Reversible Data Hiding in Encrypted Images Based on Chinese Remainder Theorem

To deal with the development of the distributed server, this article proposes a new method for reversible data hiding in encrypted images based on the Chinese Remainder Theorem (CRT), encrypting and sharing one image to multiple data hiders through $(k,n)$-threshold secret sharing. First, an original image is divided into the most significant bit (MSB) compression area and the least significant bit (LSB) area by utilizing the spatial correlation. The $l$-MSB layers are predicted to obtain prediction errors, and these prediction errors are compressed by Huffman coding. Then according to the value of $k$, CRT and secret sharing scheme are performed on the $(8-l)$-LSB layers to generate the shared bitstream. Finally, $n$ encrypted images for sharing consist of MSB compression bitstreams and shared bitstreams, whose size is adjusted based on $k$ value. Each data hider can independently embed secret data after having one of the encrypted images, while the receiver can recover the original image only after receiving $k$ or more encrypted images. Experimental results show that the proposed algorithm not only provides a large embedding space for secret data, but is also able to complete the inverse operation of data hiding and realize the lossless recovery of the original image with $(k,n)$-threshold secret sharing.