Cryptography

Mathematics

Economic growth

Operating system

Algorithm

Mathematical optimization

Regular polygon

Optimization problem

Convex function

Encryption

News aggregator

Homomorphic encryption

Economics

Computational complexity theory

Information exchange

Geometry

Convergence (economics)

Computer science

Computer security

Telecommunications

IEEE Transactions on Information Forensics and Security

Privacy preservation is addressed for decentralized optimization, where $N$ agents cooperatively minimize the sum of $N$ convex functions private to these individual agents. In most existing decentralized optimization approaches, participating agents exchange and disclose states explicitly, which may not be desirable when the states contain sensitive information of individual agents. The problem is more acute when adversaries exist which try to steal information from other participating agents. To address this issue, we propose a privacy-preserving decentralized optimization approach based on alternating direction method of multipliers (ADMM) and partially homomorphic cryptography. To the best of our knowledge, this is the first time that cryptographic techniques are incorporated in a fully decentralized setting to enable privacy preservation in decentralized optimization in the absence of any third party or aggregator. To facilitate the incorporation of encryption in a fully decentralized manner, we introduce a new ADMM, which allows time-varying penalty matrices and rigorously prove that it has a convergence rate of $O(1/t)$ . Numerical and experimental results confirm the effectiveness and low-computational complexity of the proposed approach.

ADMM Based Privacy-Preserving Decentralized Optimization