The explosion in volume and variety of data offers enormous potential for research and commercial use. Increased availability of personal data is of particular interest in enabling highly customised services tuned to individual needs. Preserving the privacy of individuals against reidentification attacks in this fast-moving ecosystem poses significant challenges for a one-size fits all approach to anonymisation. In this paper we present ( @math , @math )-anonymisation, an approach that combines the @math -anonymisation and @math -differential privacy models into a single coherent framework, providing privacy guarantees at least as strong as those offered by the individual models. Linking risks of less than 5 are observed in experimental results, even with modest values of @math and @math . Our approach is shown to address well-known limitations of @math -anonymity and @math -differential privacy and is validated in an extensive experimental campaign using openly available datasets.
@cite_7 the authors present a comparison between the privacy guarantees provided by applying @math -anonymity and @math -differential privacy. Also, the authors provide a mechanism to approximate the equivalent @math parameter of a @math -closeness setting and vice-versa.
@cite_7
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It is not uncommon in the data anonymization literature to oppose the "old" @math k -anonymity model to the "new" differential privacy model, which offers more robust privacy guarantees. Yet, it is often disregarded that the utility of the anonymized results provided by differential privacy is quite limited, due to the amount of noise that needs to be added to the output, or because utility can only be guaranteed for a restricted type of queries. This is in contrast with @math k -anonymity mechanisms, which make no assumptions on the uses of anonymized data while focusing on preserving data utility from a general perspective. In this paper, we show that a synergy between differential privacy and @math k -anonymity can be found: @math k -anonymity can help improving the utility of differentially private responses to arbitrary queries. We devote special attention to the utility improvement of differentially private published data sets. Specifically, we show that the amount of noise required to fulfill @math ? -differential privacy can be reduced if noise is added to a @math k -anonymous version of the data set, where @math k -anonymity is reached through a specially designed microaggregation of all attributes. As a result of noise reduction, the general analytical utility of the anonymized output is increased. The theoretical benefits of our proposal are illustrated in a practical setting with an empirical evaluation on three data sets. This paper investigates the relation between three different notions of privacy: identifiability, differential privacy, and mutual-information privacy. Under a unified privacy-distortion framework, where the distortion is defined to be the expected Hamming distance between the input and output databases, we establish some fundamental connections between these three privacy notions. Given a maximum allowable distortion @math , we define the privacy-distortion functions @math , @math , and @math to be the smallest (most private best) identifiability level, differential privacy level, and mutual information between the input and the output, respectively. We characterize @math and @math , and prove that @math for @math within certain range, where @math is a constant determined by the prior distribution of the original database @math , and diminishes to zero when @math is uniformly distributed. Furthermore, we show that @math and @math can be achieved by the same mechanism for @math within certain range, i.e., there is a mechanism that simultaneously minimizes the identifiability level and achieves the best mutual-information privacy. Based on these two connections, we prove that this mutual-information optimal mechanism satisfies @math -differential privacy with @math . The results in this paper reveal some consistency between two worst case notions of privacy, namely, identifiability and differential privacy, and an average notion of privacy, mutual-information privacy. k-anonymity and e-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 e-differential privacy are strongly related to one another when it comes to anonymizing data sets. Specifically, k-anonymity for the quasi-identifiers combined with e-differential privacy for the confidential attributes yields stochastic t-closeness (an extension of t-closeness), with t a function of k and e. Conversely, t-closeness can yield e-differential privacy when t=exp(e 2) and the assumptions made by t-closeness about the prior and posterior views of the data hold. A mechanism for releasing information about a statistical database with sensitive data must resolve a trade-off between utility and privacy. Privacy can be rigorously quantified using the framework of differential privacy , which requires that a mechanism's output distribution is nearly the same whether or not a given database row is included or excluded. The goal of this paper is strong and general utility guarantees, subject to differential privacy. We pursue mechanisms that guarantee near-optimal utility to every potential user, independent of its side information (modeled as a prior distribution over query results) and preferences (modeled via a loss function). Our main result is: for each fixed count query and differential privacy level, there is a geometric mechanism @math -- a discrete variant of the simple and well-studied Laplace mechanism -- that is simultaneously expected loss-minimizing for every possible user, subject to the differential privacy constraint. This is an extremely strong utility guarantee: every potential user @math , no matter what its side information and preferences, derives as much utility from @math as from interacting with a differentially private mechanism @math that is optimally tailored to @math .