Reversible data hiding in encrypted image (RDHEI) is advantageous to scenarios where complete recovery of the original cover image and additional data are required. In some of the existing RDHEI schemes, the image pre-processing step involved is an overhead for the resource-constrained devices on the sender’s side. In this paper, an efficient separable reversible data hiding scheme over a homomorphically encrypted image that assures privacy preservation of the contents in the cloud environment is proposed. This proposed scheme comprises three stakeholders: content-owner, data hider, and receiver. Initially, the content-owner encrypts the original image and sends the encrypted image to the data hider. The data hider embeds the encrypted additional data into the encrypted image and then sends the marked encrypted image to the receiver. On the receiver’s side, both additional data and the original image are extracted in a separable manner, i.e., additional data and the original image are extracted independently and completely from the marked encrypted image. The present scheme uses public key cryptography and facilitates the encryption of the original image on the content-owner side, without any pre-processing step involved. In addition, our experiment used distinct images to demonstrate the image-independency and the obtained results show high embedding rate where the peak signal noise ratio (PSNR) is +∞ dB for the directly decrypted image. Finally, a comparison is drawn, which shows that the proposed scheme is an optimized approach for resource-constrained devices as it omits the image pre-processing step.