Anonymity under flow insertion: A game theoretic approach

The problem of anonymous wireless networking is considered when an adversary is capable of controlling a subset of routes in the network. For a desired quality-of-service (QoS), as measured by network throughput, the problem of maximizing anonymity is studied from a game-theoretic perspective. Anonymity is quantified using conditional entropy of the routes given the adversary's observation. The problem of optimizing anonymity is posed as a two player zero-sum game between the network designer and the adversary; the task of the adversary is to choose a subset of flows to control so that anonymity of routes is minimum whereas the task of the network designer is to maximize anonymity by choosing a subset of nodes to evade flow detection by generating independent transmission schedules. It is shown that a unique Nash equilibrium exists for the game in the class of randomized strategies. The Nash equilibrium conditions are then used to derive properties of the optimal strategies of the network designer and the adversary.