Improving the proof of "Privacy-preserving attribute-keyword based data publish-subscribe service on cloud platforms"

Most recently, Kan Yang et al. proposed an attribute-keyword based encryption scheme for data publish-subscribe service(AKPS), which is highly useful for cloud storage scenario. Unfortunately, we discover that there is a flaw in the security proof of indistinguishability of the tag and trapdoor against chosen keyword attack under the Bilinear Diffie-Hellman (BDH) assumption. As the security proof is a key component for a cryptographic scheme, based on the Decisional Diffie-Hellman (DDH) assumption, we improve the security proof method and give a new security proof of the AKPS scheme for indistinguishability of the tag and trapdoor in our proposal, which is more rigorous than the original one. Furthermore, we also demonstrate that the AKPS scheme is secure against data Replayable Chosen Ciphertext Attack (RCCA).