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An efficient pixel-level chaotic image encryption algorithm

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A Correction to this article was published on 31 October 2018

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Abstract

In this paper, a new and efficient pixel-level image encryption algorithm is presented. In contrast to the traditional permutation–diffusion architecture, the proposed method enhances the connection between position shuffling for pixels and value changing for grayness. As a result, the separate attack becomes more difficult when attacking our structure of permutation–rewriting–diffusion (PRD). Before the diffusion operation, a rewriting function is applied to the permuted image in a simple way, which can be seen as a remedy for permutation’s inability to change the frequency of pixels. Moreover, the keystream is designed dependent upon the plain-image. Therefore, the proposed method can disturb the chosen plain-image and known plain-image attacks. Experimental results together with security analysis also show good efficiency of the PRD mechanism. Compared to some bit-level-based image encryption algorithms, our method shows increased faster speed and satisfies the performance requirements of real-time communication.

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  • 31 October 2018

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References

  1. Zhang, L.Y., Liu, Y.S., Pareschi, F., Zhang, Y.S., Wong, K.W., Rovatti, R., Setti, G.: On the security of a class of diffusion mechanisms for image encryption. IEEE Trans. Cybernetics 48, 1163–1175 (2018)

    Article  Google Scholar 

  2. Liu, H., Wan, H.B., Tse, C.K., Lü, J.H.: An encryption scheme based on synchronization of two-layered complex dynamical networks. IEEE Trans. Circuits-I 63, 2010–2021 (2016)

    Article  Google Scholar 

  3. Chou, H.G., Chuang, C.F., Wang, W.J., Lin, J.C.: A fuzzy-model-based chaotic synchronization and its implementation on a secure communication system. IEEE Trans. Inf. Foren. Sec. 8, 2177–2185 (2013)

    Article  Google Scholar 

  4. Bhatnagar, G., Wu, Q.M.J.: Chaos-based security solution for fingerprint data during communication and transmission. IEEE Trans. Instrum. Meas. 61, 876–887 (2012)

    Article  Google Scholar 

  5. Yang, Y.G., Tian, J., Lei, H., Zhou, Y.H., Shi, W.M.: Novel quantum image encryption using one-dimensional quantum cellular automata. Inf. Sci. 345, 257–270 (2016)

    Article  Google Scholar 

  6. Chai, X.L., Gan, Z.H., Yang, K., Chen, Y.R., Liu, X.X.: An image encryption algorithm based on the memristive hyperchaotic system, cellular automata and DNA sequence operations. Signal Process-Image 52, 6–19 (2017)

    Article  Google Scholar 

  7. Ye, G.D., Huang, X.L.: A feedback chaotic image encryption scheme based on both bit-level and pixel-level. J. Vib. Control 22, 1171–1180 (2016)

    Article  MathSciNet  Google Scholar 

  8. Enayatifar, R., Abdullah, A.H., Isnin, I.F.: Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence. Opt. Laser. Eng. 56, 83–93 (2014)

    Article  Google Scholar 

  9. Wu, X.J., Kan, H.B., 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)

    Article  Google Scholar 

  10. Hua, Z.Y., Zhou, Y.C.: Image encryption using 2D logistic-adjusted-Sine map. Inf. Sci. 339, 237–253 (2016)

    Article  Google Scholar 

  11. Murillo-Escobara, M.A., Cruz-Hernándezb, C., Abundiz-Péreza, F., López-Gutiérreza, R.M., Acosta Del Campo, O.R.: A RGB image encryption algorithm based on total plain image characteristics and chaos. Signal Process. 109, 119–131 (2015)

    Article  Google Scholar 

  12. Huang, X.L., Ye, G.D.: An efficient self-adaptive model for chaotic image encryption algorithm. Commun. Nonlinear SCI. 19, 4094–4104 (2014)

    Article  Google Scholar 

  13. Seyedzadeh, S.M., Norouzi, B., Mosavi, M.R., Mirzakuchaki, S.: A novel color image encryption algorithm based on spatial permutation and quantum chaotic map. Nonlinear Dyn. 81, 511–529 (2015)

