The existing outsourcing algorithms for modular exponentiations has some problems such as low security

low probability of validation and wrong calculation results. a CP-ABE (Ciphertext-Policy Attribute-Based Encryption) scheme with verifiable outsourced encryption and decryption is proposed with the help of the improved algorithm for secure outsourcing of modular exponentiations. The scheme outsources attribute-related key subitems

outsources half of the computing tasks of shared ciphertext subitems

and verifies all the outsourced results. Theoretical and experimental analysis show that compared with the existing related schemes

both in key generation and encryption

the computing overhead of both authority centers and user clients of the proposed scheme has been significantly reduced. Security analysis shows that the proposed scheme can defend against chosen plaintext attacks.