Skip to main content
SpringerLink
Log in

Improvement of a chaotic maps-based three-party password-authenticated key exchange protocol without using server’s public key and smart card

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Three-party password-authenticated key exchange (3PAKE) protocol allows two users to establish a secure session key over an insecure communication channel with the help of a trusted server. Recently, Farash and Attari proposed a chaotic maps-based 3PAKE protocol without using server’s public key, smart card and symmetric cryptosystems and claimed its security by providing well-organized security proof. Unfortunately, in this paper, we demonstrate that their protocol cannot resist impersonation attack and off-line password guessing attack. To overcome their security weaknesses, we propose an improved chaotic maps-based 3PAKE protocol with the same advantages. Further, we apply the pi calculus-based formal verification tool ProVerif to show that our 3PAKE protocol achieves authentication and security and show that our protocol is more efficient than Farash and Attari’s protocol in terms of computation and communication costs.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baptista, M.S.: Cryptography with chaos. Phys. Lett. A 240(1–2), 50–54 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Özkaynak, F., Yavuz, S.: Designing chaotic S-boxes based on time-delay chaotic system. Nonlinear Dyn. 74(3), 551–557 (2013)

    Article  Google Scholar 

  3. Hussain, I., Shah, T., Gondal, M., Mahmood, H.: An efficient approach for the construction of LFT S-boxes using chaotic logistic map. Nonlinear Dyn. 71(1–2), 133–140 (2013)

    Article  MathSciNet  Google Scholar 

  4. Hussain, I., Shah, T., Gondal, M.: A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm. Nonlinear Dyn. 70(3), 1791–1794 (2012)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  6. Khan, M., Shah, T., Mahmood, H., Gondal, M.: An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dyn. 71(3), 489–492 (2013)

    Article  MathSciNet  Google Scholar 

  7. Anees, A., Siddiqui, A.M., Ahmed, F.: Chaotic substitution for highly autocorrelated data in encryption algorithm. Commun. Nonlinear Sci. Numer. Simul. 19(9), 3106–3118 (2014)

    Article  MathSciNet  Google Scholar 

  8. Huang, X., Ye, G.: An efficient self-adaptive model for chaotic image encryption algorithm. Commun. Nonlinear Sci. Numer. Simul. 19(12), 4094–4104 (2014)

    Article  Google Scholar 

  9. Hussain, I., Gondal, M.A.: An extended image encryption using chaotic coupled map and S-box transformation. Nonlinear Dyn. 76(2), 1355–1363 (2014)

    Article  Google Scholar 

  10. Chen, J.X., Zhu, Z.L., Fu, C., Yu, H.: A fast image encryption scheme with a novel pixel swapping-based confusion approach. Nonlinear Dyn. 77(4), 1191–1207 (2014)

    Article  Google Scholar 

  11. Chain, K., Kuo, W.C.: A new digital signature scheme based on chaotic maps. Nonlinear Dyn. 74(4), 1003–1012 (2013)

  12. Deng, S., Li, Y., Xiao, D.: Analysis and improvement of a chaos-based Hash function construction. Commun. Nonlinear Sci. Numer. Simul. 15(5), 1338–1347 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  13. Jabbari, A., Bagherzadeh, J.: A revised key agreement protocol based on chaotic maps. Nonlinear Dyn. (2014). doi:10.1007/s11071-014-1467-1

    MathSciNet  Google Scholar 

  14. Farash, M.S., Attari, m A.: Cryptanalysis and improvement of a chaotic map-based key agreement protocol using Chebyshev sequence membership testing. Nonlinear Dyn. 76(2), 1203–1213 (2014)

    Article  MathSciNet  Google Scholar 

  15. Lee, C.C., Lou, D.C., Li, C.T., Hsu, C.W.: An extended chaotic-maps-based protocol with key agreement for multiserver environments. Nonlinear Dyn. 76(1), 853–866 (2014)

    Article  MathSciNet  Google Scholar 

  16. Islam, S.H.: Provably secure dynamic identity-based three-factor password authentication scheme using extended chaotic maps. Nonlinear Dyn. (2014). doi:10.1007/s11071-014-1584-x

    Google Scholar 

  17. Xiao, D., Liao, X., Deng, S.: Using time-stamp to improve the security of a chaotic maps-based key agreement protocol. Inf. Sci. 178(6), 1598–1602 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  18. Han, S., Chang, E.: Chaotic map based key agreement with/out clock synchronization. Chaos Solitons Fractals 39(3), 1283–1289 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  19. Guo, X., Zhang, J.: Secure group key agreement protocol based on chaotic Hash. Inf. Sci. 180(20), 4069–4074 (2010)

    Article  MATH  Google Scholar 

  20. He, D., Chen, Y., Chen, Y.: Cryptanalysis and improvement of an extended chaotic maps-based key agreement protocol. Nonlinear Dyn. 69(3), 1149–1157 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  21. Gong, P., Li, P., Shi, W.: A secure chaotic maps-based key agreement protocol without using smart cards. Nonlinear Dyn. 70(4), 2401–2406 (2012)

