Reversible Data Hiding Algorithm in Homomorphic Encrypted Domain Based on EC-EG

Abstract

This paper proposes a reversible data hiding algorithm in homomorphic encrypted domain based on EC-EG. First, original image is segmented. The square grid pixel group randomly selected by image owner has one reference pixel and eight target pixels. The n least significant bits (LSBs) of reference pixel and all bits of target pixel are self-embedded into other parts of the image by predictive error expansion (PEE). The n LSBs of reference pixel are reset to zero before encryption for the purpose of avoiding overflow when embedding data. Then, the pixel values of image are encrypted after encoded onto the points of elliptic curve. The encrypted reference pixel replaces the encrypted target pixels surrounding it. Thence, mirror central ciphertext (MCC) is constructed. In a set of MCC, data hider embeds the encrypted extra data into the n LSBs of target pixels by homomorphic addition in ciphertexts, while the reference pixel remains unchanged. Receiver can directly extract extra data by homomorphic subtraction in ciphertexts between target pixels and corresponding reference pixel, and can extract the extra data by subtraction in plaintexts with the directly decrypted image, and can restore the original image without loss. The experimental results show that the proposed algorithm has higher security than the similar algorithms, and the average embedding rate of algorithm is 0.25 bpp.