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A parallel image encryption algorithm based on chaotic Duffing oscillators

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Abstract

Image encryption has been a popular research field in recent decades. This paper presents a novel parallel image encryption algorithm, which is based on the chaotic duffing oscillators. Image encryption systems based on chaotic Duffing oscillators are show some better performances. In order to be more efficient and secure, we divided the plain-images (original-image) into several pieces. The speed of encryption and decryption is very fast. We use well-known ways to perform the security and performance analysis of the proposed image encryption scheme. The results of the fail-safe analysis are inspiring and it can be concluded that, the proposed scheme is efficient and secure.

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References

  1. Ahmad B, Alsaedi A, Alghamdi BS (2008) Analytic approximation of solutions of the forced duffing equation with integral boundary conditions. Nonlinear Anal Real World Appl 9(4):1727–1740

    Article  MathSciNet  MATH  Google Scholar 

  2. Akhavan A, Samsudin A, Akhshani A (2011) A symmetric image encryption scheme based on combination of nonlinear chaotic maps. J Frankl Inst 348(8):1797–1813

    Article  MathSciNet  Google Scholar 

  3. Akhshani A, Mahmodi H, Akhavan A (2006) A novel block cipher based on hierarchy of one-dimensional composition chaotic maps. In: IEEE international conference on image processing, pp 1993–1996

  4. Behnia S, Akhshani A, Ahadpour S, Mahmodi H, Akhavan A (2007) A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps. Phys Lett A 366(4–5):391–396

    Article  MATH  Google Scholar 

  5. Belazi A, El-Latif AAA, Belghith S (2016) A novel image encryption scheme based on substitution-permutation network and chaos. Signal Process 128:155–170

    Article  Google Scholar 

  6. Bender CM, Orszag SA (1978) Advanced mathematical methods for scientists and engineers i. Math Gaz 63(424):xiv–140

    MATH  Google Scholar 

  7. Bruce S (1995) In: Sutherland P (ed) Applied cryptography: protocols, algorithms, and source code in C. Wiley, New York

  8. Carroll TL, Pecora LM (2002) Synchronizing chaotic circuits. IEEE Trans Circuits Syst 38(4):453–456

    Article  MATH  Google Scholar 

  9. Chen G, Mao Y, Chui CK (2004) A symmetric image encryption scheme based on 3d chaotic cat maps. Chaos Solitons Fractals 21(3):749–761

    Article  MathSciNet  MATH  Google Scholar 

  10. Dachselt F, Schwarz W (2002) Chaos and cryptography. IEEE Trans Circuits Syst I Fundam Theory Appl 48(12):1498–1509

    Article  MathSciNet  MATH  Google Scholar 

  11. Deckard ND (2016) Book review: elementary statistics: a step by step approach. Teach Sociol 44(4):296–298

  12. Dong C (2014) Color image encryption using one-time keys and coupled chaotic systems. Signal Process Image Commun 29(5):628–640

    Article  MathSciNet  Google Scholar 

  13. El-Latif AAA, Li L, Niu X (2014) A new image encryption scheme based on cyclic elliptic curve and chaotic system. Multimed Tools Appl 70(3):1559–1584

    Article  Google Scholar 

  14. Elgendy F, Sarhan AM, Eltobely TE, El-Zoghdy SF, El-Sayed HS, Faragallah OS (2015) Chaos-based model for encryption and decryption of digital images. Multimed Tools Appl (18):1–25

  15. Hsiao HI, Lee J (2015) Color image encryption using chaotic nonlinear adaptive filter. Signal Process 117(C):281–309

    Article  Google Scholar 

  16. Jiang ZP (2002) Advanced feedback control of the chaotic duffing equation. IEEE Trans Circuits Syst I Fundam Theory Appl 49(2):244–249

    Article  MathSciNet  MATH  Google Scholar 

  17. Li C, Luo G, Qin K, Li C (2017) An image encryption scheme based on chaotic tent map. Nonlinear Dyn 87(1):127–133

    Article  Google Scholar 

  18. Liu H, Kadir A, Gong P (2015) A fast color image encryption scheme using one-time s-boxes based on complex chaotic system and random noise. Opt Commun 338:340–347

    Article  Google Scholar 

  19. Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20(2):130–141

    Article  MATH  Google Scholar 

  20. Loria A, Panteley E, Nijmeijer H (1997) Control of the chaotic duffing equation with uncertainty in all parameters. IEEE Trans Circuits Syst I Fundam Theory Appl 45(12):1252–1255

