Secure Average Consensus Algorithm with Dynamics-Based Privacy Preservation for Unbalanced Digraphs

Core Concepts

The core message of this article is to develop a novel privacy-preserving average consensus algorithm for unbalanced digraphs. The algorithm carefully embeds randomness in mixing weights and introduces an auxiliary parameter to mask the state-update rule in the initial iterations, while exploiting the intrinsic robustness of consensus dynamics to guarantee the exact average consensus.

Abstract

The article presents a new privacy-preserving average consensus algorithm for unbalanced digraphs. The key highlights are:

The algorithm has two stages:

The first K iterations inject randomness into the mixing weights and the state-update rule to preserve privacy.
The remaining iterations follow the conventional push-sum protocol to ensure exact average consensus.

The algorithm can achieve linear convergence rate to the exact average consensus value, and the convergence rate is explicitly characterized by the mixing matrix and network connectivity structure.

The article introduces new privacy notions for honest-but-curious attacks and eavesdropping attacks, which are more generalized than the existing notions that only consider the exact inference of initial values.

The algorithm is shown to preserve the privacy of agents against both honest-but-curious and eavesdropping attacks by carefully designing the weight generation mechanism and the state-update rule.

The article also presents a vector-state version of the privacy-preserving algorithm and discusses its convergence and privacy properties.

Numerical experiments validate the correctness of the theoretical findings on convergence and privacy preservation.

Stats

The algorithm can achieve linear convergence rate to the exact average consensus value, where the convergence rate is characterized by ρ = (1 - ηN^-1)^(1/(N-1)), and η is a parameter in the weight generation mechanism.

Quotes

"The core message of this article is to develop a novel privacy-preserving average consensus algorithm for unbalanced digraphs."
"The algorithm carefully embeds randomness in mixing weights and introduces an auxiliary parameter to mask the state-update rule in the initial iterations, while exploiting the intrinsic robustness of consensus dynamics to guarantee the exact average consensus."

Key Insights Distilled From

Dynamics-Based Algorithm-Level Privacy Preservation for Push-Sum Average Consensus

by Huqi... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2304.08018.pdf

Deeper Inquiries

How can the proposed algorithm be extended to handle time-varying network topologies or asynchronous updates

To extend the proposed algorithm to handle time-varying network topologies or asynchronous updates, one approach could be to incorporate adaptive mechanisms that adjust the mixing weights based on the changing network structure. For time-varying topologies, the algorithm could periodically update the mixing weights to adapt to the new network configuration. Asynchronous updates can be addressed by introducing synchronization mechanisms or timestamping to ensure that agents are updating their states based on the most recent information available. Additionally, the algorithm could be modified to include resilience mechanisms that can handle delays or inconsistencies in the communication between agents.

What are the potential applications of the privacy-preserving average consensus algorithm in real-world distributed systems

The privacy-preserving average consensus algorithm has a wide range of potential applications in real-world distributed systems. One key application is in the field of smart grids, where multiple energy sources need to reach a consensus on energy production or distribution without revealing sensitive information about their capacities or operations. In sensor networks, the algorithm can be used to aggregate data from multiple sensors while preserving the privacy of individual sensor readings. In healthcare systems, it can enable collaborative analysis of patient data without compromising the confidentiality of personal health information. Other applications include financial systems, supply chain management, and decentralized decision-making processes.

Can the dynamics-based privacy preservation technique be applied to other distributed optimization or control problems beyond average consensus

The dynamics-based privacy preservation technique used in the average consensus algorithm can be applied to various other distributed optimization or control problems beyond average consensus. For example, in distributed optimization tasks such as distributed machine learning or parameter estimation, the dynamics-based approach can help protect the privacy of individual data points or model parameters while achieving a consensus on the global model. In decentralized control systems, the technique can be used to ensure that control decisions are made collaboratively without revealing sensitive information about the system's dynamics or state variables. Overall, the dynamics-based privacy preservation technique has the potential to enhance the security and privacy of a wide range of distributed systems and applications.