A reserving room before encryption (RRBE) framework is proposed to provide separable reversible data hiding for encrypted images in this paper. A combination of Interpolative AMBTC and Huffman coding is used to enhance the hiding capacity. In our scheme, a receiver with only the hiding key can extract the secret data without knowing about the content. If the receiver has only the encryption key, it is not possible to extract the hidden secret data, but it is possible to decrypt an image similar to the original image. Only when the receiver has both the hiding key and the encryption key, it is possible to extract the secret data and completely recover the original content without any error. The experimental results demonstrated the efficiency of our proposed high payload reversible data hiding scheme for encrypted images (HP-RDHEI), especially with respect to the data embedding rate.