Cloud computing, which provides adequate storage and computation capability, has been a prevalent information infrastructure. Secure data sharing is a basic demand when data was outsourced to a cloud server. Attribute-based proxy re-encryption has been a promising approach that allows secure encrypted data sharing on clouds. With attribute-based proxy re-encryption, a delegator can designate a set of shared users through issuing a re-encryption key which will be used by the cloud server to transform the delegator's encrypted data to the shared users'. However, the existing attribute-...