Abstract
With the widespread adoption of cloud computing, it is a popular trend to migrate shortest path and distance (SPD) retrieval on large-scale graphs to cloud environments, harnessing their immense computational capabilities. To protect sensitive information, these graphs are usually encrypted before being outsourced to the cloud. A significant challenge is how to answer SPD retrieval in a secure, efficient, and accurate manner. However, recent works have yet to concurrently tackle all three aspects to meet this challenge. To address this challenge, we design, implement, and evaluate Crypt-Graph, the first scheme simultaneously allowing private, efficient, and accurate retrieval over encrypted graphs. CryptGraph leverages additive homomorphic encryptions to protect graphs and client information. A series of secure protocols are tailored based on the two-cloud (i.e., server) model. Supported by these protocols, Crypt-Graph converts SPD retrieval from the ciphertext domain to both the plaintext (for vertices) and secret-sharing (for weights) domains, achieving access pattern protection and remarkable efficiency close to plain retrieval. The security of CryptGraph is formally analyzed under the semi-honest adversary model. Extensive experiments are conducted on both synthetic and real-world graph datasets, demonstrating millisecond-level efficiency and 100% accuracy rates.