A Reversible Data Hiding Scheme in Encrypted Domain for Secret Image Sharing Based on Chinese Remainder Theorem

Abstract

Schemes of reversible data hiding in encrypted domain (RDH-ED) based on symmetric or public key encryption are mainly applied in the scenarios of end-to-end communication. To provide security guarantees for the multi-party scenarios, a RDH-ED scheme for secret image sharing based on Chinese remainder theorem (CRT) is presented. In the application of (<inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>) secret image sharing, an image is first shared into <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> different shares of ciphertext. Only when not less than <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> shares obtained, can the image be reconstructed. In our scheme, additional data could be embedded into the image shares. To realize data extraction from the image shares and the reconstructed image separably, two data hiding methods are proposed: one is homomorphic difference expansion in encrypted domain (HDE-ED) that supports data extraction from the reconstructed image by utilizing the addition homomorphism of CRT secret sharing; the other is difference expansion in image shares (DE-IS) that supports the data extraction from the marked shares before image reconstruction. Experimental results demonstrate that the proposed scheme could not only maintain the security and the threshold function of secret sharing system, but also obtain a better reversibility and efficiency compared with most existing RDH-ED algorithms. The maximum embedding rate of HDE-ED could reach 0.500 bits per pixel and the average embedding rate of DE-IS could reach 0.4652 bits per pixel.