Abstract
This article addresses a gap between legal and technical conceptions of data privacy and demonstrates how it can be minimized. The article focuses on “singling out,” which is a concept appearing in the GDPR. Our analysis draws on the legislation, regulatory guidance, and mathematical reasoning to derive a technical concept—“predicate singling out”—aimed at capturing a core part of GDPR’s intent. Examination of predicate singling out sheds light on the concept of singling out and the question of whether existing technologies protect against such a threat. Conceptually, this work demonstrates the role that principled analysis supported by mathematical argument can and should play in articulating and informing public policy at the interface between law and technology.
There is a significant conceptual gap between legal and mathematical thinking around data privacy. The effect is uncertainty as to which technical offerings meet legal standards. This uncertainty is exacerbated by a litany of successful privacy attacks demonstrating that traditional statistical disclosure limitation techniques often fall short of the privacy envisioned by regulators. We define “predicate singling out,” a type of privacy attack intended to capture the concept of singling out appearing in the General Data Protection Regulation (GDPR). An adversary predicate singles out a dataset x using the output of a data-release mechanism M(x) if it finds a predicate p matching exactly one row in x with probability much better than a statistical baseline. A data-release mechanism that precludes such attacks is “secure against predicate singling out” (PSO secure). We argue that PSO security is a mathematical concept with legal consequences. Any data-release mechanism that purports to “render anonymous” personal data under the GDPR must prevent singling out and, hence, must be PSO secure. We analyze the properties of PSO security, showing that it fails to compose. Namely, a combination of more than logarithmically many exact counts, each individually PSO secure, facilitates predicate singling out. Finally, we ask whether differential privacy and k-anonymity are PSO secure. Leveraging a connection to statistical generalization, we show that differential privacy implies PSO security. However, and in contrast with current legal guidance, k-anonymity does not: There exists a simple predicate singling out attack under mild assumptions on the k-anonymizer and the data distribution.
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