# Reversible Data Hiding Scheme in Homomorphic Encrypted Image Based on EC-EG
## 4 Simulation Experiment and Theoretical Analysis
### Performance Comparison  
Currently, reversible data hiding in homomorphic encrypted image mostly utilizes the Paillier cryptosystem. Table 4 summarizes some of the literature on the reversible data hiding in encrypted  
Figure 6: Different stages of images Lena, F-16, Man and Hill with 4095 bits of hidden data under \(n=3\) and PSNR values of the Directly decrypted image are 54.719 dB, 44.913 dB, 47.637 dB and 54.526 dB, respectively: (**a**) [PERSON]’s original image; (**b**) [PERSON]’s encrypted image; (**c**) [PERSON]’s encrypted image with hidden data; (**d**) [PERSON]’s directly decrypted image; (**e**) [PERSON]’s restored image without loss; (**f**) F-16’s original image; (**g**) F-16’s encrypted image; (**h**) F-16’s encrypted image with hidden data; (**i**) F-16’s directly decrypted image; (**j**) F-16’s restored image without loss; (**k**) [PERSON]’s original image; (**l**) [PERSON]’s encrypted image; (**m**) [PERSON]’s encrypted image with hidden data; (**n**) [PERSON]’s directly decrypted image; (**o**) [PERSON]’s restored image without loss; (**p**) [PERSON]’s original image; (**q**) [PERSON]’s encrypted image; (**r**) [PERSON]’s encrypted image with hidden data; (**s**) [PERSON]’s directly decrypted image; and (**t**) [PERSON]’s restored image without loss. \begin{table}
\begin{tabular}{c c} \hline \hline
**Image** & **(bits)** \\ \hline [PERSON] & 33 \\ F-16 & 670 \\ [PERSON] & 755 \\ [PERSON] & 128 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum size of images’ _L_map_. image using homomorphic property. [PERSON] et al. (2019), using VRAE; our scheme; and [PERSON] et al. (2019), using VRBE, could keep the amount of data transmitted unchanged. All of the algorithms in Table 4 have separable properties. In our proposed scheme, after the space is reserved and encrypted, the MCC is constructed. The extra information is embedded into the bit plane of the corresponding plaintext by homomorphic addition. The receiver extracts extra information by homomorphic subtraction in ciphertexts. [PERSON] et al. (2019) used WPC coding to perform two information embedding. The computational complexity is \(O(k^{3})\) and \(k\) is the embedded capacity. Our algorithm and the one in ([PERSON] et al., 2019) use homomorphic addition in ciphertexts to embed information. [PERSON] et al. (2019) used Homomorphic multiplication in ciphertexts to embed information. The computational complexity of them is \(O(k)\). [PERSON] et al. (2019) combined WPC coding and Paillier homomorphic encryption to embed additional information into the corresponding bit plane of the ciphertext. In the encrypted domain, the embedded information is protected by the WPC encoding mechanism, and the receiver cannot extract the embedded information without the key. However, when the receiver receives the ciphertext image, the same method can be used to forge the information, and the original embedded information may be overwritten or replaced. [PERSON] et al. (2019) used the homomorphic and probabilistic properties of Paillier encryption to protect the embedded extra information. In ([PERSON] et al., 2019), a high-capacity RDH-HEI algorithm is proposed by using the SHE homomorphism. The image owner divides the image pixels into groups of three, and then encrypts them with SHE, and the ciphertext expansion is small. The data hider sorts the absolute differences of each set of ciphertext pixels and generates an absolute difference histogram, embedding additional data by moving the ciphertext absolute difference histogram. The proposed scheme uses the homomorphic addition feature of EC-EG to protect the embedded extra information. When there is no shared parameter, the receiver cannot find the ciphertext embedded with the information, let alone extract, tamper or replace the additional information. Figure 7 shows the PSNR performance comparison between the proposed scheme and the ones in ([PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2019).