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A novel cascade encryption algorithm for digital images based on anti-synchronized fractional order dynamical systems

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Abstract

In this paper, an active control technique is employed for anti-synchronization between two identical fractional order reverse butterfly-shaped hyperchaotic systems. We have shown that the convergence rate of anti-synchronization error is very faster by increasing the value of an active controller gain. A new algorithm for image encryption and decryption is introduced and established by anti-synchronized fractional order dynamical systems. Experimental results show that the proposed encryption algorithm has high level security against various attacks. Further, it confirms that the new algorithm is more efficient compared to other existing algorithms.

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References

  1. Aghababa MP, Borjkhani M (2014) Chaotic fractional-order model for muscular blood vessel and its control via fractional control scheme. Complexity 20(2):37–46

    Article  MathSciNet  Google Scholar 

  2. Asheghan MM, Delshad SS, Beheshti MTH, Tavazoei MS (2013) Non-fragile control and synchronization of a new fractional order chaotic system. Appl Math Comput 222:712–721

    MATH  MathSciNet  Google Scholar 

  3. Balasubramaniam P, Muthukumar P, Ratnavelu K (2015) Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system. Nonlinear Dyn 80(1-2):249–267

    Article  MATH  MathSciNet  Google Scholar 

  4. Bhalekar S (2014) Synchronization of non-identical fractional order hyperchaotic systems using active control. World J Modell Simul 10:60–68

    Google Scholar 

  5. Caputo M (1967) Linear models of dissipation whose q is almost frequency independentii. Geophys J Int 13(5):529–539

    Article  Google Scholar 

  6. Chen D, Zhao W, Sprott JC, Ma X (2013) Application of takagi–sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization. Nonlinear Dyn 73(3):1495–1505

    Article  MATH  MathSciNet  Google Scholar 

  7. Delavari H, Lanusse P, Sabatier J (2013) Fractional order controller design for a flexible link manipulator robot. Asian J Control 15(3):783–795

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  9. Guesmi R, Farah MAB, Kachouri A, Samet M (2016) Hash key-based image encryption using crossover operator and chaos. Multimed tools Appl 75(8):4753–4769

    Article  MATH  Google Scholar 

  10. He J, Yu S, Cai J (2015) A method for image encryption based on fractional-order hyperchaotic systems. J Appl Anal Comput 5(2):197–209

    MATH  MathSciNet  Google Scholar 

  11. Huang X, Ye G (2014) An image encryption algorithm based on hyper-chaos and dna sequence. Multimed Tools Appl 72(1):57–70

    Article  Google Scholar 

  12. Huang X, Sun T, Li Y, Liang J (2014) A color image encryption algorithm based on a fractional-order hyperchaotic system. Entropy 17(1):28–38

    Article  Google Scholar 

  13. Jian X (2011) Anti-synchronization of uncertain rikitake systems via active sliding mode control. Int J Phys Sci 6(10):2478–2482

    Google Scholar 

  14. Khan M, Shah T, Batool SI (2016) Construction of s-box based on chaotic boolean functions and its application in image encryption. Neural Comput Appl 27 (3):677–685

    Article  Google Scholar 

  15. Kwuimy CK, Litak G, Nataraj C (2015) Nonlinear analysis of energy harvesting systems with fractional order physical properties. Nonlinear Dyn 80(1-2):491–501

    Article  Google Scholar 

  16. Li HL, Jiang YL, Wang ZL (2015) Anti-synchronization and intermittent anti-synchronization of two identical hyperchaotic chua systems via impulsive control. Nonlinear Dyn 79(2):919–925

    Article  MATH  MathSciNet  Google Scholar 

  17. Li R, Chen W (2014) Lyapunov-based fractional-order controller design to synchronize a class of fractional-order chaotic systems. Nonlinear Dyn 76(1):785–795

    Article  MATH  MathSciNet  Google Scholar 

  18. Liang Y, Liu G, Zhou N, Wu J (2015) Color image encryption combining a reality-preserving fractional dct with chaotic mapping in hsi space. Multimed Tools Appl:1–16

  19. Liu H, Kadir A, Niu Y (2014) Chaos-based color image block encryption scheme using s-box. AEU-Int J Electron Commun 68(7):676–686

    Article  Google Scholar 

  20. 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 

  21. Lopes AM, Machado JT (2016) Integer and fractional-order entropy analysis of earthquake data series. Nonlinear Dynam 84(1):79–90

    Article  MathSciNet  Google Scholar 

  22. Matignon D (1996) Stability results for fractional differential equations with applications to control processing. In: Computational Engineering in Systems Applications, vol 2. Citeseer, pp 963–968

