Practical and Provably Secure Onion Routing

In an onion routing protocol, messages travel through several intermediaries before arriving at their destinations, they are wrapped in layers of encryption (hence they are called "onions"). The goal is to make it hard to establish who sent the message. It is a practical and widespread tool for creating anonymous channels. For the standard adversary models --- network, passive, and active --- we present practical and provably secure onion routing protocols. Akin to Tor, in our protocols each party independently chooses the routing paths for his onions. For security parameter $\lambda$, our differentially private solution for the active adversary takes $O(\log^2\lambda)$ rounds and requires every participant to transmit $O(\log^{4} \lambda)$ onions in every round.