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Multimedia Tools and Applications

, Volume 78, Issue 2, pp 1265–1287 | Cite as

Polynomial-based extended secret image sharing scheme with reversible and unexpanded covers

  • Lintao LiuEmail author
  • Yuliang Lu
  • Xuehu Yan
Article
  • 39 Downloads

Abstract

In comparison with traditional secret image sharing (SIS), extended secret image sharing (ESIS) can encrypt the secret image into several meaningful shadow images rather than noise-like shares, which both decrease enemies’ suspects and make them more manageable for participants. However, a majority of current ESISs are based on a combination between SIS and steganography, which result in the limited performance such as the small capacity of secret information and the large cost for decryption. In this paper, we propose a (k, n) threshold extended polynomial-based ESIS, namely EPSIS, completely based on Shamir’s classic PSIS without the help of steganography. Firstly, novel concepts, such as the sharing map and sharing pool, are defined to reconstruct the sharing and recovery phases of PSIS; secondly, the secret image and halftone binary cover images act on the sharing phase to generate meaningful grayscale shares from the novel view of PSIS based on the sharing map; finally, in order to achieve the same effects but without the huge sharing map, a filtering procedure for appropriate shared values is added into the sharing phase of natural PSIS, which aims to make the most significant bit of pixel in each share equal to bit in corresponding binary cover. In comparison with current ESISs, the proposed EPSIS not only has advantages in the traditional properties, such (k, n) threshold, capacity, visual quality and computational cost, but also owns two unique properties about covers, including no restrictive requirements on the selection of covers and reversible recovery of cover with the single related share. These significant properties are beneficial for searchable encryption in the area of cloud storage. Furthermore, the security condition of the proposed EPSIS is discussed in detail, and then simulations are provided to verify the security and effectiveness.

Keywords

Secret sharing Polynomial-based scheme Extended secret image sharing Meaningful shares Reversible cover images 

Notes

Acknowledgements

This project is supported by the National Natural Science Foundation of China (Grant No.61602491). Thanks for the anonymous reviewers’ constructive comments and suggestions.

