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Homomorphic Encryption-Based Reversible Data Hiding for 3D Mesh Models

  • Research Article - Computer Engineering and Computer Science
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Abstract

Reversible data hiding in the encrypted domain (RDH-ED) reversibly encode and decode information to an encrypted cover medium without decrypting it. With the rapid development of multimedia applications, 3D models are considered as potential cover media for reversible data hiding due to their intrinsic capacity and potential applications in various areas such as military and medicine. In this paper, we propose a two-tier RDH-ED framework for 3D mesh models using the homomorphic Paillier cryptosystem. Two homomorphic properties of the underlying cryptosystem are utilized to propose a two-tier RDH-ED framework for end-to-end authentication and cloud data management. The proposed framework is successfully implemented on various simple and dense meshes. The performance evaluation of the proposed framework shows high embedding rates. Furthermore, it produces high-quality directly decrypted meshes from which information bits are extracted error-free and the original meshes are recovered losslessly.

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References

  1. Cox, I.; Miller, M.; Bloom, J.; Fridrich, J.; Kalker, T.: Digital Watermarking and Steganography. Morgan Kaufmann, Burlington (2007)

    Google Scholar 

  2. Fridrich, J.: Steganography in Digital Media: Principles, Algorithms, and Applications. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  3. Tian, J.: Reversible data embedding using a difference expansion. IEEE Trans. Circuits Syst. Video Technol. 13(8), 890–896 (2003)

    Article  Google Scholar 

  4. Ni, Z.; Shi, Y.-Q.; Ansari, N.; Su, W.: Reversible data hiding. IEEE Trans. Circuits Syst. Video Technol. 16(3), 354–362 (2006)

    Article  Google Scholar 

  5. Avci, E.; Tuncer, T.; Avci, D.: A novel reversible data hiding algorithm based on probabilistic XOR secret sharing in wavelet transform domain. Arab. J. Sci. Eng. 41(8), 3153–3161 (2016)

    Article  Google Scholar 

  6. Celik, M.U.; Sharma, G.; Tekalp, A.M.; Saber, E.: Lossless generalized-LSB data embedding. IEEE Trans. Image Process. 14(2), 253–266 (2005)

    Article  Google Scholar 

  7. Weng, S.; Zhao, Y.; Pan, J.-S.; Ni, R.: Reversible watermarking based on invariability and adjustment on pixel pairs. IEEE Signal Process. Lett. 15, 721–724 (2008)

    Article  Google Scholar 

  8. Wang, X.; Li, X.; Yang, B.; Guo, Z.: Efficient generalized integer transform for reversible watermarking. IEEE Signal Process. Lett. 17(6), 567–570 (2010)

    Article  Google Scholar 

  9. Qiu, Y.; Qian, Z.; Yu, L.: Adaptive reversible data hiding by extending the generalized integer transformation. IEEE Signal Process. Lett. 23(1), 130–134 (2016)

    Article  Google Scholar 

  10. Coltuc, D.: Low distortion transform for reversible watermarking. IEEE Trans. Image Process. 21(1), 412–417 (2012)

    Article  MathSciNet  Google Scholar 

  11. Thodi, D.M.; Rodriguez, J.J.: Prediction-error based reversible watermarking. In: Image Processing, 2004. ICIP’04. 2004 International Conference on, pp. 1549-1552. IEEE (2004)

  12. Thodi, D.M.; Rodríguez, J.J.: Expansion embedding techniques for reversible watermarking. IEEE Trans. Image Process. 16(3), 721–730 (2007)

    Article  MathSciNet  Google Scholar 

  13. Zhang, W.; Hu, X.; Li, X.; Yu, N.: Recursive histogram modification: establishing equivalency between reversible data hiding and lossless data compression. IEEE Trans. Image Process. 22(7), 2775–2785 (2013)

