Privacy-Preserving Any-Hop Cover Shortest Distance Queries on Encrypted Graphs

Graphs are an essential data representation method and are widely used in many scenarios. Shortest distance query is one of the most fundamental operations on a graph and has thus attracted much research attention. While various graph encryption schemes supporting shortest distance query have been proposed, there remain considerable challenges, such as information leakage, approximate query results, and large computational errors. Furthermore, existing schemes can only address 2-hop cover shortest distance queries on encrypted graphs and do not allow shortest distance queries by others. Therefore, only the graph owner (GO) can query the shortest distance based on encrypted data. To overcome these limitations, we propose a privacy-preserving any-hop cover shortest distance query scheme on encrypted graphs, called AHCSDQ. Matrices are used to compute any-hop cover shortest distance (AHCSD) between any two vertices. Our scheme preprocesses graph data and store the preprocessed results in a server, and query users can retrieve the corresponding encoding value from the appropriate matrix. This scheme enable accurate AHCSD queries while protecting graph data privacy. In addition, the GO only needs to preprocess graph data once, and the preprocessing result can be provided to multiple users for multiple queries. Furthermore, a single shortest distance query only needs the query user one encryption operation, also significantly reduces the computational cost for query users. In this article, we establish the security of our proposed scheme using a widely accepted simulation paradigm and present experimental results to demonstrate the high efficiency of scheme.