A Combinatorial Approach to Measuring Anonymity

In this paper we define a new metric for quantifying the degree of anonymity collectively afforded to users of an anonymous communication system. We show how our metric, based on the permanent of a matrix, can be useful in evaluating the amount of information needed by an observer to reveal the communication pattern as a whole. We also show how our model can be extended to include probabilistic information learned by an attacker about possible sender-recipient relationships. Our work is intended to serve as a complementary tool to existing information-theoretic metrics, which typically consider the anonymity of the system from the perspective of a single user or message.