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Variations of Diffie-Hellman Problem

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Information and Communications Security (ICICS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2836))

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Abstract

This paper studies various computational and decisional Diffie-Hellman problems by providing reductions among them in the high granularity setting. We show that all three variations of computational Diffie-Hellman problem: square Diffie-Hellman problem, inverse Diffie-Hellman problem and divisible Diffie-Hellman problem, are equivalent with optimal reduction. Also, we are considering variations of the decisional Diffie-Hellman problem in single sample and polynomial samples settings, and we are able to show that all variations are equivalent except for the argument DDH \(\Leftarrow\) SDDH. We are not able to prove or disprove this statement, thus leave an interesting open problem.

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Author information

Authors and Affiliations

  1. Infocomm Security Department, Institute for Infocomm Research, 21 Heng Mui Keng Terrace, Singapore, 119613

    Feng Bao, Robert H. Deng & HuaFei Zhu

Authors
  1. Feng Bao
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  2. Robert H. Deng
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  3. HuaFei Zhu
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Editor information

Editors and Affiliations

  1. Institute of Softwear, Chinese Academy of Sciences, 100080, Beijing, China

    Sihan Qing

  2. Institute for Security in Distributed Applications, Hamburg University of Technology, 21071, Hamburg, Germany

    Dieter Gollmann

  3. Cryptography and Security Department Institute for Infocomm Research, Singapore

    Jianying Zhou

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© 2003 Springer-Verlag Berlin Heidelberg

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Bao, F., Deng, R.H., Zhu, H. (2003). Variations of Diffie-Hellman Problem. In: Qing, S., Gollmann, D., Zhou, J. (eds) Information and Communications Security. ICICS 2003. Lecture Notes in Computer Science, vol 2836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39927-8_28

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  • DOI: https://doi.org/10.1007/978-3-540-39927-8_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20150-2

  • Online ISBN: 978-3-540-39927-8

  • eBook Packages: Springer Book Archive

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