Privacy-Preserving Edge-Aided Eigenvalue Decomposition in Internet of Things

Eigenvalue decomposition (EVD) is a fundamental yet time-consuming operation with extensive applications in Internet of Things (IoT). When the matrix dimension reaches millions, resource-limited IoT devices struggle to perform such computationally expensive operations. Edge computing, with its plentiful computing resources, offers an effective solution to this problem. However, privacy concerns arise because outsourced tasks may contain sensitive user data. In this article, we propose the first privacy-preserving, edge-assisted EVD outsourcing scheme that securely enables users to outsource EVD tasks to edge servers. We design a privacy-preserving matrix transformation method to encode the original data, ensuring that edge servers cannot access users' private information. Additionally, we design a verification scheme that enables the user to verify the correctness of the results returned by the edge servers. Our protocol supports parallel computation by multiple edge servers, thus enhancing the efficiency of EVD. The feasibility of our proposed scheme is demonstrated through both theoretical and experimental perspectives.