Multimedia Tools and Applications

, Volume 76, Issue 5, pp 7087–7103 | Cite as

A secret image sharing scheme based on piecewise linear chaotic map and Chinese remainder theorem

Article

Abstract

In this paper, a secret image sharing scheme, by combining arithmetic compression coding and Chinese remainder theorem (CRT) is proposed. It is well known that arithmetic compression coding method for image has a good compressibility, and it can reduce the size of the shadow image, which consists of sharing values. Usually, a smaller shadow image is convenient to store and transmit. The piecewise linear map is applied to design compression coding scheme, which has the same properties as the conventional arithmetic compression coding. The CRT is used to construct the sharing scheme for compression codes. Meanwhile, it also has encryption effects in the process of sharing. Finally, the security and the effectiveness of the secret image sharing scheme are confirmed by some computer simulation results.

Keywords

Piecewise linear map Chinese remainder theorem (CRT) Compression coding scheme Sharing scheme 

References

  1. 1.
    Bao L, Zhou Y, Chen CLP (2014) A lossless (2,8)-chaos-based secret image sharing Scheme. IEEE International Conference on Systems, Man, and CyberneticsGoogle Scholar
  2. 2.
    Bose R, Pathak S (2006) A novel compression and encryption scheme using variable model arithmetic coding and coupled chaotic system. IEEE Trans Circuits and Systems-I: Regular Papers 53(4):848–857MathSciNetCrossRefGoogle Scholar
  3. 3.
    Chang CC, Lin CC, Lin CH, Chen YH (2008) A novel secret image sharing scheme in color images using small shadow images. Inf Sci 178(11):2433–2447CrossRefGoogle Scholar
  4. 4.
    Chen GR, Mao YB, Chui CK (2004) A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos, Solitons and Fractals 21(3):749–761MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Chien MC, Ing j, Hwang G (2012) Secret image sharing using (t,n) threshold scheme with lossless recovery. IEEE International Congress on Image and Signal ProcessingGoogle Scholar
  6. 6.
    Devaki P, Rao GR (2012) Lossless reconstruction of secret image using threshold secret sharing and transformation. International Journal of Network Security and Its Applications 4(3):111–119CrossRefGoogle Scholar
  7. 7.
    Duan LL, Liao XF, Xiang T (2011) A secure arithmetic coding based on Markov model. Commun Nonlinear Sci Numer Simul 16(6):2554–2562MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Eslami Z, Ahmadabadi JZ (2010) A verifiable multi-secret sharing scheme based on cellular automata. Inf Sci 180(15):2889–2894MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Harn L, Lin CL (2010) Strong (n,t,n) verifiable secret sharing scheme. Inf Sci 180(16):3059–3064MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Huang XL, Ye GD (2014) An image encryption algorithm based on hyper-chaos and DNA sequence. Multimedia tools and applications 72(1):57–70CrossRefGoogle Scholar
  11. 11.
    Iftene S, Boureanu IC (2005) Weighted threshold secret sharing based on the Chinese remainder theorem. Scientific Annals of Cuza University 15:161–172MathSciNetMATHGoogle Scholar
  12. 12.
    Kwok HS, Tang WKS (2007) A fast image encryption system based on chaotic maps with finite precision representation. Chaos, Solitons and Fractals 32(4):1518–1529MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Li S, Zhao YH, Qu BY, Wang JA (2013) Image scrambling based on chaotic sequences and Veginre cipher. Multimedia tools and applications 66(3):573–588CrossRefGoogle Scholar
  14. 14.
    Lin QZ, Wong KW, Chen JY (2013) An enhanced variable-length arithmetic coding and encryption scheme using chaotic maps. J Syst Softw 86(5):1384–1389CrossRefGoogle Scholar
  15. 15.
    Luca MB, Serbanescu A, Azou S, Burel G (2004) A new compression method using a chaotic symbolic approach. In: Proceedings of IEEE Commun. Conf., Bucharest, RomaniaGoogle Scholar
  16. 16.
    Mi B, Liao XF, Chen Y (2008) A novel chaotic encryption scheme based on arithmetic coding. Chaos, Solitons and Fractals 38(5):1523–1531CrossRefGoogle Scholar
  17. 17.
    Nagaraj N, Vaidya PG, Bhat KG (2009) Arithmetic coding as a non-linear dynamical system. Commun Nonlinear Sci Numer Simul 14(4):1013–1020MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Norouzi B, Mirzakuchaki S, Seyedzadeh SM, Mosavi MR (2014) A simple, sensitive and secure image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Multimedia Tools and Applications 71(3):1469–1497CrossRefGoogle Scholar
  19. 19.
    Rehman AU, Liao XF, Kulsoom A, Abbas SA (2015) Selective encryption for gray images based on chaos and DNA complementary rules. Multimedia Tools and Applications 74(1):4655– 4677CrossRefGoogle Scholar
  20. 20.
    Sharma S (2013) An implementation of a novel secret image sharing algorithm. International Journal of Computer Science and Mobile Computing 2(4):263–268Google Scholar
  21. 21.
    Shamir A (1979) How to share a secret. Commun ACM 22(11):612–613MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Shyu SJ, Chen YR (2008) Threshold secret image sharing by chinese remainder theorem. IEEE Asia-Pacific Services Computing ConferenceGoogle Scholar
  23. 23.
    Shyu SJ (2013) Visual cryptograms of random grids for general access structures. IEEE Transactions on Circuits and Systems for Video Technology 23(3):414–424CrossRefGoogle Scholar
  24. 24.
    Thien CC, Lin JC (2002) Secret image sharing. Comput Graph 26(5):765–770CrossRefGoogle Scholar
  25. 25.
    Thien CC, Lin JC (2003) An image-sharing method with user-friendly shadow images. IEEE Transactions on Circuits and Systems for Video Technology 13 (12):1161–1169CrossRefGoogle Scholar
  26. 26.
    Wang RZ, Su CH (2006) Secret image sharing with smaller shadow images. Pattern Recogn Lett 27(6):551–555CrossRefGoogle Scholar
  27. 27.
    Wong KW, Lin QZ, Chen JY (2010) Simultaneous arithmetic coding and encryption using chaotic maps. IEEE Trans Circults and Systems-II: Express Briefs 57 (2):146–150CrossRefGoogle Scholar
  28. 28.
    Wu KS (2013) A secret image sharing scheme for light images. EURASIP Journal on Advances in Signal Processing 2013(1):1–5CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.College of Electronic and Information EngineeringSouthwest UniversityChongqingChina

Personalised recommendations