A New Image Encryption Algorithm Based on One-Dimensional Polynomial Chaotic Maps

  • Amir Akhavan
  • Hadi Mahmodi
  • Afshin Akhshani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4263)


In recent years, a growing number of cryptosystems based on chaos have been proposed, however, most of them encounter with some problems such as: low level of security and small key space. Chaotic maps have good properties such as ergodicity, sensitivity to initial conditions and control parameters, etc. Due to these features, they are good candidate for information encryption. In this paper, encryption based on the Polynomial Chaotic Maps (PCMs) is proposed. The theoretic and simulation results state that the proposed algorithm has many properties such as high speed and large key space and high security. Therefore it is suitable for practical use in the secure communications.


Invariant Measure Image Encryption Adjacent Pixel Encrypt Image Cipher Image 


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  1. 1.
    Brown, R., Chua, L.O.: Clarifying chaos: Examples and counterexamples. Int. J. Bifur. Chaos 6(2), 219–242 (1996)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Fridrich, J.: Symmetric ciphirs based on two-dimensional chaotic maps. Int. J. Bifurcation and Chaos 8(6), 1259–1284 (1998)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Baptista, M.S.: Cryptography with chaos. Physics Letters A 240, 50–54 (1998)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Wong, W.-K., Lee, L.-P., Wong, K.-W.: A modified chaotic cryptographic method. Comput. Phys. Commun. 138, 234 (2001)MATHCrossRefGoogle Scholar
  5. 5.
    Wong, K.-W.: A fast chaotic cryptographic scheme with dynamic look-up table. Phys. Lett. A 298, 238 (2002)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Guan, Z.-H., Huang, F., Guan, W.: Chaos-based image encryption algorithm. Phys. Lett. A 346, 153–157 (2005)CrossRefMATHGoogle Scholar
  7. 7.
    Ponomarenko, V.I., Prokhorov, M.D.: Extracting information masked by the chaotic signal of a time-delay system. Phys. Rev. E. 66, 026215–026221 (2002)Google Scholar
  8. 8.
    Jafarizadeh, M.A., Behnia, S., Khorram, S., Nagshara, H.: Hierarchy of Chaotic Maps with an Invariant Measure. J. Stat. Phys. 104(516), 1013 (2001)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Umeno, K.: Method of constructing exactly solvable chaos. Phys. Rev. E 55, 5280–5284 (1997)CrossRefGoogle Scholar
  10. 10.
    Gilbert, T., Ferguson, C.D., Dorfman, J.R.: Field driven thermostated systems: A nonlinear multibaker map. Phys. Rev. E 59, 364–371 (1999)CrossRefGoogle Scholar
  11. 11.
    Keller, G.: Equilibrium States in a Ergodic Theory, pp. 23–30. Cambrige University Press, Cambrige (1998)Google Scholar
  12. 12.
    Wong, K.-W., Ho, S.-W., Yung, C.-K.: A chaotic cryptography scheme for generating short ciphertext. Phys. Lett. A 310, 67 (2003)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Xiang, T., Liao, X., Tang, G., Chen, Y., Wong, K.-W.: A novel block cryptosystem based on iterating a chaotic map. Physics Letters A 349, 109–115 (2006)CrossRefMATHGoogle Scholar
  14. 14.
    Chen, G., Mao, Y., Chui, C.: A symmetric image encryption scheme based on 3d chaotic cat maps. Chaos Solitons Fractals 21, 749–761 (2004)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Jafarizadeh, M.A., Behnia, S.: Hierarchy of Chaotic Maps with an Invariant Measure and their Compositions. J. Nonlinear Math.Phys. 9(1), 1–16 (2002)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Amir Akhavan
    • 1
  • Hadi Mahmodi
    • 2
  • Afshin Akhshani
    • 2
  1. 1.Department of EngineeringIAUUrmiaIran
  2. 2.Department of PhysicsIAUUrmiaIran

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