Concurrent Composition Theorems for Differential Privacy (2207.08335v3)

Abstract: We study the concurrent composition properties of interactive differentially private mechanisms, whereby an adversary can arbitrarily interleave its queries to the different mechanisms. We prove that all composition theorems for non-interactive differentially private mechanisms extend to the concurrent composition of interactive differentially private mechanisms, whenever differential privacy is measured using the hypothesis testing framework of $f$-DP, which captures standard $(\eps,\delta)$-DP as a special case. We prove the concurrent composition theorem by showing that every interactive $f$-DP mechanism can be simulated by interactive post-processing of a non-interactive $f$-DP mechanism. In concurrent and independent work, Lyu~\cite{lyu2022composition} proves a similar result to ours for $(\eps,\delta)$-DP, as well as a concurrent composition theorem for R\'enyi DP. We also provide a simple proof of Lyu's concurrent composition theorem for R\'enyi DP. Lyu leaves the general case of $f$-DP as an open problem, which we solve in this paper.