Privacy: From database reconstruction to legal theorems

There are significant gaps between legal and technical thinking around data privacy. Technical standards are described using mathematical language whereas legal standards are not rigorous from a mathematical point of view and often resort to concepts which they only partially define. As a result, arguments about the adequacy of technical privacy measures for satisfying legal privacy often lack rigor, and their conclusions are uncertain. The uncertainty is exacerbated by a litany of successful privacy attacks on privacy measures thought to meet legal expectations but then shown to fall short of doing so. As computer systems manipulating individual privacy-sensitive data become integrated in almost every aspect of society, and as such systems increasingly make decisions of legal significance, the need to bridge the diverging, and sometimes conflicting legal and technical approaches becomes urgent. We formulate and prove formal claims - "legal theorems'' - addressing legal questions such as whether the use of technological measures satisfies the requirements of a legal privacy standard. In particular, we analyze the notion of singling out from the GDPR and whether technologies such as k-anonymity and differential privacy prevent singling out. Our long-term goal is to develop concepts which are on one hand technical, so they can be integrated in the design of computer systems, and can be used in legal reasoning and for policymaking on the other hand.