VTRQ: Enabling Verifiable Trajectory Range Queries in Hybrid-Storage Blockchains

Due to their increasingly large volumes, outsourcing of trajectory storage and querying to third-party service providers has become attractive. However, in such outsourced environments, service providers may return incorrect, e.g., incomplete, tampered, or invalid query results, making verifiability of query results an important consideration. Existing hybrid-storage blockchains offer limited support for trajectory data, lacking authenticated data structures (ADS) that enable efficient verification. For example, ADSs designed for queries on one-dimensional data are unsuitable for queries on multidimensional trajectory data, while ADSs tailored for discrete data may yield incomplete results when applied to continuous trajectory data. We propose the first framework for verifiable trajectory range queries in hybrid-storage blockchains, called VTRQ. It features two efficient ADSs: (i) a spatial ADS for road networks that leverages hierarchical organization to aggregate trajectory, edge, and node hashes, thus reducing redundant computations and improving spatial verification efficiency; and (ii) a temporal ADS based on interval trees, which indexes only the start and end times of trajectories, thereby enabling pruning and efficient temporal verification. By separating spatial and temporal indexing, the method reduces the need for data comparison, enhancing both query and verification efficiency. To aggregate spatial and temporal query results, VTRQ provides a spatio-temporal edge aggregation mechanism that combines temporal verification of spatial nodes, spatial intersection computation, and temporal intersection analysis to achieve spatio-temporal filtering.