    Article  MathSciNet  MATH  Google Scholar 

  21. Mao Y, Chen G, Lian S (2004) A novel fast image encryption scheme based on 3d chaotic baker maps. Int J Bifurc Chaos 14(10):3613–3624

    Article  MathSciNet  MATH  Google Scholar 

  22. Matthews RAJ (1993) The use of genetic algorithms in cryptanalysis. Cryptologia 17(2):187–201

    Article  Google Scholar 

  23. Mirzaei O, Yaghoobi M, Irani H (2012) A new image encryption method: parallel sub-image encryption with hyper chaos. Nonlinear Dyn 67(1):557–566

    Article  MathSciNet  Google Scholar 

  24. Mollaeefar M, Sharif A, Nazari M (2017) A novel encryption scheme for colored image based on high level chaotic maps. Multimedia Tools & Applications 76:1–23

    Article  Google Scholar 

  25. Nijmeijer H, Berghuis H (1995) On lyapunov control of the duffing equation. IEEE Trans Circuits Syst I Fundam Theory Appl 42(8):473–477

    Article  MathSciNet  MATH  Google Scholar 

  26. Ott E, Grebogi C, Yorke JA (1990) Controlling chaos. Phys Rev Lett 64 (11):1196

    Article  MathSciNet  MATH  Google Scholar 

  27. Pareek NK, Patidar V, Sud KK (2006) Image encryption using chaotic logistic map. Image Vis Comput 24(9):926–934

    Article  Google Scholar 

  28. Parvin Z, Seyedarabi H, Shamsi M (2016) A new secure and sensitive image encryption scheme based on new substitution with chaotic function. Multimed Tools Appl 75(17):10631–10648

    Article  Google Scholar 

  29. Saberikamarposhti M, Mohammad D, Rahim MSM, Yaghobi M (2014) Using 3-cell chaotic map for image encryption based on biological operations. Nonlinear Dyn 75(3):407–416

    Article  Google Scholar 

  30. Shannon CE (1949) Communication theory of secrecy systems*. Bell Syst Tech J 28(4):656–715

    Article  MathSciNet  MATH  Google Scholar 

  31. Smart N et al (2010) Ecrypt ii yearly report on algorithms and keysizes (2009–2010). Framework 116

  32. Stoyanov B, Kordov K (2014) Novel image encryption scheme based on chebyshev polynomial and duffing map. Sci World J (2014-3-26) 2014:283,639

    Google Scholar 

  33. Ued Y (1991) Survey of regular and chaotic phenomena in the forced duffing oscillator. Chaos Solitons Fractals 1(3):199–231

    Article  MathSciNet  Google Scholar 

  34. Wang W, Tan H, Sun P, Pang Y, Ren B (2016) A novel digital image encryption algorithm based on wavelet transform and multi-chaos. In: International conference on wireless communication and sensor network, pp 711–719

  35. Wang W, Si M, Pang Y, Ran P, Wang H, Jiang X, Liu Y, Wu J, Wu W, Chilamkurti N (2017) An encryption algorithm based on combined chaos in body area networks. Comput Electr Eng. https://doi.org/10.1016/j.compeleceng.2017.07.026

  36. Yusufoğlu E (2006) Numerical solution of duffing equation by the laplace decomposition algorithm. Appl Math Comput 177(2):572–580

    MathSciNet  MATH  Google Scholar 

  37. Zaher AA, Harb AM, Zohdy MA (2007) Recursive backstepping control of chaotic duffing oscillators. Chaos Solitons Fractals 34(2):639–645

    Article  MATH  Google Scholar 

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Acknowledgements

This work is supported by the foundation of science and technology department of Sichuan province NO.2015SZ0231 and NO.2015SZ0045.

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Authors and Affiliations

  1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, People’s Republic of China

    Chunhu Li, Guangchun Luo & Chunbao Li

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  1. Chunhu Li
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  2. Guangchun Luo
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  3. Chunbao Li
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Correspondence to Chunhu Li.

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Li, C., Luo, G. & Li, C. A parallel image encryption algorithm based on chaotic Duffing oscillators. Multimed Tools Appl 77, 19193–19208 (2018). https://doi.org/10.1007/s11042-017-5391-5

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  • DOI: https://doi.org/10.1007/s11042-017-5391-5

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