Privacy-preserving local clustering coefficient query on structured encrypted graphs

Graphs and graph databases serve as the fundamental building blocks for various network structures. In real-world network scenarios, nodes often aggregate due to their approximate organizational associations with each other. The local clustering coefficient, which evaluates the proximity of nodes within a graph, plays an important role in quantifying the structural properties of graphs in scrutinizing network robustness and understanding its intricate dynamics. Despite the growing popularity of easily accessible cloud services among small and medium-sized enterprises as well as individuals, the potential risk of data privacy disclosure when outsourcing large graphs to third-party servers is increasing. It is vital to explore a technique for executing queries on encrypted graph data. In this paper, we propose a structured encryption scheme to achieve privacy-preserving local clustering coefficient query ($\mathrm{STE}\text{-}\mathrm{CC}$) on the outsourced encrypted graphs. To calculate the clustering coefficient, we design the ${\mathrm{PSI}}_{\mathrm{sum}}$ protocol to sum the number of intersections, in which the basic private set intersection (PSI) protocol combines Bloom filter (BF) and garbled Bloom filter (GBF) to perform the private matching for counting the number of common neighbors. When configured with appropriate parameters, it can achieve no false negatives and negligible false positives. Finally, the security analysis and experimental evaluation on real-world graph data substantiate the effectiveness and efficiency of our approach.