# Shuffle Gaussian Mechanism for Differential Privacy

arXiv: https://arxiv.org/abs/2206.09569 · HTML: https://mlsanity.com/paper/2206.09569/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 20 Jun 2022.

## Builds on (most cited first, 28 of 28)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Opacus: User-Friendly Differential Privacy Library in PyTorch](https://mlsanity.com/paper/2109.12298/) (2021)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018)
- [Numerical Composition of Differential Privacy](https://mlsanity.com/paper/2106.02848/) (2021)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2102.06387/) (2021)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Hiding Among the Clones: A Simple and Nearly Optimal Analysis of Privacy Amplification by Shuffling](https://mlsanity.com/paper/2012.12803/) (2020)
- [Optimal Accounting of Differential Privacy via Characteristic Function](https://mlsanity.com/paper/2106.08567/) (2021)
- [Hypothesis Testing Interpretations and Renyi Differential Privacy](https://mlsanity.com/paper/1905.09982/) (2019)
- [The Privacy Blanket of the Shuffle Model](https://mlsanity.com/paper/1903.02837/) (2019)
- [Prochlo: Strong Privacy for Analytics in the Crowd](https://mlsanity.com/paper/1710.00901/) (2017)
- [Encode, Shuffle, Analyze Privacy Revisited: Formalizations and Empirical Evaluation](https://mlsanity.com/paper/2001.03618/) (2020)
- [Privacy Amplification via Random Check-Ins](https://mlsanity.com/paper/2007.06605/) (2020)
- [On the Renyi Differential Privacy of the Shuffle Model](https://mlsanity.com/paper/2105.05180/) (2021)
- [Differential Privacy in the Shuffle Model: A Survey of Separations](https://mlsanity.com/paper/2107.11839/) (2021)
- [Renyi Differential Privacy of the Subsampled Shuffle Model in Distributed Learning](https://mlsanity.com/paper/2107.08763/) (2021)
- [Network Shuffling: Privacy Amplification via Random Walks](https://mlsanity.com/paper/2204.03919/) (2022)
- [Tight Accounting in the Shuffle Model of Differential Privacy](https://mlsanity.com/paper/2106.00477/) (2021)

## Built on by (most cited first, 4 of 4)

- [Privacy amplification by random allocation](https://mlsanity.com/paper/2502.08202/) (2025)
- [Leveraging Randomness in Model and Data Partitioning for Privacy Amplification](https://mlsanity.com/paper/2503.03043/) (2025)
- [Trade-off Functions for DP-SGD with Subsampling based on Random Allocation: Tight Upper and Lower Bounds](https://mlsanity.com/paper/2605.06259/) (2026)
- [Closed-Form Noise Calibration Against Membership Inference for Random-Allocation DP-SGD](https://mlsanity.com/paper/2610.09651/) (2026)

## Abstract (arXiv)

We study Gaussian mechanism in the shuffle model of differential privacy (DP). Particularly, we characterize the mechanism's R'enyi differential privacy (RDP), showing that it is of the form:  ε(λ) ≤ frac1λ-1logleft(frace-λ/2σ2nλ sum_substackk1+dotsc+kn = λ; k1,dotsc,kn≥ 0binomλk1,dotsc,kne^sumi=1nki2/2σ2right)  We further prove that the RDP is strictly upper-bounded by the Gaussian RDP without shuffling. The shuffle Gaussian RDP is advantageous in composing multiple DP mechanisms, where we demonstrate its improvement over the state-of-the-art approximate DP composition theorems in privacy guarantees of the shuffle model. Moreover, we extend our study to the subsampled shuffle mechanism and the recently proposed shuffled check-in mechanism, which are protocols geared towards distributed/federated learning. Finally, an empirical study of these mechanisms is given to demonstrate the efficacy of employing shuffle Gaussian mechanism under the distributed learning framework to guarantee rigorous user privacy.