From t-Closeness to PRAM and Noise Addition Via Information Theory

t-Closeness is a privacy model recently defined for data anonymization. A data set is said to satisfy t-closeness if, for each group of records sharing a combination of key attributes, the distance between the distribution of a confidential attribute in the group and the distribution of the attribute in the data is no more than a threshold t. We state here the t-closeness property in terms of information theory and then use the tools of that theory to show that t-closeness can be achieved by the PRAM masking method in the discrete case and by a form of noise addition in the general case.