Threshold changeable secret image sharing scheme based on interpolation polynomial

  • Yan-Xiao LiuEmail author
  • Ching-Nung Yang
  • Chi-Ming Wu
  • Qin-Dong Sun
  • Wei Bi


In previous (k,n) secret image sharing scheme, the threshold k is decided by dealer according to the security requirement, and this threshold value is fixed without considering the dynamic secure environment in future. In this work, we propose a novel threshold changeable secret image sharing scheme where the threshold value can be changed according to the changeable security requirement. In our scheme, each participant only needs to keep one initial shadow. When reconstructing image, the dealer decides the threshold according to security level. If the threshold is unchanged, any k or more initial shadows can recover the image; else if the threshold is increased or decreased, dealer publishes additional information, each participant update their shadows accordingly such that the threshold of updated shadows is changed correspondingly. The contribution of our work is that the threshold of shadows can be changed flexibly to satisfy the dynamic secure environment, and each participant only need to keep one initial shadows. The feature of threshold changeable makes our scheme more practical than previous secret image sharing in some complicated applications.


Secret image sharing Threshold changeable Interpolation polynomial 



The research presented in this paper is supported in part by the China National Natural Science Foundation (No.: 61502384, 61571360, 61872289), Shaanxi Science and Technology Co-ordination and Innovation Project (No.: 2016KTZDGY05-09), and the Innovation Project of Shaanxi Provincial Department of Education (No.: 17JF023). This research was supported in part by Ministry of Science and Technology (MOST), under Grant 107-2221-E-259-007.


