A Hierarchical Key Assignment Scheme: A Unified Approach for Scalability and Efficiency

This study introduces a hierarchical key assignment scheme (HKAS) based on the closest vector problem in an inner product space (CVP-IPS). The proposed scheme offers a comprehensive solution with scalability, flexibility, cost-effectiveness, and high performance. The key features of the scheme include CVP-IPS based construction, the utilization of two public keys by the scheme, a distinct basis set designated for each class, a direct access scheme to enhance user convenience, and a rigorous mathematical and algorithmic presentation of all processes. This scheme eliminates the need for top-down structures and offers a significant benefit in that the lengths of the basis sets defined for classes are the same and the costs associated with key derivation are the same for all classes, unlike top-down approaches, where the higher class in the hierarchy generally incurs much higher costs. The scheme excels in both vertical and horizontal scalability due to its utilization of the access graph and is formally proven to achieve strong key indistinguishability security (S-KI-security). This research represents a significant advancement in HKAS systems, providing tangible benefits and improved security for a wide range of use cases.