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Attributed-based encryption (ABE) is a promising cryptographic access control mechanism with a rich expressiveness of ABE policies. Due to the high complexities of encryption and decryption, users are burdened with large computation cost. Fortunately, outsourcing technologies can be used to reduce the computation overhead for the ABE schemes. In the recent decade, the achievements of the outsourced ciphertext-policy ABE (CP-ABE) schemes are inspiring. But, the outsourcing encryption algorithms for CP-ABE schemes are not addressed properly since the encryption exponents are dynamic. In this paper, we present an efficient outsourced CP-ABE scheme with checkability, where the number of the exponential operations in the encryption can be reduced to a constant by introducing a blinding algorithm. Meanwhile, the ciphertext size is not increased. Furthermore, to guarantee the correctness of our scheme, we provide the verification mechanism based on a collision-resistance hash function, which allows the users to efficiently check the validity of messages and outsourced computation results. Besides, the proposed scheme is secure against replayable chosen ciphertext attacks based on Green’s outsourcing security model. Intensive experiments are carried out to illustrate the efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]