The identical operands commutative encryption and watermarking based on homomorphism


Aiming at the requirement of comprehensive security protection for multimedia information, this paper proposes a new algorithm to realize the combination of encryption and watermarking based on the homomorphism. Under the proposed algorithm scheme, the plaintext watermark embedding operations are mapped to the ciphertext domain by homomorphism to achieve the plaintext watermark embedding in the ciphertext domain; at the same time, the embedded plaintext watermarks are also mapped to the ciphertext domain by homomorphism to achieve the ciphertext watermarking embedding. According to the experimental results, by the proposed algorithm, the order of watermark embedding and data encrypting does not affect the production of the same encrypted-watermarked data, meanwhile, whether the encrypted-watermarked data being decrypted or not does not affect the extraction of embedded watermark. For the operands of encryption and watermarking being the same data, the proposed algorithm has higher security compared with the existing mainstream independent operands based communicative encryption and watermarking.

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  1. 1.

    Battisti F, Cancellaro M, Boato G et al (2009) Joint watermarking and encryption of color images in the fibonacci-haar domain. EURASIP J Adv Sign Process: 1–13

  2. 2.

    Bender W, Gruhl D, Morimoto N (1995) Technique for data hiding. Proceeding of the SPIE 2420, storage and retrieval for image and video database III: 164–173

  3. 3.

    Boato G, Conci N, Conotter V, Natale FGBD, Fontanari C (2008) Multimedia asymmetric watermarking and encryption. Electron Lett 44:601–603

    Article  Google Scholar 

  4. 4.

    Brakerski Z, Gentry C, Vaikuntanathan V (2014) Fully homomorphic encryption without bootstraooing. ACM Trans Comput Theory 6(3):13

    Article  Google Scholar 

  5. 5.

    Cancellaro M, Battisti F, Carli M, Boato G, Natale FGBD, Neri A (2011) A commutative digital image watermarking and encryption method in the tree structured Haar transform domain. Signal Process Image Commun 26(1):1–12

    Article  Google Scholar 

  6. 6.

    Chang F, Huang H, Hang H (2005) Combined encryption and watermarking approaches for scalable multimedia coding. Adv Multimed Info Process 3333:356–363

    Google Scholar 

  7. 7.

    Chang F, Huang H, Hang H (2005) Layered access control schemes on watermarked scalable media. J VLSI Sign Process 49(3):4983–4986

    Google Scholar 

  8. 8.

    Chauhan DS, Singh AK, Kumar B et al (2017) Quantization based multiple medical information watermarking for secure e-health, Multimedia tools and applications

  9. 9.

    Dijk MV, Gentry C, Halevi S, Vaikuntanathan V (2010) Fully homomorphic encryption over the integers. Adv Cryptol – EUROCRYPT 6110(2010):24–43

    MathSciNet  MATH  Google Scholar 

  10. 10.

    Gentry C (2009) A fully homomorphic encryption scheme. PhD thesis, Stanford University

  11. 11.

    Gentry C, Halevi S (2011) Fully homomorphic encryption without squashing using depth-3 arithmetic circuits. IEEE symposium on foundations of computer. Science 47(10):107–109

    MATH  Google Scholar 

  12. 12.

    Jiang L, Xu Z (2010) Combination algorithm of active and passive security protection for image based on arnold transform. Proc. of 2010 IEEE Int. Conf. Multimedia Information Networking and Security: 625–629

  13. 13.

    Jiang L, Xu Z, Xu Y (2014) Commutative encryption and watermarking based on orthogonal decomposition. Multimed Tools Appl 70(3):1617–1635

    Article  Google Scholar 

  14. 14.

    Kalker T (2005) Secure watermark detection. Proc 43rd Ann Allerton Conf Commun, Contrl, Comput, Monticello: 1511–1520

  15. 15.

    Li Z, Zhu X, Lian Y et al (2007) Constructing secure content-dependent watermarking scheme using homomorphic encryption, Multimed Expo: 627–630

  16. 16.

