To ensure the security of digital information, information needs to be stored and processed in the encryption domain during the cloud storage process, during which the user does not allow the cloud provider (CP) to access the image contents, and the CP must embed additional information in the image. Therefore, reversible data hiding in an encryption domain (RDHEI) has emerged. This paper presents an adaptive and separable multiary RDHEI method. First, the image is divided into two parts that consist of reference pixels and non-reference pixels. Next, we compute the prediction errors of the non-reference pixels, followed by a replacement of the original non-reference values with the computed prediction errors. Then, the entire image is encrypted with a specially designed stream cipher strategy so that the CP can embed additional information by modifying the prediction errors without knowing the original image. In addition, although our method vacates space before encryption, the CP can adaptively control the reserved space, unlike traditional RDHEI schemes which also vacate space before encryption. Because our method is separable, the embedded message can be extracted from both encryption and plaintext domains accurately. The experimental results demonstrate the efficacy of the proposed method.