Concurrent Composition of Differential Privacy

Abstract:

We initiate a study of the composition properties of interactive dierentially private mechanisms. An interactive dierentially private mechanism is an algorithm that allows an analyst to adaptively ask queries about a sensitive dataset, with the property that an adversarial

analyst's view of the interaction is approximately the same regardless of whether or not any individual's data is in the dataset. Previous studies of composition of dierential privacy have focused on non-interactive algorithms, but interactive mechanisms are needed to capture many of the intended applications of dierential privacy and a number of the important dierentially private primitives.

We focus on concurrent composition, where an adversary can arbitrarily interleave its queries to several dierentially private mechanisms, which may be feasible when dierentially private query systems are deployed in practice. We prove that when the interactive mechanisms being composed are pure dierentially private, their concurrent composition achieves privacy parameters (with respect to pure or approximate dierential privacy) that match the (optimal) composition theorem for noninteractive dierential privacy. We also prove a composition theorem for interactive mechanisms that satisfy approximate dierential privacy. That bound is weaker than even the basic (suboptimal) composition theorem for noninteractive dierential privacy, and we leave closing the gap as a direction for future research, along with understanding concurrent composition for other variants of dierential privacy.