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In this paper, a new mathematical formulation for the problem ofde-anonymizing social network users by actively querying their membership insocial network groups is introduced. In this formulation, the attacker hasaccess to a noisy observation of the group membership of each user in thesocial network. When an unidentified victim visits a malicious website, theattacker uses browser history sniffing to make queries regarding the victim'ssocial media activity. Particularly, it can make polar queries regarding thevictim's group memberships and the victim's identity. The attacker receivesnoisy responses to her queries. The goal is to de-anonymize the victim with theminimum number of queries. Starting with a rigorous mathematical model for thisactive de-anonymization problem, an upper bound on the attacker's expectedquery cost is derived, and new attack algorithms are proposed which achievethis bound. These algorithms vary in computational cost and performance. Theresults suggest that prior heuristic approaches to this problem providesub-optimal solutions.

An Information Theoretic Framework for Active De-anonymization in Social Networks Based on Group Memberships