Nonlinear Dynamics

, Volume 93, Issue 4, pp 2399–2413 | Cite as

Cryptanalysis and improvement in an image encryption scheme using combination of the 1D chaotic map

  • Junxin Chen
  • Fangfang Han
  • Wei Qian
  • Yu-Dong Yao
  • Zhi-liang ZhuEmail author
Original Paper


In this paper, we evaluate the security of an image cipher recently proposed. Three different cryptographic primitives, i.e., permutation, diffusion, and cyclic rotation, were integrated in this cipher so as to obtain a satisfactory security performance within a single encryption round. It is found that the equivalent key stream elements can be derived under chosen-plaintext attack. Both mathematical proof and experimental validation are given in detail. Concerning the presented analysis and some common defects of chaos-based image ciphers, an enhanced image cryptosystem based on the single-round permutation–diffusion structure is further developed. Natural and medical images are introduced for experimental verification and performance comparison. The results demonstrate the security superiority of the improved cryptosystem.


Image encryption Cryptanalysis Improved diffusion Plaintext-related permutation 



This work is funded by the China Postdoctoral Science Foundation (No. 2018M630301), the Fundamental Research Funds for the Central Universities (Nos. N171903003, N171904009, N151903001), the National Natural Science Foundation of China (Nos. 61672146, 61771121). Thanks to Dr. Leo Yu Zhang ( for his valuable suggestions and selfless contribution, which are much help ful for promoting the manuscript.

Compliance with ethical standards

Conflicts of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.


