Skip to main content
SpringerLink
Log in

A secure image encryption scheme with compression-confusion-diffusion structure

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

This paper presents a novel image compression-encryption scheme, which has the compression-confusion-diffusion Structure. Firstly, based on Chebyshev chaotic map, a Gauss measurement matrix is constructed and optimized, which is applied to compressive sensing. Then, an image compression-encryption algorithm is proposed by using a six-dimensional discrete chaotic map. In the proposed scheme, the original image is transformed into a sparse coefficient matrix by discrete wavelet transform, and the sparse coefficients are measured by using the optimized Gauss measurement matrix to get the measured values. Then, the measured values are quantized into integer values and the compressed image is obtained. Furtherly, the compressed image is encrypted by using a six-dimensional chaotic map. In the process of encryption, the plaintext image is divided into two parts, when encrypting the second part, the first part is used as part of the key. While encrypting the first part, the ciphertext of the second part is used as part of the key. Thus, the algorithm has strong confusion and diffusion effect and makes ciphertext sensitive to plaintext. Experimental results such as effects of compression-encryption, key space analysis, key sensitivity analysis, differential analysis, histograms analysis, information entropy analysis, and correlation coefficients analysis show that the proposed scheme is secure and has high application potential.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Alvarez G, Li S (2006) Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurcation Chaos 16(8):2129–2151. https://doi.org/10.1142/s0218127406015970

    Article  MathSciNet  MATH  Google Scholar 

  2. Belazi A, El-Latif AAA (2017) A simple yet efficient S-box method based on chaotic sine map. Optik 130:1438–1444. https://doi.org/10.1016/j.ijleo.2016.11.152

    Article  Google Scholar 

  3. Candes EJ, Tao T (2006) Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans Inf Theory 52(12):5406–5425. https://doi.org/10.1109/tit.2006.885507

    Article  MathSciNet  MATH  Google Scholar 

  4. Candes EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489–509. https://doi.org/10.1109/tit.2005.862083

    Article  MathSciNet  MATH  Google Scholar 

  5. Chai X, Fu X, Gan Z, Lu Y, Chen Y (2019) A color image cryptosystem based on dynamic DNA encryption and chaos. Signal Process 155:44–62. https://doi.org/10.1016/j.sigpro.2018.09.029

    Article  Google Scholar 

  6. Chai X, Wu H, Gan Z, Zhang Y, Chen Y, Nixon KW (2020) An efficient visually meaningful image compression and encryption scheme based on compressive sensing and dynamic LSB embedding. Opt Lasers Eng 124:105837. https://doi.org/10.1016/j.optlaseng.2019.105837

    Article  Google Scholar 

  7. Chen GR, Mao YB, Chui CK (2004) A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Solitons Fractals 21(3):749–761. https://doi.org/10.1016/j.chaos.2003.12.022

    Article  MathSciNet  MATH  Google Scholar 

  8. Deng J, Zhao S, Wang Y, Wang L, Wang H, Sha H (2017) Image compression-encryption scheme combining 2D compressive sensing with discrete fractional random transform. Multimed Tools Appl 76(7):10097–10117. https://doi.org/10.1007/s11042-016-3600-2

    Article  Google Scholar 

  9. Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306. https://doi.org/10.1109/tit.2006.871582

    Article  MathSciNet  MATH  Google Scholar 

  10. Fridrich J (1998) Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifurcation Chaos 8(6):1259–1284

    Article  MathSciNet  Google Scholar 

  11. Gong L, Qiu K, Deng C, Zhou N (2019) An image compression and encryption algorithm based on chaotic system and compressive sensing. Opt Laser Technol 115:257–267. https://doi.org/10.1016/j.optlastec.2019.01.039

    Article  Google Scholar 

  12. Hua ZY, Zhou YC (2018) One-dimensional nonlinear model for producing Chaos. IEEE Transactions on Circuits and Systems I-Regular Papers 65(1):235–246. https://doi.org/10.1109/tcsi.2017.2717943

    Article  Google Scholar 

  13. Li J, Huang XY, Li JW, Chen XF, Xiang Y (2014) Securely outsourcing attribute-based encryption with Checkability. IEEE Transactions on Parallel and Distributed Systems 25(8):2201–2210. https://doi.org/10.1109/tpds.2013.271

