Reversible Data Hiding in Encrypted Images Based on Chinese Remainder Theorem

To deal with the development of the distributed server, this paper 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(k,n)$</tex-math></inline-formula>-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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l$</tex-math></inline-formula>-MSB layers are predicted to obtain prediction errors, and these prediction errors are compressed by Huffman coding. Then according to the value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>, CRT and secret sharing scheme are performed on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(8-l)$</tex-math></inline-formula>-LSB layers to generate the shared bitstream. Finally, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> encrypted images for sharing consist of MSB compression bitstreams and shared bitstreams, whose size is adjusted based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(k,n)$</tex-math></inline-formula>-threshold secret sharing.