Abstract
Attribute-Based Encryption (ABE) plays an important role in current secure data sharing through fine-grained customizable policies. However, the existing ABE schemes only support simple predicates, = and ≠, but cannot express a more general membership predicates, ∈ and ∉, in policies. The low expressivity of ABE will enlarge the ciphertext storage and reduce the communication efficiency. To overcome this problem, we propose an ABE supporting Dual Membership (DM-ABE). The core problem for implementing this scheme is how to use cryptographic methods to decide the membership between the verified element and the given set. In order to solve this problem, we design a cryptographic algorithm, called Secure Decision of Membership (SDM), based on aggregation functions. In this algorithm, any set can be aggregated into one cryptographic element, and the verified element and the given set can be converted into another cryptographic element in decision process. The membership between them can be decided by the above two cryptographic elements. Furthermore, we construct the DM-ABE by using SDM. Because of the good expressivity of our DM-ABE, we further propose a novel cryptographic data sharing framework by integrating DM-ABE and attribute-based access control to provide fine-grained access control and security protection for private data. In the security proof of DM-ABE, we prove that the DM-ABE satisfies the semantic security against chosen-plaintext attacks under the DBDHE assumption in the standard model through a unified way, considering both two encryption methods for ∈ and ∉ at the same time. Finally, we analyze our scheme in terms of time and space complexity, and compare it with some existing schemes. The results show that our DM-ABE has a better expressive ability on the boolean logic of general membership predicates, ∈ and ∉.