Reliable access control is a major challenge of cloud storage services. This paper presents a cloud-based file-sharing architecture with ciphertext-policy Attribute-based encryption (CP-ABE) access control mechanism. In CP-ABE, the data owner can specify the ciphertext access structure, and if the user key satisfies this access structure, the user can decrypt the ciphertext. The trusted authority embeds the private key of each Attribute in a so-called Attribute access polynomial and stores its coefficients publicly on the cloud. By means of the access polynomial, each authorized user will be able to retrieve the private key of the Attribute by using her/his owned pre-shard key. In contrast, the data owner encrypts the file with a randomly selected key, namely the cipher key. The data owner encrypts the cipher key by CP-ABE scheme with the desired policies. Further, the data owner can create a different polynomial called query access polynomial for multi-keyword searching. Finally, the data owner places the encrypted file along the encrypted cipher key and query access polynomial in the cloud. The proposed scheme supports fast Attribute Revocation using updating the corresponding access polynomial and re-encrypting the affected cipher keys by the cloud server. Moreover, most of the calculations at the decryption and searching phases are outsourced to the cloud server, thereby allowing the lightweight nodes with limited resources to act as data users. Our analysis shows that the proposed scheme is both secure and efficient.