# Infinitely Divisible Noise in the Low Privacy Regime

arXiv: https://arxiv.org/abs/2110.06559 · HTML: https://mlsanity.com/paper/2110.06559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 41 references that are in the map.
- First posted on arXiv 13 Oct 2021.

## Builds on (most cited first, 14 of 14)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [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)
- [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)
- [Private Summation in the Multi-Message Shuffle Model](https://mlsanity.com/paper/2002.00817/) (2020)
- [Differentially Private Aggregation in the Shuffle Model: Almost Central Accuracy in Almost a Single Message](https://mlsanity.com/paper/2109.13158/) (2021)
- [Optimality of the Laplace Mechanism in Differential Privacy](https://mlsanity.com/paper/1504.00065/) (2015)
- [Private Aggregation from Fewer Anonymous Messages](https://mlsanity.com/paper/1909.11073/) (2019)
- [Pure Differentially Private Summation from Anonymous Messages](https://mlsanity.com/paper/2002.01919/) (2020)

## Abstract (arXiv)

Federated learning, in which training data is distributed among users and never shared, has emerged as a popular approach to privacy-preserving machine learning. Cryptographic techniques such as secure aggregation are used to aggregate contributions, like a model update, from all users. A robust technique for making such aggregates differentially private is to exploit infinite divisibility of the Laplace distribution, namely, that a Laplace distribution can be expressed as a sum of i.i.d. noise shares from a Gamma distribution, one share added by each user. However, Laplace noise is known to have suboptimal error in the low privacy regime for varepsilon-differential privacy, where varepsilon > 1 is a large constant. In this paper we present the first infinitely divisible noise distribution for real-valued data that achieves varepsilon-differential privacy and has expected error that decreases exponentially with varepsilon.