CT Image Secret Sharing Based on Chaotic Map and Singular Value Decomposition

  • Feixiang Zhao
  • Mingzhe LiuEmail author
  • Xianghe Liu
  • Xin Jiang
  • Zhirong Tang
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 895)


In order to prevent CT images from being stolen and tampered in telemedicine, a secret sharing method of (n, n) structure is designed and combined with the classical chaotic digital image encryption method. The method consists of three parts: In the first part, singular value decomposition is used to generate the key of the Henon chaotic map and CT subgraphs; in the second part, the Henon map is used to generate chaotic sequences of scramble CT subgraphs. Then a valueless image selected by the user is used as an impurity image, the diffusing operation is completed by a XOR operation between the impurity image and the image obtained by the scrambling operation. Finally, the image obtained by the diffusing operation is divided into multiple parts by the secret sharing method designed in this paper and embedded into the cover images selected by the user to generate several shadow images. The third part is the decryption part, and the decryptor completes the decryption when all the shadow images, impurity image and keys are collected. Several experiments have shown that this method has excellent performance in the test of ciphertext statistical characteristics, sensitivity, PSNR and other typical indicators for measuring the performance of image encryption methods.


Singular value decomposition Chaotic map Secret sharing CT image 


  1. 1.
    Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurcat. Chaos 08, 1259–1284 (1998)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Wang, X., Yang, L., Liu, R., Kadir, A.: A chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn. 62, 615–621 (2010)CrossRefGoogle Scholar
  3. 3.
    Kanso, A., Ghebleh, M.: A novel image encryption algorithm based on a 3D chaotic map. Commun. Nonlinear Sci. Numer. Simul. 17, 2943–2959 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chen, G., Mao, Y., Chui, C.: A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Solitons Fractals 21, 749–761 (2004)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Liu, L., Zhang, Q., Wei, X., Zhou, C.: Image encryption algorithm based on chaotic modulation of Arnold dual scrambling and DNA computing. Adv. Sci. Lett. 4, 3537–3542 (2011)CrossRefGoogle Scholar
  6. 6.
    Wu, Y., Zhou, Y., Noonan, J., Agaian, S.: Design of image cipher using latin squares. Inf. Sci. 264, 317–339 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Lafe, O.: Data compression and encryption using cellular automata transforms. Eng. Appl. Artif. Intell. 10, 581–591 (1997)CrossRefGoogle Scholar
  8. 8.
    Chen, R., Lai, J.: Image security system using recursive cellular automata substitution. Pattern Recogn. 40, 1621–1631 (2007)CrossRefGoogle Scholar
  9. 9.
    Machkour, M., Saaidi, A., Benmaati, M.: A novel image encryption algorithm based on the two-dimensional logistic map and the latin square image cipher. 3D Res. 6, 18 (2015)CrossRefGoogle Scholar
  10. 10.
    Bakhshandeh, A., Eslami, Z.: An authenticated image encryption scheme based on chaotic maps and memory cellular automata. Opt. Lasers Eng. 51, 665–673 (2013)CrossRefGoogle Scholar
  11. 11.
    Panduranga, H., Naveen Kumar, S., Kiran: Image encryption based on permutation-substitution using chaotic map and Latin Square Image Cipher. Eur Phys. J. Spec. Top. 223, 1663–1677 (2014)Google Scholar
  12. 12.
    Liao, X., Lai, S., Zhou, Q.: A novel image encryption algorithm based on self-adaptive wave transmission. Signal Process. 90, 2714–2722 (2010)CrossRefGoogle Scholar
  13. 13.
    Kekre, H., Sarode, T., Halarnkar, P.: Partial image scrambling using walsh sequency in sinusoidal wavelet transform domain. Intell. Syst. Technol. Appl. 384, 471–484 (2016)Google Scholar
  14. 14.
    Lai, S., Liao, X., Zhou, Q.: Novel image encryption algorithm based on wave transmission. J. Comput. Appl. 29, 2210–2212 (2009)Google Scholar
  15. 15.
    Ye, G.: A block image encryption algorithm based on wave transmission and chaotic systems. Nonlinear Dyn. 75, 417–427 (2013)CrossRefGoogle Scholar
  16. 16.
    Shamir, A.: How to share a secret. Commun. ACM 22, 612–613 (1979)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Naor, M., Shamir, A.: Visual cryptography. In: Lecture Notes in Computer Science, vol. 950, pp. 1–12. Springer, Berlin (1994)Google Scholar
  18. 18.
