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Privacy-Preserving Distributed Maximum Consensus Without Accuracy Loss

Wenrui Yu, Richard Heusdens, Jun Pang, Qiongxiu Li

TL;DR

This work proposes a novel distributed optimization-based approach that preserves privacy without sacrificing accuracy, and derives a sufficient condition to protect private data against both passive and eavesdropping adversaries.

Abstract

In distributed networks, calculating the maximum element is a fundamental task in data analysis, known as the distributed maximum consensus problem. However, the sensitive nature of the data involved makes privacy protection essential. Despite its importance, privacy in distributed maximum consensus has received limited attention in the literature. Traditional privacy-preserving methods typically add noise to updates, degrading the accuracy of the final result. To overcome these limitations, we propose a novel distributed optimization-based approach that preserves privacy without sacrificing accuracy. Our method introduces virtual nodes to form an augmented graph and leverages a carefully designed initialization process to ensure the privacy of honest participants, even when all their neighboring nodes are dishonest. Through a comprehensive information-theoretical analysis, we derive a sufficient condition to protect private data against both passive and eavesdropping adversaries. Extensive experiments validate the effectiveness of our approach, demonstrating that it not only preserves perfect privacy but also maintains accuracy, outperforming existing noise-based methods that typically suffer from accuracy loss.

Privacy-Preserving Distributed Maximum Consensus Without Accuracy Loss

TL;DR

This work proposes a novel distributed optimization-based approach that preserves privacy without sacrificing accuracy, and derives a sufficient condition to protect private data against both passive and eavesdropping adversaries.

Abstract

In distributed networks, calculating the maximum element is a fundamental task in data analysis, known as the distributed maximum consensus problem. However, the sensitive nature of the data involved makes privacy protection essential. Despite its importance, privacy in distributed maximum consensus has received limited attention in the literature. Traditional privacy-preserving methods typically add noise to updates, degrading the accuracy of the final result. To overcome these limitations, we propose a novel distributed optimization-based approach that preserves privacy without sacrificing accuracy. Our method introduces virtual nodes to form an augmented graph and leverages a carefully designed initialization process to ensure the privacy of honest participants, even when all their neighboring nodes are dishonest. Through a comprehensive information-theoretical analysis, we derive a sufficient condition to protect private data against both passive and eavesdropping adversaries. Extensive experiments validate the effectiveness of our approach, demonstrating that it not only preserves perfect privacy but also maintains accuracy, outperforming existing noise-based methods that typically suffer from accuracy loss.
Paper Structure (14 sections, 1 theorem, 11 equations, 5 figures, 1 algorithm)

This paper contains 14 sections, 1 theorem, 11 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem formulation
  4. A/PDMM with linear equality and inequality constraints
  5. Adversary model and evaluation metrics
  6. Proposed approach
  7. Output accuracy
  8. Individual privacy
  9. Simulation results
  10. Information leakage via mutual information
  11. Performance comparison
  12. Conclusion
  13. Appendix
  14. Proof of Theorem \ref{['thm.1']}

Key Result

Theorem 1

Given $i\in{\cal V}_h$. If

Figures (5)

  • Figure 1: (a) Example of the original graph $\mathcal{G}$; (b) Example of the augmented graph $\mathcal{G}^\prime$ including dummy nodes.
  • Figure 2: Normalized mutual information (NMI) $\frac{I(S_i;Z^{(0)}_{i|i^\prime}+\frac{1}{2}cS_i)}{I(S_i;S_i)}$ as a function of variance $\sigma_z$
  • Figure 3: LHS of \ref{['eq:cond']} as a function of $t$ for three values of $c$, where the blue lines are the results for the node having the maximum value and the others for nodes having $s_i < s_{\rm max}$.
  • Figure 4: Performance comparison of the proposed approach with two existing approaches under various privacy levels.
  • Figure 5: Convergence of the optimization variable $x^{(t)}$ for three nodes with minimum, median and maximum value of three algorithms, respectively.

Theorems & Definitions (2)

  • Theorem 1
  • proof