Hierarchical Identity-Based Encryption with Tight Multi-challenge Security

Abstract

We construct the first hierarchical identity-based encryption (HIBE) scheme with tight adaptive security in the multi-challenge setting, where adversaries are allowed to ask for ciphertexts for multiple adaptively chosen identities. Technically, we develop a novel technique that can tightly introduce randomness into user secret keys for hierarchical identities in the multi-challenge setting, which cannot be easily achieved by the existing techniques for tightly multi-challenge secure IBE. In contrast to the previous constructions, the security of our scheme is independent of the number of user secret key queries and that of challenge ciphertext queries. We prove the tight security of our scheme based on the Matrix Decisional Diffie-Hellman Assumption, which is an abstraction of standard and simple decisional Diffie-Hellman assumptions, such as the k-Linear and SXDH assumptions. Finally, we also extend our ideas to achieve tight chosen-ciphertext security and anonymity, respectively. These security notions for HIBE have not been tightly achieved in the multi-challenge setting before.