Progressive reversible data hiding in encrypted images based on polynomial secret sharing and Chinese remainder theorem

In the current distributed environment, reversible data hiding in encrypted images has the disadvantages of low security and nonprogressivity. To address this problem, a homomorphic embedding algorithm is proposed based on polynomial secret sharing (PSS) and Chinese remainder theorem. First, the image owner encrypts the carrier image in streaming encryption and sends it to the data hider. Then, the data hider utilizes PSS to split the carrier image into n shares. At the same time, extra secrets after SS are embedded into the carrier shares using homomorphism. After splitting by Chinese remainder theorem, every share of the embedded data is divided into some sub-shares and then distributed to the participants. The participants that satisfy the threshold condition provide part or all of the sub-shares according to the authority of the data extractor. If each participant provides all sub-shares, the secrets and carrier image can be reconstructed completely. If each participant provides part of the sub-shares, the secrets and carrier image can be reconstructed partly. The experimental results show that the proposed scheme has progressivity, high security, and a large embedding rate (ER). Meanwhile, the ER is not affected by the carrier image.