  1. 1.
    Blundo C, Cresti A, Santis A, Vaccaro U (1994) Fully dynamic secret sharing schemes. In: Advances in cryptology CRYPTO’92: proceedings of the 13th annual international cryptology conference, London, pp 110–125Google Scholar
  2. 2.
    Chao H, Fan TY (2017) Random-grid based progressive visual secret sharing scheme with adaptive priority. Digital Signal Process 68:69–80CrossRefGoogle Scholar
  3. 3.
    Chao K, Lin JC (2009) Secret image sharing: a Boolean-operations-based approach combining benefits of polynomial-based and fast Approaches. Int J Pattern Recognit Artif Intell 23:263–285CrossRefGoogle Scholar
  4. 4.
    Gong X, Hu P, Shum K, Sung CW (2018) A Zigzag-Decodable ramp secret sharing scheme. IEEE Trans Inf Forensics Secur 13(8):1906–1916CrossRefGoogle Scholar
  5. 5.
    Harn L, Hsu CF (2015) Dynamic threshold secret reconstruction and its application to the threshold cryptography. Inf Process Lett 115(11):851–857MathSciNetCrossRefGoogle Scholar
  6. 6.
    Li P, Yang C, Wu, Kong Q, Ma Y (2013) Essential secret image sharing scheme with different importance of shadows. J Vis Commun Image Represent 24(7):1106–1114CrossRefGoogle Scholar
  7. 7.
    Liu Y, Nie L, Han L, Zhang L, Rosenblum DS (2015) Action2activity: recognizing complex activities from sensor data. In: Proceedings of the twenty-fourth international joint conference of artificial intelligence (IJCAI), pp 1617–1623Google Scholar
  8. 8.
    Liu Y, Nie L, Liu L, Rosenblum DS (2016) From action to activity: Sensor-based activity recognition. Neurocomputing 181:108–115CrossRefGoogle Scholar
  9. 9.
    Liu Y, Yang C, Wu S, Chou YS (2018) Progressive (k,n) secret image sharing schemes based on Boolean operations and covering codes. Signal Process Image Commun 66:77–86CrossRefGoogle Scholar
  10. 10.
    Liu Y, Yang C, Yeh PH (2014) Reducing shadow size in smooth scalable secret image sharing. Security and Communication Networks 7(12):2237–2244CrossRefGoogle Scholar
  11. 11.
    Liu Y, Yang CN (2017) Scalable secret image sharing scheme with essential shadows. Signal Process Image Commun 58:49–55CrossRefGoogle Scholar
  12. 12.
    Naor M, Shamir A (1995) Visual cryptography. Proc Eurocrypt94, LNCS 950:1–12MathSciNetzbMATHGoogle Scholar
  13. 13.
    Shamir A (1979) How to share a secret. Commun ACM 22(11):612–613MathSciNetCrossRefGoogle Scholar
  14. 14.
    Steinfeld R, Pieprzyk J, Wang HX (2006) Lattice-based threshold-changeability for standard crt secret- sharing schemes. Finite Fields Appl 12(4):653–680MathSciNetCrossRefGoogle Scholar
  15. 15.
    Steinfeld R, Pieprzyk J, Wang HX (2007) Lattice-based threshold changeability for standard shamir secret-sharing schemes. IEEE Trans Inf Theory 53(7):2542–2559MathSciNetCrossRefGoogle Scholar
  16. 16.
    Thien, Lin JC (2002) Secret image sharing. Comput Graph 26(5):765–770CrossRefGoogle Scholar
  17. 17.
    Wang H, Wong DS (2008) On secret reconstruction in secret sharing schemes. IEEE Trans Inf Theory 54(1):473–480MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wang R, Shyu SJ (2007) Scalable secret image sharing. Signal Process Image Commun 22(4):363–373CrossRefGoogle Scholar
  19. 19.
    Wang RZ (2009) Region incrementing visual cryptography. IEEE Signal Process Lett 16(8):659–662CrossRefGoogle Scholar
  20. 20.
    Wang Z, Di Y, Li, Chang, Liu H (2016) Progressive secret image sharing scheme using meaningful shadows. Security and Communication Networks 9 (17):4075–4088CrossRefGoogle Scholar
  21. 21.
    Xiao H, Wang H, Wang B (2016) Quantum ramp secret sharing scheme and quantum operations. Int J Theor Phys 55(9):3807–3815MathSciNetCrossRefGoogle Scholar
  22. 22.
    Yan X, Wang S, Niu XM (2016) Threshold progressive visual cryptography construction with unexpanded shares. Mutimedia Tools and Applications 75(14):8657–8674CrossRefGoogle Scholar
  23. 23.
    Yang C, Chu YY (2011) A general (k,n) scalable secret image sharing scheme with the smooth scalability. J Syst Softw 84 (10):1726–1733CrossRefGoogle Scholar
  24. 24.
    Yang C, Huang SM (2010) Constructions and properties of k out of n scalable secret image sharing. Opt Commun 283(9):1750–1762CrossRefGoogle Scholar
  25. 25.
    Yang C, Ouyang J, Harn L (2012) Steganography and authentication in image sharing without parity bits. Opt Commun 285(7):1725–1735CrossRefGoogle Scholar
  26. 26.
    Yang C, Shih H, Wu, Harn L (2012) K out of n region incrementing scheme in visual cryptography. IEEE Trans Circuits Syst Video Technol 22(5):799–809CrossRefGoogle Scholar
  27. 27.
    Yuan L, Li M, Guo C, Choo K.-K., Ren Y (2016) Novel threshold changeable secret sharing schemes based on polynomial interpolation. PloS One 11 (10):1–19Google Scholar
  28. 28.
    Yuan L, Li M, Guo C, Hu W, Luo XJ (2016) Secret image sharing scheme with threshold changeable capability. Math Probl Eng 2016:1–11MathSciNetzbMATHGoogle Scholar
  29. 29.
    Zhang Z, Chee Y, Ling S, Liu M, Wang H (2012) Threshold changeable secret sharing schemes revisited. Theor Comput Sci 418:106–115MathSciNetCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.XI’AN University of TechnologyXi’anChina
  2. 2.Department of CSIENational Dong Hwa UniversityHualien CountryTaiwan
  3. 3.SeeleTech CorporationSan FranciscoUSA

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