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Anonymous communication (AC) protocols such as the widely used Tor network have been designed to provide anonymity over the Internet to their participating users. While AC protocols have been the subject of several security and anonymity analyses in the last years, there still does not exist a framework for analyzing these complex systems and their different anonymity properties in a unified manner.

In this work we present AnoA: a generic framework for defining, analyzing, and quantifying anonymity properties for AC protocols. In addition to quantifying the (additive) advantage of an adversary in an indistinguishability-based definition, AnoA uses a multiplicative factor, inspired from differential privacy. AnoA enables a unified quantitative analysis of well-established anonymity properties, such as sender anonymity, sender unlinkability, and relationship anonymity. AnoA modularly specifies adversarial capabilities by a simple wrapper-construction, called adversary classes. We examine the structure of these adversary classes and identify conditions under which it suffices to establish anonymity guarantees for single messages in order to derive guarantees for arbitrarily many messages. This then leads us to the definition of Plug'n'Play adversary classes (PAC), which are easy-to-use, expressive, and satisfy this condition. We prove that our framework is compatible with the universal composability (UC) framework and show how to apply AnoA to a simplified version of Tor against passive adversaries, leveraging a recent realization proof in the UC framework.