Concurrent Composition Theorems for Differential Privacy

TL;DR

This paper extends composition theorems for differential privacy to interactive mechanisms under concurrent queries using the $f$-DP framework, showing they can be simulated by non-interactive mechanisms, thus broadening privacy guarantees.

Contribution

It proves that all composition theorems for non-interactive mechanisms extend to interactive mechanisms under concurrent composition within the $f$-DP framework, solving an open problem.

Findings

Concurrent composition theorems extend to interactive mechanisms.

Every interactive $f$-DP mechanism can be simulated by non-interactive $f$-DP mechanisms.

Provides a simple proof of Lyu's Rènyi DP composition theorem.

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.