Peer-to-peer approaches to anonymous communication promise to eliminate the scalability concerns and central vulnerability points of current networks such as Tor. However, the P2P setting introduces many new opportunities for attack, and previous designs do not provide an adequate level of anonymity. We propose ShadowWalker: a new low-latency P2P anonymous communication system, based on a random walk over a redundant structured topology. We base our design on shadows that redundantly check and certify neighbor information; these certifications enable nodes to perform random walks over the structured topology while avoiding route capture and other attacks. We analytically calculate the anonymity provided by ShadowWalker and show that it performs well for moderate levels of attackers, and is much better than the state of the art. We also design an extension that improves forwarding performance at a slight anonymity cost, while at the same time protecting against selective DoS attacks. We show that our system has manageable overhead and can handle moderate churn, making it an attractive new design for P2P anonymous communication.