Percolation framework reveals limits of privacy in Conspiracy, Dark Web, and Blockchain networks

We consider the limits of privacy based on the knowledge of interactions in anonymous networks. In many anonymous networks, such as blockchain cryptocurrencies, dark web message boards, and other illicit networks, nodes are anonymous to outsiders, however the existence of a link between individuals is observable. For example, in blockchains, transactions between anonymous accounts are published openly. Here we consider what happens if one or more individuals in such a network are deanonymized by an outside investigator. These compromised individuals could then potentially leak information about others with whom they interacted, leading to a cascade of nodes’ identities being revealed. We map this scenario to percolation and analyze its consequences on three real anonymous networks—(1) a blockchain transaction network, (2) interactions on the dark web, and (3) a political conspiracy network. We quantify, for different likelihoods of individuals possessing information on their neighbors, p, the fraction of accounts that can be identified in each network. We then estimate the minimum and most probable number of steps to a desired anonymous node, a measure of the effort to deanonymize that node. In all three networks, we find that it is possible to deanonymize a significant fraction of the network ($>50\%$ > 50 % ) within less than 5 steps for values of $p>0.4$ p > 0.4 . We show how existing measures and approaches from percolation theory can help investigators quantify the chances of deanonymizing individuals, as well as how users can maintain privacy.