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Published in:
2014 | OriginalPaper | Chapter
Why Proving HIBE Systems Secure Is Difficult
Authors : Allison Lewko, Brent Waters
Published in: Advances in Cryptology – EUROCRYPT 2014
Publisher: Springer Berlin Heidelberg
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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, we 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 work, we 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. We show that any simple black box reduction to a non-interactive assumption for a HIBE or ABE system that contains this property will suffer an exponential degradation of security.