    Article  MathSciNet  Google Scholar 

  14. Wu, Y., Hua, Z.Y., Zhou, Y.C.: \(n\)-dimensional discrete cat map generation using Laplace expansions. IEEE Trans. Cybern. 46, 2622–2633 (2016)

    Article  Google Scholar 

  15. Pareschi, F., Setti, G., Rovatti, R.: Implementation and testing of high-speed CMOS true random number generators based on chaotic systems. IEEE Trans. Circuits-I 57, 3124–3137 (2010)

    Article  MathSciNet  Google Scholar 

  16. Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurcat. Chaos 8, 1259–1284 (1998)

    Article  MathSciNet  Google Scholar 

  17. Ye, G.D., Huang, X.L.: Spatial image encryption algorithm based on chaotic map and pixel frequency. Sci. China Inf. Sci. 61, 058104 (2018)

    Article  MathSciNet  Google Scholar 

  18. Huang, X.L., Ye, G.D.: An image encryption algorithm based on hyper-chaos and DNA sequence. Multimed. Tools Appl. 72, 57–70 (2014)

    Article  Google Scholar 

  19. Liu, H.J., Kadir, A.: Asymmetric color image encryption scheme using 2D discrete-time map. Signal Process. 113, 104–112 (2015)

    Article  Google Scholar 

  20. Pak, C., Huang, L.L.: A new color image encryption using combination of the 1D chaotic map. Signal Process. 138, 129–137 (2017)

    Article  Google Scholar 

  21. Tong, X.J., Liu, Y., Zhang, M., Xu, H., Wang, Z.: An image encryption scheme based on hyperchaotic Rabinovich and exponential chaos maps. Entropy 17, 181–196 (2015)

    Article  Google Scholar 

  22. Zhang, W., Yu, H., Zhu, Z.L.: Color image encryption based on paired interpermuting planes. Opt. Commun. 338, 199–208 (2015)

    Article  Google Scholar 

  23. Liu, H.J., Wang, X.Y.: Color image encryption based on one-time keys and robust chaotic maps. Comput. Math. Appl. 59, 3320–3327 (2010)

    Article  MathSciNet  Google Scholar 

  24. Liu, H.J., Wang, X.Y.: Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt. Commun. 284, 3895–3903 (2011)

    Article  Google Scholar 

  25. Liu, H.J., Wang, X.Y., Kadir, A.: Image encryption using DNA complementary rule and chaotic maps. Appl. Soft Comput. 12, 1457–1466 (2012)

    Article  Google Scholar 

  26. Wang, X.Y., Yang, L., Liu, R., Kadir, A.: A chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn. 62, 615–621 (2010)

    Article  Google Scholar 

  27. Xiao, D., Wang, L., Xiang, T., Wang, Y.: Multi-focus image fusion and robust encryption algorithm based on compressive sensing. Opt. Laser Technol. 91, 212–225 (2017)

    Article  Google Scholar 

  28. Zhang, L.Y., Wong, K.W., Zhang, Y.S., Zhou, J.T.: Bi-level protected compressive sampling. IEEE Trans. Multimedia 18, 1720–1732 (2016)

    Article  Google Scholar 

  29. Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurcat. Chaos 16, 2129–2151 (2006)

    Article  MathSciNet  Google Scholar 

  30. Zhou, N.R., Hua, T.X., Gong, L.H., Pei, D.J., Liao, Q.H.: Quantum image encryption based on generalized Arnold transform and double random-phase encoding. Quantum Inf. Process. 14, 1193–1213 (2015)

    Article  MathSciNet  Google Scholar 

  31. Zhou, N.R., Pan, S.M., Cheng, S., Zhou, Z.H.: Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing. Opt. Laser Technol. 82, 121–133 (2016)

    Article  Google Scholar 

  32. Zhou, N.R., Li, H.L., Wang, D., Pan, S.M., Zhou, Z.H.: Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform. Opt. Commun. 343, 10–21 (2015)

