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

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