Backward Private Graph Searchable Encryption Supporting Exact Shortest Distance Query

Graph searchable encryption (GSE) ensures privacy protection for graphs while maintaining search functionality. A key aspect of GSE is exact shortest distance search, which identifies the closest relation between nodes in an encrypted graph. However, even minimal leakage from updates and queries can be exploited by attackers to infer the database or query content. Current GSE schemes supporting exact shortest distance queries overlook the potential information leakage from frequent relationship changes, particularly edge deletions, which compromise data privacy. This paper introduces the concept of backward privacy in GSE and formalizes three types of backward privacy (type-I, type-II, and type-III), a novel contribution. We then propose two backward-private GSE schemes, Bayonet and Baccarat. Bayonet offers fine-grained control over data decryption with type-III backward privacy, while Baccarat enhances type-II backward privacy by delegating edge deletion to a non-collusive proxy. We provide formal security proofs for both schemes and evaluate their efficiency on ten real-world graph datasets. Experimental results show that Bayonet sacrifices server storage and computational overhead for type-III backward privacy, while Baccarat achieves higher security and matches the query efficiency of the state-of-the-art GSE scheme with only forward privacy, incurring minimal proxy storage and computational costs.