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A chaos-based image encryption scheme using 2D rectangular transform and dependent substitution

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Abstract

Chaos-based image cryptosystems usually adopt the traditional confusion-diffusion architecture which is considered insecure against known/chosen plaintext attacks. To overcome this drawback, this paper proposes a novel chaos-based image encryption scheme, in which the two-dimensional rectangular transform is employed to directly scramble the image of any rectangular size, and the dependent substitution is introduced to substitute for each pixel according to the image pixels. This scheme comprises two stages of encryption processes. Each stage provides the confusion and diffusion simultaneously in one traverse of image pixels. As a result, the proposed scheme has high speed and achieves a satisfactory security performance. Experimental results and various types of security analysis indicate that this scheme is efficient and secure enough to be used for practical image encryption and transmission.

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References

  1. Arroyo D, Li C, Li S, Alvarez G, Halang WA (2009) Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm. Chaos Soliton Fract 41(5):2613–2616

    Article  MATH  Google Scholar 

  2. Chen G, Mao Y, Chui C (2004) A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Soliton Fract 21(3):749–761

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen G, Chen Y, Liao X (2007) An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps. Chaos Soliton Fract 31(3):571–579

    Article  MathSciNet  MATH  Google Scholar 

  4. El-Latif A A A, Li L, Niu X (2012) A new image encryption scheme based on cyclic elliptic curve and chaotic system. Multimed Tools Appl. doi:10.1007/s11042-012-1173-2

  5. Fouda J S A E, Effa J Y, Sabat SL, Ali M (2014) A fast chaotic block cipher for image encryption. Commun Nonlinear Sci 19(3):578–588

    Article  MathSciNet  Google Scholar 

  6. Fridrich J (1998) Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifurcat Chaos 8(06):1259–1284

    Article  MathSciNet  MATH  Google Scholar 

  7. Fu C, Chen J, Zou H, Meng W, Zhan Y, Yu Y (2012) A chaos-based digital image encryption scheme with an improved diffusion strategy. Opt Express 20(3):2363–2378

    Article  Google Scholar 

  8. Huang X, Ye G (2012) An image encryption algorithm based on hyper-chaos and DNA sequence. Multimed Tools Appl. doi:10.1007/s11042-012-1331-6

  9. Hussain I, Shah T, Gondal MA (2012) An efficient image encryption algorithm based on S 8 S-box transformation and NCA map. Opt Commun 285:4887–4890

    Article  Google Scholar 

  10. Hussain I, Shah T, Gondal MA (2013) Application of S-box and chaotic map for image encryption. Math Comput Model 57(9–10):2576–2579

    Article  MATH  Google Scholar 

  11. Jolfaei A, Mirghadri A (2011) Image encryption using chaos and block cipher. Comput Inform Sci 4(1):172–185

    Google Scholar 

  12. Khan M, Shah T, Mahmood H, Gondal MA (2013) An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dyn 71(3):489–492

    Article  MathSciNet  Google Scholar 

  13. Kumar A, Ghose MK (2011) Extended substitution-diffusion based image cipher using chaotic standard map. Commun Nonlinear Sci 16(1):372–382

    Article  MathSciNet  MATH  Google Scholar 

  14. Li C, Lo K (2011) Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process 91(4):949–954

    Article  MATH  Google Scholar 

  15. Li S, Li C, Chen G, Bourbakis NG, Lo K (2008) A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process-Image 23(3):212–223

    Article  Google Scholar 

  16. Li H, Wang Y, Yan H, Li L, Li Q, Zhao X (2013) Double-image encryption by using chaos-based local pixel scrambling technique and gyrator transform. Opt Laser Eng 51(12):1327–1331

    Article  Google Scholar 

  17. Liu H, Liu Y (2014) Security assessment on block-Cat-map based permutation applied to image encryption scheme. Opt Laser Technol 56:313–316

    Article  Google Scholar 

  18. Liu H, Wang X (2013) Triple-image encryption scheme based on one-time key stream generated by chaos and plain images. J Syst Software 86(3):826–834

    Article  Google Scholar 

  19. Matthews R (1989) On the derivation of a chaotic encryption algorithm. Cryptologia 13(1):29–42

    Article  MathSciNet  Google Scholar 

  20. Norouzi B, Seyedzadeh S M, Mirzakuchaki S, Mosavi MR (2013) A novel image encryption based on row-column, masking and main diffusion processes with hyper chaos. Multimed Tools Appl. doi:10.1007/s11042-013-1699-y