  1. 1.
    Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc Chaos 16(08), 2129–2151 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Chai, X., Gan, Z., Chen, Y., Zhang, Y.: A visually secure image encryption scheme based on compressive sensing. Signal Process. 134, 35–51 (2017)CrossRefGoogle Scholar
  3. 3.
    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)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Chen, J., Zhang, Y., Qi, L., Fu, C., Xu, L.: Exploiting chaos-based compressed sensing and cryptographic algorithm for image encryption and compression. Optics Laser Technol. 99, 238–248 (2018)CrossRefGoogle Scholar
  5. 5.
    Chen, J., Zhu, Z., Zhang, L., Zhang, Y., Yang, Bq: Exploiting self-adaptive permutationdiffusion and DNA random encoding for secure and efficient image encryption. Signal Process. 142, 340–353 (2018)CrossRefGoogle Scholar
  6. 6.
    Chen, J., Zhu, Zl, Fu, C., Yu, H.: A fast image encryption scheme with a novel pixel swapping-based confusion approach. Nonlinear Dyn. 77(4), 1191–1207 (2014)CrossRefGoogle Scholar
  7. 7.
    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)zbMATHCrossRefGoogle Scholar
  8. 8.
    Diaconu, A.V.: Circular inter-intra pixels bit-level permutation and chaos-based image encryption. Inf. Sci. 355, 314–327 (2016)CrossRefGoogle Scholar
  9. 9.
    Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurc. Chaos 8(06), 1259–1284 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Fu, C., Meng, W., Zhan, Y., Zhu, Z., Lau, F.C.M., Chi, K.T., Ma, H.F.: An efficient and secure medical image protection scheme based on chaotic maps. Comput. Biol. Med. 43(8), 1000–1010 (2013)CrossRefGoogle Scholar
  11. 11.
    Guesmi, R., Farah, M., Kachouri, A., Samet, M.: A novel chaos-based image encryption using DNA sequence operation and secure hash algorithm SHA-2. Nonlinear Dyn. 3(83), 1123–1136 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Guesmi, R., Farah, M.A.B., Kachouri, A., Samet, M.: A novel chaos-based image encryption using DNA sequence operation and secure hash algorithm SHA-2. Nonlinear Dyn. 83(3), 1123–1136 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Hamdi, M., Rhouma, R., Belghith, S.: A selective compression-encryption of images based on SPIHT coding and Chirikov standard map. Signal Process. 131, 514–526 (2017)CrossRefGoogle Scholar
  14. 14.
    Hu, G., Xiao, D., Wang, Y., Li, X.: Cryptanalysis of a chaotic image cipher using Latin square-based confusion and diffusion. Nonlinear Dyn. 2(88), 1305–1316 (2017)zbMATHCrossRefGoogle Scholar
  15. 15.
    Hu, G., Xiao, D., Zhang, Y., Xiang, T.: An efficient chaotic image cipher with dynamic lookup table driven bit-level permutation strategy. Nonlinear Dyn. 2(87), 1359–1375 (2016)Google Scholar
  16. 16.
    Hu, T., Liu, Y., Gong, L.H., Ouyang, C.J.: An image encryption scheme combining chaos with cycle operation for DNA sequences. Nonlinear Dyn. 87(1), 51–66 (2017)CrossRefGoogle Scholar
  17. 17.
    Hua, Z., Yi, S., Zhou, Y.: Medical image encryption using high-speed scrambling and pixel adaptive diffusion. Signal Process. 144, 134–144 (2018)CrossRefGoogle Scholar
  18. 18.
    Hua, Z., Zhou, Y.: Design of image cipher using block-based scrambling and image filtering. Inf. Sci. 396, 97–113 (2017)CrossRefGoogle Scholar
  19. 19.
    Hussain, I.: Optical image encryption based on s-box transformation and fractional Hartley transform. J. Vib. Control 22(4), 1143–1146 (2016)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Hussain, I., Ahmed, J., Hussain, A.: An image encryption technique based on coupled map lattice and one-time s-boxes based on complex chaotic system. J. Intell. Fuzzy Syst. 29(4), 1493–1500 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Hussain, I., Gondal, M.A.: An extended image encryption using chaotic coupled map and s-box transformation. Nonlinear Dyn. 76(2), 1355–1363 (2014)CrossRefGoogle Scholar
  22. 22.
    Hussain, I., Shah, T., Gondal, M.A.: An efficient image encryption algorithm based on S8 S-box transformation and NCA map. Optics Commun. 285(24), 4887–4890 (2012)CrossRefGoogle Scholar
  23. 23.
    Hussain, I., Shah, T., Gondal, M.A.: Image encryption algorithm based on pgl(2, gf(28)) s-boxes and td-ercs chaotic sequence. Nonlinear Dyn. 70(1), 181–187 (2012)CrossRefGoogle Scholar
  24. 24.
    Hussain, I., Shah, T., Gondal, M.A.: Application of s-box and chaotic map for image encryption. Math. Comput. Model. 57(9), 2576–2579 (2013)zbMATHCrossRefGoogle Scholar
  25. 25.
    Hussain, I., Shah, T., Gondal, M.A.: Image encryption algorithm based on total shuffling scheme and chaotic s-box transformation. J. Vib. Control 20(14), 2133–2136 (2014)CrossRefGoogle Scholar
  26. 26.
    Li, C.: Cracking a hierarchical chaotic image encryption algorithm based on permutation. Signal Process. 118, 203–210 (2016)CrossRefGoogle Scholar
  27. 27.
    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)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Li, C., Lo, K.T.: Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal process. 91(4), 949–954 (2011)zbMATHCrossRefGoogle Scholar
  29. 29.
    Li, C., Xie, T., Liu, Q., Cheng, G.: Cryptanalyzing image encryption using chaotic logistic map. Nonlinear Dyn. 78(2), 1545–1551 (2014)CrossRefGoogle Scholar
  30. 30.
