Efficient Ciphertext Policy Attribute-Based Encryption with Constant-Size Ciphertext and Constant Computation-Cost

Attribute-based encryption provides good solutions to the problem of anonymous access control by specifying access policies among private keys or ciphertexts over encrypted data. In ciphertext-policy attribute-based encryption (CP-ABE), each user is associated with a set of attributes, and data is encrypted with access structures on attributes. A user is able to decrypt a ciphertext if and only if his attributes satisfy the ciphertext access structure. CF-ABE is very appealing since the ciphertext and data access policies are integrated together in a natural and effective way. Most current CF-ABE schemes incur large ciphertext size and computation costs in the encryption and decryption operations which depend at least linearly on the number of attributes involved in the access policy. In this paper, we present two new CF-ABE schemes, which have both constant-size ciphertext and constant computation costs for a non-monotone AND gate access policy, under chosen plaintext and chosen ciphertext attacks. The security of first scheme can be proven CPA-secure in standard model under the decision n-BDHE assumption. And the security of second scheme can be proven CCA-secure in standard model under the decision n-BDHE assumption and the existence of collision-resistant hash functions. Our scheme can also be extended to the decentralizing multi-authority setting.