  21. Özkaynak F, Özer AB (2010) A method for designing strong S-boxes based on chaotic Lorenz system. Phys Lett A 374(36):3733–3738

    Article  MATH  Google Scholar 

  22. Shao L, Qin Z, Liu B, et al. (2009) 2D bi-scale rectangular mapping and its application in image scrambling. J Comput Aided Des Comput Graph 21(7):1025–1034. in Chinese

    Google Scholar 

  23. Tang Z, Zhang X, Lan W (2014) Efficient image encryption with block shuffling and chaotic map. Multimed Tools Appl. doi:10.1007/s11042-014-1861-1

    Google Scholar 

  24. Wang X, Wang Q (2014) A novel image encryption algorithm based on dynamic S-boxes constructed by chaos. Nonlinear Dyn 75(3):567–576

    Article  Google Scholar 

  25. Wang Y, Wong K, Liao X, Xiang T (2009) A block cipher with dynamic S-boxes based on tent map. Commun Nonlinear Sci 14(7):3089–3099

    Article  MathSciNet  MATH  Google Scholar 

  26. Wang Y, Wong K, Liao X, Chen G (2011) A new chaos-based fast image encryption algorithm. Appl soft comput 11(1):514–522

    Article  Google Scholar 

  27. Wang Y, Wong K. W, Li C, Li Y (2012) A novel method to design S-box based on chaotic map and genetic algorithm. Phys Lett A 376(6):827–833

    Article  MATH  Google Scholar 

  28. Wei X, Guo L, Zhang Q, Zhang J, Lian S (2012) A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system. J Syst Software 85(2):290–299

    Article  Google Scholar 

  29. Ye G (2010) Image scrambling encryption algorithm of pixel bit based on chaos map. Pattern Recogn Lett 31(5):347–354

    Article  Google Scholar 

  30. Zhang Y, Xiao D, 2013 Cryptanalysis of S-box-only chaotic image ciphers against chosen plaintext attack. Nonlinear Dyn 72(4):751–756

  31. Zhang X, Zhao Z (2014) Chaos-based image encryption with total shuffling and bidirectional diffusion. Nonlinear Dyn 75(1-2):319–330

    Article  Google Scholar 

  32. Zhang W, Wong K, Yu H, Zhu Z (2013) An image encryption scheme using reverse 2-dimensional chaotic map and dependent diffusion. Commun Nonlinear Sci 18(8):2066–2080

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhang Q, Liu L, Wei X (2014) Improved algorithm for image encryption based on DNA encoding and multi-chaotic maps. AEU-Int J Electron Commun 68(3):186–192

    Article  Google Scholar 

  34. Zhang X, Shao L, Zhao Z, Liang Z (2014) An image encryption scheme based on constructing large permutation with chaotic sequence. Comput Electr Eng 40(3):931–941

    Article  Google Scholar 

  35. Zhua Z, Zhang W, Wong K, Yu H (2011) A chaos-based symmetric image encryption scheme using a bit-level permutation. Inform Sciences 181(6):1171–1186

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No: 61100239), the Ph.D. Programs Foundation of Ministry of Education of China (Grant No: 20100201110063), the Shaanxi Provincial Natural Science Foundation of China (Grant No: 2014JM8322, 2014JM8350).

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Authors and Affiliations

  1. Department of Computer Science and Technology, Xi’an Jiaotong University, Xi’an, 710049, China

    Xuanping Zhang, Xing Fan & Zhongmeng Zhao

  2. The Genome Institute, Washington University in St. Louis, St. Louis, MO, 63108, USA

    Jiayin Wang

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  1. Xuanping Zhang
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  2. Xing Fan
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  3. Jiayin Wang
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  4. Zhongmeng Zhao
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Correspondence to Xuanping Zhang.

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Zhang, X., Fan, X., Wang, J. et al. A chaos-based image encryption scheme using 2D rectangular transform and dependent substitution. Multimed Tools Appl 75, 1745–1763 (2016). https://doi.org/10.1007/s11042-014-2372-9

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  • DOI: https://doi.org/10.1007/s11042-014-2372-9

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