    Ma, J., Tang, J.: A review for dynamics in neuron and neuronal network. Nonlinear Dyn. 89(3), 1569–1578 (2017)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Norouzi, B., Mirzakuchaki, S., Seyedzadeh, S.M., Mosavi, M.R.: A simple, sensitive and secure image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Multimed. Tools Appl. 71(3), 1469 (2014)CrossRefGoogle Scholar
  32. 32.
    Özkaynak, F.: Brief review on application of nonlinear dynamics in image encryption. Nonlinear Dyn. 92(2), 305–313 (2018)CrossRefGoogle Scholar
  33. 33.
    Pak, C., Huang, L.: A new color image encryption using combination of the 1D chaotic map. Signal Process. 138, 129–137 (2017)CrossRefGoogle Scholar
  34. 34.
    Patidar, V., Pareek, N., Sud, K.: A new substitution-diffusion based image cipher using chaotic standard and logistic maps. Commun. Nonlinear Sci. Numer. Simul. 14(7), 3056–3075 (2009)CrossRefGoogle Scholar
  35. 35.
    Paul, S., Preneel, B.: Solving systems of differential equations of addition. In: Proceedings of the 10th Australasian Conference on Information Security and Privacy, pp. 75–88 (2005)Google Scholar
  36. 36.
    Solak, E., Çokal, C., Yildiz, O.T., BIYIKOĞLU, T.: Cryptanalysis of Fridrich’s chaotic image encryption. Int. J. Bifurc. Chaos 20(05), 1405–1413 (2010)Google Scholar
  37. 37.
    Tong, X.J., Zhang, M., Wang, Z., Ma, J.: A joint color image encryption and compression scheme based on hyper-chaotic system. Nonlinear Dyn. 4(84), 2333–2356 (2016)CrossRefGoogle Scholar
  38. 38.
    Wang, H., Xiao, D., Chen, X., Huang, H.: Cryptanalysis and enhancements of image encryption using combination of the 1d chaotic map. Signal Process. 144, 444–452 (2018)CrossRefGoogle Scholar
  39. 39.
    Wang, X., Liu, C., Zhang, H.: An effective and fast image encryption algorithm based on chaos and interweaving of ranks. Nonlinear Dyn. 84(3), 1595–1607 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Wen, W., Zhang, Y., Su, M., Zhang, R., Chen, Jx, Li, M.: Differential attack on a hyper-chaos-based image cryptosystem with a classic bi-modular architecture. Nonlinear Dyn. 1(87), 383–390 (2016)Google Scholar
  41. 41.
    Wu, J., Liao, X., Yang, B.: Color image encryption based on chaotic systems and elliptic curve Elgamal scheme. Signal Process. 141, 109–124 (2017)CrossRefGoogle Scholar
  42. 42.
    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)CrossRefGoogle Scholar
  43. 43.
    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, 137–153 (2016)CrossRefGoogle Scholar
  44. 44.
    Wu, X., Wang, K., Wang, X., Kan, H.: Lossless chaotic color image cryptosystem based on DNA encryption and entropy. Nonlinear Dyn. 90(2), 855–875 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  45. 45.
    Wu, Y., Noonan, J.P., Agaian, S.: NPCR and UACI randomness tests for image encryption. Cyber J Multidiscip. J. Sci. Technol. J. Sel. Areas Telecommun. (JSAT) 1, 31–38 (2011)Google Scholar
  46. 46.
    Wu, Y., Zhou, Y., Noonan, J.P., Agaian, S.: Design of image cipher using latin squares. Inf. Sci. 264, 317–339 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    Yap, W.S., Phan, R.C.W.: Commentary on a block chaotic image encryption scheme based on self-adaptive modelling[Applied Soft Computing 22 (2014) 351–357]. Appl. Soft Comput. 52, 501–504 (2017)CrossRefGoogle Scholar
  48. 48.
    Ye, G., Zhao, H., Chai, H.: Chaotic image encryption algorithm using wave-line permutation and block diffusion. Nonlinear Dyn. 4(83), 2067–2077 (2016)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Zhang, L., Zhu, Z., Yang, B., Liu, W., Zhu, H., Zou, M.: Cryptanalysis and improvement of an efficient and secure medical image protection scheme. Math. Problems Eng. 2015, 1–11 (2015)Google Scholar
  50. 50.
    Zhang, L.Y.: Design and analysis of multimedia cryptosystems. Ph.D. thesis, City University of HongkongGoogle Scholar
  51. 51.
    Zhang, L.Y., Liu, Y., Wang, C., Zhou, J., Zhang, Y., Chen, G.: Improved known-plaintext attack to permutation-only multimedia ciphers. Inf. Sci. 430–431, 228–239 (2018)MathSciNetCrossRefGoogle Scholar
  52. 52.
    Zhang, L.Y., Liu, Y., Wong, K.W., Pareschi, F., Zhang, Y., Rovatti, R., Setti, G.: On the security of a class of diffusion mechanisms for image encryption. IEEE Trans. Cybern. 99, 1–13 (2017)Google Scholar
  53. 53.
    Zhang, Y., Li, C., Li, Q., Zhang, D., Shu, S.: Breaking a chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn. 69(3), 1091–1096 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  54. 54.
    Zhang, Y., Xiao, D., Shu, Y., Li, J.: A novel image encryption scheme based on a linear hyperbolic chaotic system of partial differential equations. Signal Process. Image Commun. 28(3), 292–300 (2013)CrossRefGoogle Scholar
  55. 55.
    Zhang, Y., Xiao, D., Wen, W., Li, M.: Breaking an image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Nonlinear Dyn. 3(76), 1645–1650 (2014)CrossRefGoogle Scholar
  56. 56.
    Zhang, Y., Xiao, D., Wen, W., Wong, K.W.: On the security of symmetric ciphers based on DNA coding. Inf. Sci. 289, 254–261 (2014)zbMATHCrossRefGoogle Scholar
  57. 57.
    Zhou, N., Pan, S., Cheng, S., Zhou, Z.: Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing. Optics Laser Technol. 82, 121–133 (2016)CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Junxin Chen
    • 1
  • Fangfang Han
    • 1
  • Wei Qian
    • 1
  • Yu-Dong Yao
    • 1
  • Zhi-liang Zhu
    • 2
    Email author
  1. 1.Sino-Dutch Biomedical and Information Engineering SchoolNortheastern UniversityShenyangChina
  2. 2.Software CollegeNortheastern UniversityShenyangChina

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