Paper 2008/365

Entropy Bounds for Traffic Confirmation

Luke O'Connor

Abstract

Consider an open MIX-based anonymity system with $N$ participants and a batch size of $b$. Assume a global passive adversary who targets a given participant Alice with a set ${\cal R}_A$ of $m$ communicating partners. Let $H( {\cal R}_A \mid {\cal B}_t)$ denote the entropy of ${\cal R}_A$ as calculated by the adversary given $t$ message sets (MIX batches) where Alice is a sender in each message set. Our main result is to express the rate at which the anonymity of Alice (as measured by ${\cal R}_A$) degrades over time as a function of the main parameters $N$, $b$ and $m$.