Nowadays, mobile cloud storage has become increasingly prevalent for processing mobile data due to its convenience and resources. Towards the right to restriction of processing in current data regulations, some solutions have been proposed to empower data owners with identity-based hierarchical control for equality, comparison, and plaintext analytics operations. However, existing solutions either rely on specific hardware environments (i.e., trusted execution environments) or face two significant issues: identity privacy breaches, where attackers can identify targeted users, and excessive overhead in multi-user scenarios, as each user requires a distinct ciphertext. In this paper, we leverage multiple cryptographic primitives to introduce PODS, an efficient and secure hierarchical data processing control scheme for multi-user mobile cloud storage. PODS allows the data owner to generate a single ciphertext for multiple users without hardware reliance. Technically, we reconstruct identity-based encryption by leveraging well-designed common and private parameters, thereby shifting the focus from data itself to data processing operations. Then, we encode multiple targeted identities as polynomial coefficients and integrate these coefficients into identity-based data processing control. We achieve threefold benefits, effectively reducing overhead, hierarchically processing users' rights, and concealing the identities of targeted users to protect privacy. Security analysis proves the security of PODS. Experiments demonstrate that PODS achieves around$8\times$and$37\times$improvement in computation and communication compared to existing related works.

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.