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 R\`enyi 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.

翻译：我们研究不同互动的私人机制的并行构成特性,使对手可以任意将其询问分散到不同机制。我们证明,非互动的、有差异的私人机制的所有组成理论都适用于互动的、有差异的私营机制的并行组成,只要使用美元-DP的假设测试框架来衡量有差异的隐私,这个假设测试框架将标准$(eps,\delta)$-DP作为一个特例。我们通过显示每个互动的美元-DP机制都可以通过互动后处理非互动的美元-DP机制来模拟。在同时和独立的工作中,Lyu\cite{clyu2022composition}证明了我们对于美元(eps,\delta)$-DP的类似结果,以及同时构成R ⁇ enyi DP(我们也在本文早先的版本中声称,但有不正确的证据)的并行构成。 Lyu留下美元-DP的一般案例,这是我们在本文中解决的公开问题。