Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove that there is no fully black-box construction of collision-resistant hash functions CRH from hierarchical identity-based encryption HIBE with arbitrary polynomial number of identity levels. To the best of our knowledge this is the first limitation proved for HIBE. As a corollary,  obtain a series of separations that are not directly about HIBE or CRH but are interesting on their own right. Namely,  show that primitives such as IBE and CCA-secure public-key encryption cannot be used in a black-box way to construct fully homomorphic encryption or any primitive that implies CRH in a black-box way.#R##N##R##N#Our proof relies on the reconstruction paradigm of Gennaro and Trevisan FOCS 2000 and Haitner eti¾?al. FOCS 2007 and extends their techniques for one-way and trapdoor permutations to the setting of HIBE. A main technical challenge in the proof of our separation stems from the adaptivity of the HIBE adversary who is allod to obtain keys for different identities before she selects the attacked identity. Our main technical contribution is to develop compression/reconstruction techniques that can be achieved relative to such adaptive attackers.
['Mohammad Mahmoody', 'Ameer Mohammed']
I am writing a research paper on a idea On the Power of Hierarchical Identity-Based Encryption
[{"from": "human", "value": "I am writing a research paper on a idea On the Power of Hierarchical Identity-Based Encryption"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove that there is no fully black-box construction of collision-resistant hash functions CRH from hierarchical identity-based encryption HIBE with arbitrary polynomial number of identity levels. To the best of our knowledge this is the first limitation proved for HIBE. As a corollary,  obtain a series of separations that are not directly about HIBE or CRH but are interesting on their own right. Namely,  show that primitives such as IBE and CCA-secure public-key encryption cannot be used in a black-box way to construct fully homomorphic encryption or any primitive that implies CRH in a black-box way.#R##N##R##N#Our proof relies on the reconstruction paradigm of Gennaro and Trevisan FOCS 2000 and Haitner eti\u00be?al. FOCS 2007 and extends their techniques for one-way and trapdoor permutations to the setting of HIBE. A main technical challenge in the proof of our separation stems from the adaptivity of the HIBE adversary who is allod to obtain keys for different identities before she selects the attacked identity. Our main technical contribution is to develop compression/reconstruction techniques that can be achieved relative to such adaptive attackers."}]