Reversible Data Hiding (RDH) should be secured as per requirements to protect content in open environments such as the cloud and internet. Integrity and undetectability of steganographic images are amongst the main concerns in any RDH scheme. As steganographic encryption using linear prediction over bit-planes is challenging, so the security and embedding capacity of the existing RDH techniques could not be adequate. Therefore, a new steganographic technique is proposed which provides better security, higher embedding capacity and visual quality to the RDH scheme. In this technique, the cover image is divided into n-bit planes (nBPs) and linear prediction is applied to it. Next, the histogram of the residual nBPs image is taken, and secret data bits are encrypted using the RC4 cryptographic algorithm. To embed the encrypted secret data bits, the histogram shifting process is applied. This is achieved by using peak and zero pairs of residual nBPs images. This scheme provides security to the cover image and hidden data. The proposed RDH scheme is capable of extracting the embedded secret data accurately and recovering the original cover or residual nBPs image.