Cryptography-Based Privacy-Preserving Method for Distributed Optimization over Time-Varying Directed Graphs with Enhanced Efficiency

TL;DR

This paper introduces a secure, efficient privacy-preserving distributed optimization algorithm based on AES, suitable for time-varying directed networks, with proven privacy protection and linear convergence.

Contribution

A novel AES-based privacy-preserving algorithm for distributed optimization over dynamic directed graphs with rigorous privacy and convergence guarantees.

Findings

Protects agent privacy with at least one legitimate neighbor initially

Achieves linear convergence under strong convexity and Lipschitz smoothness

Demonstrates effectiveness through sensor fusion simulations

Abstract

In this paper, we study the privacy-preserving distributed optimization problem, aiming to prevent attackers from stealing the private information of agents. For this purpose, we propose a novel privacy-preserving algorithm based on the Advanced Encryption Standard (AES), which is both secure and computationally efficient. By appropriately constructing the underlying weight matrices, our algorithm can be applied to time-varying directed networks. We show that the proposed algorithm can protect an agent's privacy if the agent has at least one legitimate neighbor at the initial iteration. Under the assumption that the objective function is strongly convex and Lipschitz smooth, we rigorously prove that the proposed algorithm has a linear convergence rate. Finally, the effectiveness of the proposed algorithm is demonstrated by numerical simulations of the canonical sensor fusion problem.