Towards an Information Theoretic Metric for Anonymity

In this paper we look closely at the popular metric of anonymity, the anonymity set, and point out a number of problems associated with it. We then propose an alternative information theoretic measure of anonymity which takes into account the probabilities of users sending and receiving the messages and show how to calculate it for a message in a standard mix-based anonymity system. We also use our metric to compare a pool mix to a traditional threshold mix, which was impossible using anonymity sets. We also show how the maximum route length restriction which exists in some fielded anonymity systems can lead to the attacker performing more powerful traffic analysis. Finally, we discuss open problems and future work on anonymity measurements.