This paper proposes a novel scheme of reversible data hiding in encrypted images using distributed source coding. After the original image is encrypted by the content owner using a stream cipher, the data-hider compresses a series of selected bits taken from the encrypted image to make room for the secret data. The selected bit series is Slepian-Wolf encoded using low-density parity check codes. On the receiver side, the secret bits can be extracted if the image receiver has the embedding key only. In case the receiver has the encryption key only, he/she can recover the original image approximately with high quality using an image estimation algorithm. If the receiver has both the embedding and encryption keys, he/she can extract the secret data and perfectly recover the original image using the distributed source decoding. The proposed method outperforms the previously published ones.