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In this paper we define a new metric for quantifying formally define our proposed anonymity metric. We then show the degree of anonymity collectively afforded to users of an how our model can be generalized to include probabilistic anonymous communication system. We show how our metric, information in Section III. We demonstrate how to apply our based on the permanent of a matrix, can be useful in evaluating the amount of information needed by an observer to reveal the metio some common type o me istin iV. In communication pattern as a whole. We also show how our model Section V, we compare our metric to some existing metrics to can be extended to include probabilistic information learned illustrate the more important differences. Section VI describes by an attacker about possible sender-recipient relationships. how we can obtain a lower-bound on the anonymity level Our work is intended to serve as a complementary tool to of a system while avoiding some computational complexity existing information-theoretic metrics, which typically consider the anonymity of the system from the perspective of a single user inheren in ctin tnr a or message.conclude in Section VII.A. Related Work Diaz et al. [7] independently proposed a similar entropy-The rest of this paper is structured as follows. First, we will based metric they refer to as the degree of anonymity, a term review some of the previous work done to establish measures first introduced by Reiter and Rubin in the Crowds design [8].Of anonymity. In Section II, we introduce our model and They define the degree of anonymity d as

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