Skip to main content
SpringerLink
Log in

A robust image encryption scheme using chaotic tent map and cellular automata

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper suggests a unique image encryption scheme based on key-based block ciphering followed by shuffling of ciphered bytes with variable-sized blocks, which makes this scheme substantially robust compared to other contemporary schemes available. Another distinguishing feature of this scheme is the usage of variable-sized key streams for consecutive blocks. Based on the elementary cellular automata with chaotic tent map, distinct key streams are used to cipher individual blocks. In the subsequent step, the bytes of the ciphered block so obtained are further shuffled to make the scheme more diffused. The block size varies with the varying key stream, which is again dependent on the preceding key stream as well as the plain image. It needs to be mentioned that the size of the first block and the key stream are generated from a 64-byte secret key and the plain image. Values of correlation and the number of pixel change rate between the original and the encrypted images are 0.000479 and 99.620901, respectively. Both of the above results along with other relevant experimental results strongly establish the robustness of the proposed scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. National Bureau of Standards: Data encryption standard. Fed. Inf. Process. Stand. Publ. 46(3), 1–22 (1999)

    Google Scholar 

  2. Barker, W.C., Barker, E.: Recommendation for the triple data encryption algorithm (TDEA) block cipher. NIST Special Publication 800, 1–26, Rev.2 (2012)

  3. Daemen, J., Rijmen, V.: Rijndael—the advanced encryption standard. Dr. Dobb’s J. 137–139 (2001)

  4. Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)

    MathSciNet  MATH  Google Scholar 

  5. Alvarez, E., Fernàndez, A., Garcìa, P., Jimènez, J., Marcano, A.: New approach to chaotic encryption. J. Phys. Lett. A 263(4–6), 373–375 (1999)

    Google Scholar 

  6. Chen, G., Mao, Y., Chui, C.K.: A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Solitons Fractals 21(3), 749–761 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Tong, X., Cui, M., Wang, Z.: A new feedback image encryption scheme based on perturbation with dynamical compound chaotic sequence cipher generator. J. Opt. Commun. 282(14), 2722–2728 (2009)

    Google Scholar 

  8. Wei, X., Guo, L., Zhang, Q., Zhang, J., Lian, S.: A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system. J. Syst. Softw. 85(2), 290–299 (2012)

    Google Scholar 

  9. Gao, H., Zhang, Y., Liang, S., Li, D.: A new chaotic algorithm for image encryption. Chaos Solitons Fractals 29(2), 393–399 (2006)

    MATH  Google Scholar 

  10. Pareek, N.K., Patidar, V., Sud, K.K.: Image encryption using chaotic logistic map. Image Vis. Comput. 24(9), 926–934 (2006)

    Google Scholar 

  11. Kanso, A., Smaoui, N.: Logistic chaotic maps for binary numbers generations. Chaos Solitons Fractals 40(5), 2557–2568 (2009)

    MATH  Google Scholar 

  12. Sathiskumar, G.A., Bagan, K.B.: A novel image encryption algorithm using pixel shuffling and base 64 encoding based chaotic block cipher (IMPSBEC). WSEAS Trans. Comput. 10(6), 169–178 (2011)

    Google Scholar 

  13. Wang, X., Teng, L., Qin, X.: A novel colour image encryption algorithm based on chaos. J. Signal Process. 92(4), 1101–1108 (2012)

    MathSciNet  Google Scholar 

  14. Zhou, Y., Bao, L., Chen, C.L.P.: Image encryption using a new parametric switching chaotic system. J. Signal Process. 93(11), 3039–3052 (2013)

    Google Scholar 

  15. Arroyo, D., Diaz, J., Rodriguez, F.B.: Cryptanalysis of a one round chaos-based substitution permutation network. J. Signal Process. 93(5), 1358–1364 (2013)

    Google Scholar 

  16. Lian, S., Sun, J., Wang, Z.: A block cipher based on a suitable use of chaotic standard map. Chaos Solitons Fractals 26(1), 117–129 (2005)

    MATH  Google Scholar 

  17. Yoon, J.W., Kim, H.: An image encryption scheme with a pseudorandom permutation based on chaotic maps. Commun. Nonlinear Sci. Numer. Simul. 15(12), 3998–4006 (2010)

    MathSciNet  MATH  Google Scholar 

  18. Borujeni, S.E., Eshghi, M.: Chaotic image encryption system using phase-magnitude transformation and pixel substitution. J. Telecommun. Syst. 52(2), 525–537 (2011)

    Google Scholar 

  19. Zhang, G., Liu, Q.: A novel image encryption method based on total shuffling scheme. J. Opt. Commun. 284, 2775–2780 (2011)

