The burgeoning complexity of communication necessitates a high demand for security. Access control encryption is a promising primitive to meet the security demand but the bulk of its constructions rely on formulating the access control policy with identities. Attribute-based access control policy in attribute-based encryption (ABE) is known to be more expressive without relying on enumerating identities. We propose a generic framework to build attribute-based access control encryption from ciphertext-policy ABE. Our instantiations prioritize different emphases on expressiveness and efficiency. The first instantiation supports multi-valued AND-gate access control structures, while the second supports the linear-secret-sharing access structure. Both are prototyped with efficiency validated empirically.