Nonlinear Dynamics

, Volume 93, Issue 3, pp 1165–1181 | Cite as

A parallel image encryption algorithm based on the piecewise linear chaotic map and hyper-chaotic map

  • Yuling Luo
  • Ronglong Zhou
  • Junxiu Liu
  • Yi Cao
  • Xuemei Ding
Original Paper


This paper proposes a parallel digital image encryption algorithm based on a piecewise linear chaotic map (PWLCM) and a four-dimensional hyper-chaotic map (FDHCM). Firstly, two decimals are obtained based on the plain-image and external keys, using a novel parallel quantification method. They are used as the initial value and control parameter for the PWLCM. Then, an encryption matrix and four chaotic sequences are constructed using the PWLCM and FDHCM, which control the permutation and diffusion processes. The proposed algorithm is implemented and tested in parallel based on a graphics processing unit device. Numerical analysis and experimental results show that the proposed algorithm achieves a high encryption speed and a good security performance, which provides a potential solution for real-time image encryption applications.


Image security Chaotic encryption Parallel encryption GPU Security analysis 



This research is supported by the National Natural Science Foundation of China under Grants 61661008 and 61603104, the Guangxi Natural Science Foundation under Grants 2017GXNSFAA198180, 2015GXNSFBA139256 and 2016GXNSFCA380017, the funding of Overseas 100 Talents Program of Guangxi Higher Education, the Research Project of Guangxi University of China under Grant KY2016YB059, Guangxi Key Lab of Multi-source Information Mining and Security under Grant MIMS15-07, the Doctoral Research Foundation of Guangxi Normal University, the Innovation Project of Guangxi Graduate Education under Grant YCSZ2017055, the Scientific Research Funds for the Returned Overseas Chinese Scholars from State Education Ministry, the Funds for Young Key Program of Education Department from Fujian Province, China (Grant No. JZ160425), Program of Education Department of Fujian Province, China (Grant No. I201501005).


