propose three approximation methods for discrete-time infinite-horizon POMDPs. One of the main contributions of our work is high-quality approximation solution for finite-space POMDPs with the average cost criterion, and their extension to DEC-POMDPs. The solution of the first algorithm is built out of the observable portion when the underlying MDP operates optimally. The other two methods presented here can be classified as the policy-based approximation schemes, in which we formulate the POMDP planning as a quadratically constrained linear program (QCLP), which defines an optimal controller of a desired size. This representation allows a wide range of powerful nonlinear programming (NLP) algorithms to be used to solve POMDPs. Simulation results for a set of benchmark problems illustrate the effectiveness of the proposed method. We show how this tool could be used to design a network security framework.