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A Novel Image Encryption Framework Based on Markov Map and Singular Value Decomposition

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6754))

Abstract

In this paper, a novel yet simple encryption technique is proposed based on toral automorphism, Markov map and singular value decomposition (SVD). The core idea of the proposed scheme is to scramble the pixel positions by the means of toral automorphism and then encrypting the scrambled image using Markov map and SVD. The combination of Markov map and SVD changed the pixels values significantly in order to confuse the relationship among the pixels. Finally, a reliable decryption scheme is proposed to construct original image from encrypted image. Experimental results demonstrate the efficiency and robustness of the proposed scheme.

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References

  1. Maniccam, S.S., Bourbakis, N.G.: Image and Video Encryption using Scan Patterns. Pattern Recognition 37, 725–737 (2004)

    Article  MATH  Google Scholar 

  2. Bourbakis, N.: Image Data Compression Encryption using G-SCAN Patterns. In: Proceedings of IEEE Conference on SMC, Orlando, FL, pp. 1117–1120 (1997)

    Google Scholar 

  3. Guan, Z.H., Huang, F., Guan, W.: Chaos-based Image Encryption Algorithm. Physics Letters A 346, 153–157 (2005)

    Article  MATH  Google Scholar 

  4. Gao, H., Zhang, Y., Liang, S., Li, D.: A New Chaotic Algorithm for Image Encryption. Chaos, Solitons and Fractals 29(2), 393–399 (2005)

    Article  MATH  Google Scholar 

  5. Tong, X., Cui, M.: Image encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator. Signal Processing 89(4), 480–491 (2009)

    Article  MATH  Google Scholar 

  6. Gaoa, T., Chen, Z.: A new image encryption algorithm based on hyper-chaos. Physics Letters A 372(4), 394–400 (2008)

    Article  Google Scholar 

  7. Gao, H., Zhang, Y., Liang, S., Li, D.: A new chaotic algorithm for image encryption. Chaos, Solitons and Fractals 29(2), 393–399 (2006)

    Article  MATH  Google Scholar 

  8. Gao, T.G., Chen, Z.Q.: Image encryption based on a new total shuffling algorithm. Chaos, Solitons and Fractals 38(1), 213–220 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chang, L.: Large Encrypting of Binary Images with Higher Security. Pattern Recognition Letters 19(5), 461–468 (1998)

    Article  MATH  Google Scholar 

  10. Li, X.: Image Compression and Encryption using Tree Structures. Pattern Recognition Letters 18(11), 1253–1259 (1997)

    Article  Google Scholar 

  11. Chuang, T., Lin, J.: New Approach to Image Encryption. Journal of Electronic Imaging 7(2), 350–356 (1998)

    Article  Google Scholar 

  12. Chuang, T., Lin, J.: A New Multiresolution Approach to Still Image Encryption. Pattern Recognition and Image Analysis 9(3), 431–436 (1999)

    Google Scholar 

  13. Pollicott, M., Yuri, M.: Dynamical systems and ergodic theory, Cambridge. London Mathematical Society Student Text Series (1998)

    Google Scholar 

  14. Golub, G.H., Reinsch, C.: Singular value decomposition and least squares solutions. Numerische Mathematik 14(5), 403–420 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  15. Schuster, H.G., Just, W.: Deterministic Chaos. Wiley-VCH (2005)

    Google Scholar 

  16. Tefas, A., Nikolaidis, A., Nikolaidis, N., Solachidis, V., Tsekeridou, S., Pitas, I.: Performance analysis of correlation-based watermarking schemes employing markov chaotic sequences. IEEE Transactions on Signal Processing 51(7), 1979–1994 (2003)

    Article  MATH  Google Scholar 

  17. Bhatnagar, G., Raman, B.: Distributed multiresolution discrete Fourier transform and its application to watermarking. International Journal of Wavelets, Multiresolution and Information Processing 8(2), 225–241 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang, Z., Bovik, A.C.: A Universal Image Quality Index. IEEE Signal Processing Letters 9(3), 81–84 (2002)

    Article  Google Scholar 

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© 2011 Springer-Verlag Berlin Heidelberg

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Bhatnagar, G., Jonathan Wu, Q.M., Raman, B. (2011). A Novel Image Encryption Framework Based on Markov Map and Singular Value Decomposition. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2011. Lecture Notes in Computer Science, vol 6754. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21596-4_29

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  • DOI: https://doi.org/10.1007/978-3-642-21596-4_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21595-7

  • Online ISBN: 978-3-642-21596-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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