An information theoretic approach for privacy metrics

Organizations often need to release microdata without revealing sensitive information. To this scope, data are anonymized and, to assess the quality of the process, various privacy metrics have been proposed, such as k-anonymity, l-diversity, and t-closeness. These metrics are able to capture different aspects of the disclosure risk, imposing minimal requirements on the association of an individual with the sensitive attributes. If we want to combine them in a optimization problem, we need a common framework able to express all these privacy conditions. Previous studies proposed the notion of mutual information to measure the different kinds of disclosure risks and the utility, but, since mutual information is an average quantity, it is not able to completely express these conditions on single records. We introduce here the notion of one-symbol information (i.e., the contribution to mutual information by a single record) that allows to express and compare the disclosure risk metrics. In addition, we obtain a relation between the risk values t and l, which can be used for parameter setting. We also show, by numerical experiments, how l-diversity and t-closeness can be represented in terms of two different, but equally acceptable, conditions on the information gain..