Auditable $\sigma $ -Time Outsourced Attribute-Based Encryption for Access Control in Cloud Computing

As a sophisticated mechanism for secure fine-grained access control over encrypted data, ciphertext-policy attribute-based encryption (CP-ABE) is one of the highly promising candidates for cloud computing applications. However, there exist two main long-lasting open problems of CP-ABE that may limit its wide deployment in commercial applications. One is that decryption yields expensive pairing cost which often grows with the increase of access policy size. The other is that one is granted access privilege for unlimited times as long as his attribute set satisfies the access policy of a given ciphertext. Such powerful access rights, which are provided by CP-ABE, may be undesirable in real-world applications (e.g., pay-as-you-use). To address the above drawbacks, in this paper, we propose a new notion called <italic>auditable <inline-formula> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula>-time outsourced CP-ABE</italic>, which is believed to be applicable to cloud computing. In our notion, expensive pairing operation incurred by decryption is offloaded to cloud and meanwhile, the correctness of the operation can be audited efficiently. Moreover, the notion provides <inline-formula> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula><italic>-time</italic> <italic>fine-grained access control</italic>. The cloud service provider may limit a particular set of users to enjoy access privilege for at most <inline-formula> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> times within a specified period. As of independent interest, the notion also captures <italic>key-leakage resistance</italic>. The leakage of a user’s decryption key does not help a malicious third party in decrypting the ciphertexts belonging to the user. We design a concrete construction (satisfying our notion) in the key encapsulation mechanism setting based on Rouselakis and Waters (prime order) CP-ABE, and further present security and extensive experimental analysis to highlight the scalability and efficiency of our construction.