    Article  Google Scholar 

  33. Liu, Z.J., Guo, C., Tan, J.B., Liu, W., Wu, J.J., Wu, Q., Pan, L.Q., Liu, S.T.: Securing color image by using phase-only encoding in Fresnel domains. Opt. Lasers Eng. 68, 87–92 (2015)

    Article  Google Scholar 

  34. Parvin, Z., Seyedarabi, H., Shamsi, M.: A new secure and sensitive image encryption scheme based on new substitution with chaotic function. Multimed. Tools Appl. 75, 10631–10648 (2016)

    Article  Google Scholar 

  35. Norouzi, B., Mirzakuchaki, S.: Breaking an image encryption algorithm based on the new substitution stage with chaotic functions. Optik 127, 5695–5701 (2016)

    Article  Google Scholar 

  36. Wang, X.Y., Xu, D.H.: A novel image encryption scheme based on Brownian motion and PWLCM chaotic system. Nonlinear Dyn. 75, 345–353 (2014)

    Article  Google Scholar 

  37. Zhu, C.X., Xu, S.Y., Hu, Y.P., Sun, K.H.: Breaking a novel image encryption scheme based on Brownian motion and PWLCM chaotic system. Nonlinear Dyn. 79, 1511–1518 (2015)

    Article  Google Scholar 

  38. Zhy, H.G., Zhao, C., Zhang, X.D.: A novel image encryption-compression scheme using hyper-chaos and Chinese remainder theorem. Signal Process.-Image 28, 670–680 (2013)

    Article  Google Scholar 

  39. Li, C.Q., Liu, Y.S., Zhang, L.Y., Wong, K.W.: Cryptanalyzing a class of image encryption schemes based on Chinese remainder theorem. Signal Process.-Image 29, 914–920 (2014)

    Article  Google Scholar 

  40. Diaconu, A.V.: Circular inter–intra pixels bit-level permutation and chaos-based image encryption. Inf. Sci. 355–356, 314–327 (2016)

    Article  Google Scholar 

  41. Belazi, A., Khan, M., El-Latif, A.A.A., Belghith, S.: Efficient cryptosystem approaches: S-boxes and permutation-substitution-based encryption. Nonlinear Dyn. 87, 337–361 (2017)

    Article  Google Scholar 

  42. Kocarev, L., Galias, Z., Lian, S.G.: Intelligent Computing Based on Chaos, pp. 333–354. Springer, Berlin (2009)

    Book  Google Scholar 

  43. Xie, E.Y., Li, C.Q., Yu, S.M., Lü, J.H.: On the cryptanalysis of Fridrich’s chaotic image encryption scheme. Signal Process. 132, 150–154 (2017)

    Article  Google Scholar 

  44. Abanda, Y., Tiedeu, A.: Image encryption by chaos mixing. IET Image Process. 10, 742–750 (2016)

    Article  Google Scholar 

  45. Li, C.Q., Lin, D.D., Lü, J.H.: Cryptanalyzing an image-scrambling encryption algorithm of pixel bits. IEEE MultiMedia 24, 64–71 (2017)

    Article  Google Scholar 

  46. Li, X.W., Xiao, D., Wang, Q.H.: Error-free holographic frames encryption with CA pixel-permutation encoding algorithm. Opt. Lasers Eng. 100, 200–207 (2018)

    Article  Google Scholar 

  47. Zhang, Y.S., Xiao, D., Wen, W.Y., Li, M.: Breaking an image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Nonlinear Dyn. 76, 1645–1650 (2014)

    Article  Google Scholar 

  48. Zhang, Y.Q., Wang, X.Y.: A new image encryption algorithm based on non-adjacent coupledmap lattices. Appl. Soft Comput. 26, 10–20 (2015)

    Article  Google Scholar 

  49. Zhang, Y.Q., Wang, X.Y.: A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice. Inf. Sci. 273, 329–351 (2014)

    Article  Google Scholar 

  50. Li, S.J., Chen, G.R., Mou, X.Q.: On the dynamical degradation of digital piecewise linear chaotic maps. Int. J. Bifurcat. Chaos 15, 3119 (2005)

