MU-MRQ: Enabling Multi-User Verifiable and Secure Multi-Dimensional Range Query Over Encrypted Data

In recent years, multi-dimensional range query (MRQ) over encrypted data has been increasingly applied in various scenarios, making it one of the mainstream services for secure large-scale data storage and sharing in cloud computing. However, although existing privacy-preserving MRQ schemes can ensure query and data privacy, they still fail to fully protect single-dimensional privacy and path pattern. Moreover, most schemes lack mechanisms to verify the completeness and correctness of query results, making it impossible to guarantee their validity. To address these issues, this paper proposes a secure and efficient MRQ scheme with result verification for multiple users (MU-MRQ). First, we design a secure and efficient multi-dimensional data index based on the G-tree, incorporating a timestamp mechanism to verify the correctness and completeness of query results. Additionally, we propose two novel intersection predicate encryption protocols to achieve efficient retrieval while preserving single-dimensional privacy and path pattern. Rigorous security analysis demonstrates that our MU-MRQ scheme achieves security under the known background model. Comprehensive experiments on real-world datasets validate the efficiency of the MU-MRQ scheme.