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Proxy re-encryption (PRE) allows a ciphertext computed under Alice's public key to be transformed to those which can be decrypted by Bob. In PKC'08, Libert and Vergnaud proposed the first unidirectional RCCA-secure PRE scheme in the standard model. They left the open problem of constructing unidirectional CCA-secure PRE scheme in the standard model open. Until recently, this open problem was solved by Weng et al. and Shao et al. independently. In this paper, based on Shao et al.'s proposal, we give a new efficient CCA-secure PRE scheme without random oracles and prove its security.