Optimal De-Anonymization in Random Graphs with Community Structure

TL;DR

This paper analyzes the limits of de-anonymization attacks on social network graphs with community structure, providing theoretical bounds and optimal strategies for identifying users based on correlated graphs.

Contribution

It characterizes the MAP estimates for user identities and establishes conditions for successful de-anonymization in graphs with community structure, extending prior Erdős-Rényi models.

Findings

Derived maximum a posteriori estimates for user re-identification.

Established sufficient conditions for successful de-anonymization.

Proved the optimality of existing attack strategies.

Abstract

Anonymized social network graphs published for academic or advertisement purposes are subject to de-anonymization attacks by leveraging side information in the form of a second, public social network graph correlated with the anonymized graph. This is because the two are from the same underlying graph of true social relationships. In this paper, we (i) characterize the maximum a posteriori (MAP) estimates of user identities for the anonymized graph and (ii) provide sufficient conditions for successful de-anonymization for underlying graphs with community structure. Our results generalize prior work that assumed underlying graphs of Erd\H{o}s-R\'enyi type, in addition to proving the optimality of the attack strategy adopted in the prior work.