On the privacy offered by (k, δ)-anonymity

The widespread deployment of technologies with tracking capabilities, like GPS, GSM, RFID and on-line social networks, allows mass collection of spatio-temporal data about their users. As a consequence, several methods aimed at anonymizing spatio-temporal data before their publication have been proposed in recent years. Such methods are based on a number of underlying privacy models. Among these models, image claims to extend the widely used k-anonymity concept by exploiting the spatial uncertainty image in the trajectory recording process. In this paper, we prove that, for any image (that is, whenever there is actual uncertainty), image does not offer trajectory k-anonymity, that is, it does not hide an original trajectory in a set of k indistinguishable anonymized trajectories. Hence, the methods based on image, like Never Walk Alone (NWA) and Wait For Me (W4M) can offer trajectory k-anonymity only when image (no uncertainty). Thus, the idea of exploiting the recording uncertainty image to achieve trajectory k-anonymity with information loss inversely proportional to image turns out to be flawed.