    Wang, D., Zhang, L., Ma, N., Li, X.: Two secret sharing schemes based on Boolean operations. Pattern Recogn. 40, 2776–2785 (2007)CrossRefGoogle Scholar
  19. 19.
    Wu, H., Wang, H., Yu, R.: Color visual cryptography scheme using meaningful shares. In: Eighth International Conference on Intelligent Systems Design and Applications. pp. 173–178. IEEE (2008)Google Scholar
  20. 20.
    Yang, C., Yang, Y.: New extended visual cryptography schemes with clearer shadow images. Inf. Sci. 271, 246–263 (2014)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zhou, Y., Agaian, S., Joyner, V., Panetta, K.: Two Fibonacci P-code based image scrambling algorithms. In: Astola, J., Egiazarian, K., Dougherty, E. (eds.) Image Processing: Algorithms and Systems VI. SPIE (2008)Google Scholar
  22. 22.
    Podoba, T., Giesl, J., Vlcek, K.: Image encryption in wavelet domain based on chaotic maps. In: 2009 2nd International Congress on Image and Signal Processing, pp. 1–5. IEEE (2009)Google Scholar
  23. 23.
    Gu, G.S., Han, G.Q.: The application of chaos and DWT in image scrambling. In: 5th International Conference on Machine Learning and Cybernetics, pp. 3729–3733. IEEE (2006)Google Scholar
  24. 24.
    Yang, C., Huang, S.: Constructions and properties of k out of n scalable secret image sharing. Opt. Commun. 283, 1750–1762 (2010)CrossRefGoogle Scholar
  25. 25.
    Thien, C.C., Lin, J.C.: Secret image sharing. Comput. Graph. 26, 765–770 (2002)CrossRefGoogle Scholar
  26. 26.
    Wang, R., Su, C.: Secret image sharing with smaller shadow images. Pattern Recogn. Lett. 27, 551–555 (2006)CrossRefGoogle Scholar
  27. 27.
    Wu, K.: A secret image sharing scheme for light images. EURASIP J. Adv. Signal Process. 2013, 49 (2013)CrossRefGoogle Scholar
  28. 28.
    Liu, Y., Zhong, Q., Shen, J., Chang, C.: A novel image protection scheme using bit-plane compression and secret sharing. J. Chin. Inst. Eng. 40, 161–169 (2017)CrossRefGoogle Scholar
  29. 29.
    Liu, Y., Wu, Z.: An improved threshold multi-level image recovery scheme. J. Inf. Secur. Appl. 40, 166–172 (2018)Google Scholar
  30. 30.
    Ahmad, M., Ahmad, F.: Cryptanalysis of image encryption based on permutation-substitution using chaotic map and latin square image cipher. In: 3rd International Conference on Frontiers of Intelligent Computing: Theory and Applications, pp. 481–488. Springer, Berlin (2014)Google Scholar
  31. 31.
    Rhouma, R., Belghith, S.: Cryptanalysis of a new image encryption algorithm based on hyper-chaos. Phys. Lett. A 372, 5973–5978 (2008)CrossRefGoogle Scholar
  32. 32.
    Çokal, C., Solak, E.: Cryptanalysis of a chaos-based image encryption algorithm. Phys. Lett. A 373, 1357–1360 (2009)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Zhang, Y.: Cryptanalysis of an image encryption algorithm based on chaotic modulation of Arnold dual scrambling and DNA computing. Adv. Sci. Focus 2, 67–82 (2014)CrossRefGoogle Scholar
  34. 34.
    Xie, T., Liu, Y., Tang, J.: Breaking a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Optik Int. J. Light Electron Optics 125, 7166–7169 (2014)CrossRefGoogle Scholar
  35. 35.
    Wu, J., Liao, X., Yang, B.: Cryptanalysis and enhancements of image encryption based on three-dimensional bit matrix permutation. Signal Process. 142, 292–300 (2018)CrossRefGoogle Scholar
  36. 36.
    Grassberger, P., Kantz, H., Moenig, U.: On the symbolic dynamics of the henon map. J. Phys. A: Gen. Phys. 22(22), 5217 (1989)CrossRefGoogle Scholar
  37. 37.
    Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurcat. Chaos 16, 2129–2151 (2006)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Li, C., Lo, K.: Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process. 91, 949–954 (2011)CrossRefGoogle Scholar
  39. 39.
    Lan, R., He, J., Wang, S., Liu, Y., Luo, X.: A parameter-selection-based chaotic system. IEEE Trans. Circuits Syst. II Express Briefs PP, 1 (2018)Google Scholar
  40. 40.
    Lan, R., He, J., Wang, S., Gu, T., Luo, X.: Integrated chaotic systems for image encryption. Signal Process. 147, 133–145 (2018)CrossRefGoogle Scholar
  41. 41.
    Hua, Z., Jin, F., Xu, B., Huang, H.: 2D Logistic-Sine-coupling map for image encryption. Signal Process. 149, 148–161 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Feixiang Zhao
    • 1
  • Mingzhe Liu
    • 1
    Email author
  • Xianghe Liu
    • 1
  • Xin Jiang
    • 1
  • Zhirong Tang
    • 1
  1. 1.State Key Laboratory of Geohazard Prevention and Geoenvironment ProtectionChengdu University of TechnologySichuanChina

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