Skip to main content
SpringerLink
Log in

Exploiting 2D compressed sensing and information entropy for secure color image compression and encryption

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Compared to 1D compressed sensing (CS), 2D CS is more efficient for compressing the plaintext image from two directions, but security level of current 2D CS-based ciphers is unsatisfactory. To solve this problem, this paper presents a novel color image compression and encryption algorithm by combining 2D CS, information entropy and chaos. Firstly, the color image is decomposed into red, green and blue components, then they are sparsely transformed by the discrete wavelet transform (DWT) to get three sparse matrices. Next, the obtained matrices are observed by two asymptotical deterministic random measurement matrices based on information entropy and counter (ADMMIC), which not only encrypts the plaintext image, but also compresses it in proportion to reduce the transmission bandwidth and storage space. Subsequently, the corresponding measurement value matrices are shuffled by a double random scrambling based on Arnold map and index vector (DRSAIV) to eliminate the correlation between adjacent pixels. Furthermore, the obtained permutated matrices are diffused by a simultaneous multiple random diffusion of inter–intra components (SMRDIC) to obtain the final cipher image, the plaintext pixel to be diffused, the key matrix involved in diffusion and the position of the obtained ciphertext pixel are all unpredictable, which makes statistical attack invalid. In addition, information entropy values of plaintext image are obtained to generate the initial values of the used chaotic systems, which greatly improve the ability to resist the known-plaintext and chosen-plaintext attacks. Simulation results and security analyses verify that this algorithm has good compression and high security.

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

Similar content being viewed by others

References

  1. Zhang Y (2020) The fast image encryption based on lifting scheme and chaos. Inf Sci 520:177–194

    Article  MathSciNet  Google Scholar 

  2. Wen WY, Wei KK, Zhang YS, Fang YM, Li M (2020) Colour light field image encryption based on DNA sequences and chaotic systems. Nonlinear Dyn 99:1587–1600

    Article  Google Scholar 

  3. Xu QY, Sun KH, He SB, Zhu CX (2020) An effective image encryption algorithm based on compressive sensing and 2D-SLIM. Opt Laser Eng 134:106178

    Article  Google Scholar 

  4. Zhang YS, Wang P, Huang H, Zhu YW, Xiao D, Xiang Y (2020) Privacy-assured FogCS: chaotic compressive sensing for secure industrial big image data processing in fog computing. Ind. Inform, IEEE T. https://doi.org/10.1109/TII.2020.3008914

    Book  Google Scholar 

  5. Hadj Brahim A, Ali Pacha A, Hadj Said N (2020) Image encryption based on compressive sensing and chaos systems. Opt Laser Technol 132:106489

    Article  Google Scholar 

  6. Wang J, Zhang LY, Chen JX, Hua G, Zhang YS, Xiang Y (2019) Compressed sensing based selective encryption with data hiding capability. IEEE T Ind Inform 15:6560–6571

    Article  Google Scholar 

  7. Ye GD, Pan C, Dong YX, Shi Y, Huang XL (2020) Image encryption and hiding algorithm based on compressive sensing and random numbers insertion. Signal Process 172:107563

    Article  Google Scholar 

  8. Wen WY, Hong YK, Fang YM, Li M, Li M (2020) A visually secure image encryption scheme based on semi-tensor product compressed sensing. Signal Process 173:107580

    Article  Google Scholar 

  9. Yao SY, Chen LF, Zhong Y (2019) An encryption system for color image based on compressed sensing. Opt Laser Technol 120:105703

    Article  Google Scholar 

  10. Wang H, Xiao D, Li M, Xiang YP, Li XY (2019) A visually secure image encryption scheme based on parallel compressed sensing. Signal Process 155:218–232

    Article  Google Scholar 

  11. Chai XL, Gan ZH, Chen YR, Zhang YS (2017) A visually secure image encryption scheme based on compressed sensing. Signal Process 134:35–51

    Article  Google Scholar 

  12. Chai XL, Wu HY, Gan ZH, Han DJ, Zhang YS, Chen YR, Nixon KW (2020) An efficient visually meaningful image compression and encryption scheme based on compressive sensing and dynamic LSB embedding. Opt Laser Eng 124:105837

    Article  Google Scholar 

  13. Gan ZH, Chai XL, Zhang JT, Zhang YS, Chen YR (2020) An effective image compression-encryption scheme based on compressive sensing (CS) and game of life (GOL). Neural Comput Appl 32:14113–14141

    Article  Google Scholar 

  14. Chen G, Li DF, Zhang JS (2014) Iterative gradient projection algorithm for two-dimensional compressed sensing sparse image reconstruction. Signal Process 104:15–26

    Article  Google Scholar 

  15. Eftekhari A, Babaie-Zadeh M, Abrishami Moghaddam H (2011) Two-dimensional random projection. Signal Process 91(7):1589–1603

    Article  Google Scholar 

  16. Zhou NR, Pan SM, Cheng S, Zhou ZH (2016) Image compression-encryption scheme based on hyper-chaotic system and 2D compressed sensing. Opt Laser Technol 82:121–133

    Article  Google Scholar 

  17. Zhou NR, Li HL, Wang D, Pan SM, Zhou ZH (2015) Image compression and encryption scheme based on 2D compressed sensing and fractional Mellin transform. Opt Commun 343:10–21

    Article  Google Scholar 

  18. Deng J, Zhao S, Wang Y, Wang L, Wang H, Sha H (2017) Image compression-encryption scheme combining 2D compressed sensing with discrete fractional random transform. Multimed Tools Appl 76:10097–10117

    Article  Google Scholar 

  19. Zhang D, Liao XF, Yang B, Zhang YS (2018) A fast and efficient approach to color-image encryption based on compressed sensing and fractional Fourier transform. Multimed Tools Appl 77:2191–2208

    Article  Google Scholar 

  20. Yang YG, Guan BW, Li J, Li D, Zhou YH, Shi WM (2019) Image compression-encryption scheme based on fractional order hyper-chaotic systems combined with 2D compressed sensing and DNA encoding. Opt Laser Technol 119:105661

    Article  Google Scholar 

  21. Chai XL, Wu HY, Gan ZH, Han DJ, Zhang YS, Chen YR (2020) An efficient approach for encrypting double color images into a visually meaningful cipher image using 2D compressive sensing. Sci, Inf. https://doi.org/10.1016/j.ins.2020.10.007

    Book  Google Scholar 

  22. Candes EJ (2008) The restricted isometry property and its implications for compressed sensing. Compt Rendus Math 346(9):589–592

    Article  MathSciNet  Google Scholar 

  23. Pati Y C, Rezaiifar R, and Krishnaprasad P S. Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In Asilomar Conference on Signals Systems and Computers, 1993: 40–44

  24. Dai W, Milenkovic O (2009) Subspace pursuit for compressed sensing signal reconstruction. IEEE Trans Inf Theory 55:2230–2249

    Article  Google Scholar 

  25. Zhou NR, Yang JP, Tan CF, Pan SM, Zhou ZH (2015) Double-image encryption scheme combining DWT-based compressed sensing with discrete fractional random transform. Opt Commun 354:112–121

    Article  Google Scholar 

  26. Prousalis DA, Volos CK, Stouboulos IN, Kyprianidis IM (2017) Hyperchaotic memristive system with hidden attractors and its adaptive control scheme. Nonlinear Dyn 90(3):1681–1694

    Article  MathSciNet  Google Scholar 

  27. Hua ZY, Jin F, Xu BX, Huang HJ (2018) 2D Logistic-Sine-coupling map for image encryption. Signal Process 149:148–161

    Article  Google Scholar 

  28. Wu Y, Zhou YC, Noonan JP, Agaian S (2014) Design of image cipher using latin squares. Inf Sci 264(6):317–339

    Article  MathSciNet  Google Scholar 

  29. Pak C, An K, Jang P, Kim J, Kim S (2019) A novel bit-level color image encryption using improved 1D chaotic map. Multimed Tools Appl 78:12027–12042

    Article  Google Scholar 

  30. Gong LH, Qiu KD, Deng CZ, Zhou NR (2019) An optical image compression and encryption scheme based on compressed sensing and RSA algorithm. Opt Laser Eng 121:169–180

    Article  Google Scholar 

  31. Zhou KL, Fan JJ, Fan HJ, Li M (2020) Secure image encryption scheme using double random-phase encoding and compressed sensing. Opt Laser Technol 121:105769

    Article  Google Scholar 

  32. Chai XL, Fu XL, Gan ZH, Lu Y, Chen YR (2019) A color image cryptosystem based on dynamic DNA encryption and chaos. Signal Process 155:44–62

    Article  Google Scholar 

  33. Chai XL, Gan ZH, Lu Y, Zhang MH, Chen YR (2016) A novel color image encryption algorithm based on genetic recombination and the four-dimensional memristive hyperchaotic system. Chin Phys B 25(10):76–88

    Article  Google Scholar 

  34. Wang XY, Zhao HY, Wang MX (2019) A new image encryption algorithm with nonlinear-diffusion based on Multiple coupled map lattices. Opt Laser Technol 115:42–57

    Article  Google Scholar 

  35. Khan M, Rasheed A (2019) Permutation-based special linear transforms with application in quantum image encryption algorithm. Quantum Inf Process 18:298

    Article  Google Scholar 

  36. Wu XJ, Kan HB, Kurths J (2015) A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps. Appl Soft Comput 37:24–39

    Article  Google Scholar 

  37. Liu HJ, Zhang YQ, Kadir A, Xu YQ (2019) Image encryption using complex hyper chaotic system by injecting impulse into parameters. Appl Math Comput 360:83–93

    Article  MathSciNet  Google Scholar 

  38. Azimi Z, Ahadpour S (2019) Color image encryption based on DNA encoding and pair coupled chaotic maps. Multimed Tools Appl. https://doi.org/10.1007/s11042-019-08375-6

    Article  Google Scholar 

  39. Zhang YQ, He Y, Li P, Wang XY (2020) A new color image encryption scheme based on 2DNLCML system and genetic operations. Opt Laser Eng 128:106040

    Article  Google Scholar 

  40. Wu XJ, Li Y, Kurths J (2015) A new color image encryption scheme using CML and a fractional-order chaotic system. PLoS ONE 10(3):e0119660

    Article  Google Scholar 

  41. Chai XL, Bi JQ, Gan ZH, Liu XX, Zhang YS, Chen YR (2020) Color image compression and encryption scheme based on compressive sensing and double random encryption strategy. Signal Process 176:107684

    Article  Google Scholar 

  42. Suryanto Y, Suryadi RK (2017) A new image encryption using color scrambling based on chaotic permutation multiple circular shrinking and expanding. Multimed Tools Appl 76(15):16831–16854

    Article  Google Scholar 

  43. Ouyang X, Luo YL, Liu JX, Cao LC, Liu YQ (2020) A color image encryption method based on memristive hyperchaotic system and DNA encryption. Int J Mod Phys B 34:2050014

    Article  MathSciNet  Google Scholar 

  44. Qin Y, Wang ZQ, Pan QN, Gong Q (2016) Optical color-image encryption in the diffractive-imaging scheme. Opt Laser Eng 77:191–202

    Article  Google Scholar 

Download references

Acknowledgements

All the authors are deeply grateful to the editors for smooth and fast handling of the manuscript. The authors would also like to thank the anonymous referees for their valuable suggestions to improve the quality of this paper. This work is supported by the National Natural Science Foundation of China (Grant No. 61802111, 61872125, 61871175), Science and Technology Foundation of Henan Province of China (Grant No. 182102210027, 182102410051), China Postdoctoral Science Foundation (Grant No. 2018T110723, 2016M602235), Key Scientific Research Projects for Colleges and Universities of Henan Province (Grant No. 19A413001), Sponsored by Natural Science Foundation of Henan (Grant No. 182300410164), Graduate Education Innovation and Quality Improvement Project of Henan University (Grant No. SYL18020105), and Henan Higher Education Teaching Reform Research and Practice Project (Graduate Education) (Grant No. 2019SJGLX080Y).

Author information

Authors and Affiliations

  1. School of Software, Intelligent Data Processing Engineering Research Center of Henan Province, Henan University, Kaifeng, 475004, China

    Zhihua Gan

  2. School of Computer and Information Engineering, Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng, 475004, China

    Jianqiang Bi, Wenke Ding & Xiuli Chai

  3. School of Artificial Intelligence, Henan University, Kaifeng, 475004, China

    Xiuli Chai

Authors
  1. Zhihua Gan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianqiang Bi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenke Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiuli Chai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Wenke Ding or Xiuli Chai.

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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gan, Z., Bi, J., Ding, W. et al. Exploiting 2D compressed sensing and information entropy for secure color image compression and encryption. Neural Comput & Applic 33, 12845–12867 (2021). https://doi.org/10.1007/s00521-021-05937-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-021-05937-4

Keywords

Search

Navigation