    Lian S, Liu Z, Ren Z et al (2006) Commutative watermarking and encryption for media data. Opt Eng 45(8):0805101–0805103

    Article  Google Scholar 

  17. 17.

    Lian S, Liu Z, Ren Z et al (2007) Commutative encryption and watermarking in video compression. IEEE Circ Syst Video Technol 17(6):774–778

    Article  Google Scholar 

  18. 18.

    Lu Z, Xu D, Sun S (2005) Multipurpose image watermarking algorithm based on multistage vector quantization. IEEE Trans Image Process 14(6):822–832

    Article  Google Scholar 

  19. 19.

    Otto-von-Guericke University at Magdeburg (GAUSS) (2005) First summary report on hybrid systems, TR: IST-2002-507932 [R]. ECRYPT European Network of Excellence in Cryptology.

  20. 20.

    Paillier P (1999) Public-key cryptosystems based on composite degree residuosity classes. Lect Notes Comput Sci 1592:223–238

    MathSciNet  Article  Google Scholar 

  21. 21.

    Park S, Shin S (2008) Combined scheme of encryption and watermarking in H.264/scalable video coding (SVC). New Direct Intell Interact Multimed 142(2008):351–361

    Article  Google Scholar 

  22. 22.

    Puech W, Rodrigues JM (2004) A new crypto-watermarking method for medical images safe transfer. In: Proc of the 12th European signal processing conference, pp 1481–1484

    Google Scholar 

  23. 23.

    Puech W, Rodrigues JM, Develay-Morice JE (2007) A new fast reversible method for image safe transfer. J Real-Time Image Proc 2(1):55–65

    Article  Google Scholar 

  24. 24.

    Puech W, Chaumont M, Strauss O (2008) A reversible data hiding method for encrypted images. In: Proc of SPIE: lirmm-00293090

  25. 25.

    Rivest R, Adleman L, Dertouzos ML (1978) On data banks and privacy homomorphisms. Academic Press, New York, pp 169–179

    Google Scholar 

  26. 26.

    Rivest R, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public-key cryptosystems. Commun ACM 21(2):120–126

    MathSciNet  Article  Google Scholar 

  27. 27.

    Singh AK, Dave M, Mohan A (2016) Hybrid technique for robust and imperceptible multiple watermarking using medical images. Multimed Tools Appl 75:8381–8401

    Article  Google Scholar 

  28. 28.

    Smart NP, Vercauteren F (2010) Fully homomorphic encryption with relatively small key and ciphertext sizes. Public Key Cryptography – PKC 6056(2010):420–443

    MathSciNet  MATH  Google Scholar 

  29. 29.

    Stinson DR (1995) Cryptography: theory and practice. CRC Press, Inc, Boca Raton, FL, USA

    Google Scholar 

  30. 30.

    The USC-SIPI Image Database:

  31. 31.

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

    Article  Google Scholar 

  32. 32.

    Xu Y, Xu Z, Zhang Y (2012) Content security protection for remote sensing images integrating selective content encryption and digital fingerprint. J Appl Remote Sens 6(1):1–15

    Article  Google Scholar 

  33. 33.

    Zhang X (2012) Separable reversible data hiding in encrypted image. IEEE Trans Info Forensics Sec 7(2):826–832

    Article  Google Scholar 

  34. 34.

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

    Article  Google Scholar 

  35. 35.

    Zheng P, Huang J (2013) Discrete wavelet transform and data expansion reduction in homomorphic encrypted domain. IEEE Trans Image Process 22(6):2455–2468

    MathSciNet  Article  Google Scholar 

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The authors would like to acknowledge the help of Dr. Zhi Quan in editing of the paper. And this work was supported by the National Natural Science Foundation of China under Grant 61402421, 61331021.

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Correspondence to Li Jiang.

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Jiang, L. The identical operands commutative encryption and watermarking based on homomorphism. Multimed Tools Appl 77, 30575–30594 (2018).

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  • Multimedia information security
  • Homomorphism
  • Commutative encryption and watermarking