    Article  MathSciNet  Google Scholar 

  22. Niu, Y., Wang, X.: An anonymous key agreement protocol based on chaotic maps. Commun. Nonlinear Sci. Numer. Simulat. 16(4), 1986–92 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  23. Xue, K., Hong, P.: Security improvement on an anonymous key agreement protocol based on chaotic maps. Commun. Nonlinear Sci. Numer. Simul. 17(7), 2969–2977 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  24. Yoon, E.: Efficiency and security problems of anonymous key agreement protocol based on chaotic maps. Commun. Nonlinear Sci. Numer. Simul. 17(7), 2735–2740 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  25. Tan, Z.: A chaotic maps-based authenticated key agreement protocol with strong anonymity. Nonlinear Dyn. 72(1–2), 311–320 (2013)

    Article  MATH  Google Scholar 

  26. Lee, C., Hsu, C.: A secure biometric-based remote user authentication with key agreement scheme using extended chaotic maps. Nonlinear Dyn. 71(1–2), 201–211 (2013)

    Article  MathSciNet  Google Scholar 

  27. Guo, C., Chang, C.C.: Chaotic maps-based password-authenticated key agreement using smart cards. Commun. Nonlinear Sci. Numer. Simul. 18(6), 1433–1440 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  28. Lin, H.Y.: Improved chaotic maps-based password-authenticated key agreement using smart cards. Commun. Nonlinear Sci. Numer. Simul. 20(2), 482–488 (2015)

    Article  MATH  Google Scholar 

  29. Yau, W.C., Phan, R.C.W.: Cryptanalysis of a chaotic map-based password-authenticated key agreement protocol using smart cards. Nonlinear Dyn. (2014). doi:10.1007/s11071-014-1704-7

    Google Scholar 

  30. Xie, Q., Dong, N., Tan, X., Wong, D.S., Wang, G.L.: Improvement of a three-party password-based key exchange protocol with formal verification. Inf. Technol. Control 42(3), 231–237 (2013)

    Google Scholar 

  31. Wang, X., Zhao, J.: An improved key agreement protocol based on chaos. Commun. Nonlinear Sci. Numer. Simul. 15(12), 4052–4057 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  32. Yoon, E., Jeon, I.: An efficient and secure Diffie–Hellman key agreement protocol based on Chebyshev chaotic map. Commun. Nonlinear Sci. Numer. Simul. 16(6), 2383–2389 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  33. Lai, H., Xiao, J., Li, L., Yang, Y.: Applying semigroup property of enhanced Chebyshev polynomials to anonymous authentication protocol. Math. Probl. Eng. (2012). doi:10.1155/2012/454823

    MathSciNet  Google Scholar 

  34. Zhao, F., Gong, P., Li, S., Li, M., Li, P.: Cryptanalysis and improvement of a three-party key agreement protocol using enhanced Chebyshev polynomials. Nonlinear Dyn. 74(1–2), 419–427 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  35. Lee, C., Li, C., Hsu, C.: A three-party password-based authenticated key exchange protocol with user anonymity using extended chaotic maps. Nonlinear Dyn. 73(1–2), 125–132 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  36. Hu, X., Zhang, Z.F.: Cryptanalysis and enhancement of a chaotic maps-based three-party password authenticated key exchange protocol. Nonlinear Dyn. (2014). doi:10.1007/s11071-014-1515-x

    Google Scholar 

  37. Xie, Q., Hu, B., Dong, N., Wong, D.S.: Anonymous three-party password-authenticated key exchange scheme for telecare medical information systems. PLoS One 9(7), e102747 (2014). doi:10.1371/journal.pone.0102747

    Article  Google Scholar 

  38. Xie, Q., Zhao, J., Yu, X.: Chaotic maps-based three-party password-authenticated key agreement scheme. Nonlinear Dyn. 74(4), 1021–1027 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  39. Lai, H., Orgun, M.A., Xiao, J.H., Pieprzyk, J., Xue, L.Y., Yang, Y.X.: Provably secure three-party key agreement protocol using Chebyshev chaotic maps in the standard model. Nonlinear Dyn. 77(4), 1427–1439 (2014)

    Article  MathSciNet  Google Scholar 

  40. Farash, M.S., Attari, M.A.: An efficient and provably secure three-party password-based authenticated key exchange protocol based on Chebyshev chaotic maps. Nonlinear Dyn. 77(1–2), 399–411 (2014)

  41. Abadi, M., Fournet, C.: Mobile values, new names, and secure communication. In: Proceedings of the 28th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 104–115. New York, USA (2001)

  42. Abadi, M., Blanchet, B., Lundh, H.C.: Models and proofs of protocol security: a progress report. In: 21st International Conference on Computer Aided Verification, , pp. 35–49. Grenoble, France (2009)

  43. Dolev, D., Yao, A.C.: On the security of public key protocols. IEEE Trans. Inf. Theory 29(2), 198–208 (1983)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This research was supported by Natural Science Foundations of Zhejiang Province (Nos. LZ12F02005, LY12F02006), the Major State Basic Research Development (973) Program of China (No. 2013CB834205), and National Natural Science Foundation of China (No. 61070153).

Author information

Authors and Affiliations

  1. Hangzhou Key Laboratory of Cryptography and Network Security, Hangzhou Normal University, Hangzhou, 311121, China

    Qi Xie & Bin Hu

  2. School of Computer Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Ting Wu

Authors
  1. Qi Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bin Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ting Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qi Xie.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xie, Q., Hu, B. & Wu, T. Improvement of a chaotic maps-based three-party password-authenticated key exchange protocol without using server’s public key and smart card. Nonlinear Dyn 79, 2345–2358 (2015). https://doi.org/10.1007/s11071-014-1816-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1816-0

Keywords

Search

Navigation