Cloud data storage environments allow the data providers to store and share large amounts of datasets generated from various resources. However, outsourcing private data to a cloud server is insecure without an efficient access control strategy. Thus, it is important to protect the data and privacy of user with a fine-grained access control policy. In this article, a Bloom Filter-based Ciphertext-Policy Attribute-Based Encryption (BF-CP-ABE) technique is presented to provide data security to cloud datasets with a Linear Secret Sharing Structure (LSSS) access policy. This fine-grained access control scheme hides the whole attribute set in the ciphertext, whereas in previous CP-ABE methods, the attributes are partially hidden in the ciphertext which in turn leaks private information about the user. Since the attribute set of the BF-CP-ABE technique is hidden, bloom filters are used to identify the authorized users during data decryption. The BF-CP-ABE technique is designed to be selective secure under an Indistinguishable-Chosen Plaintext attack and the simulation results show that the communication overhead is significantly reduced with the adopted LSSS access policy.