Network Consensus with Privacy: A Secret Sharing Method

TL;DR

This paper presents a novel privacy-preserving network consensus method inspired by secret sharing, ensuring agreement among nodes without exposing individual states, and resilient to node failures and eavesdropping.

Contribution

It introduces a new secret sharing-based algorithm for privacy-preserving consensus that is resilient to node failures and collusion, advancing secure distributed network protocols.

Findings

Achieves consensus and average consensus almost surely.

Resistant to collusion and eavesdropping.

Supports node failure recovery through neighbor information.

Abstract

In this work, inspired by secret sharing schemes, we introduce a privacy-preserving approach for network consensus, by which all nodes in a network can reach an agreement on their states without exposing the individual state to neighbors. With the privacy degree defined for the agents, the proposed method makes the network resistant to the collusion of any given number of neighbors, and protects the consensus procedure from communication eavesdropping. Unlike existing works, the proposed privacy-preserving algorithm is resilient to node failures. When a node fails, the method offers the possibility of rebuilding the lost node via the information kept in its neighbors, even though none of the neighbors knows the exact state of the failing node. Moreover, it is shown that the proposed method can achieve consensus and average consensus almost surely, when the agents have arbitrary privacy degrees and a common privacy degree, respectively. To illustrate the theory, two numerical examples are presented.