Cloud computing is one term that has evolved drastically over the years. It involves deploying groups of remote servers and software that are networked, that will allow centralised data storage and online access to computer services or resources. However, an important problem in public clouds is how to selectively share data based on fine-grained attribute-based access control policies while at the same time assuring confidentiality of the data and preserving the privacy of users from the cloud. Keeping in mind the confidentiality of data that must be provided, many schemes and encryption algorithms have been implemented, but most of those schemes have high computational costs and overload on the data owner. In this paper, we are proposing a hierarchy-based privacy preserving access control scheme, in which data is encrypted and decrypted by the cloud using the blinded encryption and decryption technique that retains the constant computation cost to the owner and the user for any large file size, thus it makes our scheme suitable for energy deficient devices. The experimental result shows that our scheme is more suitable for energy deficient devices without compromising the security of data. Copyright © 2017 Inderscience Enterprises Ltd.