Security analysis for a ciphertext-policy attribute-based encryption scheme

In the ciphertext-policy ABE (CP-ABE) schemes, attributes are associated with secret keys and access structures are associated with ciphertexts. The access structures are described with the attributes and therefore the concept of CP-ABE is closely related to Role-Based Access Control. Because it requires both of the encryptor and the key generalization center meeting the construction, it will be more difficult to design. Ibraimi et al.[7] allegedly proposed an efficient and provable secure CP-ABE schemes. They require that the simulator can not send back the private keys of attributes which overlap with challenging access attributes. We point out their fault of security proof and their requirement is a small probability event and it is unreasonable to reduce to standard DBDH assumption. However, we give a proof in the generic bilinear group model, which is weaker than DBDH assumption.