Cloud-assisted Internet of Things (IoT) has become the core infrastructure of smart society since it solves the computational power, storage, and collaboration bottlenecks of traditional IoT through resource decoupling and capability complementarity. The development of a graph database and cloud-assisted IoT promotes the research of privacy preserving graph computation. We propose a secure graph intersection scheme that supports multi-user intersection queries in cloud-assisted IoT in this article. The existing work on graph encryption for intersection queries is designed for a single user, which will bring high computational and communication costs for data owners, or cause the risk of secret key leaking if directly applied to multi-user scenarios. To solve these problems, we employ the proxy re-encryption (PRE) that transforms the encrypted graph data with a re-encryption key to enable the graph intersection results to be decrypted by an authorized IoT user using their own private key, while data owners only encrypt their graph data on IoT devices once. In our scheme, different IoT users can query for the intersection of graphs flexibly, while data owners do not need to perform encryption operations every time an IoT user makes a query. Theoretical analysis and simulation results demonstrate that the graph intersection scheme in this paper is secure and practical.
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