Geometric Range Searchable Encryption with Forward and Backward Security

Geometric range query is a general query algorithm over spatial data and applies to many real-world applications, such as location-based services. Considering the sensitivity of location information, how to guarantee the confidentiality of the location information while providing efficient query service becomes a big concern. Several cryptographic solutions are proposed to solve this problem, particularly those dynamic searchable encryption schemes with forward and backward privacy that provides strong security guarantees for encrypted spatial databases that support data deletion and addition. Despite the increasing efforts, recent studies show that existing solutions with these two securities either use less secure property-preserving encryption for efficiency and flexibility or intuitively build a binary tree for each dimension, which leads to poor scalability. This paper proposes a novel forward and backward secure geometric range searchable encryption scheme on encrypted spatial data. Specifically, we build a two-level index for first-step rough navigation and second-step precise testing to get accurate search results. Detailed theoretical analysis and experimental evaluation demonstrate that compared with related work, our scheme achieves strong security and sub-linear search efficiency while boosting the average update time by 70 times.