  1. 1.
    Abanda, Y., Tiedeu, A.: Image encryption by chaos mixing. IET Image Process. 10, 742–750 (2016)CrossRefGoogle Scholar
  2. 2.
    Arroyo, D., Li, C., Li, S., Alvarez, G., Halang, W.A.: Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm. Chaos Solitons Fractals 41(5), 2613–2616 (2009)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chai, X., Chen, Y., Broyde, L.: A novel chaotic image encryption scheme using dna sequence operations. Opt. Lasers Eng. 73, 53–61 (2015)CrossRefGoogle Scholar
  4. 4.
    Chai, X.L., Gan, Z.H., Yuan, K., Lu, Y., Chen, Y.R.: An image encryption scheme based on three-dimensional brownian motion and chaotic system. Chin. Phys. B 26, 020,504 (2017)CrossRefGoogle Scholar
  5. 5.
    Chen, J., Zhu, Z., Fu, C., Zhang, L., Yu, H.: Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains. Opt. Lasers Eng. 66, 1–9 (2015)CrossRefGoogle Scholar
  6. 6.
    Chen, L., Ma, B., Zhao, X., Wang, S.: Differential cryptanalysis of a novel image encryption algorithm based on chaos and line map. Nonlinear Dyn. 87(3), 1797–1807 (2017)CrossRefzbMATHGoogle Scholar
  7. 7.
    Chen, L., Wang, S.: Differential cryptanalysis of a medical image cryptosystem with multiple rounds. Comput. Biol. Med. 65, 69–75 (2015)CrossRefGoogle Scholar
  8. 8.
    Choi, J., Seok, S., Seo, H., Kim, H.: A fast arx model-based image encryption scheme. Multimed. Tools Appl. 2, 14685–14706 (2016)CrossRefGoogle Scholar
  9. 9.
    Dong, C.: Color image encryption using one-time keys and coupled chaotic systems. Sig. Process. Image Commun. 29, 628–640 (2014)CrossRefGoogle Scholar
  10. 10.
    Elgendy, F., Sarhan, A.M., Eltobely, T.E., El-Zoghdy, S.F., El-sayed, H.S., Faragallah, O.S.: Chaos-based model for encryption and decryption of digital images. Multimed. Tools Appl. 75, 11529–11553 (2016)CrossRefGoogle Scholar
  11. 11.
    Fu, C., Meng, Wh, Zhan, Yf, Zhu, Zl, Lau, F.C.M., Tse, C.K., Ma, Hf: An efficient and secure medical image protection scheme based on chaotic maps. Comput. Biol. Med. 43, 1000–10 (2013)CrossRefGoogle Scholar
  12. 12.
    Gu, G., Ling, J.: Optik a fast image encryption method by using chaotic 3d cat maps. Optik 125, 4700–4705 (2014)CrossRefGoogle Scholar
  13. 13.
    Hua, Z., Zhou, Y.: Image encryption using 2D logistic-adjusted-sine map. Inf. Sci. 339, 237–253 (2016)CrossRefGoogle Scholar
  14. 14.
    Hua, Z., Zhou, Y.: Design of image cipher using block-based scrambling and image filtering. Inf. Sci. 396, 97–113 (2017)CrossRefGoogle Scholar
  15. 15.
    Huang, R., Rhee, K., Uchida, S.: A parallel image encryption method based on compressive sensing. Multimed. Tools Appl. 72, 71–93 (2014)CrossRefGoogle Scholar
  16. 16.
    Huang, X., Ye, G.: An image encryption algorithm based on hyper-chaos and dna sequence. Multimed. Tools Appl. 72, 57–70 (2014)CrossRefGoogle Scholar
  17. 17.
    Kadir, A., Hamdulla, A., Guo, W.Q.: Color image encryption using skew tent map and hyper chaotic system of 6th-order cnn. Optik 125, 1671–1675 (2014)CrossRefGoogle Scholar
  18. 18.
    Kamel Mohamed, F.: A parallel block-based encryption schema for digital images using reversible cellular automata. Eng. Sci. Technol. Int. J. 17, 85–94 (2014)CrossRefGoogle Scholar
  19. 19.
    Lee, J., Yi, F., Saifullah, R., Moon, I.: Graphics processing unit caccelerated double random phase encoding for fast image encryption. Opt. Eng. 53, 112,308 (2014)CrossRefGoogle Scholar
  20. 20.
    Li, C., Li, S., Chen, G., Halang, Wa: Cryptanalysis of an image encryption scheme based on a compound chaotic sequence. Image Vis. Comput. 27, 1035–1039 (2009)CrossRefGoogle Scholar
  21. 21.
    Li, C., Liu, Y., Xie, T., Chen, M.Z.Q.: Breaking a novel image encryption scheme based on improved hyperchaotic sequences. Nonlinear Dyn. 73(3), 2083–2089 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Li, C., Liu, Y., Zhang, L.Y., Wong, K.W.: Cryptanalyzing a class of image encryption schemes based on Chinese Remainder Theorem. Sig. Process. Image Commun. 29(8), 914–920 (2014)CrossRefGoogle Scholar
  23. 23.
    Li, C., Lo, K.T.: Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process. 91, 949–954 (2011)CrossRefzbMATHGoogle Scholar
  24. 24.
    Li, C., Xie, T., Liu, Q., Cheng, G.: Cryptanalyzing image encryption using chaotic logistic map. Nonlinear Dyn. 78(2), 1545–1551 (2014)CrossRefGoogle Scholar
  25. 25.
    Li, Y., Wang, C., Chen, H.: A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation. Opt. Lasers Eng. 90, 238–246 (2017)CrossRefGoogle Scholar
  26. 26.