    Article  Google Scholar 

  14. Hu, X.; Zhang, W.; Hu, X.; Yu, N.; Zhao, X.; Li, F.: Fast estimation of optimal marked-signal distribution for reversible data hiding. IEEE Trans. Inf. Forensics Secur. 8(5), 779–788 (2013)

    Article  Google Scholar 

  15. Zhang, W.; Hu, X.; Li, X.; Nenghai, Y.: Optimal transition probability of reversible data hiding for general distortion metrics and its applications. IEEE Trans. Image Process. 24(1), 294–304 (2015)

    Article  MathSciNet  Google Scholar 

  16. Jiang, R.; Zhou, H.; Zhang, W.; Yu, N.-H.: Reversible data hiding in encrypted 3D mesh models. IEEE Trans. Multimedia 20(1), 55–67 (2017)

    Article  Google Scholar 

  17. Ma, K.; Zhang, W.; Zhao, X.; Yu, N.; Li, F.: Reversible data hiding in encrypted images by reserving room before encryption. IEEE Trans. Inf. Forensics Secur. 8(3), 553–562 (2013)

    Article  Google Scholar 

  18. Zhang, W.; Ma, K.; Yu, N.: Reversibility improved data hiding in encrypted images. Signal Process. 94, 118–127 (2014)

    Article  Google Scholar 

  19. Cao, X.; Du, L.; Wei, X.; Meng, D.; Guo, X.: High capacity reversible data hiding in encrypted images by patch-level sparse representation. IEEE Trans. Cybern. 46(5), 1132–1143 (2016)

    Article  Google Scholar 

  20. Zhang, X.: Reversible data hiding in encrypted image. IEEE Signal Process. Lett. 18(4), 255–258 (2011)

    Article  Google Scholar 

  21. Liao, X.; Shu, C.: Reversible data hiding in encrypted images based on absolute mean difference of multiple neighboring pixels. J. Vis. Commun. Image Represent. 28, 21–27 (2015)

    Article  Google Scholar 

  22. Zhou, J.; Sun, W.; Dong, L.; Liu, X.; Au, O.C.; Tang, Y.Y.: Secure reversible image data hiding over encrypted domain via key modulation. IEEE Trans. Circuits Syst. Video Technol. 26(3), 441–452 (2016)

    Article  Google Scholar 

  23. Zheng, S.; Li, D.; Hu, D.; Ye, D.; Wang, L.; Wang, J.: Lossless data hiding algorithm for encrypted images with high capacity. Multimedia Tools Appl. 75(21), 13765–13778 (2016)

    Article  Google Scholar 

  24. Qian, Z.; Zhang, X.: Reversible data hiding in encrypted images with distributed source encoding. IEEE Trans. Circuits Syst. Video Technol. 26(4), 636–646 (2016)

    Article  Google Scholar 

  25. Chen, Y.-C.; Shiu, C.-W.; Horng, G.: Encrypted signal-based reversible data hiding with public key cryptosystem. J. Vis. Commun. Image Represent. 25(5), 1164–1170 (2014)

    Article  Google Scholar 

  26. Wu, X.; Chen, B.; Weng, J.: Reversible data hiding for encrypted signals by homomorphic encryption and signal energy transfer. J. Vis. Commun. Image Represent. 41, 58–64 (2016)

    Article  Google Scholar 

  27. Wu, H.-T.; Cheung, Y.-M.; Huang, J.: Reversible data hiding in Paillier cryptosystem. J. Vis. Commun. Image Represent. 40, 765–771 (2016)

    Article  Google Scholar 

  28. Zhang, X.; Long, J.; Wang, Z.; Cheng, H.: Lossless and reversible data hiding in encrypted images with public-key cryptography. IEEE Trans. Circuits Syst. Video Technol. 26(9), 1622–1631 (2016)

    Article  Google Scholar 

  29. Xiang, S.; Luo, X.: Efficient reversible data hiding in encrypted image with public key cryptosystem. EURASIP J. Adv. Signal Process. 2017(1), 59 (2017)

