On the measurement of privacy as an attacker’s estimation error

A wide variety of privacy metrics have been proposed in the literature to evaluate the level of protection offered by privacy enhancing-technologies. Most of these metrics are specific to concrete systems and adversarial models, and are difficult to generalize or translate to other contexts. Furthermore, a better understanding of the relationships between the different privacy metrics is needed to enable more grounded and\udsystematic approach to measuring privacy, as well as to assist system designers in selecting the most appropriate metric for a\udgiven application.\udIn this work we propose a theoretical framework for privacypreserving\udsystems, endowed with a general definition of privacy in terms of the estimation error incurred by an attacker who aims\udto disclose the private information that the system is designed to conceal. We show that our framework permits interpreting and\udcomparing a number of well-known metrics under a common perspective.\udThe arguments behind these interpretations are based on fundamental results related to the theories of information, probability and Bayes decision.Preprin