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

    Article  MathSciNet  Google Scholar 

  24. Murillo-Escobar M, Cruz-Hernández C, Abundiz-Pérez F, López-Gutiérrez R, Del Campo OA (2015) A rgb image encryption algorithm based on total plain image characteristics and chaos. Signal Process 109:119–131

    Article  Google Scholar 

  25. Muthukumar P, Balasubramaniam P (2013) Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography. Nonlinear Dyn 74(4):1169–1181

    Article  MATH  MathSciNet  Google Scholar 

  26. Muthukumar P, Balasubramaniam P, Ratnavelu K (2014a) Synchronization and an application of a novel fractional order king cobra chaotic system. Chaos: An Interdisc J Nonlinear Sci 24(3):033,105

    Article  MathSciNet  MATH  Google Scholar 

  27. Muthukumar P, Balasubramaniam P, Ratnavelu K (2014b) Synchronization of a novel fractional order stretch-twist-fold (stf) flow chaotic system and its application to a new authenticated encryption scheme (aes). Nonlinear Dyn 77(4):1547–1559

    Article  MATH  MathSciNet  Google Scholar 

  28. Muthukumar P, Balasubramaniam P, Ratnavelu K (2015a) Fast projective synchronization of fractional order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (dob). Nonlinear Dyn 80(4):1883–1897

    Article  MATH  Google Scholar 

  29. Muthukumar P, Balasubramaniam P, Ratnavelu K (2015b) Sliding mode control design for synchronization of fractional order chaotic systems and its application to a new cryptosystem. International Journal of Dynamics and Control:1–9

  30. Norouzi B, Mirzakuchaki S (2015) Breaking a novel image encryption scheme based on an improper fractional order chaotic system. Multimedia Tools and Applications:1–10

  31. Qin W, Jiao X, Sun T (2014) Synchronization and anti-synchronization of chaos for a multi-degree-of-freedom dynamical system by control of velocity. J Vib Control 20(1):146–152

    Article  MathSciNet  Google Scholar 

  32. Razminia A, Baleanu D (2013) Fractional hyperchaotic telecommunication systems: a new paradigm. J Comput Nonlinear Dyn 8(3):031, 012

    Article  Google Scholar 

  33. Srivastava M, Ansari S, Agrawal S, Das S, Leung A (2014) Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method. Nonlinear Dyn 76(2):905–914

    Article  MathSciNet  Google Scholar 

  34. Tavazoei MS, Haeri M (2007) A necessary condition for double scroll attractor existence in fractional-order systems. Phys Lett A 367(1):102–113

    Article  MATH  Google Scholar 

  35. Wu GC, Baleanu D, Lin ZX (2016) Image encryption technique based on fractional chaotic time series. J Vib Control 22(8):2092–2099

    Article  MathSciNet  Google Scholar 

  36. Wu X, Bai C, Kan H (2014) A new color image cryptosystem via hyperchaos synchronization. Commun Nonlinear Sci Numer Simul 19(6):1884–1897

    Article  Google Scholar 

  37. Wu X, Li Y, Kurths J (2015) A new color image encryption scheme using cml and a fractional-order chaotic system. PloS one 10(3):e0119, 660

    Article  Google Scholar 

  38. Xu J, Cai G, Zheng S (2009) A novel hyperchaotic system and its control. J Uncertain Syst 3(2):137–144

    Google Scholar 

  39. Xu Y, Wang H, Li Y, Pei B (2014) Image encryption based on synchronization of fractional chaotic systems. Commun Nonlinear Sci Numer Simul 19(10):3735–3744

    Article  MathSciNet  Google Scholar 

  40. Yao W, Zhang X, Zheng Z, Qiu W (2015) A colour image encryption algorithm using 4-pixel feistel structure and multiple chaotic systems. Nonlinear Dynx 81(1-2):151–168

    Article  MathSciNet  Google Scholar 

  41. Zhang R, Gong J (2014) Synchronization of the fractional-order chaotic system via adaptive observer. Syst Sci Control Eng: Open Access J 2(1):751–754

    Article  Google Scholar 

  42. Zhong J, Li L (2015) Tuning fractional-order controllers for a solid-core magnetic bearing system. IEEE Trans Control Syst Technol 23(4):1648–1656

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the University of Malaya HIR Grant UM.C/625/1/HIR/MOHE/SC/13, Malaysia.

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Correspondence to P. Balasubramaniam.

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Muthukumar, P., Balasubramaniam, P. & Ratnavelu, K. A novel cascade encryption algorithm for digital images based on anti-synchronized fractional order dynamical systems. Multimed Tools Appl 76, 23517–23538 (2017). https://doi.org/10.1007/s11042-016-4052-4

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  • DOI: https://doi.org/10.1007/s11042-016-4052-4

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