A general cipher for individual data anonymization

Abstract: Over the years, the literature on individual data anonymization has burgeoned in many directions. Borrowing from several areas of other sciences, the current diversity of concepts, models and tools available contributes to understanding and fostering individual data dissemination in a privacy-preserving way, as well as unleashing new sources of information for the benefits of society at large. However, such diversity doesn't come without some difficulties. Currently, the task of selecting the optimal analytical environment to conduct anonymization is complicated by the multitude of available choices. Based on recent contributions from the literature and inspired by cryptography, this paper proposes the first cipher for data anonymization. The functioning of this cipher shows that, in fact, every anonymization method can be viewed as a general form of rank swapping with unconstrained permutation structures. Beyond all the currently existing methods that it can mimic, this cipher offers a new way to practice data anonymization, notably by performing anonymization in an ex ante way, instead of being engaged in several ex post evaluations and iterations to reach the protection and information properties sought after. Moreover, the properties of this cipher point to some previously unknown general insights into the task of data anonymization considered at a general level of functioning. Finally, and to make the cipher operational, this paper proposes the introduction of permutation menus in data anonymization, where recently developed universal measures of disclosure risk and information loss are used ex ante for the calibration of permutation keys. To justify the relevance of their uses, a theoretical characterization of these measures is also proposed.