A system-wide anonymity metric with message multiplicities

An important goal of an anonymity system is to hide the level of communication between two users, i.e., the number of messages one user sent to another. We construct an anonymity metric thatmeasures the extent towhich the system-wide communication pattern of all users of an anonymity system is hidden, among other possible patterns, in the aftermath of an attack. Ourmodel allows users to send or receive multiple messages via the anonymity system, and our metric handles attacks that are capable of determining infeasibility of some of the system’s input-output message combinations. We also analyse two earlier attempts in the literature at arriving at such a metric, and show that one of those attempts is limited to only a small class of such attacks, while the other fails to take any attack into account. In comparison, our metric is comprehensive, as it is applicable to all attacks mentioned above.