    Google Scholar 

  20. Huang, C.K., Liao, C.W., Hsu, S.L., Jeng, Y.C.: Implementation of gray image encryption with pixel shuffling and gray-level encryption by single chaotic system. J. Telecommun. Syst. 52(2), 563–571 (2011)

    Google Scholar 

  21. Zhu, C.: A novel image encryption scheme based on improved hyperchaotic sequences. J. Opt. Commun. 285(1), 29–37 (2012)

    Google Scholar 

  22. Mirzaei, O., Yaghoobi, M., Irani, H.: A new image encryption method: parallel sub-image encryption with hyper chaos. Nonlinear Dyn. 67, 557–566 (2012)

    MathSciNet  Google Scholar 

  23. Huang, X.: Image encryption algorithm using chaotic chebyshev generator. J. Nonlinear Dyn. 67(4), 2411–2417 (2012)

    MathSciNet  Google Scholar 

  24. Norouzi, B., Seyedzadeh, S.M., Mirzakuchaki, S., Mosavi, M.R.: A novel image encryption based on hash function with only two-round diffusion process. Multimed. Syst. 20(1), 45–64 (2013)

    MATH  Google Scholar 

  25. Ye, G.: A block image encryption algorithm based on wave transmission and chaotic systems. Nonlinear Dyn. 75(3), 417–427 (2014)

    Google Scholar 

  26. Wang, X., Wang, Q.: A novel image encryption algorithm based on dynamic S-boxes constructed by chaos. Nonlinear Dyn. 75, 567–576 (2014)

    Google Scholar 

  27. Naskar, P.K., Chaudhuri, A.: A robust image encryption technique using dual chaotic map. Int. J. Electron. Secur. Digit. Forensics 7(4), 358–380 (2015)

    Google Scholar 

  28. Zhang, Q., Guo, L., Wei, X.: Image encryption using DNA addition combining with chaotic maps. J. Math. Comput. Model. 52(11), 2028–2035 (2010)

    MathSciNet  MATH  Google Scholar 

  29. Enayatifar, R., Abdullah, A.H., Isnin, I.F.: Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence. Opt. Lasers Eng. 56, 83–93 (2014)

    Google Scholar 

  30. Enayatifar, R., Sadaei, H.J., Abdullah, A.H., Lee, M., Isnin, I.F.: A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata. Opt. Lasers Eng. 71, 33–41 (2015)

    Google Scholar 

  31. Huang, X., Ye, G.: An image encryption algorithm based on hyper-chaos and DNA sequence. Multimed. Tools Appl. 72(1), 57–70 (2014)

    Google Scholar 

  32. Tuncer, T., Avci, E.: A reversible data hiding algorithm based on probabilistic DNA-XOR secret sharing scheme for color images. Displays 41, 1–8 (2016)

    Google Scholar 

  33. Wu, X., Wang, K., Wang, X., Kan, H.: Lossless chaotic color image cryptosystem based on DNA encryption and entropy. Nonlinear Dyn. 90(2), 855–875 (2017)

    MathSciNet  MATH  Google Scholar 

  34. Jin, J.: An image encryption based on elementary cellular automata. Opt. Lasers Eng. 50(12), 1836–1843 (2012)

    Google Scholar 

  35. Abdo, A.A., Lian, S., Ismail, I.A., Amin, M., Diab, H.: A cryptosystem based on elemetary cellular automata. Commun. Nonlinear Sci. Numer. Simul. 18, 136–147 (2013)

    MathSciNet  MATH  Google Scholar 

  36. Zhang, X., Wang, C., Zhong, S., Yao, Q.: Image encryption scheme based on balanced two-dimensional cellular automata. Math. Probl. Eng. 2013, 1–10 (2013)

    MATH  Google Scholar 

  37. Tralic, D., Grgic, S.: Robust image encryption based on balanced cellular automaton and pixel separation. Radioengineering 25(3), 548–555 (2016)

    Google Scholar 

  38. Naskar, P.K., Chaudhuri, A.: Secured secret sharing technique based on chaotic map and DNA encoding with application on secret image. Imaging Sci. J. 94(8), 460–470 (2016)

    Google Scholar 

  39. Naskar, P.K., Khan, H.N., Roy, U., Chaudhuri, A., Chaudhuri, A.: Secret image sharing with embedded session key. Int. Conf. CISIM 245, 289–294 (2011)

    Google Scholar 

  40. Tso, H.K.: Meaningful image sharing scheme using total automorphism. Nonlinear Dyn. 75(1–2), 1–6 (2014)

    Google Scholar 

  41. Xiao, X.L., Mou, H., Zhang, R.: A verifiable secret image sharing scheme based on compressive sensing. Wuhan Univ. J. Nat. Sci. 23(3), 219–224 (2018)

