Abstract:

This paper investigates a Hierarchical Identity Based Encryption (HIBE) scheme, with emphasis on the construction of D. Cash, D. Hofheinz, E. Kiltz, and Ch. Peikert. The scheme is founded on q-ary lattices and its security relies on the hardness of the Learning With Errors (LWE) problem, which is regarded as resistant to all known quantum algorithms. We propose a modified variant of the original design and provide a formal security analysis in the random oracle model, confirming that the modification preserves its theoretical guarantees. The central contribution of the study, however, lies in the implementation. We evaluate the scheme with respect to correctness, execution time, and computational overhead, offering a concrete assessment of its efficiency and scalability. The results show that the modified scheme combines post-quantum security with practical performance, making it a compelling candidate for applications that require hierarchical key management in a quantum aware environment.