Document Type



Doctor of Philosophy


Electrical Engineering

First Adviser

Venkitasubramaniam, Parv

Other advisers/committee members

Yukich, Joseph; Blum, Rick; Dobric, Vladimir


Timing analysis has long been used to compromise users' anonymity in networks. Even when data is encrypted, an adversary can track flows from sources to the corresponding destinations by merely using the correlation between the inter-packet timing on incoming and outgoing streams at intermediate routers. Anonymous network systems, where users communicate without revealing their identities, rely on the idea of Chaum mixing to hide `networking information'. Chaum mixes are routers or proxy servers that randomly reorder the outgoing packets to prevent an eavesdropper from tracking the flow of packets. The effectiveness of such mixing strategies is, however, diminished under constraints on network Quality of Services (QoS)s such as memory, bandwidth, and fairness. In this work, two models for studying anonymity, packet based anonymity and flow based anonymity, are proposed to address these issues quantitatively and a trade-off between network constraints and achieved anonymity is studied. Packet based anonymity model is proposed to study the short burst traffic arrival models of users such as in web browsing. For packet based anonymity, an information theoretic investigation of mixes under memory constraint and fairness constraint is established. Specifically, for memory constrained mixes, the first single letter characterization of the maximum achievable anonymity for a mix serving two users with equal arrival rates is provided. Further, for two users with unequal arrival rates the anonymity is expressed as a solution to a series of finite recursive equations. In addition, for more than two users and arbitrary arrival rates, a lower bound on the convergence rate of anonymity is derived as buffer size increases and it is shown that under certain arrival configurations the lower bound is tight. The adverse effects of requirement of fairness in data networking on anonymous networking is also studied using the packet based anonymity model and a novel temporal fairness index is proposed to compare the tradeoff between fairness and achieved anonymity of three diverse and popular fairness paradigms: First Come First Serve, Fair Queuing and Proportional Method. It is shown that FCFS and Fair Queuing algorithms have little inherent anonymity. A significant improvement in anonymity is therefore achieved by relaxing the fairness paradigms. The analysis of the relaxed FCFS criterion, in particular, is accomplished by modeling the problem as a Markov Decision Process (MDP). The proportional method of scheduling, while avoided in networks today, is shown to significantly outperform the other fair scheduling algorithms in anonymity, and is proven to be asymptotically optimal as the buffer size of the scheduler is increased. Flow based anonymity model is proposed to study long streams traffic models of users such as in media streaming. A detection theoretic measure of anonymity is proposed to study the optimization of mixing strategies under network constraints for this flow based anonymity model. Specifically, using the detection time of the adversary as a metric, the effectiveness of mixing strategies is maximized under constraints on memory and throughput. A general game theoretic model is proposed to study the mixing strategies when an adversary is capable of capturing a fraction of incoming packets. For the proposed multistage game, existence of a Nash equilibrium is proven, and the optimal strategies for the mix and adversary were derived at the equilibrium condition.It is noted in this work that major literature on anonymity in Internet is focused on achieving anonymity using third parties like mixes or onion routers, while the contributions of users' individual actions such as accessing multiple websites to hide the targeted websites, using multiple proxy servers to hide the traffic routes are overlooked. In this thesis, signaling game model is proposed to study specifically these kind of problems. Fundamentally, signaling games consist of two players: senders and receivers and each sender belongs to one of multiple types. The users who seek to achieve anonymity are modeled as the sender of a signaling game and their types are identified by their personal information that they want to hide. The eavesdroppers are modeled as the receiver of the signaling game. Senders transmit their messages to receivers. The transmission of these messages can be seen as inevitable actions that a user have to take in his/her daily life, like the newspapers he/she subscribes on the Internet, online shopping that he/she does, but these messages are susceptible to reveal the user identity such as his/her political affiliation or his/her affluence level. The receiver (eavesdropper) uses these messages to interpret the senders' type and take optimal actions according to his belief of senders' type. Senders choose their messages to increase their reward given that they know the optimal policies of the receivers for choosing the action based on the transmitted message. However, sending the messages that increases senders' reward may reveal their type to receivers thus violating their privacy and can be used by eavesdropper in future to harm the senders. In this work, the payoff of a signalling game is adjusted to incorporate the information revealed to an eavesdropper such that this information leakage is minimized from the users' perspective. The existence of Bayesian-Nash equilibrium is proven in this work for the signaling games even after the incorporation of users' anonymity. It is also proven that the equilibrium point is unique if the desired anonymity is below a certain threshold.