Reversible Data Hiding in Encrypted Images Based on Binary Symmetric Channel Model and Polar Code

For vacating-room-after-encryption reversible data hiding in encrypted images (VRAE RDHEI), an essential problem is how to address potential errors in data extraction and image recovery. This problem significantly limits the capacities of the existing VRAE RDHEI methods. To solve the problem while losing as little capacity as possible, in this article, a novel method is proposed that uses the ideas of noisy channel model and channel code. By designing the data hiding mechanism appropriately, the embedding and extraction of data in the proposed method can be equivalent to the input and output of a virtual binary symmetric channel (BSC) model, so that the errors in data extraction are equivalent to the bit transitions in BSC. Based on the virtual BSC model, polar code is used to encode the secret data in the data hider's side. With the help of polar code, the receiver can decode the extracted bits containing errors to obtain correct secret data, then recover the error-free original image based on the corrected secret data. The experimental results proved that, compared with the existing VRAE methods, the proposed method can significantly improve the capacity and the quality of the decrypted images under the premise of complete reversibility.