PMkR: Privacy-preserving multi-keyword top-k reachability query

Privacy-preserving reachability query can determine whether one vertex is reachable from another vertex, which is applied in many domains. Due to the growing size of graphs, more and more users upload blinded graphs to the cloud, which can reduce the computation and storage burden for users. While privacy-preserving reachability query schemes have been proposed, they do not consider the keyword information in vertices. In this paper, we propose a privacy-preserving multi-keyword top-$k$ reachability query scheme (PM$k$R), which can find $k$ vertices nearest to the source vertex, and containing the given keywords. In order to achieve the multi-keyword reachability query, we build the secure indexes based on the 2-hop labeling and the balanced binary tree. The 2-hop labeling index can help quickly determine whether two vertices are reachable and the distance between them. We convert the inclusion relationship between vertices and keywords into vectors, and store in the tree index. We use the secure Euclidean distance calculation to protect data privacy, which can judge whether the vertices contain the query keywords by secure inner product computation. To avoid the cloud learning the correspondence between vertices in the tree index and 2-hop index, we perform two-layer blinding on the vertices. The security analysis and extensive experiments on real-world datasets show that our scheme is secure and efficient.