From t-closeness to differential privacy and vice versa in data anonymization

TL;DR

This paper explores the theoretical relationships between t-closeness and differential privacy, showing how they can be transformed into each other under certain conditions, thereby unifying two major data anonymization models.

Contribution

It establishes formal links between t-closeness and differential privacy, demonstrating how one can be derived from the other under specific assumptions and parameter settings.

Findings

k-anonymity combined with differential privacy yields stochastic t-closeness

t-closeness can imply differential privacy when t = exp(ε/2)

The models are strongly related but not fully equivalent

Abstract

k-Anonymity and {\epsilon}-differential privacy are two mainstream privacy models, the former introduced to anonymize data sets and the latter to limit the knowledge gain that results from including one individual in the data set. Whereas basic k-anonymity only protects against identity disclosure, t-closeness was presented as an extension of k-anonymity that also protects against attribute disclosure. We show here that, if not quite equivalent, t-closeness and {\epsilon}-differential privacy are strongly related to one another when it comes to anonymizing data sets. Specifically, k-anonymity for the quasi-identifiers combined with {\epsilon}-differential privacy for the confidential attributes yields stochastic t-closeness (an extension of t-closeness), with t a function of k and {\epsilon}. Conversely, t-closeness can yield {\epsilon}- differential privacy when t = exp({\epsilon}/2) and the assumptions made by t-closeness about the prior and posterior views of the data hold