A Novel Cryptography-Based Privacy-Preserving Decentralized Optimization Paradigm

Abstract

Existing large-scale optimization schemes are challenged by both scalability and cyber-security. With the favorable scalability, adaptability, and flexibility, decentralized and distributed optimization paradigms are widely adopted in cyberphysical system applications. However, most existing approaches heavily rely on explicit information exchange between agents or between agents and the system operator, leading the entire framework prone to privacy risks. To tackle this issue, this paper synthesizes cryptography and decentralized optimization techniques to develop a novel privacy-preserving decentralized optimization paradigm. The proposed paradigm is generically applicable to strongly coupled convex optimization problems with nonseparable objective functions and linearly coupled constraints. The security and accuracy of the proposed paradigm are verified via numerical examples.

Privacy-Preserving Decentralized Multi-Agent Cooperative Optimization -- Paradigm Design and Privacy Analysis

“…However, we claim that this case rarely happens in a large-scale network because of the agents' huge population size. Remark 3: Comparing with the private key based algorithms, e.g., SingleMod-based method in [5], [16], the proposed public key based paradigm has enhanced security. Lu et al [5] proposed a nonoverlapping partition of the coefficients in the first-order gradients of the Lagrangian to avoid repeated encryption due to the lack of semantic security.…”

“…However, as the decision variables converge, it is inevitable to encrypt the same decision variables multiple times. Our preliminary work [16] designed a privacypreserving paradigm which naturally avoids the repeated encryption of the coefficients. However, in both [5] and [16], if the SO has access to the update rule of the decision variables, it can use the collected data to estimate the agents' true decision variables.…”

“…Our preliminary work [16] designed a privacypreserving paradigm which naturally avoids the repeated encryption of the coefficients. However, in both [5] and [16], if the SO has access to the update rule of the decision variables, it can use the collected data to estimate the agents' true decision variables. In contrast, Paradigm 1 that is developed based on the Paillier cryptosystem is semantically secure, and the transmitted ciphertexts reveal nothing to the external eavesdroppers or the SO.…”