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International Conference on Field Programmable Logic and Applications

FPL 2004: Field Programmable Logic and Application pp 911–916Cite as

Implementation of the Extended Euclidean Algorithm for the Tate Pairing on FPGA

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3203))

Abstract

The Tate pairing is a mapping which has good functionality for constructing elliptic cryptosystems, while its computation is a hard task. Especially, calculation of an inverse element using the extended Euclidean algorithm over a finite field \({\Bbb F}_p\) tends to be a bottleneck. In this paper, several kinds of implementation of the extended Euclidean algorithm on an FPGA are shown and compared. Effects of introducing Montgomery multiplication methods are also analyzed.

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Author information

Authors and Affiliations

  1. Department of Computer and Information Sciences, Nagasaki University,  

    Takehiro Ito, Yuichiro Shibata & Kiyoshi Oguri

Authors
  1. Takehiro Ito
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  2. Yuichiro Shibata
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  3. Kiyoshi Oguri
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Editor information

Editors and Affiliations

  1. ITIV - Universitaet Karlsruhe (TH),  

    Jürgen Becker

  2. University of Paderborn,  

    Marco Platzner

  3. IMEC, Kapeldreef 75, Leuven, Leuven, Belgium

    Serge Vernalde

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© 2004 Springer-Verlag Berlin Heidelberg

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Ito, T., Shibata, Y., Oguri, K. (2004). Implementation of the Extended Euclidean Algorithm for the Tate Pairing on FPGA. In: Becker, J., Platzner, M., Vernalde, S. (eds) Field Programmable Logic and Application. FPL 2004. Lecture Notes in Computer Science, vol 3203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30117-2_98

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  • DOI: https://doi.org/10.1007/978-3-540-30117-2_98

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22989-6

  • Online ISBN: 978-3-540-30117-2

  • eBook Packages: Springer Book Archive

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