Cloud computing is an effective framework to enable on demand network access for sharing configurable computing resources such as applications, network, servers, services, and storages. Cloud technology offers the users to store and retrieve their data easily in a remote manner. However, privacy and security are considered as the most challenging concerns in cloud data storage. In this paper, a novel Privacy and Security aware Cryptographic Algorithm (PSCA) for data storage is proposed which is based on Invertible Non-linear Function (INF). In proposed technique, the encrypted data is only stored at the cloud storage without key and the encryption is done by the data authorities who also secure the decryption key. The end user has to send request to the data authority and after all verification process the encrypted data is given and with the obtained key and the knowledge of inverse INF the decryption is performed. Thus, both the internal and external attacks are avoided and its detailed analysis is given in the proposed security evaluation. In experimental results, the file size is plotted against encryption time, decryption time, uploading time, and downloading time respectively. The observed results are plotted and the proposed technique is compared with the existing AES and RSA techniques. From the results, it is observed that the proposed PSCA has better performance in terms of reduced time in all four parameters.