Reversible Data Hiding in Encrypted Images with Secret Sharing and Multivariate Linear Equation

Reversible data hiding in encrypted images (RDHEI) is an essential data security technique. Most RDHEI methods with secret sharing cannot perform well on the images with low redundancy, such as the complex texture images. To address this issue, we propose an RDHEI method with ($n$, $k$) threshold-secret sharing (SS), which is universal for the images with diverse content since it is unrelated with the image content. Specifically, the original image is shared by polynomials over Galois field GF($2^{8}$) to generate $n$ image shares. Two kinds of reference matrices are elaborated to guide data embedding and extraction in image shares, one for higher capacity and the other for less communication overhead. At the decoder stage, the marked pixel shares are viewed as the unknowns to construct the multivariate linear equation (MLE) and the original image can be recovered by solving MLE. Experiment results show that the proposed method outperforms some state-of-the-art SS-based RDHEI methods.