Mobile Mixing

We consider a process during which encoded messages are processed through a network; at one step a message can be delivered only to a neighbor of the current node; at each node a message is recoded cryptographically so that an external observer cannot link the messages before and after re-coding. The goal of re-coding is to hide origins of the messages from an adversary who monitors the traffic. Recoding becomes useful, if at least two messages simultaneously enter a node – then the node works like a mix server. We investigate how long the route of messages must be so that traffic analysis does not provide any substantial information for the adversary. Anonymity model we consider is very strong and concerns distance between a priori probability distribution describing origins of each message, and the same probability distribution but conditioned upon the traffic information. We provide a rigid mathematical proof that for a certain route length, expressed in terms of mixing time of the network graph, variation distance between the probability distributions mentioned above is small with high probability (over possible traffic patterns). While the process concerned is expressed in quite general terms, it provides tools for proving privacy and anonymity features of many protocols. For instance, our analysis extends results concerning security of an anonymous communication protocol based on onion encoding – we do not assume, as it is done in previous papers, that a message can be sent directly between arbitrary nodes. However, the most significant application now might be proving immunity against traffic analysis of RFID tags with universal re-encryption performed for privacy protection.