Cryptanalysis of Two Efficient HIBE Schemes in the Standard Model

In Informatica 32 (2008), Ren and Gu proposed an anonymous hierarchical identity based encryption scheme based on the q-ABDHE problem with full security in the standard model. Later in Indocrypt’08, they proposed another secure hierarchical identity based encryption scheme based on the q-TBDHE problem with full security in the standard model. They claimed that their schemes have short parameters, high efficiency and tight reduction. However, in this paper we give attacks to show their schemes are not secure at all. Concretely, from any first level private key, the adversary can easily derive a “private key” which can decrypt any ciphertexts for the target identity. That is to say, a query on any first level identity is enough to decrypt any ciphertext in the system.