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Comparative Analysis of Calculations in Cryptographic Protocols Using a Combination of Different Bases of Finite Fields

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Advances in Dependability Engineering of Complex Systems (DepCoS-RELCOMEX 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 582))

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Abstract

The chapter introduces a comparative analysis of the complexity of the Tate pairing operation on a supersingular elliptic curve and the complexity of the final exponentiation in the tripartite key agreement cryptographic protocol. The analysis takes into account a possibility of using different bases of finite fields in combination. Operations of multiplication and multiple squaring in the field \( GF(2^{n} ) \) and its 4-degree extension, of Tate pairing on supersingular elliptic curve and of final exponentiation are considered separately and in combination. We conclude that the best complexity bound for the pairing and the final exponentiation in the cryptographically significant field \( GF(2^{191} ) \) is provided by the combination of the polynomial basis of this field and 1-type optimal basis of the field expansion.

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Acknowledgements

This research was supported by the Russian Foundation for Basic Research, project 17-01-00485a. The authors are grateful to Igor Sergeev for editing and anonymous reviewers for comments.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University - MSU, GSP-1, 1 Leninskiye Gory, Main Building, Moscow, 119991, Russia

    Sergey Gashkov

  2. National Research University Moscow Power Engineering Institute, Krasnokazarmennaya, 14, Moscow, 111250, Russian Federation

    Alexander Frolov

Authors
  1. Sergey Gashkov
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  2. Alexander Frolov
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Corresponding author

Correspondence to Sergey Gashkov .

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Editors and Affiliations

  1. Department of Computer Engineering, Wrocław University of Technology Department of Computer Engineering, Wrocław, Poland

    Wojciech Zamojski

  2. Department of Computer Engineering, Wrocław University of Technology Department of Computer Engineering, Wrocław, Poland

    Jacek Mazurkiewicz

  3. Department of Computer Engineering, Wrocław University of Technology, Wroclaw, Poland

    Jarosław Sugier

  4. Department of Computer Engineering, Wrocław University of Technology Department of Computer Engineering, Wrocław, Poland

    Tomasz Walkowiak

  5. Systems Research Institute, Polish Academy of Sciences Systems Research Institute, Warsaw, Poland

    Janusz Kacprzyk

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Gashkov, S., Frolov, A. (2018). Comparative Analysis of Calculations in Cryptographic Protocols Using a Combination of Different Bases of Finite Fields. In: Zamojski, W., Mazurkiewicz, J., Sugier, J., Walkowiak, T., Kacprzyk, J. (eds) Advances in Dependability Engineering of Complex Systems. DepCoS-RELCOMEX 2017. Advances in Intelligent Systems and Computing, vol 582. Springer, Cham. https://doi.org/10.1007/978-3-319-59415-6_16

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  • DOI: https://doi.org/10.1007/978-3-319-59415-6_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59414-9

  • Online ISBN: 978-3-319-59415-6

  • eBook Packages: EngineeringEngineering (R0)

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