International Association for Cryptologic Research
Proving security of Hierarchical Identity-Based Encryption (HIBE) and attribution based encryption scheme is a challenging problem. There are multiple well-known schemes in the literature where the best known (adaptive) security proofs degrade exponentially in the maximum hierarchy depth. However, the authors do not have a rigorous understanding of why better proofs are not known. (For ABE, the analog of hierarchy depth is the maximum number of attributes used in a ciphertext). In this paper, they define a certain commonly found checkability property on ciphertexts and private keys. Roughly the property states that any two different private keys that are both \"Supposed to\" decrypt a ciphertext will decrypt it to the same message.