    Article  MathSciNet  Google Scholar 

  51. Ghebleh, M., Kanso, A., Stevanovic, D.: A novel image encryption algorithm based on piecewise linear chaotic maps and least squares approximation. Multimed. Tools Appl. 77, 7305–7326 (2018)

    Article  Google Scholar 

  52. Chen, J.X., Zhu, Z.L., Zhang, L.B., Zhang, Y.S., Yang, B.Q.: Exploiting self-adaptive permutation-diffusion and DNA random encoding for secure and efficient image encryption. Signal Process. 142, 340–353 (2018)

    Article  Google Scholar 

  53. Chen, J.X., Zhu, Z.L., Fu, C., Yu, H., Zhang, Y.S.: Reusing the permutation matrix dynamically for efficient image cryptographic algorithm. Signal Process. 111, 294–307 (2015)

    Article  Google Scholar 

  54. Wang, X.Y., Liu, C.M., Xu, D.H., Liu, C.X.: Image encryption scheme using chaos and simulated annealing algorithm. Nonlinear Dyn. 84, 1417–1429 (2016)

    Article  MathSciNet  Google Scholar 

  55. Wang, X.Y., Liu, L.T., Zhang, Y.Q.: A novel chaotic block image encryption algorithm based on dynamic random growth technique. Opt. Lasers Eng. 66, 10–18 (2015)

    Article  Google Scholar 

  56. Wang, X.Y., Zhang, Y.Q., Bao, X.M.: A novel chaotic image encryption scheme using DNA sequence operations. Opt. Lasers Eng. 73, 53–61 (2015)

    Article  Google Scholar 

  57. Huang, X.L.: Image encryption algorithm using chaotic Chebyshev generator. Nonlinear Dyn. 67, 2411–2417 (2012)

    Article  MathSciNet  Google Scholar 

  58. Liu, Y.Q., Luo, Y.L., Song, S.X., Cao, L.C., Liu, J.X., Harkin, J.: Counteracting dynamical degradation of digital chaotic Chebyshev map via perturbation. Int. J. Bifurcat. Chaos 27, 1750033 (2017)

    Article  MathSciNet  Google Scholar 

  59. Addabbo, T., Member, S., Alioto, M., Fort, A., Pasini, A., Rocchi, S., Vignoli, V.: A class of maximum-period nonlinear congruential generators derived from the Rényi chaotic map. IEEE Trans. Circuits Syst.-I: Reg. Pap. 54, 816–828 (2007)

    Article  Google Scholar 

  60. Wang, X.Y., Teng, L., Qin, X.: A novel colour image encryption algorithm based on chaos. Signal Process. 92, 1101–1108 (2012)

    Article  Google Scholar 

  61. Özkaynak, F.: Brief review on application of nonlinear dynamics in image encryption. Nonlinear Dyn. 92, 305–313 (2018)

    Article  Google Scholar 

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Acknowledgements

The work described in this paper was supported by the National Natural Science Foundations of China (Nos. 61602124, 61702116), the Postdoctoral Science Foundation of China (No. 2017M611991), the Natural Science Foundations of Guangdong Province of China (Nos. 2016A030310333, 2015A030313614, 2015A030313620), the Science and Technology Planning Project of Guangdong Province of China (No. 2017A010101025), the Program for Scientific Research Start-up Funds of Guangdong Ocean University of China (No. R17037), the Special Funding Program for Excellent Young Scholars of Guangdong Ocean University of China (No. HDYQ2017006), and the Project of Enhancing School With Innovation of Guangdong Ocean University of China (GDOU2016050228).

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang, 524088, China

    Guodong Ye

  2. College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, 310027, China

    Guodong Ye, Chen Pan, Xiaoling Huang & Qixiang Mei

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  1. Guodong Ye
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  2. Chen Pan
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  3. Xiaoling Huang
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Correspondence to Guodong Ye.

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Ye, G., Pan, C., Huang, X. et al. An efficient pixel-level chaotic image encryption algorithm. Nonlinear Dyn 94, 745–756 (2018). https://doi.org/10.1007/s11071-018-4391-y

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