    MathSciNet  MATH  Google Scholar 

  42. Ahmadian, A.M., Amirmazlaghani, M.: A novel secret image sharing with steganography scheme utilizing optimal asymmetric encryption padding and information dispersal algorithms. Signal Process. Image Commun. 74, 78–88 (2019)

    Google Scholar 

  43. Li, C., Luo, G., Qin, K., Li, C.: An image encryption scheme based on chaotic tent map. Nonlinear Dyn. 87(1), 127–133 (2017)

    Google Scholar 

  44. Zhu, H., Zhang, X., Yu, H., Zhao, C., Zhu, Z.: An image encryption algorithm based on compound homogeneous hyper-chaotic system. Nonlinear Dyn. 89(1), 61–79 (2017)

    Google Scholar 

  45. Ye, G., Pan, C., Huang, X., Mei, Q.: An efficient pixel-level chaotic image encryption algorithm. Nonlinear Dyn. 94(1), 745–756 (2018)

    Google Scholar 

  46. Li, B., Liao, X., Jiang, Y.: A novel image encryption scheme based on improved random number generator and its implementation. Nonlinear Dyn. 95(3), 1781–1805 (2018)

    MATH  Google Scholar 

  47. Luo, Y., Zhou, R., Liu, J., Cao, Y., Ding, X.: A parallel image encryption algorithm based on the piecewise linear chaotic map and hyper-chaotic map. Nonlinear Dyn. 93(3), 1165–1181 (2018)

    Google Scholar 

  48. Wang, Y., Zhao, Y., Zhou, Q., Lin, Z.: Image encryption using partitioned cellular automata. Neurocomputing 275, 1318–1332 (2018)

    Google Scholar 

  49. Raza, S.F., Satpute, V.: A novel bit permutation-based image encryption algorithm. Nonlinear Dyn. 95(2), 859–873 (2018)

    Google Scholar 

  50. Wang, X., Feng, L., Li, R., Zhang, F.: A fast image encryption algorithm based on non-adjacent dynamically coupled map lattice model. Nonlinear Dyn. 95(4), 2797–2824 (2019)

    Google Scholar 

  51. Chen, J., Chen, L., Zhang, L.Y., Zhu, Z.: Medical image cipher using hierarchical diffusion and non-sequential encryption. Nonlinear Dyn. 96(1), 301–322 (2019)

    Google Scholar 

  52. Chai, X., Gan, Z., Yuan, K., Chen, Y., Liu, X.: A novel image encryption scheme based on DNA sequence operations and chaotic systems. Neural Comput. Appl. 31(1), 219–237 (2017)

    Google Scholar 

  53. Guesmi, R., Farah, M.A.B., Kachouri, A., Samet, M.: Hash key-based image encryption using crossover operator and chaos. Multimed. Tools Appl. 75(8), 4753–4769 (2015)

    MATH  Google Scholar 

  54. Guesmi, R., Farah, M.A.B., Kachouri, A., Samet, M.: A novel chaos-based image encryption using DNA sequence operation and Secure Hash Algorithm SHA-2. Nonlinear Dyn. 83(3), 1123–1136 (2015)

    MathSciNet  MATH  Google Scholar 

  55. Rehman, A-u, Liao, X., Kulsoom, A., Ullah, S.: A modified (dual) fusion technique for image encryption using SHA-256 hash and multiple chaotic maps. Multimed. Tools Appl. 75(18), 11241–11266 (2015)

    Google Scholar 

  56. Patro, K.A.K., Acharya, B.: An efficient colour image encryption scheme based on 1-d chaotic maps. J. Inf. Secur. Appl. 46, 23–41 (2019)

    Google Scholar 

  57. Li, C., Lin, D., Feng, B., Lu, J., Hao, F.: Cryptanalysis of a chaotic image encryption algorithm based on information entropy. IEEE Access 6, 75834–75842 (2018)

    Google Scholar 

  58. Ye, G.: A chaotic image encryption algorithm based on information entropy. Int. J. Bifurc. Chaos 28(1), 1850010(1–11) (2018)

    MathSciNet  MATH  Google Scholar 

  59. Li, C., Lin, D., Lu, J., Hao, F.: Cryptanalyzing an image encryption algorithm based on autoblocking and electrocardiography. IEEE Multimed. 25(4), 46–56 (2018)

    Google Scholar 

  60. Ye, G., Huang, X.: An image encryption algorithm based on autoblocking and electrocardiography. IEEE Multimed. 23(2), 64–71 (2016)

