Analysis of an ABE Scheme with Verifiable Outsourced Decryption

Attribute-based encryption (ABE) is a popular cryptographic technology to protect the security of users' data in cloud computing. In order to reduce its decryption cost, outsourcing the decryption of ciphertexts is an available method, which enables users to outsource a large number of decryption operations to the cloud service provider. To guarantee the correctness of transformed ciphertexts computed by the cloud server via the outsourced decryption, it is necessary to check the correctness of the outsourced decryption to ensure security for the data of users. Recently, Li et al. proposed a full verifiability of the outsourced decryption of ABE scheme (ABE-VOD) for the authorized users and unauthorized users, which can simultaneously check the correctness of the transformed ciphertext for both them. However, in this paper we show that their ABE-VOD scheme cannot obtain the results which they had shown, such as finding out all invalid ciphertexts, and checking the correctness of the transformed ciphertext for the authorized user via checking it for the unauthorized user. We first construct some invalid ciphertexts which can pass the validity checking in the decryption algorithm. That means their "verify-then-decrypt" skill is unavailable. Next, we show that the method to check the validity of the outsourced decryption for the authorized users via checking it for the unauthorized users is not always correct. That is to say, there exist some invalid ciphertexts which can pass the validity checking for the unauthorized user, but cannot pass the validity checking for the authorized user.