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In ciphertext policy attribute-based encryption (CP-ABE), every secret key is associated with a set of attributes, and every ciphertext is associated with an access structure on attributes. Decryption is enabled if and only if the user's attribute set satisfies the ciphertext access structure. This provides fine-grained access control on shared data in many practical settings, e.g., secure database and IP multicast.
Cheung et al. (Sun,) studied this question.