# Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation

arXiv: https://arxiv.org/abs/2202.10618 · HTML: https://mlsanity.com/paper/2202.10618/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 22 Feb 2022.

## Builds on (most cited first, 15 of 15)

- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [cpSGD: Communication-efficient and differentially-private distributed SGD](https://mlsanity.com/paper/1805.10559/) (2018)
- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Hiding Among the Clones: A Simple and Nearly Optimal Analysis of Privacy Amplification by Shuffling](https://mlsanity.com/paper/2012.12803/) (2020)
- [Turbo-Aggregate: Breaking the Quadratic Aggregation Barrier in Secure Federated Learning](https://mlsanity.com/paper/2002.04156/) (2020)
- [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)
- [Prio: Private, Robust, and Scalable Computation of Aggregate Statistics](https://mlsanity.com/paper/1703.06255/) (2017)
- [Private Summation in the Multi-Message Shuffle Model](https://mlsanity.com/paper/2002.00817/) (2020)
- [Manipulation Attacks in Local Differential Privacy](https://mlsanity.com/paper/1909.09630/) (2019)
- [Differentially Private Aggregation in the Shuffle Model: Almost Central Accuracy in Almost a Single Message](https://mlsanity.com/paper/2109.13158/) (2021)
- [Private Aggregation from Fewer Anonymous Messages](https://mlsanity.com/paper/1909.11073/) (2019)
- [Differentially Private Multi-party Computation: Optimality of Non-Interactive Randomized Response](https://mlsanity.com/paper/1407.1546/) (2014)

## Built on by (most cited first, 5 of 5)

- [Samplable Anonymous Aggregation for Private Federated Data Analysis](https://mlsanity.com/paper/2307.15017/) (2023)
- [Private Vector Mean Estimation in the Shuffle Model: Optimal Rates Require Many Messages](https://mlsanity.com/paper/2404.10201/) (2024)
- [Correlated Privacy Mechanisms for Differentially Private Distributed Mean Estimation](https://mlsanity.com/paper/2407.03289/) (2024)
- [PREAMBLE: Private and Efficient Aggregation via Block Sparse Vectors](https://mlsanity.com/paper/2503.11897/) (2025)
- [Differentially Private Secure Multiplication: Hiding Information in the Rubble of Noise](https://mlsanity.com/paper/2309.16105/) (2023)

## Abstract (arXiv)

Computing the noisy sum of real-valued vectors is an important primitive in differentially private learning and statistics. In private federated learning applications, these vectors are held by client devices, leading to a distributed summation problem. Standard Secure Multiparty Computation (SMC) protocols for this problem are susceptible to poisoning attacks, where a client may have a large influence on the sum, without being detected. In this work, we propose a poisoning-robust private summation protocol in the multiple-server setting, recently studied in PRIO. We present a protocol for vector summation that verifies that the Euclidean norm of each contribution is approximately bounded. We show that by relaxing the security constraint in SMC to a differential privacy like guarantee, one can improve over PRIO in terms of communication requirements as well as the client-side computation. Unlike SMC algorithms that inevitably cast integers to elements of a large finite field, our algorithms work over integers/reals, which may allow for additional efficiencies.