Abstract: To improve the encryption efficiency, the online/offline cryptography was extended to ABE and the primitive of attribute-based online/offline encryption (ABOOE) was proposed. The ABOOE non-trivially splited the encryption process into two phases: the offline phase first executed most of heavy computations prior to knowing the message and the attributes’ set; and then the online phase only performed light computations to produce the ciphertext once the attributes’ set and the message get available. An ABOOE scheme was first constructed with the CPA security. To enhance its security, the primitive of attribute-based online/offline KEM (ABOOKEM) was also introduced and a concrete ABOOKEM scheme was given, and then a generic transformation was proposed to get security against chosen-ciphertext attack (CCA) for ABOOE from any ABOOKEM with one-wayness. This transformation greatly improved the security for ABOOE without increasing the amount of computation. Compared with the famous ABE schemes, the proposed schemes improved the encryption efficiency and get suitable for power-constrained devices.