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.
Since Sweeney et. al. @cite_12 proposed the @math -anonymity model, numerous extensions to that model have been proposed to address its weaknesses. As an example, @cite_8 proposes @math -diversity and @cite_8 proposes @math -closeness, both of which protect against inference-based attacks. None of the proposed models consider the combination of other anonymisation protocols.
@cite_12 @cite_8
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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. The k-anonymity privacy requirement for publishing microdata requires that each equivalence class (i.e., a set of records that are indistinguishable from each other with respect to certain “identifying” attributes) contains at least k records. Recently, several authors have recognized that k-anonymity cannot prevent attribute disclosure. The notion of l-diversity has been proposed to address this; l-diversity requires that each equivalence class has at least l well-represented (in Section 2) values for each sensitive attribute. In this paper, we show that l-diversity has a number of limitations. In particular, it is neither necessary nor sufficient to prevent attribute disclosure. Motivated by these limitations, we propose a new notion of privacy called “closeness.” We first present the base model t-closeness, which requires that the distribution of a sensitive attribute in any equivalence class is close to the distribution of the attribute in the overall table (i.e., the distance between the two distributions should be no more than a threshold t). We then propose a more flexible privacy model called (n,t)-closeness that offers higher utility. We describe our desiderata for designing a distance measure between two probability distributions and present two distance measures. We discuss the rationale for using closeness as a privacy measure and illustrate its advantages through examples and experiments. K-Anonymity has been proposed as a mechanism for protecting privacy in microdata publishing, and numerous recoding "models" have been considered for achieving 𝑘anonymity. This paper proposes a new multidimensional model, which provides an additional degree of flexibility not seen in previous (single-dimensional) approaches. Often this flexibility leads to higher-quality anonymizations, as measured both by general-purpose metrics and more specific notions of query answerability. Optimal multidimensional anonymization is NP-hard (like previous optimal 𝑘-anonymity problems). However, we introduce a simple greedy approximation algorithm, and experimental results show that this greedy algorithm frequently leads to more desirable anonymizations than exhaustive optimal algorithms for two single-dimensional models. The k-anonymity privacy requirement for publishing microdata requires that each equivalence class (i.e., a set of records that are indistinguishable from each other with respect to certain "identifying" attributes) contains at least k records. Recently, several authors have recognized that k-anonymity cannot prevent attribute disclosure. The notion of l-diversity has been proposed to address this; l-diversity requires that each equivalence class has at least l well-represented values for each sensitive attribute. In this paper we show that l-diversity has a number of limitations. In particular, it is neither necessary nor sufficient to prevent attribute disclosure. We propose a novel privacy notion called t-closeness, which requires that the distribution of a sensitive attribute in any equivalence class is close to the distribution of the attribute in the overall table (i.e., the distance between the two distributions should be no more than a threshold t). We choose to use the earth mover distance measure for our t-closeness requirement. We discuss the rationale for t-closeness and illustrate its advantages through examples and experiments.