The Encrypted Image Reversible Data Hiding (EIRDH) is a hot area of research in multimedia outsourcing scenarios. In such a setting, a content owner possesses confidential images that he wants to upload to an untrusted server. The server is supposed to embed a secret message in the images before sending them to potential receivers, and the receivers expect to recover the original images without any distortion. EIRDH schemes are designed to meet reversible data hiding goals while preserving the confidentiality of the host images. Confidentiality is provided by means of encryption algorithms; however, these algorithms, in turn, introduce the challenge of dealing with ciphered images in both embedding and extraction phases. The current paper tries to propose a privacy-preserving reversible data hiding scheme for JPEG images without the need for any levels of decompression. We propose an elliptic curve-based asymmetric, commutative, and separable EIRDH method, in which no entities other than the sender and the eligible receiver of the hidden message (embedded in the encrypted image) are able to recognize its existence. In particular, even the server that performs the embedding remains completely unaware of the content of the images. An important security feature of our scheme involves the security of its multiple encryptions against Chosen-Plaintext Attack (CPA), which is an attack model that assumes the adversary can obtain the encryptions of the images on his choice to achieve possible extra information to attack. Experimental results show that our scheme achieves full reversibility and a satisfactory level of capacity, while it accurately extracts all the hidden bits.