References

  1. 1.
    Ateniese G, Blundo C, De Santis A, Stinson DR (1996) Visual cryptography for general access structures. Inf Comput 129(2):86–106MathSciNetCrossRefGoogle Scholar
  2. 2.
    Ateniese G, Blundo C, Santis AD, Stinson DR (2001) Extended capabilities for visual cryptography. Theor Comput Sci 250(1-2):143–161.  https://doi.org/10.1016/S0304-3975(99)00127-9. http://www.sciencedirect.com/science/article/pii/S0304397599001279 MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Cheng TF, Chang CC, Liu L (2017) Secret sharing: using meaningful image shadows based on gray code. Multimedia Tools and Applications 76(7):9337–9362CrossRefGoogle Scholar
  4. 4.
    He J, Lan W, Tang S (2017) A secure image sharing scheme with high quality stego-images based on steganography. Multimedia Tools and Applications 76 (6):7677–7698CrossRefGoogle Scholar
  5. 5.
    Huynh NT, Bharanitharan K, Chang CC (2015) Quadri-directional searching algorithm for secret image sharing using meaningful shadows. J Vis Commun Image Represent 28:105–112.  https://doi.org/10.1016/j.jvcir.2015.01.011 CrossRefGoogle Scholar
  6. 6.
    Li P, Ma PJ, Su XH, Yang CN (2012) Improvements of a two-in-one image secret sharing scheme based on gray mixing model. J Vis Commun Image Represent 23 (3):441–453CrossRefGoogle Scholar
  7. 7.
    Li P, Yang CN, Kong Q (2018) A novel two-in-one image secret sharing scheme based on perfect black visual cryptography. J Real-Time Image Proc 14(1):41–50CrossRefGoogle Scholar
  8. 8.
    Lin PY, Chan CS (2010) Invertible secret image sharing with steganography. Pattern Recogn Lett 31(13):1887–1893CrossRefGoogle Scholar
  9. 9.
    Lin SJ, Lin JC (2007) Vcpss: a two-in-one two-decoding-options image sharing method combining visual cryptography (vc) and polynomial-style sharing (pss) approaches. Pattern Recogn 40(12):3652–3666CrossRefGoogle Scholar
  10. 10.
    Liu F, Wu C (2011) Embedded extended visual cryptography schemes. IEEE Trans Inf Forensics Secur 6(2):307–322CrossRefGoogle Scholar
  11. 11.
    Liu F, Yan WQ (2014) . In: Visual cryptography for image processing and security: theory, methods, and applications. Springer.  https://doi.org/10.1007/978-3-319-09644-5
  12. 12.
    Liu F, Wu CK, Lin XJ (2008) Colour visual cryptography schemes. IET Inf Secur 2(4):151–165CrossRefGoogle Scholar
  13. 13.
    Liu X, Wang S, Sang J, Zhang W (2018) A novel mapping-based lossless recovery algorithm for vss. J Real-Time Image Proc 14(1):51–61.  https://doi.org/10.1007/s11554-016-0644-5 CrossRefGoogle Scholar
  14. 14.
    Liu X, Wang S, Sang J, Zhang W (2017) A novel lossless recovery algorithm for basic matrix-based vss. Multimedia Tools and Applications (2):1–16Google Scholar
  15. 15.
    Naor M, Shamir A (1994) Visual cryptography. In: Workshop on the theory and application of of cryptographic techniques. Springer, pp 1–12Google Scholar
  16. 16.
    Ni Z, Shi YQ, Ansari N, Su W (2006) Reversible data hiding. IEEE Trans Circuits Syst Video Technol 16(3):354–362CrossRefGoogle Scholar
  17. 17.
    Ou D, Sun W, Wu X (2015) Non-expansible XOR-based visual cryptography scheme with meaningful shares. Signal Process 108:604–621.  https://doi.org/10.1016/j.sigpro.2014.10.011 CrossRefGoogle Scholar
  18. 18.
    Shen G, Liu F, Fu Z, Yu B (2016) Perfect contrast xor-based visual cryptography schemes via linear algebra. Des Codes Crypt 85(1):1–23MathSciNetzbMATHGoogle Scholar
  19. 19.
    Shin SH, Jung KH (2016) Reversible secret image sharing scheme in encrypted images. Multimedia Tools and Applications 75(21):13,931–13,949CrossRefGoogle Scholar
  20. 20.
    Thien CC, Lin JC (2002) Secret image sharing. Comput Graph 26(5):765–770CrossRefGoogle Scholar
  21. 21.
    Wang Z, Arce GR (2006) Halftone visual cryptography through error diffusion. In: Proceedings - international conference on image processing, ICIP, pp 109–112.  https://doi.org/10.1109/ICIP.2006.312384
  22. 22.
    Wang DS, Yi F, Li X (2009) On general construction for extended visual cryptography schemes. Pattern Recogn 42(11):3071–3082.  https://doi.org/10.1016/j.patcog.2009.02.015 CrossRefzbMATHGoogle Scholar
  23. 23.
    Weir J, Yan WQ (2009) Sharing multiple secrets using visual cryptography. In: IEEE international symposium on circuits and systems, pp 509–512Google Scholar
  24. 24.
    Weir J, Yan W (2010) A comprehensive study of visual cryptography. In: Transactions on data hiding and multimedia security V. Springer, pp 70–105Google Scholar
  25. 25.
    Wu X, Sun W (2013) Generalized random grid and its applications in visual cryptography. IEEE Trans Inf Forensics Secur 8(9):1541–1553CrossRefGoogle Scholar
  26. 26.
    Wu X, Ou D, Liang Q, Sun W (2012) A user-friendly secret image sharing scheme with reversible steganography based on cellular automata. J Syst Softw 85(8):1852–1863.  https://doi.org/10.1016/j.jss.2012.02.046 CrossRefGoogle Scholar
  27. 27.
    Wu X, Weng J, Yan W (2018) Adopting secret sharing for reversible data hiding in encrypted images. Signal Process 143:269–281CrossRefGoogle Scholar
  28. 28.
    Yan X, Liu X, Yang CN (2015) An enhanced threshold visual secret sharing based on random grids. J Real-Time Image Proc 14:61–63.  https://doi.org/10.1007/s11554-015-0540-4 CrossRefGoogle Scholar
  29. 29.
    Yan X, Wang S, Niu X, Yang CN (2015) Generalized random grids-based threshold visual cryptography with meaningful shares. Signal Process 109:317–333.  https://doi.org/10.1016/j.sigpro.2014.12.002 CrossRefGoogle Scholar
  30. 30.
    Yan X, Wang S, Niu X, Yang CN (2015) Halftone visual cryptography with minimum auxiliary black pixels and uniform image quality. Digital Signal Processing: A Review Journal 38:53–65.  https://doi.org/10.1016/j.dsp.2014.12.002 CrossRefGoogle Scholar
  31. 31.
    Yang CN (2004) New visual secret sharing schemes using probabilistic method. Pattern Recogn Lett 25(4):481–494MathSciNetCrossRefGoogle Scholar
  32. 32.
    Yang CN, Chen TS, Yu KH, Wang CC (2007) Improvements of image sharing with steganography and authentication. J Syst Softw 80(7):1070–1076CrossRefGoogle Scholar
  33. 33.
    Zhang X (2011) Reversible data hiding in encrypted image. IEEE Signal Process Lett 18(4):255–258CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National University of Defense TechnologyHefeiChina

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