    Article  Google Scholar 

  14. Li J, Li YK, Chen XF, Lee PPC, Lou WJ (2015) A hybrid cloud approach for secure authorized Deduplication. IEEE Transactions on Parallel and Distributed Systems 26(5):1206–1216. https://doi.org/10.1109/tpds.2014.2318320

    Article  Google Scholar 

  15. Li C, Zhang Y, Xie EY (2019) When an attacker meets a cipher-image in 2018: a year in review. Journal of Information Security and Applications 48:1–9. https://doi.org/10.1016/j.jisa.2019.102361

    Article  Google Scholar 

  16. Lian SG, Sun JS, Wang ZQ (2005) A block cipher based on a suitable use of the chaotic standard map. Chaos Solitons Fractals 26(1):117–129. https://doi.org/10.1016/j.chaos.2004.11.096

    Article  MATH  Google Scholar 

  17. Lu Q, Zhu C, Wang G (2019) A novel S-box design algorithm based on a new compound chaotic system. Entropy 21(10). https://doi.org/10.3390/e21101004

  18. Lu Q, Zhu C, Deng X (2020) An efficient image encryption scheme based on the LSS chaotic map and single S-box. IEEE Access 8(1):25664–25678. https://doi.org/10.1109/access.2020.2970806

    Article  Google Scholar 

  19. Orsdemir A, Altun HO, Sharma G, Bocko MF (2008) On the security and robustness of encryption via compressed sensing. In: 2008 IEEE military communications conference: Milcom 2008, vols 1-7. IEEE Military Communications Conference. IEEE, pp 1040–1046

  20. Peng Y, He Y (2012) A reconstruction algorithm for compressed sensing noise signal. Journal of Computational Information Systems 8(14):6025–6031

    Google Scholar 

  21. Rachlin Y, Baron D (2008) The secrecy of compressed sensing measurements. Paper presented at the 2008 46th annual Allerton conference on communication, control, and computing, vols 1–3. IEEE

  22. Rehman AU, Khan JS, Ahmad J, Hwang SO (2016) A new image encryption scheme based on dynamic S-boxes and chaotic maps. 3D Research 7(1):UNSP 7. https://doi.org/10.1007/s13319-016-0084-9

    Article  Google Scholar 

  23. Ren Y-M, Zhang Y-N, Li Y (2014) Advances and perspective on compressed sensing and application on image processing. Acta Automat Sin 40(8):1563–1575

    MATH  Google Scholar 

  24. Wang X, Teng L, Qin X (2012) A novel colour image encryption algorithm based on chaos. Signal Process 92(4):1101–1108. https://doi.org/10.1016/j.sigpro.2011.10.023

    Article  MathSciNet  Google Scholar 

  25. Wong KW, Kwok BSH, Law WS (2008) A fast image encryption scheme based on chaotic standard map. Phys Lett A 372(15):2645–2652. https://doi.org/10.1016/j.physleta.2007.12.026

    Article  MATH  Google Scholar 

  26. Xiao D, Wang L, Xiang T, Wang Y (2017) Multi-focus image fusion and robust encryption algorithm based on compressive sensing. Opt Laser Technol 91:212–225. https://doi.org/10.1016/j.optlastec.2016.12.024

    Article  Google Scholar 

  27. Xu L, Gou X, Li Z, Li J (2017) A novel chaotic image encryption algorithm using block scrambling and dynamic index based diffusion. Opt Lasers Eng 91:41–52. https://doi.org/10.1016/j.optlaseng.2016.10.012

    Article  Google Scholar 

  28. Xu Q, Sun K, Cao C, Zhu C (2019) A fast image encryption algorithm based on compressive sensing and hyperchaotic map. Opt Lasers Eng 121:203–214. https://doi.org/10.1016/j.optlaseng.2019.04.011

    Article  Google Scholar 

  29. Zhang LY, Wong K-W, Zhang Y, Zhou J (2016) Bi-level protected compressive sampling. IEEE Transactions on Multimedia 18(9):1720–1732. https://doi.org/10.1109/tmm.2016.2581593

    Article  Google Scholar 

  30. Zhou NR, Zhang AD, Zheng F, Gong LH (2014) Novel image compression-encryption hybrid algorithm based on key-controlled measurement matrix in compressive sensing. Opt Laser Technol 62:152–160. https://doi.org/10.1016/j.optlastec.2014.02.015

