This paper proposes a lossless, a reversible, and a combined data hiding schemes for ciphertext images encrypted by public key cryptosystems with probabilistic and homomorphic properties. In the lossless scheme, the ciphertext pixels are replaced with new values to embed the additional data into several LSB-planes of ciphertext pixels by multi-layer wet paper coding. Then, the embedded data can be directly extracted from the encrypted domain, and the data embedding operation does not affect the decryption of original plaintext image. In the reversible scheme, a preprocessing is employed to shrink the image histogram before image encryption, so that the modification on encrypted images for data embedding will not cause any pixel oversaturation in plaintext domain. Although a slight distortion is introduced, the embedded data can be extracted and the original image can be recovered from the directly decrypted image. Due to the compatibility between the lossless and reversible schemes, the data embedding operations in the two manners can be simultaneously performed in an encrypted image. With the combined technique, a receiver may extract a part of embedded data before decryption, and extract another part of embedded data and recover the original plaintext image after decryption.

Reversible data hiding, Lossless data hiding, Image encryption

[I] X Zhang, "Separable Reversible Data Hiding in Encrypted Image", IEEE transactions on infonnation forensics and security, vol. 7, no. 2, pp. 826-832, Apr.2012.
[2] Z. Ni, Y-Q. Shi, N. Ansali, and W. Su, "Reversible data hiding," IEEE Trans. Circuits Syst. Video Technol., vol.` 16, no. 3 , pp. 354-362, Mar.2006.
[3] X. Zhang, "Reversible data hiding in encrypted image," IEEE Signal Process. Lett., vol. 18, no. 4, pp. 255-258, Apr. 2011.
[4] RiniJ ,4th Semester M.Tech ,Dept. of Computer Science and Information Systems FISAT Angamaly ,Kerala, India "Study on Separable Reversible Data Hiding in Encrypted Images" International Journal of Advancements in Research &Teclmology, Volume 2, Issue 12, December-2013 Copyright © 2013 SciResPub. IJOART
[5] VinitAghamDepaltment of Computer Engineeling R C Patel Institute of Technology, Shirpur.Dist. Dhule, Maharashtra, India.TareekPattewar Department oflnfonnation Technology R C Patel Institute of Technology, Shirpur. Dist. Dhule, Maharashtra, India" A Novel Approach Towards Separable Reversible Data Hiding Technique" 2014 Intemational Conference on Issues and Challenges in Intelligent Computing Techniques (IClCT).
[6] Rengarajaswamy I Assistant Professor, Department of Electronics and Communication Engineeling, M.A.M School of Engineering, Trichy, Tamil Nadu "OFT Based Individual Extraction Of Steganographic Compression Oflmages", : IJRET Feb-14.
[7] VinitAghamDepaltment of Computer Engineering R C Patel Institute of Technology, Shirpur.Dist. Dhule, Maharashtra, India.TareekPattewar Department of Infonnation Technology R C Patel Institute of Technology, Shirpur. Dis!.Dhule, Maharashtra, India " A Novel Approach Towards Separable Reversible Data Hiding Technique" 2014 International Conference on Issues and Challenges in Intelligent Computing Techniques (lClCT).
[8] Ming Li, Di Xiao, ZhongxianPeng, and Hai Nan, “A modified reversible data hiding in encrypted images using random diffusion and accurate prediction,” ETRIJournal, vol. 36, no. 2, pp. 325–328, 2014.
[9] J. Zhou, W. Sun, L. Dong, X. Liu, O. C. Au, and Y. Y. Tang, “Secure reversible image data hiding over encrypted domain via key modulation,” IEEE Transactionson Circuits and Systems for Video Technology, vol. PP, no. 99, pp. 1–1, 2015.
[10] Xinpeng Zhang, “Separable reversible data hiding in encrypted image,” IEEE Transactions on InformationForensics and Security, vol. 7, no. 2, pp. 826–832, 2012.
[11] Xinpeng Zhang, ZhenxingQian, GuoruiFeng, and YanliRen, “Efficient reversible data hiding in encrypted images,” Journal of Visual Communication and ImageRepresentation, vol. 25, no. 2, pp. 322–328, 2014.
[12] ShuliZheng, Dandan Li, Donghui Hu, Dengpan Ye, Lina Wang, and Jinwei Wang, “Lossless data hiding algorithm for encrypted images with high capacity,” MultimediaTools and Applications, pp. 1–14, 2015.
[13] Xinpeng Zhang, Chuan Qin, and Guangling Sun, “Reversible data hiding in encrypted images using pseudorandom
sequence modulation,” Digital Forensics and Watermaking, vol. 7809, pp. 358–367, 2013.
[14] Zhaoxia Yin, Bin Luo, and Wien Hong, “Separable and error-free reversible data hiding in encrypted image with high payload,” The Scientific World Journal, vol. 2014, pp. 8, 2014.
[15] Zhaoxia Yin, Huabin Wang, Haifeng Zhao, Bin Luo, and Xinpeng Zhang, “Complete separable reversible data hiding in encrypted image,” Cloud Computing andSecurity: First International Conference, ICCCS 2015, pp. 101–110, 2015.
[16] Xiaotian Wu and Wei Sun, “High-capacity reversible data hiding in encrypted images by prediction error,” Signal Processing, vol. 104, pp. 387–400, 2014.
[17] Xinpeng Zhang, Chuan Qin, and Guangling, “Reversible data hiding in encrypted images using pseudorandom
sequence modulation,” Digital Forensics and Watermaking, vol. 7809, pp. 358–367, 2013.
[18] Chong Fu, Jun-jie Chen, HaoZou, Wei-hongMeng, Yong-feng Zhan, and Ya-wen Yu, “A chaos-based digital image encryption scheme with an improved diffusion strategy,” Optics Express, vol. 20, no. 3, pp. 2363–2378, 2012.
[19] Zhicheng Ni, Yun-Qing Shi, N. Ansari, and Wei Su, “Reversible data hiding,” IEEE Transactions on Circuitsand Systems for Video Technology, vol. 16, no. 3, pp. 354–362, 2006.
[20] Y. Q. Shi, X. Li, X. Zhang, H. Wu, and Ma B., “Reversible data hiding: Advances in the past two decades,” IEEE Access, vol. PP, no. 99, pp. 1–1, 2016, doi:10.1109/ACCESS.2016.2573308.
[21] Xinpeng Zhang, “Reversible data hiding in encrypted image,” IEEE Signal Processing Letters, vol. 18, no. 4, pp. 255–258, 2011.
[22] K. Ma, Weiming Zhang, Xianfeng Zhao, Nenghai Yu, and Fenghua Li, “Reversible data hiding in encrypted images by reserving room before encryption,” IEEE.
[23] M. N. Islam,M. S. Alam, and M. A. Karim, _Optical security system employing quadrature multiplexing,_ Optical Engineering, vol. 47, 2008, Paper No. 048201.
[24] Z. Liu and S. Liu, _Double image encryption based on iterative fractional Fourier transform,_ Optics Communications, vol. 275, 2007, pp. 324-329.
[25] Z. H. Guan, F. Huang, and W. Guan, _Chaos-based image encryption algorithm,_ Physics Letters A, vol. 346, 2005, pp. 153-157.
[26] N. Y. Pareek, V. Patidar, and K. K. Sud, _Image encryption using chaotic logistic map,_ Image and Vision Computing, vol. 24, 2006, pp. 926-934.