We propose separable reversible data hiding in an encrypted signal with public key cryptography. In our separable framework, the image owner encrypts the original image by using a public key. On receipt of the encrypted signal, the data-hider embeds data in it by using a data-hiding key. The image decryption and data extraction are independent and separable at the receiver side. Even though the receiver, who has only the data-hiding key, does not learn about the decrypted content, he can extract data from the received marked encrypted signal. However, the receiver who has only the private key cannot extract the embedded data, but he can directly decrypt the received marked encrypted signal to obtain the original image without any error. Compared with other schemes using a cipher stream to encrypt the image, the proposed scheme is more appropriate for cloud services without degrading the security level.