    Liu, Y., Fan, H., Xie, E.Y., Cheng, G., Li, C.: Deciphering an image cipher based on mixed transformed logistic maps. Int. J. Bifurc. Chaos 25(13), 1550188 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Luo, Y., Cao, L., Qiu, S., Lin, H., Harkin, J., Liu, J.: A chaotic map-control-based and the plain image-related cryptosystem. Nonlinear Dyn. 83, 2293–2310 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Luo, Y., Du, M., Liu, J.: A symmetrical image encryption scheme in wavelet and time domain. Commun. Nonlinear Sci. Numer. Simul. 20, 447–460 (2014)CrossRefGoogle Scholar
  29. 29.
    Matthews, R.: on the derivation of a chaotic encryption algorithm. Cryptologia 13(1), 29–42 (1989)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Mirzaei, O., Yaghoobi, M., Irani, H.: A new image encryption method: Parallel sub-image encryption with hyper chaos. Nonlinear Dyn. 67, 557–566 (2012)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Murillo-Escobar, M., Cruz-Hernández, C., Abundiz-Pérez, F., López-Gutiérrez, R., Del Campo, O.A.: A rgb image encryption algorithm based on total plain image characteristics and chaos. Signal Process. 109, 119–131 (2015)CrossRefGoogle Scholar
  32. 32.
    Qiu, H., Memmi, G.: Fast selective encryption method for bitmaps based on gpu acceleration. In: 2014 IEEE International Symposium on Multimedia, pp. 155–158 (2014)Google Scholar
  33. 33.
    Saikumar, N.: An encryption approach for security enhancement in images using key based partitioning technique. In: 2016 International Conference on Circuit, Power and Computing Technologies (ICCPCT), pp. 1–3 (2016)Google Scholar
  34. 34.
    Singh, H., Yadav, A.K., Vashisth, S., Singh, K.: Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane. Opt. Lasers Eng. 67, 145–156 (2015)CrossRefGoogle Scholar
  35. 35.
    Wang, Q., Yu, S., Li, C., Lü, J., Fang, X., Guyeux, C., Bahi, J.M.: Theoretical design and FPGA-based implementation of higher-dimensional digital chaotic systems. IEEE Trans Circuits Syst I-Regul Papers 63(3), 401–412 (2016)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Wang, X., Yang, L., Liu, R., Kadir, A.: A chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn. 62(3), 615–621 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    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, 290–299 (2012)CrossRefGoogle Scholar
  38. 38.
    Wu, X., Wang, D., Kurths, J., Kan, H.: A novel lossless color image encryption scheme using 2D DWT and 6D hyperchaotic system. Inf. Sci. 349–350, 137–153 (2016)CrossRefGoogle Scholar
  39. 39.
    Xie, E.Y., Li, C., Yu, S., Lü, J.: On the cryptanalysis of Fridrich’s chaotic image encryption scheme. Signal Process. 132, 150–154 (2017)CrossRefGoogle Scholar
  40. 40.
    Xie, K., Wu, P., Yang, S.: Gpu and cpu cooperation parallel visualisation for large seismic data. Electron. Lett. 46, 1196 (2010)CrossRefGoogle Scholar
  41. 41.
    Yaghouti Niyat, A., Moattar, M.H., Niazi Torshiz, M.: Color image encryption based on hybrid hyper-chaotic system and cellular automata. Opt. Lasers Eng. 90, 225–237 (2017)CrossRefGoogle Scholar
  42. 42.
    Ye, G.D., Huang, X.L., Zhang, L.Y., Wang, Z.X.: A self-cited pixel summation based image encryption algorithm. Chin. Phys. B 26, 010,501 (2017)CrossRefGoogle Scholar
  43. 43.
    Zhang, W., Yu, H., Zhao, Y., Zhu, Z.: Image encryption based on three-dimensional bit matrix permutation. Signal Process. 118, 36–50 (2016)CrossRefGoogle Scholar
  44. 44.
    Zhang, Y.Q., Wang, X.Y.: A chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn. 77, 687–698 (2014)CrossRefGoogle Scholar
  45. 45.
    Zheng, Y., Jin, J.: A novel image encryption scheme based on henon map and compound spatiotemporal chaos. Multimed. Tools Appl. 74, 7803–7820 (2014)CrossRefGoogle Scholar
  46. 46.
    Zhu, C.: A novel image encryption scheme based on improved hyperchaotic sequences. Opt. Commun. 285, 29–37 (2012)Google Scholar
  47. 47.
    Zhu, Z., Zhang, W., Wong, K., Yu, H.: A chaos-based symmetric image encryption scheme using a bit-level permutation. Inf. Sci. 181, 1171–1186 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Guangxi Key Lab of Multi-Source Information Mining and Security, Faculty of Electronic EngineeringGuangxi Normal UniversityGuilinChina
  2. 2.Department of Business Transformation and Sustainable Enterprise, Surrey Business SchoolUniversity of SurreySurreyUK
  3. 3.School of Computing, Engineering and Intelligent SystemsUlster UniversityDerryUK
  4. 4.College of Mathematics and InformaticsFujian Normal UniversityFuzhouChina

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