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Nonlinear Dynamics

, Volume 77, Issue 4, pp 1427–1439 | Cite as

Provably secure three-party key agreement protocol using Chebyshev chaotic maps in the standard model

  • Hong Lai
  • Mehmet A. Orgun
  • Jinghua Xiao
  • Josef Pieprzyk
  • Liyin Xue
  • Yixian Yang
Original Paper

Abstract

Recently, several key agreement protocols based on Chebyshev chaotic maps have been proposed in the literature. However, they can normally achieve “heuristic” security, that is, once drawbacks are found in these protocols, they are either modified to resist the new attacks, or are discarded. Under these circumstances, it is necessary and significant to define standard security models that can precisely characterize the capabilities of the participants and a potent adversary. Hence, we propose to use public key encryption based on enhanced Chebyshev chaotic maps and pseudo-random function ensembles to construct an efficient three-party key agreement protocol under the standard model, in which the adversary is able to make a wider range of queries and have more freedom than the other proposed schemes. In the design of our protocol, we follow the ideas in the recent key agreement protocol of Yang and Cao’s. The proposed protocol is shown to be provably secure if decisional Diffie–Hellman problem, which is based on Chebyshev chaotic maps, is computationally infeasible. To the best of our knowledge, our protocol is the first provably secure 3PAKE protocol using Chebyshev chaotic maps under the standard model.

Keywords

Heuristic security Standard model Enhanced Chebyshev chaotic maps Pseudo-random function ensembles Decisional Diffie–Hellman 

Notes

Acknowledgments

The authors are grateful to the two anonymous referees for their valuable comments and suggestions which helped us to improve the presentation of this paper. Hong Lai has been supported in part by an International Macquarie University Research Excellence Scholarship (iMQRES). This work is also supported by the National Basic Research Program of China (973 Program) (Grant No. 2010CB923200) and the National Natural Science Foundation of China (No. 61377067, 61121061). The work is also supported by Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), P. R. China.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Hong Lai
    • 1
    • 2
  • Mehmet A. Orgun
    • 2
  • Jinghua Xiao
    • 1
  • Josef Pieprzyk
    • 2
  • Liyin Xue
    • 3
  • Yixian Yang
    • 4
  1. 1.School of ScienceBeijing University of Posts and TelecommunicationsBeijing China
  2. 2.Department of ComputingMacquarie UniversitySydneyAustralia
  3. 3.Corporate Analytics The Australian Taxation OfficeSydneyAustralia
  4. 4.Information Security CenterBeijing University of Posts and TelecommunicationsBeijing China

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