Advertisement

A Weighted Threshold Visual Cryptography

  • Tai-Yuan Tu
  • Tzung-Her Chen
  • Ji-min Yang
  • Chih-Hung WangEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1013)

Abstract

Over the past years, a visual secret sharing scheme gave each share the same ability to reconstruct the secret image. That means each participant had the same significance to reveal the secret. However, it is not realistic in real world for some applications. In this paper, the weighted \( (k,n) \)-threshold visual cryptography scheme is proposed, in which the secret image is encoded into some shares with different weights and the sum of weights for all shares has to be equal to \( n \), according to the share-holders of different priority levels. In the decoding phase, when the shares with different weights are superimposed and the sum of weights of all stacking shares is equal to or larger than \( k \), the secret is then visually recognizable. Otherwise, no information about secret image is revealed. The proposed scheme is the first weighted \( (k,n) \)-threshold visual cryptography method with no pixel expansion. It is suitable for applications in the real life.

Keywords

Cryptography Visual cryptography Weighted visual secret sharing Probabilistic visual secret sharing 

Notes

Acknowledgements

This research was partially supported by Ministry of Science Technology, Taiwan, R.O.C., under contract no. MOST 105-2221-E-415 -012.

References

  1. 1.
    Blakley, G.: Safeguarding cryptographic keys. In: Proceedings AFIPS 1979 National Computer Conference, pp. 313–317, AFIPS Press, New York (1979)Google Scholar
  2. 2.
    Blundo, C., Santis, A.D., Stinson, D.R.: On the contrast in visual cryptography schemes. J. Crypt. 12, 261–289 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Chao, K.Y., Lin, J.C.: User-friendly sharing of images: progressive approach based on modulus operation. J. Electronic Imaging 18(3), 0330081–0330089 (2009)CrossRefGoogle Scholar
  4. 4.
    Chen, S.K.: Weighted visual cryptography with non-expansible shares. J. Image Process. Commun. 5(1), 1–6 (2013)Google Scholar
  5. 5.
    Chen, T.H., Lee, Y.S.: Yet another friendly progressive visual secret sharing scheme. In: Fifth International Conference on Intelligent Information Hiding and Multimedia Signal Processing (2009)Google Scholar
  6. 6.
    Cimato, S., Prisco, R.D., Santis, A.D.: Probabilistic visual cryptography schemes. Comput. J. 49(1), 97–107 (2006)zbMATHCrossRefGoogle Scholar
  7. 7.
    Fang, W.P.: Friendly progressive visual secret sharing. Pattern Recogn. 41, 1410–1414 (2008)zbMATHCrossRefGoogle Scholar
  8. 8.
    Fang, W.P., Lin, J.C.: Progressive viewing and sharing of sensitive image. Pattern Recogn. Image Anal. 15(4), 632–636 (2006).  https://doi.org/10.1134/S1054661806040080CrossRefGoogle Scholar
  9. 9.
    Homiest, T., Krause, M., Simon, H.U.: Contrast optimal k out of n secret sharing schemes in visual cryptography. Theoret. Comput. Sci. 240, 471–485 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Hou, Y.C.: Visual cryptography for color images. Pattern Recogn. 36(7), 1619–1629 (2003)CrossRefGoogle Scholar
  11. 11.
    Hou, Y.C., Chang, C.Y., Hsu, C.S.: Visual cryptography for color images without pixel expansion. In: Proceeding of CISST 2001, vol. I, pp. 239–245, Las Vegas (2001)Google Scholar
  12. 12.
    Hou, Y.C., Quan, Z.Y., Tsai, C.F.: General model for the priority-based progressive visual secret sharing. Journal of C.C.I.T, 42(2), 33–48 (2013)Google Scholar
  13. 13.
    Naor, M., Shamir, A.: Visual cryptography. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 1–12. Springer, Heidelberg (1995).  https://doi.org/10.1007/BFb0053419CrossRefGoogle Scholar
  14. 14.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Thien, C.C., Lin, J.C.: Secret image sharing. Comput. Graph. 26(5), 765–770 (2002)CrossRefGoogle Scholar
  16. 16.
    Verheul, E.R., Van Tilborg, H.C.: Constructions and properties of k out of n visual secret sharing schemes. Design, Codes and Cryptography 11(2), 179–196 (1997).  https://doi.org/10.1023/A:1008280705142MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Viet, D.Q., Kurosawa, K.: Almost ideal contrast visual cryptography with reversing. In: Okamoto, T. (ed.) CT-RSA 2004. LNCS, vol. 2964, pp. 353–365. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24660-2_27CrossRefGoogle Scholar
  18. 18.
    Wang, A., Zhang, L., Ma, N., Li, X.: Two secret sharing schemes based on boolean operations. Pattern Recogn. 40, 2776–2785 (2007)zbMATHCrossRefGoogle Scholar
  19. 19.
    Yang, N.: New visual secret sharing schemes using probabilistic method. Pattern Recogn. Lett. 25(4), 481–494 (2004)CrossRefGoogle Scholar
  20. 20.
    Yang, C.N., Chen, T.S.: Aspect ratio invariant visual secret sharing schemes with minimum pixel expansion. Pattern Recogn. Lett. 26, 193–206 (2005)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Tai-Yuan Tu
    • 1
  • Tzung-Her Chen
    • 1
  • Ji-min Yang
    • 1
  • Chih-Hung Wang
    • 1
    Email author
  1. 1.Department of Computer Science and Information EngineeringNational Chiayi UniversityChiayiTaiwan

Personalised recommendations