Skip to main content
SpringerLink
Log in

A secure image encryption scheme based on a novel 2D sine–cosine cross-chaotic (SC3) map

  • Original Research Paper
  • Published:
Journal of Real-Time Image Processing Aims and scope Submit manuscript

Abstract

In this paper, we propose a new 2D sine–cosine cross-chaotic (SC3) map to design an image encryption scheme with high confusion and diffusion capability. We evaluate the maximum Lyapunov exponent (MLE) of the proposed SC3 map to measure its degree of sensitivity to initial conditions and perform bifurcation analysis to find the chaotic region. The proposed chaotic map generates two pseudo-random sequence \(R_1\) and \(R_2\), which are used in confusion (permutation) and diffusion phase, respectively. The confusion layer is designed by shuffling the image pixels, and the diffusion layer is designed by bitwise XOR operation. The strength of the proposed image encryption scheme is evaluated against resistance to the statistical attack (information entropy, correlation coefficient, and histogram analysis), differential attack (NPCR and UACI), and sensitivity to the secret key. The experimental results of both security and performance analysis show that the proposed image encryption scheme is secure enough to resist all the existing cryptanalytic attack and efficient in terms of encryption time.

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
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Daemen, J., Rijmen, V.: The Design of Rijndael: AES-the Advanced Encryption Standard. Springer Science & Business Media, New York (2013)

    MATH  Google Scholar 

  2. Coppersmith, D.: The data encryption standard (des) and its strength against attacks. IBM J. Res. Dev. 38(3), 243–250 (1994)

    Article  Google Scholar 

  3. Hell, M., Johansson, T., Meier, W.: Grain: a stream cipher for constrained environments. IJWMC 2(1), 86–93 (2007)

    Article  Google Scholar 

  4. Kocarev, L.: Chaos-based cryptography: a brief overview. IEEE Circuits Syst. Mag. 1(3), 6–21 (2001)

    Article  Google Scholar 

  5. Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc. Chaos 16(08), 2129–2151 (2006)

    Article  MathSciNet  Google Scholar 

  6. Liu, H., Kadir, A., Niu, Y.: Chaos-based color image block encryption scheme using s-box. AEU Int. J. Electron. Commun. 68(7), 676–686 (2014)

    Article  Google Scholar 

  7. Wang, M., Wang, X., Zhang, Y., Zhou, S., Zhao, T., Yao, N.: A novel chaotic system and its application in a color image cryptosystem. Opt. Lasers Eng. 121, 479–494 (2019)

    Article  Google Scholar 

  8. Shannon, C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949)

    Article  MathSciNet  Google Scholar 

  9. Zhou, Y., Bao, L., Chen, C.P.: A new 1d chaotic system for image encryption. Signal Process. 97, 172–182 (2014)

    Article  Google Scholar 

  10. Hussain, I., Shah, T., Gondal, M.A.: Application of s-box and chaotic map for image encryption. Math. Comput. Model. 57(9–10), 2576–2579 (2013)

    Article  Google Scholar 

  11. Ye, G.: Image scrambling encryption algorithm of pixel bit based on chaos map. Pattern Recognit. Lett. 31(5), 347–354 (2010)

    Article  Google Scholar 

  12. 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)

    Article  MathSciNet  Google Scholar 

  13. Diab, H.: An efficient chaotic image cryptosystem based on simultaneous permutation and diffusion operations. IEEE Access 6, 42227–42244 (2018)

    Article  Google Scholar 

  14. Diab, H., El-semary, A.M.: Secure image cryptosystem with unique key streams via hyper-chaotic system. Signal Process. 142, 53–68 (2018)

    Article  Google Scholar 

  15. Hua, Z., Zhou, Y.: Image encryption using 2D logistic-adjusted-sine map. Inf. Sci. 339, 237–253 (2016)

    Article  Google Scholar 

  16. Marton, K., Suciu, A.: On the interpretation of results from the NIST statistical test suite. Sci. Technol. 18(1), 18–32 (2015)

    Google Scholar 

  17. Li, S., Zheng, X.: Cryptanalysis of a chaotic image encryption method. In: 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat.No. 02CH37353), vol. 2, pp. II–II. IEEE (2002)

  18. Rosenstein, M.T., Collins, J.J., De Luca, C.J.: A practical method for calculating largest lyapunov exponents from small data sets. Phys. D Nonlinear Phenpomena 65(1–2), 117–134 (1993)

    Article  MathSciNet  Google Scholar 

  19. Mondal, B., Kumar, P., Singh, S.: A chaotic permutation and diffusion based image encryption algorithm for secure communications. Multimed. Tools Appl. 77(23), 31177–31198 (2018)

    Article  Google Scholar 

  20. Mondal, B., Mandal, T.: A novel chaos based secure image encryption algorithm. Int. J. Appl. Eng. Res. 11(5), 3120–3127 (2016)

    Google Scholar 

  21. Mondal, B., Singh, S., Kumar, P.: A secure image encryption scheme based on cellular automata and chaotic skew tent map. J. Inf. Secur. Appl. 45, 117–130 (2019)

    Google Scholar 

  22. Ping, P., Wu, J., Mao, Y., Xu, F., Fan, J.: Design of image cipher using life-like cellular automata and chaotic map. Signal Process. 150, 233–247 (2018)

