Skip to main content

Cryptography Based on Spatiotemporal Chaotic Systems

  • Chapter
Evolutionary Algorithms and Chaotic Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 267))

  • 1165 Accesses

Abstract

Chaos has been applied in cryptography in the past decades since there are tight relationships between chaos and cryptography. Especially, spatiotemporal chaotic systems can be used to design cryptosystems with satisfactory properties. The chapter focuses on applying a typical spatiotemporal chaotic system, i.e., a coupled map lattice (CML) in cryptography. Multiple-output pseudo-random bit generators (PRBGs) based on CMLs with various constructions and parameters values are designed. Their properties are investigated and compared to determine a certain CML with certain parameters from which the resulting PRBG have satisfactory properties. Additionally, a stream cipher based on the CML is designed and analyzed. It is shown that it has high security, high efficiency and low cost. Moreover, a multimedia cryptosystem based on the proposed stream cipher is constructed by using a field programmable gate array (FPGA). The effects of the encryptions of the text file, the audio file and the image file by using the cryptosystem is measured as effective.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baranovsky, A., Daems, D.: Design of one-dimensional chaotic maps with prescribed statistical properties. Int. J. Bifurcat Chaos Appl. Sci. Eng. 5, 1585–1598 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Batista, A.M., Pinto, S.E., Viana, R.L., Lopes, S.R.: Lyapunov spectrum and synchronization of piecewise linear map lattiecs with power-law coupling. Phys. Rev. E 65 (2002)

    Google Scholar 

  3. Baptista, M.S.: Cryptography with chaos. Phys. Lett. A 240, 50–54 (1999)

    Article  MathSciNet  Google Scholar 

  4. Chen, G., Mao, Y., Chui, C.: A symmetric image encryption scheme based on 3rd chaotic cat maps. Chaos, Solitons & Fractals 21, 749–761 (2003)

    Article  MathSciNet  Google Scholar 

  5. Garcia, P., Parravano, A., Cosenza, M., Jimenez, J., Marcano, A.: Coupled map networks as communication schemes. Phys. Rev. E 65, 195–201 (2002)

    Article  Google Scholar 

  6. Gotz, M., Kelber, K., Schwarz, W.: Discrete-time chaotic encryption systems-part i: Statistical design approach. IEEE Trans. Circ. Syst. Fund. Theor. Appl. 44(10), 963–970 (1997)

    Article  MathSciNet  Google Scholar 

  7. Kaneko, K.: Theory and Application of Coupled Map Lattices. John Wiley and Sons, New York(1993)

    Google Scholar 

  8. Kocarev, L., Jakimoski, G.: Pseudorandom bits generated by chaotic maps. IEEE Trans. Circ. Syst. Fund. Theor. Appl. 50, 123–126 (2003)

    Article  MathSciNet  Google Scholar 

  9. Kohda, T., Tsuneda, A.: Pseudonoise sequence by chaotic nonlinear maps and their correlation properties. IEICE Trans. Commun. E76-B, 855–862 (1993)

    Google Scholar 

  10. Lasota, A., Mackey, M.C.: Chaos, Fractals, and Noise: stochastic aspects of dynamics. Springer, New York (1997)

    Google Scholar 

  11. Li, P., Li, Z., Halang, W.A., Chen, G.R.: Analysis of a multiple output pseudo-randombit generator based on a spatiotemporal chaotic system. Int. J. Bifurcat Chaos Appl. Sci. Eng. 16(10), 2949–2963 (2006)

    Article  Google Scholar 

  12. Li, P., Li, Z., Halang, W.A., Chen, G.R.: A stream cipher based on a spatiotemporal chaotic system. Chaos, Solitons & Fractals 32(5), 1867–1876 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Li, S.J.: Analyses and New Designs of Digital Chaotic Ciphers. Ph.D thesis, School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an, China (2003)

    Google Scholar 

  14. Shujun, L., Xuanqin, M., Yuanlong, C.: Pseudo-random bit generator based on couple chaotic systems and its applications in stream-cipher cryptography. In: Pandu Rangan, C., Ding, C. (nteds.) INDOCRYPT 2001. LNCs, vol. 2247, pp. 316–329. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Li, S.J., Chen, G.R., Qin, M.: On the dynamical degradation of digital piecewise linear chaotic maps. Int. J. Bifurcat Chaos Appl. Sci. Eng. 15(10), 3119–3151 (2005)

