Here, we describe a new method for reversible data hiding in encrypted images (RDHEI) that aims to improve the embedding capacity (EC) and visual quality of the stego image. Most of the existing techniques for RDHEI need location maps to discriminate embedded and non-embedded pixels, which increases computational overhead and affects EC. The proposed method reserves room after encryption and converts prediction errors (PE) to odd and even numbers to discriminate between embedded and non-embedded pixels. This avoids the computational overhead caused by the use of a location map. The proposed scheme also employs double-layer encryption using random permutation and a stream cipher to secure the cover images. The method is separable, which means that the secret data and cover image can be independently extracted and recovered, depending on the availability of the data hiding and decryption keys. The scheme uses block-wise reference pixels for the calculation of PE, that enhances the EC. Experimental results indicate that the proposed scheme is more effective than existing state-of-the-art works.