A Probabilistic Analysis of Onion Routing in a Black-box Model

Every day, half a million people use the onion-routing network Tor [Dingledine et al. 2004] to anonymize their Internet communication. However, the effectiveness of this service, and of onion routing in general, is not well understood. The approach we take to this problem is to model onion routing formally all the way from the protocol details to the behavior of the users. We then analyze the resulting system and quantify the anonymity it provides. Key features of our model include i) a black-box abstraction in the Universally Composable (UC) framework [Canetti 2000] that hides the underlying operation of the protocol and ii) probabilistic user behavior and protocol operation. Systems for communication anonymity generally have at most one of two desirable properties: provable security and practicality. Systems that one can prove secure have used assumptions that make them impractical for most communication applications. Practical systems are ultimately the ones we must care about, because they are the ones that will actually be used. However, their security properties have not been rig-