Concurrent Composition Theorems for Differential Privacy
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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 (,δ)-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 <cit.> proves a similar result to ours for (,δ)-DP, as well as a concurrent composition theorem Rènyi DP (which we also claimed in an earlier version of this paper, but with an incorrect proof). Lyu leaves the general case of f-DP as an open problem, which we solve in this paper.
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