VSpatial: Enabling Private and Verifiable Spatial Keyword-based Positioning in 6G-oriented IoT

For increasing Internet of Things (IoT) devices, 6G wireless technology aims for ubiquitous communications in which positioning services are necessary. Private spatial keyword-based positioning service is promising in 6G-oriented IoT since it positions users based on spatial locations and textual keywords while protecting user privacy. However, due to economic benefits or malicious attacks, positioning service providers may return erroneous or incomplete results, which cause tremendous economic damage and security threats, e.g., always assigning a selective driver for the specific car-hailing user. A technical challenge for extending existing private schemes to enable users to verify the correctness and completeness of positioning results is the distinctive positioning paradigm between compared spatial locations and matched textual keywords. This paper proposes a private and verifiable spatial keyword positioning scheme named VSpatial in 6G-oriented IoT. VSpatial enables users to verify the correctness and completeness of spatial keyword-based positioning results while preserving user privacy. The main inspiration for addressing the technical challenge is converting both spatial locations and textual keywords into an internal status, i.e., adapting comparison and matching to existence judging by multiple cryptographic tools, such as hierarchical cube and pseudorandom function. Based on this inspiration, we design a novel private authenticated data structure (named PVTree), and then propose two constructions of VSpatial, i.e., VSpatial-S and VSpatial-D, to suit static and dynamic environments, respectively. The core idea for adapting VSpatial-S to VSpatial-D is transferring one whole PVTree into multiple exponential-size partitions. Security analysis proves the security and verifiability of VSpatial. Theoretical and experimental evaluations show that VSpatial achieves faster-than-linear positioning efficiency and linear verification overhead.