Data sharing is a handy and financial provider provided via cloud computing. Data contents privateness additionally emerges from it when you consider that the facts is outsourced to some cloud servers. To shield the precious and touchy information, more than a few methods are used to decorate get admission to manipulate on the shared data. In these techniques, Ciphertext-policy attribute-based encryption (CP-ABE) can make it extra handy and secure. Traditional CP-ABE focuses on information confidentiality merely, whilst the user's non-public privateness safety is an vital trouble at present. CP-ABE with hidden get entry to coverage ensures records confidentiality and ensures that user's privateness is no longer published as well. However, most of the present schemes are inefficient in verbal exchange overhead and computation cost. Moreover, most of these works take no consideration about authority verification or the hassle of privateness leakage in authority verification phase. To handle the troubles stated above, a privateness maintaining CP-ABE scheme with environment friendly authority verification is delivered in this paper. Additionally, the secret keys of it acquire consistent size. Meanwhile, the proposed scheme achieves the selective safety underneath the decisional n-BDHE trouble and decisional linear assumption. The computational effects affirm the deserves of the introduced scheme.