# Hiding in the Crowd: A Massively Distributed Algorithm for Private Averaging with Malicious Adversaries

## TL;DR

This paper introduces a scalable, privacy-preserving distributed algorithm for averaging data among users, resilient to malicious adversaries, enabling private data analysis without third-party reliance.

## Contribution

It presents a novel massively distributed protocol for private averaging that is robust against malicious users and does not depend on third-party authorities.

## Key findings

- The protocol achieves arbitrary accuracy in private averaging.
- It maintains privacy even against malicious adversaries.
- A verification method effectively detects malicious manipulations.

## Abstract

The amount of personal data collected in our everyday interactions with connected devices offers great opportunities for innovative services fueled by machine learning, as well as raises serious concerns for the privacy of individuals. In this paper, we propose a massively distributed protocol for a large set of users to privately compute averages over their joint data, which can then be used to learn predictive models. Our protocol can find a solution of arbitrary accuracy, does not rely on a third party and preserves the privacy of users throughout the execution in both the honest-but-curious and malicious adversary models. Specifically, we prove that the information observed by the adversary (the set of maliciours users) does not significantly reduce the uncertainty in its prediction of private values compared to its prior belief. The level of privacy protection depends on a quantity related to the Laplacian matrix of the network graph and generally improves with the size of the graph. Furthermore, we design a verification procedure which offers protection against malicious users joining the service with the goal of manipulating the outcome of the algorithm.