    Article  Google Scholar 

  31. Zhou N, Yang J, Tan C, Pan S, Zhou Z (2015) Double-image encryption scheme combining DWT-based compressive sensing with discrete fractional random transform. Opt Commun 354:112–121. https://doi.org/10.1016/j.optcom.2015.05.043

    Article  Google Scholar 

  32. Zhu C (2012) A novel image encryption scheme based on improved hyperchaotic sequences. Opt Commun 285(1):29–37. https://doi.org/10.1016/j.optcom.2011.08.079

    Article  Google Scholar 

  33. Zhu C, Sun K (2018) Cryptanalyzing and improving a novel color image encryption algorithm using RT-enhanced chaotic tent maps. IEEE Access 6:18759–18770. https://doi.org/10.1109/access.2018.2817600

    Article  Google Scholar 

  34. Zhu S, Zhu C (2018) Image encryption algorithm with an avalanche effect based on a six-dimensional discrete chaotic system. Multimed Tools Appl 77(21):29119–29142. https://doi.org/10.1007/s11042-018-6078-2

    Article  Google Scholar 

  35. Zhu S, Zhu C (2019) Plaintext-related image encryption algorithm based on block structure and five-dimensional chaotic map. IEEE Access 7:147106–147118. https://doi.org/10.1109/access.2019.2946208

    Article  Google Scholar 

  36. Zhu S, Zhu C (2019) A new image compression-encryption scheme based on compressive sensing and cyclic shift. Multimed Tools Appl 78(15):20855–20875. https://doi.org/10.1007/s11042-019-7405-y

    Article  Google Scholar 

  37. Zhu S, Zhu C, Wang W (2018) A novel image compression-encryption scheme based on Chaos and compression sensing. IEEE Access 6:67095–67107. https://doi.org/10.1109/access.2018.2874336

    Article  Google Scholar 

  38. Zhu C, Wang G, Sun K (2018) Improved cryptanalysis and enhancements of an image encryption scheme using combined 1D chaotic maps. Entropy 20(11):843. https://doi.org/10.3390/e20110843

    Article  Google Scholar 

  39. Zhu CX, Wang GJ, Sun KH (2018) Cryptanalysis and improvement on an image encryption algorithm design using a novel Chaos based S-box. Symmetry 10(9):399. https://doi.org/10.3390/sym10090399

    Article  Google Scholar 

  40. Zhu S, Wang G, Zhu C (2019) A secure and fast image encryption scheme based on double chaotic S-boxes. Entropy 21(8):790. https://doi.org/10.3390/e21080790

    Article  MathSciNet  Google Scholar 

  41. Zhu S, Zhu C, Cui H, Wang W (2019) A class of quadratic polynomial chaotic maps and its application in cryptography. IEEE Access 7:34141–34152. https://doi.org/10.1109/access.2019.2902873

    Article  Google Scholar 

Download references

Acknowledgements

This work was Supported by the Open Research Fund of Key Laboratory of Network Crime Investigation of Hunan Provincial Colleges under Grant NO. 2020WLFZZC002, in part by National innovation and entrepreneurship training program for college students under Grant NO. S201910447044 and Liaocheng University innovation and entrepreneurship training program for college students under Grant NO. cxcy2019y091.

Author information

Authors and Affiliations

  1. School of Computer Science, Liaocheng University, Liaocheng, 252059, China

    Shuqin Zhu, Yu Fu, Weimeng Zhang & Xiaoting Wu

  2. School of Computer Science and Engineering, Central South University, Changsha, 410083, China

    Congxu Zhu

  3. Key Laboratory of Network Crime Investigation of Hunan Provincial Colleges, Hunan Police Academy, Changsha, 410138, China

    Congxu Zhu

Authors
  1. Shuqin Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Congxu Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Weimeng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiaoting Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Congxu Zhu.

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

Zhu, S., Zhu, C., Fu, Y. et al. A secure image encryption scheme with compression-confusion-diffusion structure. Multimed Tools Appl 79, 31957–31980 (2020). https://doi.org/10.1007/s11042-020-09699-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-09699-4

Keywords

Search

Navigation