Enabling Privacy-Preserving K-hop Reachability Query over Encrypted Graphs

K-hop Reachability Query (KRQ) is one of fundamental graph queries, which can answer whether a node u can reach a node v within K hops. With the scale of graph data increasing, data owner desires to outsource the local graphs to cloud server. To protect the graph privacy, data owner encrypts graphs before outsourcing them to the cloud server. It imposes a great challenge to KRQ over encrypted graphs. How to realize Privacy-Preserving K-hop Reachability Query (PPKRQ) over encrypted graphs is still an unexplored problem. In this paper, we explore this problem and propose a practical scheme. In order to efficiently answer KRQ over encrypted graphs, we construct the encrypted Breadth-First Spanning Tree table and adjacent list D (BFST-D). Based on encrypted BFST table, we can directly judge whether two query nodes are reachable within K hops when they are in one spanning tree. The encrypted adjacent list D can help answer that two query nodes in different spanning trees. To protect the privacy, we utilize the Paillier cryptographic and Order-Revealing Encryption (ORE) to support the comparison and computation over ciphertexts. As a result, our scheme achieves the sensitive information privacy without losing the ability of querying over encrypted graphs. The security analysis shows that our proposed scheme is secure based on semi-honest cloud server. The extensive experiments show the efficiency of our scheme.