# Differentially Private Summation with Multi-Message Shuffling

arXiv: https://arxiv.org/abs/1906.09116 · HTML: https://mlsanity.com/paper/1906.09116/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2019.

## Built on by (most cited first, 9 of 9)

- [Shuffle Private Linear Contextual Bandits](https://mlsanity.com/paper/2202.05567/) (2022)
- [Muffliato: Peer-to-Peer Privacy Amplification for Decentralized Optimization and Averaging](https://mlsanity.com/paper/2206.05091/) (2022)
- [Differentially Private Multi-Armed Bandits in the Shuffle Model](https://mlsanity.com/paper/2106.02900/) (2021)
- [Shuffle Private Stochastic Convex Optimization](https://mlsanity.com/paper/2106.09805/) (2021)
- [On the Renyi Differential Privacy of the Shuffle Model](https://mlsanity.com/paper/2105.05180/) (2021)
- [Renyi Differential Privacy of the Subsampled Shuffle Model in Distributed Learning](https://mlsanity.com/paper/2107.08763/) (2021)
- [FedPerm: Private and Robust Federated Learning by Parameter Permutation](https://mlsanity.com/paper/2208.07922/) (2022)
- [The Sample Complexity of Distribution-Free Parity Learning in the Robust Shuffle Model](https://mlsanity.com/paper/2103.15690/) (2021)
- [Fully Decentralized Certified Unlearning](https://mlsanity.com/paper/2512.08443/) (2025)

## Abstract (arXiv)

In recent work, Cheu et al. (Eurocrypt 2019) proposed a protocol for n-party real summation in the shuffle model of differential privacy with Oε, δ(1) error and Theta(ε√n) one-bit messages per party. In contrast, every local model protocol for real summation must incur error Omega(1/√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/ε) error and O(log(n/δ)) 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.