Anonymous networking amidst active adversaries

The problem of anonymous wireless networking is considered when adversaries who monitor the transmissions in the network are also capable of compromising a fraction of nodes to extract network information. For a given level of network performance, as measured by network throughput, the problem of maximizing anonymity is studied from a game-theoretic perspective. The metric of anonymity considered is the conditional entropy of network routes given the monitored packet transmission times. In order to provide anonymity, a random subset of nodes (referred to as covert relays) are chosen to generate independent transmission schedules. These covert relays, unless compromised, can effectively hide the flow of traffic through them. Depending on the routes and the throughput requirement, the network designer needs to optimize the choice of covert relays such that anonymity is maximized. Whereas, the eavesdropper needs to optimize the choice of nodes to compromise subject to a constraint on maximum number of monitored nodes, such that the anonymity of the network routes is minimized. This problem is posed as a two player zero-sum game, and it is shown that a unique Nash equilibrium exists for a general category of finite networks. Using numerical examples, the tradeoff between the achievable anonymity and the power of the adversary is demonstrated as a function of the throughput for passive and active adversaries.