On the privacy of anonymized networks

Abstract

The proliferation of online social networks, and the concomitant accumulation of user data, give rise to hotly debated issues of privacy, security, and control. One specific challenge is the sharing or public release of anonymized data without accidentally leaking personally identifiable information (PII). Unfortunately, it is often difficult to ascertain that sophisticated statistical techniques, potentially employing additional external data sources, are unable to break anonymity.In this paper, we consider an instance of this problem, where the object of interest is the structure of a social network, i.e., a graph describing users and their links. Recent work demonstrates that anonymizing node identities may not be sufficient to keep the network private: the availability of node and link data from another domain, which is correlated with the anonymized network, has been used to re-identify the anonymized nodes. This paper is about conditions under which such a de-anonymization process is possible.We attempt to shed light on the following question: can we assume that a sufficiently sparse network is inherently anonymous, in the sense that even with unlimited computational power, deanonymization is impossible? Our approach is to introduce a random graph model for a version of the de-anonymization problem, which is parameterized by the expected node degree and a similarity parameter that controls the correlation between two graphs over the same vertex set. We find simple conditions on these parameters delineating the boundary of privacy, and show that the mean node degree need only grow slightly faster than log n with network size n for nodes to be identifiable. Our results have policy implications for sharing of anonymized network information.

Assembling a network out of ambiguous patches

“…Lemma 14: [Difference of Binomials [18]] Let X 1 and X 2 be two binomial random variables with means λ 1 and λ 2 , where λ 2 > λ 1 . Then,…”

“…Graph Alignment [18], [13] We use the results related to the graph-alignment problem introduced in [18], [13]. The BiG(G(n, p); s) edge-sampling model from [18] generates two similar graphs G 1,2 from a common vertex set.…”

“…Graph Alignment [18], [13] We use the results related to the graph-alignment problem introduced in [18], [13]. The BiG(G(n, p); s) edge-sampling model from [18] generates two similar graphs G 1,2 from a common vertex set. To elaborate on this, let G = (V, E) be a generator graph with vertex set V and edge set E. For a fixed realization of G that is an Erdös-Rényi random graph G(n, p), we generate two graphs G 1,2 = (V, E 1,2 ) by sampling the vertex set E twice.…”

“…The last follows from Equation 19 of [18] where conditions of the Theorem 4.1 from [18] are met (except the condition p → 0 that the authors never use). The second term follows from the fact that P(m < x) ≤ P(m < m(1 − t)(1 − δ)) ≤ exp − m(1 − t)δ …”

Unveiling Privacy Setting Breaches in Online Social Networks

“…There are two major research directions on the privacy and security issues in OSNs: (1) to reveal the privacy threats in OSNs by conducting surveys [16,17] and proposing attack models [26], information inference algorithms [6,8,9,13,14,19,28], de-anonymization algorithms [4,21], and re-identification algorithms [27]; and (2) to reinforce users' privacy by redesigning the OSN system structure [5,10,20,23] and conducting anonymization [22,25]. This paper investigates the privacy setting breaches, which belongs to (1).…”