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

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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.

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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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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing , 100876, China

    Hong Lai & Jinghua Xiao

  2. Department of Computing, Macquarie University, Sydney, NSW , 2109, Australia

    Hong Lai, Mehmet A. Orgun & Josef Pieprzyk

  3. Corporate Analytics The Australian Taxation Office, Sydney, NSW , 2000, Australia

    Liyin Xue

  4. Information Security Center, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing , 100876, China

    Yixian Yang

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  1. Hong Lai
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  2. Mehmet A. Orgun
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  3. Jinghua Xiao
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  4. Josef Pieprzyk
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  5. Liyin Xue
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  6. Yixian Yang
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Correspondence to Hong Lai.

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Lai, H., Orgun, M.A., Xiao, J. et al. Provably secure three-party key agreement protocol using Chebyshev chaotic maps in the standard model. Nonlinear Dyn 77, 1427–1439 (2014). https://doi.org/10.1007/s11071-014-1388-z

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  • DOI: https://doi.org/10.1007/s11071-014-1388-z

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