Anonymity of a buffer constrained chaum mix: Optimal strategy and asymptotics

As networked systems increasingly pervade every facet of life, it is quintessential for users to communicate without revealing their identities or the paths of data flow. Chaum Mixes are intermediate nodes or routers that are used to provide anonymity by using cryptographic and batching methods to hide source identities. The anonymity achievable by batching strategies, are however, severely impacted by limited buffer capacity of the mix node. This paper presents an information theoretic investigation of a buffer constrained mix, and provides the first single letter characterization of the maximum achievable anonymity as a function of buffer size for a mix serving two users with equal arrival rates. For two users with unequal arrival rates the anonymity is expressed as a solution to a series of finite recursive equations. For more than two users and arbitrary arrival rates, a lower bound on the convergence rate of anonymity is derived as buffer size increases and it is shown that under certain arrival configurations the lower bound is tight.