An entropy based method for measuring anonymity

Data holders use data masking techniques for limiting disclosure risk in releasing sensitive datasets. Disclosure risk is often expressed in terms of rareness or of probability of re-identification. We propose a novel measure of disclosure risk, based on Shannon entropy, which combines together these two approaches. This measure represents the uncertainty of the linkage of the masked record with the original dataset, and so an estimation of the disclosure risk. It is also related to the size of the support of an equivalent random process with a uniform distribution. This allows us to define for any masking transformation an effective k value in analogy to k-anonymity measure used for integrity preserving transformations. Furthermore, this measure provides a direct link to the information loss in the transformations, providing some insights about the utility. We demonstrate this approach in a toy example using a dataset masked by adding Gaussian noise.