Private Ciphertext-Policy Attribute-based Encryption Schemes With Constant-Size Ciphertext Supporting CNF Access Policy

Attribute-based encryption (ABE) is an extension of traditional public key encryption in which the encryption and decryption phases are based on user’s attributes. More precisely, we focus on ciphertext-policy ABE (CP-ABE) where the secret-key is associated to a set of attributes and the ciphertext is generated with an access policy. It then becomes feasible to decrypt a ciphertext only if one’s attributes satisfy the used access policy. In this paper, we give the first private CP-ABE constructions with a constant-size ciphertext, supporting CNF (Conjunctive Normal Form) access policy, with the simple restriction that each attribute can only appear kmax times in the access formula. Our two constructions are based on the BGW scheme at Crypto’05. The first scheme is basic selective secure (in the standard model) while our second one reaches the selective CCA security (in the random oracle model).