    Google Scholar 

  61. Yoshida, T., Mori, H., Shigematsu, H.: Analytic study of chaos of the tent map: band structures, power spectra, and critical behaviors. J. Stat. Phys. 31(2), 279–308 (1983)

    MathSciNet  Google Scholar 

  62. Kanso, A.: Self-shrinking chaotic stream ciphers. Commun. Nonlinear Sci. Numer. Simul. 16(2), 822–836 (2011)

    MathSciNet  MATH  Google Scholar 

  63. Li, S., Chen, G., Mou, X.: On the dynamical degradation of digital piecewise linear chaotic maps. Int. J. Bifurc. Chaos 15(10), 3119–3151 (2005)

    MathSciNet  MATH  Google Scholar 

  64. Li, C., Feng, B., Li, S., Kurths, J., Chen, G.: Dynamic analysis of digital chaotic maps via state-mapping networks. IEEE Trans. Circuits Syst. I Regul. Pap. 66(6), 2322–2335 (2019)

    MathSciNet  Google Scholar 

  65. Li, C., Zhang, Y., Xie, E.Y.: When an attacker meets a cipher-image in 2018: a year in review. J. Inf. Secur. Appl. 48, 1–9 (2019)

    Google Scholar 

  66. Lin, T., Chua, L.O.: On chaos of digital filters in the real world. IEEE Trans. Circuits Syst. 38(5), 557–558 (1991)

    Google Scholar 

  67. Li, C.-Y., Chen, Y.-H., Chang, T.-Y., Deng, L.-Y., To, K.: Period extension and randomness enhancement using high throughput reseeding mixing PRNG. IEEE Trans. Very Large Scale Integr. Syst. 20(2), 385–389 (2012)

    Google Scholar 

  68. Cernak, J.: Digital generators of chaos. Phys. Lett. A 214(3–4), 151–160 (1996)

    MathSciNet  MATH  Google Scholar 

  69. Hua, H., Zhou, Y.: One-dimensional nonlinear model for producing chaos. IEEE Trans. Circuits Syst. I 65(1), 235–246 (2018)

    Google Scholar 

  70. Nagaraj, N., Shastry, M.C., Vaidya, P.G.: Increasing average period lengths by switching of robust chaos maps in finite precision. Eur. Phys. J. Spec. Top. 165(1), 73–83 (2008)

    Google Scholar 

  71. Addabbo, T., Alioto, M., Fort, A., Rocchi, S., Vignoli, V.: A feedback strategy to improve the entropy of a chaos-based random bit generator. IEEE Trans. Circuits Syst. I 53(2), 326–337 (2006)

    MathSciNet  MATH  Google Scholar 

  72. Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55(3), 601–644 (1983)

    MathSciNet  MATH  Google Scholar 

  73. Naskar, P.K., Paul, S., Nandy, D., Chaudhuri, A.: DNA encoding and channel shuffling for secured encryption of audio data. Multimed. Tools Appl. 78(17), 25019–25042 (2019)

    Google Scholar 

  74. Flajolet, P., Poblete, P., Viola, A.: On the analysis of linear probing hashing. Algorithmica 22(4), 490–515 (1998)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We are thankful to the Department of Computer Science and Engineering, Government College of Engineering and Textile Technology, Serampore, Hooghly, W.B., India, and MCKV Institute of Engineering, Howrah, W.B., India, for giving us the platform for planning and developing this work using all departmental facilities. We are also deeply grateful to the editors for smooth and fast handling of the manuscript. We would also like to thank the anonymous reviewers for their valuable advices and suggestions to improve the quality of this paper.

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Government College of Engineering and Textile Technology, Serampore, Hooghly, WB, India

    Prabir Kumar Naskar & Dipta Nandy

  2. Department of Computer Science and Engineering, MCKV Institute of Engineering, Howrah, WB, India

    Surojit Bhattacharyya

  3. Veer Surendra Sai University of Technology, Burla, Odisha, India

    Atal Chaudhuri

Authors
  1. Prabir Kumar Naskar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Surojit Bhattacharyya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dipta Nandy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Atal Chaudhuri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Prabir Kumar Naskar.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Atal Chaudhuri: On lien from Department of C.S.E, Jadavpur University, Jadavpur, WB, India.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Naskar, P.K., Bhattacharyya, S., Nandy, D. et al. A robust image encryption scheme using chaotic tent map and cellular automata. Nonlinear Dyn 100, 2877–2898 (2020). https://doi.org/10.1007/s11071-020-05625-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-05625-3

Keywords

Search

Navigation