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 (epsilon, 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 (NeurIPS '22) proves a similar result to ours for (epsilon,delta)-DP, as well as a concurrent composition theorem for Renyi DP. We also provide a simple proof of Lyu's concurrent composition theorem for Renyi DP. Lyu leaves the general case of f-DP as an open problem, which we solve in this paper.
