Provably Private Distributed Averaging Consensus: An Information-Theoretic Approach

TL;DR

This paper introduces a privacy-preserving distributed averaging algorithm that achieves the same convergence rate as classic methods while minimizing information leakage, using an information-theoretic approach to balance privacy and convergence.

Contribution

It proposes a novel noisy message design framework that ensures privacy in distributed consensus without sacrificing convergence accuracy.

Findings

Achieves consensus convergence rate comparable to classic algorithms.

Provides formal privacy guarantees quantified by mutual information.

Balances privacy level with convergence time, allowing arbitrary accuracy.

Abstract

In this work, we focus on solving a decentralized consensus problem in a private manner. Specifically, we consider a setting in which a group of nodes, connected through a network, aim at computing the mean of their local values without revealing those values to each other. The distributed consensus problem is a classic problem that has been extensively studied and its convergence characteristics are well-known. Alas, state-of-the-art consensus methods build on the idea of exchanging local information with neighboring nodes which leaks information about the users' local values. We propose an algorithmic framework that is capable of achieving the convergence limit and rate of classic consensus algorithms while keeping the users' local values private. The key idea of our proposed method is to carefully design noisy messages that are passed from each node to its neighbors such that the consensus algorithm still converges precisely to the average of local values, while a minimum amount of information about local values is leaked. We formalize this by precisely characterizing the mutual information between the private message of a node and all the messages that another adversary collects over time. We prove that our method is capable of preserving users' privacy for any network without a so-called "generalized leaf", and formalize the trade-off between privacy and convergence time. Unlike many private algorithms, any desired accuracy is achievable by our method, and the required level of privacy only affects the convergence time.