    Article  MATH  Google Scholar 

  16. Li, S., Á lvarez, G., Chen, G.R.: Breaking a chaos-based secure communication scheme designed by an improved modulation method. Chaos, Soliton & Fractals 25, 109–120 (2005)

    Article  MATH  Google Scholar 

  17. Lu, H., Wang, S., Li, X., Tang, G., Kuang, J., Ye, W., Hu, G.: A new spatiotemporally chaotic cryptosystem and its security and performance analyses. Chaos 14(3), 617–629 (2004)

    Article  MathSciNet  Google Scholar 

  18. Masuda, N., Aihara, K.: Cryptosystems with discretized chaotic maps. IEEE Trans. Circ. Syst. Fund. Theor. Appl. 49(1), 28–40 (2002)

    Article  MathSciNet  Google Scholar 

  19. Menezes, A., Oorschot, P.V., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)

    MATH  Google Scholar 

  20. NIST, Security requirements for cryptographic modules (FIPS pub 140-2) (2001), http://csrc.nist.gov/publications/fips/fips140-2

    Google Scholar 

  21. Sang, T., Wang, R., Yan, Y.: Clock-controlled chaotic keystream generators. Electronics Letters 34(20), 1932–1934 (1998)

    Article  Google Scholar 

  22. Schneier, B.: Applied Cryptography: Protocols, algorithms, and source code in C. John Wiley and Sons, New York (1996)

    MATH  Google Scholar 

  23. Schuster, H.G.: Handbook of Chaos Control. WILEY-VCH, Weinheim (1999)

    Book  MATH  Google Scholar 

  24. Soto, J.: Statistical testing of random number generators (1999), http://csrc.nist.gov/rng/rng5.html

    Google Scholar 

  25. Stojanovski, T., Kocarev, L.: Chaos-based random number generators-part i: Analysis. IEEE Trans. Circ. Syst. Fund. Theor. Appl. 48(3), 281–288 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  26. Tang, G., Wang, S., Lu, H., Hu, G.: Chaos-based cryptograph incorporated with S-box algebraic operation. Phys. Lett. A 318, 388–398 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  27. Wang, S., Liu, W., Lu, H., Kuang, J., Hu, G.: Periodicity of chaotic trajectories in realizations of finite computer precisions and its implication in chaos communications. Int. J. Mod. Phys. B 18(17-19), 2617–2622 (2004)

    Article  Google Scholar 

  28. Wang, S., Ye, W., Lu, H., Kuang, J., Li, J., Luo, Y., Hu, G.: A spatiotemporal-chaosbased encryption having overall properties considerably better than advanced encryption standard. Comm. Theor. Phys. 40, 57–60 (2003)

    MATH  MathSciNet  Google Scholar 

  29. Wikipedia (2006) Chi Test, http://en.wikipedia.org/wiki/Pearson%7s-chi-square-test

    Google Scholar 

  30. Yang, T.: A survey of chaotic secure communication systems. International Journal of Computational Cognition 2(2), 81–130 (2004)

    Google Scholar 

  31. Ye, W., Dai, Q., Wang, S., Lu, H., Kuang, J., Zhao, Z., Zhu, X., Tang, G., Huang, R., Hu, G.: Experimental realization of a highly secure chaos communication under strong channel noise. Phys. Lett. A 330, 75–84 (2004)

    Article  MATH  Google Scholar 

  32. Zhang, H., Wang, H., Chen, W.: Oversampled chaotic binary sequences with good security. J. Circ. Syst. Comput. 11, 173–185 (2002)

    Google Scholar 

  33. Zhou, H., Ling, X.: Problems with the chaotic inverse system encryption approach. IEEE Trans. Circ. Syst. Fund. Theor. Appl. 44(3), 268–271 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Li, P., Li, Z., Halang, W.A., Chen, G. (2010). Cryptography Based on Spatiotemporal Chaotic Systems. In: Zelinka, I., Celikovsky, S., Richter, H., Chen, G. (eds) Evolutionary Algorithms and Chaotic Systems. Studies in Computational Intelligence, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10707-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-10707-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10706-1

  • Online ISBN: 978-3-642-10707-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics