Nonlinear Dynamics

, Volume 95, Issue 3, pp 2235–2261 | Cite as

Joint image compression–encryption scheme using entropy coding and compressive sensing

  • Yanjie Song
  • Zhiliang ZhuEmail author
  • Wei Zhang
  • Li Guo
  • Xue Yang
  • Hai Yu
Original Paper


Recently, compressive sensing (CS)-based joint compression–encryption schemes have been widely investigated due to their high efficiency and good security for images. However, the existing schemes typically have a lower compression ratio (CR), and there may be a flaw during their compression processes. Therefore, in this paper, according to the intrinsic features of images, we propose a novel compression architecture to enhance the CR. Meanwhile, based on this architecture, a joint image compression–encryption scheme using entropy coding and CS is designed to implement a complete compression and encryption process. In this joint scheme, a presented bit-level lossless compression–encryption algorithm based on entropy coding for the higher bit-planes is incorporated to improve the quality of the reconstructed image and ensure the security. Alternately, this joint scheme also contains an improved CS-based lossy compression–encryption algorithm for the lower bit-planes, which can guarantee the efficiency and security. Through the cooperation between the proposed lossless and lossy coding, the higher reconstruction performance can be achieved. SHA-256 is combined with all initial keys in the proposed joint scheme to generate the updated keys for chaos cryptosystem to maintain high security and resist some common attacks. Experimental and analytical results illustrate the superiority of the proposed joint scheme compared with the existing compression–encryption schemes and JPEG, as well as good encryption performance.


Joint image compression–encryption Compressive sensing Entropy coding Chaos Bit-plane 



This research was supported by the National Natural Science Foundation of China (Grant Nos. 61374178, 61402092, 61603182), the Online Education Research Fund of the MOE Research Center for Online Education, China (Qtone Education, Grant No. 2016ZD306), the Ph.D. Start-Up Foundation of Liaoning Province, China (Grant No. 201501141), and the Fundamental Research Funds for the Central Universities (Grant No. N171704004).

Compliance with ethical standards

Conflict of interest

Compliance with ethical standards Conflict of interest. The authors declare that they have no conflict of interest.


  1. 1.
    Tong, X., Wang, Z., Zhang, M., Liu, Y.: A new algorithm of the combination of image compression and encryption technology based on cross chaotic map. Nonlinear Dyn. 72(1), 229–241 (2013)MathSciNetGoogle Scholar
  2. 2.
    Zhang, M., Tong, X.: A new chaotic map based image encryption schemes for several image formats. J. Syst. Softw. 98, 140–154 (2014)Google Scholar
  3. 3.
    Zhang, Y., Xiao, D., Liu, H., Nan, H.: GLS coding based security solution to JPEG with the structure of aggregated compression and encryption. Commun. Nonlinear Sci. Numer. Simul. 19(5), 1366–1374 (2014)Google Scholar
  4. 4.
    Li, P., Lo, K.T.: Joint image compression and encryption based on order-8 alternating transforms. J. Visual Commun. Image Rep. 44, 61–71 (2017)Google Scholar
  5. 5.
    Candès, E.J., Tao, T.: Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Rachlin, Y., Baron, D.: The secrecy of compressed sensing measurements. In: 2008 46th Annual Allerton Conference on Communication, Control, and Computing, pp. 813–817 (2008)Google Scholar
  7. 7.
    Yu, L., Barbot, J.P., Zheng, G., Sun, H.: Compressive sensing with chaotic sequence. IEEE Signal Process. Lett. 17(8), 731–734 (2010)Google Scholar
  8. 8.
    Frunzete, M., Yu, L., Barbot, J.P., Vlad, A.: Compressive sensing matrix designed by tent map, for secure data transmission. In: 2011 15th Conference on Signal Processing: Algorithms, Architectures, Arrangements, and Applications, pp. 1–6 (2011)Google Scholar
  9. 9.
    Endra, R.S.: Compressive sensing-based image encryption with optimized sensing matrix. In: 2013 IEEE International Conference on Computational Intelligence and Cybernetics, pp. 122–125 (2013)Google Scholar
  10. 10.
    Zhou, N., Zhang, A., Wu, J., Pei, D., Yang, Y.: Novel hybrid image compression-encryption algorithm based on compressive sensing. Optik 125(18), 5075–5080 (2014)Google Scholar
  11. 11.
    Zhou, N., Zhang, A., Zheng, F., Gong, L.: Novel image compression-encryption hybrid algorithm based on key-controlled measurement matrix in compressive sensing. Opt. Laser Technol. 62, 152–160 (2014)Google Scholar
  12. 12.
    Zhou, N., Li, H., Wang, D., Pan, S., Zhou, Z.: Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform. Opt. Commun. 343, 10–21 (2015)Google Scholar
  13. 13.
    Zhou, N., Pan, S., Cheng, S., Zhou, Z.: Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing. Opt. Laser Technol. 82, 121–133 (2016)Google Scholar
  14. 14.
    Zhang, A., Zhou, N., Gong, L.: Color image encryption algorithm combining compressive sensing with Arnold transform. J. Comput. 8(11), 2857–2863 (2013)Google Scholar
  15. 15.
    Fang, H., Vorobyov, S.A., Jiang, H., Taheri, O.: Permutation meets parallel compressed sensing: How to relax restricted isometry property for 2D sparse signals. IEEE Trans. Signal Process. 62(1), 196–210 (2014)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Fang, H., Vorobyov, S.A., Jiang, H.: Permutation enhanced parallel reconstruction for compressive sampling. In: 2015 16th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, pp. 393–396 (2015)Google Scholar
  17. 17.
    Zhang, Y., Zhou, J., Chen, F., Zhang, L.Y., Wong, K.W., He, X., Xiao, D.: Embedding cryptographic features in compressive sensing. Neurocomputing 205, 472–480 (2016)Google Scholar
  18. 18.
    Chen, T., Zhang, M., Wu, J., Yuen, C., Tong, Y.: Image encryption and compression based on kronecker compressed sensing and elementary cellular automata scrambling. Opt. Laser Technol. 84, 118–133 (2016)Google Scholar
  19. 19.
    Zhang, Y., Zhang, L.Y., Zhou, J., Liu, L., Chen, F., He, X.: A review of compressive sensing in information security field. IEEE Access 4, 2507–2519 (2016)Google Scholar
  20. 20.
    Lu, P., Xu, Z., Lu, X., Liu, X.: Digital image information encryption based on compressive sensing and double random-phase encoding technique. Optik 124(16), 2514–2518 (2013)Google Scholar
  21. 21.
    Huang, R., Rhee, K.H., Uchida, S.: A parallel image encryption method based on compressive sensing. Multimed. Tools Appl. 72(1), 71–93 (2014)Google Scholar
  22. 22.
    Zhang, Y., Xu, B., Zhou, N.: A novel image compression-encryption hybrid algorithm based on the analysis sparse representation. Opt. Commun. 392, 223–233 (2017)Google Scholar
  23. 23.
    Liu, X., Mei, W., Du, H.: Simultaneous image compression, fusion and encryption algorithm based on compressive sensing and chaos. Opt. Commun. 366, 22–32 (2016)Google Scholar
  24. 24.
    Hu, G., Xiao, D., Wang, Y., Xiang, T.: An image coding scheme using parallel compressive sensing for simultaneous compression-encryption applications. J. Visual Commun. Image Rep. 44, 116–127 (2017)Google Scholar
  25. 25.
    Chai, X., Gan, Z., Chen, Y., Zhang, Y.: A visually secure image encryption scheme based on compressive sensing. Signal Process. 134, 35–51 (2017)Google Scholar
  26. 26.
    Tong, X., Zhang, M., Wang, Z., Ma, J.: A joint color image encryption and compression scheme based hyper-chaotic system. Nonlinear Dyn. 84(4), 2333–2356 (2016)Google Scholar
  27. 27.
    Tong, X., Chen, P., Zhang, M.: A joint image lossless compression and encryption method based on chaotic map. Multimed. Tools Appl. 76(12), 13995–14020 (2017)Google Scholar
  28. 28.
    Zhang, M., Tong, X.: Joint image encryption and compression scheme based on IWT and SPIHT. Opt. Lasers Eng. 90, 254–274 (2017)Google Scholar
  29. 29.
    Zhang, Y., Xiao, D., Wen, W., Nan, H., Su, M.: Secure binary arithmetic coding based on digitalized modified logistic map and linear feedback shift register. Commun. Nonlinear Sci. Numer. Simul. 27(1), 22–29 (2015)MathSciNetGoogle Scholar
  30. 30.
    Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)MathSciNetzbMATHGoogle Scholar
  31. 31.
    Candès, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(4), 489–509 (2006)MathSciNetzbMATHGoogle Scholar
  32. 32.
    Candès, E.J.: Compressive Sampling. Marta Sanz Solé 17(2), 1433–1452 (2006)Google Scholar
  33. 33.
    Zhang, W., Wong, K.W., Yu, H., Zhu, Z.: A symmetric color image encryption algorithm using the intrinsic features of bit distributions. Commun. Nonlinear Sci. Numer. Simul. 18(3), 584–600 (2013)MathSciNetzbMATHGoogle Scholar
  34. 34.
    Candès, E.J.: The restricted isometry property and its implications for compressed sensing. Comptes Rendus Math. 346(9), 589–592 (2008)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Liang, W.J., Lin, G.X., Lu, C.S.: Tree structure sparsity pattern guided convex optimization for compressive sensing of large-scale images. IEEE Trans. Image Process. 26(2), 847–859 (2017)MathSciNetzbMATHGoogle Scholar
  36. 36.
    Moshtaghpour, A., Jacques, L., Cambareri, V., Degraux, K., Vleeschouwer, C.: Consistent basis pursuit for signal and matrix estimates in quantized compressed sensing. IEEE Signal Process. Lett. 23(1), 25–29 (2016)Google Scholar
  37. 37.
    Candès, E.J., Wakin, M.B., Boyd, S.P.: Enhancing sparsity by reweighted \(l_1\) minimization. J. Fourier Anal. Appl. 14(1), 877–905 (2008)MathSciNetzbMATHGoogle Scholar
  38. 38.
    Gan, H., Li, Z., Li, J., Wang, X., Cheng, Z.: Compressive sensing using chaotic sequence based on Chebyshev map. Nonlinear Dyn. 78(4), 2429–2438 (2014)MathSciNetzbMATHGoogle Scholar
  39. 39.
    Zhao, H., Ye, H., Wang, R.: The construction of measurement matrices based on block weighing matrix in compressed sensing. Signal Process. 123, 64–74 (2016)Google Scholar
  40. 40.
    Yao, S., Wang, T., Shen, W., Pan, S., Chong, Y.: Research of incoherence rotated chaotic measurement matrix in compressed sensing. Multimed. Tools Appl. 76(17), 17699–17717 (2017)Google Scholar
  41. 41.
    Rabah, H., Amira, A., Mohanty, B.K., Almaadeed, S., Meher, P.K.: FPGA implementation of orthogonal matching pursuit for compressive sensing reconstruction. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 23(10), 2209–2220 (2015)Google Scholar
  42. 42.
    Chang, K., Ding, P.L.K., Li, B.: Compressive sensing reconstruction of correlated images using joint regularization. IEEE Signal Process. Lett. 23(4), 449–453 (2016)Google Scholar
  43. 43.
    Wang, Q., Li, D., Shen, Y.: Intelligent nonconvex compressive sensing using prior information for image reconstruction by sparse representation. Neurocomputing 224, 71–81 (2017)Google Scholar
  44. 44.
    Wang, X., Teng, L., Qin, X.: A novel colour image encryption algorithm based on chaos. Signal Process. 92(4), 1101–1108 (2012)MathSciNetGoogle Scholar
  45. 45.
    Zymnis, A., Boyd, S.P., Candès, E.J.: Compressed sensing with quantized measurements. IEEE Signal Process. Lett. 17(2), 149–152 (2010)Google Scholar
  46. 46.
