Metadata-Conscious Anonymous Messaging

Consider a line graph G(V,E) in which V = {0, 1, . . . , n, n + 1}, nodes s1 = 0 and s2 = n + 1 are spies, and E = {(i, i + 1) | i ∈ {0, . . . , n}}. One of the n nodes between the spies is chosen uniformly at random as a source, denoted by v∗ ∈ {1, . . . , n}. When the message reaches a spy si, the spy collects at least two pieces of metadata: the timestamp Tsi and the parent node psi that relayed the message. We let t0 denote the time the source starts propagating the message according to some global reference clock. Let Ts1 = T1 + t0 and Ts2 = T2 + t0 denote the timestamps when the two spy nodes receive the message, respectively. Knowing the spreading protocol and the metadata, the adversary uses the maximum likelihood estimator to optimally estimate the source.