# Differentially Private Aggregation in the Shuffle Model: Almost Central Accuracy in Almost a Single Message

arXiv: https://arxiv.org/abs/2109.13158 · HTML: https://mlsanity.com/paper/2109.13158/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2021.

## Built on by (most cited first, 18 of 18)

- [Private Non-Convex Federated Learning Without a Trusted Server](https://mlsanity.com/paper/2203.06735/) (2022)
- [Regression with Label Differential Privacy](https://mlsanity.com/paper/2212.06074/) (2022)
- [User-Level Private Learning via Correlated Sampling](https://mlsanity.com/paper/2110.11208/) (2021)
- [Network Shuffling: Privacy Amplification via Random Walks](https://mlsanity.com/paper/2204.03919/) (2022)
- [Samplable Anonymous Aggregation for Private Federated Data Analysis](https://mlsanity.com/paper/2307.15017/) (2023)
- [Optimal Unbiased Randomizers for Regression with Label Differential Privacy](https://mlsanity.com/paper/2312.05659/) (2023)
- [Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation](https://mlsanity.com/paper/2202.10618/) (2022)
- [Private Vector Mean Estimation in the Shuffle Model: Optimal Rates Require Many Messages](https://mlsanity.com/paper/2404.10201/) (2024)
- [Transfer Learning In Differential Privacy's Hybrid-Model](https://mlsanity.com/paper/2201.12018/) (2022)
- [Learning from End User Data with Shuffled Differential Privacy over Kernel Densities](https://mlsanity.com/paper/2502.14087/) (2025)
- [Multi-Message Shuffled Privacy in Federated Learning](https://mlsanity.com/paper/2302.11152/) (2023)
- [Making Old Things New: A Unified Algorithm for Differentially Private Clustering](https://mlsanity.com/paper/2406.11649/) (2024)
- [Beyond Statistical Estimation: Differentially Private Individual Computation via Shuffling](https://mlsanity.com/paper/2406.18145/) (2024)
- [PREAMBLE: Private and Efficient Aggregation via Block Sparse Vectors](https://mlsanity.com/paper/2503.11897/) (2025)
- [Shuffle and Joint Differential Privacy for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/2602.00417/) (2026)
- [Infinitely Divisible Noise in the Low Privacy Regime](https://mlsanity.com/paper/2110.06559/) (2021)
- [Differential Privacy on Trust Graphs](https://mlsanity.com/paper/2410.12045/) (2024)
- [Shuffling-Aware Optimization for Private Vector Mean Estimation](https://mlsanity.com/paper/2604.28032/) (2026)

## Abstract (arXiv)

The shuffle model of differential privacy has attracted attention in the literature due to it being a middle ground between the well-studied central and local models. In this work, we study the problem of summing (aggregating) real numbers or integers, a basic primitive in numerous machine learning tasks, in the shuffle model. We give a protocol achieving error arbitrarily close to that of the (Discrete) Laplace mechanism in the central model, while each user only sends 1 + o(1) short messages in expectation.