    Saab, R., Wang, R., Yilmaz, Ö.: From compressed sensing to compressed bit-streams: practical encoders, tractable decoders. IEEE Trans. Inf. Theory 64(9), 6098–6114 (2018)MathSciNetzbMATHGoogle Scholar
  47. 47.
    Boufounos, P.T., Baraniuk, R.G.: 1-Bit compressive sensing. In: 2008 42nd Annual Conference on Information Sciences and Systems, pp. 16–21 (2008)Google Scholar
  48. 48.
    Laska, J.N., Wen, Z., Yin, W., Baraniuk, R.G.: Trust, but verify: fast and accurate signal recovery from 1-bit compressive measurements. IEEE Trans. Signal Process. 59(11), 5289–5301 (2011)MathSciNetzbMATHGoogle Scholar
  49. 49.
    Jacques, L., Laska, J.N., Boufounos, P.T., Baraniuk, R.G.: Robust 1-bit compressive sensing via binary stable embeddings of sparse vectors. IEEE Trans. Inf. Theory 59(4), 2082–2102 (2013)MathSciNetzbMATHGoogle Scholar
  50. 50.
    Knudson, K., Saab, R., Ward, R.: One-bit compressive sensing with norm estimation. IEEE Trans. Inf. Theory 62(5), 2748–2758 (2016)MathSciNetzbMATHGoogle Scholar
  51. 51.
    Hachemi, S., Massicotte, D.: Binary input-output compressive sensing: a sub-gradient reconstruction. In: 2015 28th IEEE Canadian Conference on Electrical and Computer Engineering, pp. 565–570 (2015)Google Scholar
  52. 52.
    Shirvanimoghaddam, M., Li, Y., Vucetic, B., Yuan, J., Zhang, P.: Binary compressive sensing via analog fountain coding. IEEE Trans. Signal Process. 63(24), 6540–6552 (2015)MathSciNetzbMATHGoogle Scholar
  53. 53.
    Ahn, J.H.: Compressive sensing and recovery for binary images. IEEE Trans. Image Process. 25(10), 4796–4802 (2016)MathSciNetzbMATHGoogle Scholar
  54. 54.
    Huffman, D.A.: A method for the construction of minimum-redundancy codes. Proc. IRE 40(9), 1098–1101 (1952)zbMATHGoogle Scholar
  55. 55.
    Pennebaker, W.B., Mitchell, J.L.: JPEG: Still Image Data Compression Standard. Van Nostrand Reinhold, New York (1993)Google Scholar
  56. 56.
    Hua, Z., Zhou, Y., Pun, C., Chen, C.L.P.: 2D Sine Logistic modulation map for image encryption. Inf. Sci. 297, 80–94 (2015)Google Scholar
  57. 57.
    Hua, Z., Zhou, Y.: Image encryption using 2D Logistic-adjusted-Sine map. Inf. Sci. 339, 237–253 (2016)Google Scholar
  58. 58.
    Ye, G., Wong, K.W.: An image encryption scheme based on time-delay and hyperchaotic system. Nonlinear Dyn. 71(1), 259–267 (2013)MathSciNetGoogle Scholar
  59. 59.
    Ye, G.: A block image encryption algorithm based on wave transmission and chaotic systems. Nonlinear Dyn. 75(3), 417–427 (2014)Google Scholar
  60. 60.
    Ye, G., Pan, C., Huang, X., Zhao, Z., He, J.: A chaotic image encryption algorithm based on information entropy. Int. J. Bifurc. Chaos 28(1), 1850010 (2018)MathSciNetzbMATHGoogle Scholar
  61. 61.
    Tong, X., Wang, Z., Zhang, M., Liu, Y., Xu, H., Ma, J.: An image encryption algorithm based on the perturbed high-dimensional chaotic map. Nonlinear Dyn. 80(3), 1493–1508 (2015)MathSciNetzbMATHGoogle Scholar
  62. 62.
    Zhou, Y., Bao, L., Chen, C.L.P.: A new 1D chaotic system for image encryption. Signal Process. 97, 172–182 (2014)Google Scholar
  63. 63.
    Ullah, A., Jamal, S.S., Shah, T.: A novel scheme for image encryption using substitution box and chaotic system. Nonlinear Dyn. 91(1), 359–370 (2018)MathSciNetGoogle Scholar
  64. 64.
    Sheela, S.J., Suresh, K.V., Tandur, D.: Image encryption based on modified Henon map using hybrid chaotic shift transform. Multimed. Tools Appl. 77(19), 25223–25251 (2018)Google Scholar
  65. 65.
    Çavuşoğlu, Ü., Kaçar, S., Zengin, A., Pehlivan, I.: A novel hybrid encryption algorithm based on chaos and S-AES algorithm. Nonlinear Dyn. 92(4), 1745–1759 (2018)zbMATHGoogle Scholar
  66. 66.
    Avcibas, I., Sankur, B., Sayood, K.: Statistical evaluation of image quality measures. J. Electron. Imaging 11(2), 206–223 (2002)Google Scholar
  67. 67.
    Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., et al.: NIST Special Publication 800-22: a statistical test suite for the validation of random number generators and pseudo random number generators for cryptographic applications. National Institute of Standards and Technology (2010)Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Software CollegeNortheastern UniversityShenyangChina
  2. 2.School of Computer Science and EngineeringNortheastern UniversityShenyangChina

Personalised recommendations