Reversible Data Hiding Scheme in Homomorphic Encrypted Image Based on EC-EG

To combine homomorphic public key encryption with reversible data hiding, a reversible data hiding scheme in homomorphic encrypted image based on EC-EG is proposed. Firstly, the cover image is segmented. The square grid pixel group randomly selected by the image owner has one reference pixel and eight target pixels. The n least significant bits (LSBs) of the reference pixel and all bits of target pixel are self-embedded into other parts of the image by a method of predictive error expansion (PEE). To avoid overflowing when embedding data, the n LSBs of the reference pixel are reset to zero before encryption. Then, the pixel values of the image are encrypted after being encoded onto the points of the elliptic curve. The encrypted reference pixel replaces the encrypted target pixels surrounding it, thereby constructing the mirroring central ciphertext (MCC). In a set of MCC, the data hider embeds the encrypted additional data into the n LSBs of the target pixels by homomorphic addition in ciphertexts, while the reference pixel remains unchanged. The receiver can directly extract additional data by homomorphic subtraction in ciphertexts between the target pixels and the corresponding reference pixel; extract the additional data by subtraction in plaintexts with the directly decrypted image; and restore the cover image without loss. The experimental results show that the proposed scheme has higher security than the similar algorithms, and the average embedding rate of the scheme is 0.25 bpp under the premise of ensuring the quality of the directly decrypted image.