Probabilistic analysis of onion routing in a black-box model

We perform a probabilistic analysis of onion routing. The analysis is presented in a black-box model of anonymous communication that abstracts the essential properties of onion routing in the presence of an active adversary that controls a portion of the network and knows all a priori distributions on user choices of destination. Our results quantify how much the adversary can gain in identifying users by exploiting knowledge of their probabilistic behavior. In particular, we show that a user uâ s anonymity is worst either when the other users always choose the destination u is least likely to visit or when the other users always choose the destination u chooses. This worst-case anonymity with an adversary that controls a fraction b of the routers is comparable to the bestcase anonymity against an adversary that controls a fraction pb.