    Article  Google Scholar 

  23. Wu, X., Kan, H., Kurths, J.: A new color image encryption scheme based on dna sequences and multiple improved 1d chaotic maps. Appl. Soft Comput. 37, 24–39 (2015)

    Article  Google Scholar 

  24. Bhaskar Mondal, T.M.: A light weight secure image encryption scheme based on chaos & dna computing. J. King Saud Univ. Comput. Inf. Sci. 26, 499–504 (2016)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  26. Çavuşoğlu, U., Kaçar, S., Pehlivan, I., Zengin, A.: Secure image encryption algorithm design using a novel chaos based s-box. Chaos Solitons Fractals 95, 92–101 (2017)

    Article  Google Scholar 

  27. Silva-Garcia, V., Flores-Carapia, R., Renteria-Marquez, C., Luna-Benoso, B., Aldape-Perez, M.: Substitution box generation using chaos: an image encryption application. Appl. Math. Comput. 332, 123–135 (2018)

    MathSciNet  MATH  Google Scholar 

  28. Zhu, Z., Zhang, W., Wong, Kw., Yu, H.: A chaos-based symmetric image encryption scheme using a bit-level permutation. Inf. Sci. 181(6), 1171–1186 (2011)

    Article  Google Scholar 

  29. Belazi, A., El-Latif, A.A.A., Belghith, S.: A novel image encryption scheme based on substitution–permutation network and chaos. Signal Process. 128, 155–170 (2016)

    Article  Google Scholar 

  30. Cao, C., Sun, K., Liu, W.: A novel bit-level image encryption algorithm based on 2d-licm hyperchaotic map. Signal Process. 143, 122–133 (2018)

    Article  Google Scholar 

  31. Fu, C., Huang, J.B., Wang, N.N., Hou, Q.B., Lei, W.M.: A symmetric chaos based image cipher with an improved bit-level permutation strategy. Entropy 16(2), 770–788 (2014)

    Article  Google Scholar 

  32. Ping, P., Xu, F., Mao, Y., Wang, Z.: Designing permutation-substitution image encryption networks with henon map. Neurocomputing 283, 53–63 (2018)

    Article  Google Scholar 

  33. Kandar, S., Chaudhuri, D., Bhattacharjee, A., Dhara, B.C.: Image encryption using sequence generated by cyclic group. J. Inf. Secur. Appl. 44, 117–129 (2019)

    Google Scholar 

  34. Zhang, X., Feng, G., Ren, Y., Qian, Z.: Scalable coding of encrypted images. IEEE Trans. Image Process. 21(6), 3108–14 (2012)

    Article  MathSciNet  Google Scholar 

  35. Qin, C., Zhou, Q., Cao, F., Dong, J., Zhang, X.: Flexible lossy compression for selective encrypted image with image inpainting. In: IEEE Transactions on Circuits and Systems for Video Technology (2018)

  36. Panwar, K., Purwar, R.K., Jain, A.: Cryptanalysis and improvement of a color image encryption scheme based on DNA sequences and multiple 1D chaotic maps. Int. J. Bifurc. Chaos 29(08), 1950103 (2019)

    Article  MathSciNet  Google Scholar 

  37. Panwar, K., Purwar, R.K., Jain, A.: Cryptanalysis and improvement of an image encryption scheme using combination of one-dimensional chaotic maps. J. Electron. Imaging 27(5), 053037 (2018)

    Google Scholar 

  38. Al-Shameri, W.F.: Dynamical properties of the Hénon mapping. Int. J. Math. Anal. 6(49), 2419–30 (2012)

    MathSciNet  MATH  Google Scholar 

  39. Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E.: A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. Booz-Allen and Hamilton Inc, Mclean (2001)

    Google Scholar 

  40. Chen, J., Zhu, Z.L., Zhang, L.B., Zhang, Y., Yang, B.Q.: Exploiting self-adaptive permutation-diffusion and DNA random encoding for secure and efficient image encryption. Signal Process. 1(142), 340–53 (2018)

    Article  Google Scholar 

  41. Ping, P., Fan, J., Mao, Y., Xu, F., Gao, J.: A chaos based image encryption scheme using digit-level permutation and block diffusion. IEEE Access 6, 67581–67593 (2018)

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the editor and all anonymous reviewers for their comments and suggestions which improved both the technical and editorial quality of the paper.

Author information

Authors and Affiliations

  1. Xavier School of Computer Science and Engineering, Xavier University Bhubaneswar, Orissa, India

    Bhaskar Mondal

  2. Department of Computer Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, India

    Pratap Kumar Behera & Sugata Gangopadhyay

Authors
  1. Bhaskar Mondal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pratap Kumar Behera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sugata Gangopadhyay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pratap Kumar Behera.

Ethics declarations

Conflict of interest

The authors declared that they have no conflicts of interest to this work.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mondal, B., Behera, P.K. & Gangopadhyay, S. A secure image encryption scheme based on a novel 2D sine–cosine cross-chaotic (SC3) map. J Real-Time Image Proc 18, 1–18 (2021). https://doi.org/10.1007/s11554-019-00940-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11554-019-00940-4

Keywords

Search

Navigation