Quantitative information flow techniques for studying optimality in differential privacy

Universal optimality for differential privacy seeks to characterise the "best" mechanisms, which are the ones that provide the most utility to some class of consumers whilst simultaneously satisfying a fixed ε-differential privacy constraint. The study of universal optimality was initiated in 2009 in two important papers: the first by Ghosh et al., who discovered a universally optimal mechanism for a large class of consumers within the differential privacy constraint context of "counting queries" on statistical datasets; the second by Brenner and Nissim who found that outside of this context, no such universally optimal mechanisms exist. Since those remarkable results, there have been few advances in this field. In this article we detail some recent work which sheds new light on these results using Quantitative Information Flow (QIF), a mathematical framework for quantifying information leaks under a Bayesian adversarial model. Using standard QIF reasoning we show how the earlier results can be both generalised and extended, opening up new avenues for exploring optimality in a wide variety of differential privacy contexts.