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.

翻译：我们研究了交互式差分隐私机制的并发组合性质，其中对手可以任意交错地向不同机制发起查询。我们证明，当使用$f$-DP（该框架以$(\eps,\delta)$-DP为标准特例）的假设检验框架衡量差分隐私时，所有非交互式差分隐私机制的组合定理均能推广至交互式差分隐私机制的并发组合。我们通过证明每个交互式$f$-DP机制均可由非交互式$f$-DP机制的交互后处理模拟，从而建立了该并发组合定理。在同期独立工作中，Lyu~\cite{lyu2022composition}针对$(\eps,\delta)$-DP证明了与我们类似的结果，并给出了Rényi DP的并发组合定理。我们还为Lyu提出的Rényi DP并发组合定理提供了简洁证明。Lyu将$f$-DP的一般情形留作开放问题，而本文解决了该问题。