    Article  Google Scholar 

  30. Chou, D.; Jhou, C.-Y.; Chu, S.-C.: Reversible watermark for 3D vertices based on data hiding in mesh formation. Int. J. Innov. Comput. Inf. Control 5(7), 1893–1901 (2009)

    Google Scholar 

  31. Wu, H.-t.; Dugelay, J.-L.: Reversible watermarking of 3D mesh models by prediction-error expansion. In: Multimedia Signal Processing, 2008 IEEE 10th Workshop on, pp. 797-802. IEEE (2008)

  32. Wu, H.-T.; Cheung, Y.-m.: A reversible data hiding approach to mesh authentication. In: Proceedings of the 2005 IEEE/WIC/ACM International Conference on Web Intelligence, pp. 774–777. IEEE Computer Society (2005)

  33. Luo, H.; Lu, Z.-m.; Pan, J.-s.: A reversible data hiding scheme for 3D point cloud model. In: Signal Processing and Information Technology, 2006 IEEE International Symposium on, pp. 863–867. IEEE (2006)

  34. Luo, H.; Pan, J.-S.; Lu, Z.-M.; Huang, H.-C.: Reversible data hiding for 3D point cloud model. In: Intelligent Information Hiding and Multimedia Signal Processing, 2006. IIH-MSP’06. International Conference on, pp. 487–490. IEEE (2006)

  35. Sun, Z.; Lu, Z.-M.; Li, Z.: Reversible data hiding for 3D meshes in the PVQ-compressed domain. In: Intelligent Information Hiding and Multimedia Signal Processing, 2006. IIH-MSP’06. International Conference on, pp. 593–596. IEEE (2006)

  36. Lu, Z.-M.; Li, Z.: High capacity reversible data hiding for 3D meshes in the PVQ domain. In: Shi, Y.Q., Kim, H.J., Katzenbeisser, S. (eds.) Digital Watermarking. IWDW 2007. Lecture Notes in Computer Science, vol. 5041, pp. 233–243. Springer, Berlin, Heidelberg (2008)

    Chapter  Google Scholar 

  37. Bianchi, T.; Piva, A.; Barni, M.: On the implementation of the discrete Fourier transform in the encrypted domain. IEEE Trans. Inf. Forensics Secur. 4(1), 86–97 (2009)

    Article  Google Scholar 

  38. Deering, M.: Geometry compression. In: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, pp. 13–20. ACM (1995)

  39. Rivest, R.L.; Adleman, L.; Dertouzos, M.L.: On data banks and privacy homomorphisms. Found. Secure Comput. 4(11), 169–180 (1978)

    MathSciNet  Google Scholar 

  40. Gentry, C.; Halevi, S.: Implementing gentry’s fully-homomorphic encryption scheme. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 129–148. Springer (2011)

  41. Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: International Conference on the Theory and Applications of Cryptographic Techniques, pp. 223–238. Springer (1999)

  42. Damgård, I.; Jurik, M.: A generalisation, a simpli. cation and some applications of paillier’s probabilistic public-key system. In: International Workshop on Public Key Cryptography, pp. 119–136. Springer (2001)

  43. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31(4), 469–472 (1985)

    Article  MathSciNet  Google Scholar 

  44. Goldwasser, S.; Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)

    Article  MathSciNet  Google Scholar 

  45. Lavoué, G.; Gelasca, E.D.; Dupont, F.; Baskurt, A.; Ebrahimi, T.: Perceptually driven 3D distance metrics with application to watermarking. In: Applications of Digital Image Processing XXIX 2006, p. 63120L. International Society for Optics and Photonics

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Correspondence to Weiming Zhang.

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Shah, M., Zhang, W., Hu, H. et al. Homomorphic Encryption-Based Reversible Data Hiding for 3D Mesh Models. Arab J Sci Eng 43, 8145–8157 (2018). https://doi.org/10.1007/s13369-018-3354-4

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  • DOI: https://doi.org/10.1007/s13369-018-3354-4

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