SecGDB: Graph Encryption for Exact Shortest Distance Queries with E cient Updates

In the era of big data, graph databases have become increasingly important for NoSQL technologies, and many systems (e.g., online social networks, world-wide web and electrical grids, etc.) can be modeled as graphs for semantic queries. Meanwhile, with the advent of cloud computing, data owners are highly motivated to outsource and store their massive potentially-sensitive graph data on remote untrusted servers in an encrypted form, expecting to retain the ability to query over the encrypted graphs. To allow e↵ective and private queries over encrypted data, the most wellstudied class of structured encryption schemes are searchable symmetric encryption (SSE) designs, which encrypt search structures (e.g., inverted indexes based on keyword-file pairs) for retrieving data files of interest from remote servers. So far, however, the problem of graph data encryption that supports customized queries has received limited attention in the literature. In this paper, we tackle the challenge of designing a Secure Graph DataBase encryption scheme (SecGDB) to encrypt graph structures and enforce private graph queries over the encrypted graph database. Specifically, our construction strategically makes use of e cient additively homomorphic encryption and garbled circuits to support the shortest distance queries with optimal time and storage complexities. To achieve better amortized time complexity over multiple queries, we further propose an auxiliary data structure called query history and store it on the remote server to act as a “caching” resource. Compared with the state-of-the-art solutions, our design returns exact shortest distance query results instead of approximate ones and allows e cient graph update queries over large-scale encrypted graphs. We prove that our construction is adaptively semantically-secure in the random oracle model and finally implement and evaluate it on various representative real-world datasets, showing that our approach is practically e cient in terms of both storage and computation.