A Reversible Data hiding Scheme in Encrypted Domain for Secret Image Sharing based on Chinese Remainder Theorem

TL;DR

This paper proposes a reversible data hiding scheme in encrypted domain for secret image sharing using Chinese Remainder Theorem, enabling secure, efficient, and reversible embedding of additional data in multi-party image sharing systems.

Contribution

It introduces a novel CRT-based secret image sharing scheme with two data hiding methods supporting separable data extraction, improving reversibility and efficiency over existing algorithms.

Findings

Maximum embedding rate of 0.5 bits per pixel for HDE-ED

Average embedding rate of 0.0545 bits per bit of ciphertext for DE-IS

Maintains security and threshold function of secret sharing system

Abstract

Reversible data hiding in encrypted domain (RDH-ED) schemes based on symmetric or public key encryption are mainly applied to the security of end-to-end communication. Aimed at providing reliable technical supports for multi-party security scenarios, a separable RDH-ED scheme for secret image sharing based on Chinese remainder theorem (CRT) is presented. In the application of (t, n) secret image sharing, the image is first shared into n different shares of ciphertext. Only when not less than t shares obtained, can the original 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 0.5000 bits per pixel and the average embedding rate of DE-IS is 0.0545 bits per bit of ciphertext.