Composition Theorems for Interactive Differential Privacy
Abstract
An interactive mechanism is an algorithm that stores a data set and answers adaptively chosen queries to it. The mechanism is called differentially private, if any adversary cannot distinguish whether a specific individual is in the data set by interacting with the mechanism. We study composition properties of differential privacy in concurrent compositions. In this setting, an adversary interacts with k interactive mechanisms in parallel and can interleave its queries to the mechanisms arbitrarily. Previously, Vadhan and Wang [2021] proved an optimal concurrent composition theorem for pure-differential privacy. We significantly generalize and extend their results. Namely, we prove optimal parallel composition properties for several major notions of differential privacy in the literature, including approximate DP, Rényi DP, and zero-concentrated DP. Our results demonstrate that the adversary gains no advantage by interleaving its queries to independently running mechanisms. Hence, interactivity is a feature that differential privacy grants us for free. Concurrently and independently of our work, Vadhan and Zhang [2022] proved an optimal concurrent composition theorem for f-DP [Dong et al., 2022], which implies our result for the approximate DP case.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2022
- DOI:
- 10.48550/arXiv.2207.09397
- arXiv:
- arXiv:2207.09397
- Bibcode:
- 2022arXiv220709397L
- Keywords:
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- Computer Science - Cryptography and Security;
- Computer Science - Data Structures and Algorithms;
- Computer Science - Information Theory
- E-Print:
- To appear in NeurIPS 2022