Anonymous Stochastic Routing.

We propose and analyze a recipient-anonymous stochastic routing model to study a fundamental trade-off between anonymity and routing delay. An agent wants to quickly reach a goal vertex in a network through a sequence of routing actions, while an overseeing adversary observes the agent's entire trajectory and tries to identify her goal among those vertices traversed. We are interested in understanding the probability that the adversary can correctly identify the agent's goal (anonymity), as a function of the time it takes the agent to reach it (delay). A key feature of our model is the presence of intrinsic uncertainty in the environment, so that each of the agent's intended steps is subject to random perturbation and thus may not materialize as planned. Using large-network asymptotics, our main results provide near-optimal characterization of the anonymity-delay trade-off under a number of network topologies. We establish an asymptotically tight characterization of the anonymity-delay trade-off in complete graphs, showing that (1) any level of intrinsic uncertainty will lead to a strictly positive delay overhead for the agent, even as her delay budget tends to infinity, and (2) a carefully designed routing policy can ensure the overhead is only additive with respect to the level of the uncertainty. We further extend the results to networks generated by random graph models, and settings where the network structure can be designed. In both cases, we show it is possible to achieve an additive overhead even for relatively sparse, non-complete networks. Our main technical contributions are centered around a new class of "noise-harnessing" routing strategies that adaptively combine intrinsic uncertainty from the environment with additional artificial randomization to achieve provably efficient obfuscation.