Abstract
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.
Highlights
Data hiding (DH) and digital watermarking (DW) are two of the important contents of cyberspace security research, which have been greatly developed in recent years
The scheme in this paper uses the method of constructing mirroring central ciphertext (MCC) after elliptic curve ElGamal (EC-EG) encryption to perform reversible data hiding in encrypted image
The scheme realizes the separation of additional data extraction and cover image restoration, and improves the embedding capacity under the premise of completely recovering the cover image
Summary
Data hiding (DH) and digital watermarking (DW) are two of the important contents of cyberspace security research, which have been greatly developed in recent years. For the purposes of confidentiality and privacy protection, medical images sometimes need to be encrypted beforehand and sent to third parties such as the cloud for management. In [15], Zhang proposed a separable RDH-EI algorithm, which can extract additional data in both the encrypted domain and the plaintext domain. The above RDH-EI algorithms need to vacate room after encryption (VRAE) for data hiding, resulting in lower embedding capacity of the algorithm and higher error rate in the data extraction process. Differing from RDH-EI, Chen et al [18] firstly proposed encrypted image-based reversible data hiding with public key cryptography (EIRDH-P). Using the homomorphic characteristics of public key cryptography for RDH-EI is the latest research hotspot, which we call reversible data hiding in homomorphic encrypted image (RDH-HEI). It is important to note that a preliminary version [24] of this paper is in proceedings of the “11th Intelligent Networking and Collaborative Systems (INCoS-2019)”
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