An information theoretic framework for active de-anonymization in social networks based on group memberships

Abstract

In this paper, a new mathematical formulation for the problem of de-anonymizing social network users by actively querying their membership in social network groups is introduced. In this formulation, the attacker has access to a noisy observation of the group membership of each user in the social network. When an unidentified victim visits a malicious website, the attacker uses browser history sniffing to make queries regarding the victim's social media activity. Particularly, it can make polar queries regarding the victim's group memberships and the victim's identity. The attacker receives noisy responses to her queries. The goal is to de-anonymize the victim with the minimum number of queries. Starting with a rigorous mathematical model for this active de-anonymization problem, an upper bound on the attacker's expected query cost is derived, and new attack algorithms are proposed which achieve this bound. These algorithms vary in computational cost and performance. The results suggest that prior heuristic approaches to this problem provide sub-optimal solutions.

Optimal Active social Network De-anonymization Using Information Thresholds

“…In this section, we provide a rigorous formulation of the active fingerprinting problem. This is a generalization of the formulation provided in [11]. We model the group memberships in the social network by a bipartite graph.…”

“…The variable Z represents the correct response to the attacker's query, where Z = 1 indicates a 'yes' response, and the variable Y represents the noisy response received by the attacker after making the query. As explained in [11], the set of possible queries is divided into two categories: i) User identity (UID): a UID query asks if the unknown victim u J is user u j in the network, and ii) group Membership Queries (GM): a GM asks if the unknown victim u J is a member of the group r i . Hence, the conditional distributions P UID Y|Z and P GM Y|Z are the distribution of the response received by the attacker given the correct response to the attacker's UID and GM queries, respectively.…”

“…Hence, the conditional distributions P UID Y|Z and P GM Y|Z are the distribution of the response received by the attacker given the correct response to the attacker's UID and GM queries, respectively. Due to practical considerations explained in [11], we assume that the responses to the UID queries are received noiselessly (i.e. P UID Y|Z = I 2 , where I 2 is the unitary matrix).…”

“…In [11], we considered the de-anonymization problem under the assumption that the victim's index J, is distributed uniformly over the index set [1, m]. Here, we relax this assumption and consider the problem when the victim's index is distributed according to an arbitrary probability distribution P J which is known a-priori to the attacker.…”

“…In [11], we proposed a mathematical formulation for Wondracek et al's browser history sniffing attack [5], introduced a new strategy by making analogies to channel coding, and quantified the amount of information the attacker obtains from each query. This formulation is summarized in Section II.…”