Cloud-Based Approximate Constrained Shortest Distance Queries Over Encrypted Graphs With Privacy Protection

Constrained shortest distance (CSD) querying is one of the fundamental graph query primitives, which finds the shortest distance from an origin to a destination in a graph with a constraint that the total cost does not exceed a given threshold. CSD querying has a wide range of applications, such as routing in telecommunications and transportation. With an increasing prevalence of cloud computing paradigm, graph owners desire to outsource their graphs to cloud servers. In order to protect sensitive information, these graphs are usually encrypted before being outsourced to the cloud. This, however, imposes a great challenge to CSD querying over encrypted graphs. Since performing constraint filtering is an intractable task, existing work mainly focuses on unconstrained shortest distance queries. CSD querying over encrypted graphs remains an open research problem. In this paper, we propose Connor, a novel graph encryption scheme that enables approximate CSD querying. Connor is built based on an efficient, tree-based ciphertext comparison protocol, and makes use of symmetric-key primitives and the somewhat homomorphic encryption, making it computationally efficient. Using Connor, a graph owner can first encrypt privacy-sensitive graphs and then outsource them to the cloud server, achieving the necessary privacy without losing the ability of querying. Extensive experiments with real-world data sets demonstrate the effectiveness and efficiency of the proposed graph encryption scheme.

I. Introduction

Recent years have witnessed the prosperity of applications based on graph-structured data [1], [2], such as online social networks, road networks, web graphs [3], biological networks, and communication networks [4], [5]. Consequently, many systems for managing, querying, and analyzing massive graphs have been proposed in both academia (e.g., GraphLab [6], Pregel [7] and TurboGraph [8]) and industry (e.g., Titan, DEX and GraphBase). With the prevalence of cloud computing, graph owners (e.g., enterprises and startups for graph-based services) desire to outsource their graph databases to a cloud server, which raises a great concern regarding privacy. An intuitive way to enhance data privacy is encrypting graphs before outsourcing them to the cloud. This, however, usually comes at the price of inefficiency, because it is quite difficult to perform operations over encrypted graphs.