Differentially Private Summation with Multi-Message Shuffling

TL;DR

This paper introduces a new differentially private summation protocol in the shuffle model that reduces message complexity while maintaining privacy guarantees, improving upon previous methods.

Contribution

It presents a protocol with logarithmic message complexity and controlled error, bridging the gap between local and shuffle model summation protocols.

Findings

Achieves $O(1/\epsilon)$ error with $O(\log(n/\delta))$ messages per party.

Uses secure shuffling to simulate the Laplace mechanism in the shuffle model.

Reduces message complexity compared to previous protocols.

Abstract

In recent work, Cheu et al. (Eurocrypt 2019) proposed a protocol for $n$-party real summation in the shuffle model of differential privacy with $O_{\epsilon, \delta}(1)$ error and $\Theta(\epsilon\sqrt{n})$ one-bit messages per party. In contrast, every local model protocol for real summation must incur error $\Omega(1/\sqrt{n})$, and there exist protocols matching this lower bound which require just one bit of communication per party. Whether this gap in number of messages is necessary was left open by Cheu et al. In this note we show a protocol with $O(1/\epsilon)$ error and $O(\log(n/\delta))$ messages of size $O(\log(n))$ per party. This protocol is based on the work of Ishai et al.\ (FOCS 2006) showing how to implement distributed summation from secure shuffling, and the observation that this allows simulating the Laplace mechanism in the shuffle model.