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Constructing Symmetric Pairings over Supersingular Elliptic Curves with Embedding Degree Three

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Pairing-Based Cryptography – Pairing 2013 (Pairing 2013)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8365))

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Abstract

In the present paper, we propose constructing symmetric pairings by applying the Ate pairing to supersingular elliptic curves over finite fields that have large characteristics with embedding degree three. We also propose an efficient algorithm of the Ate pairing on these curves. To construct the algorithm, we apply the denominator elimination technique and the signed-binary approach to the Miller’s algorithm, and improve the final exponentiation. We then show the efficiency of the proposed method through an experimental implementation.

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Author information

Authors and Affiliations

  1. Research Institute for Secure Systems, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba-shi, Ibaraki-ken, 305-8568, Japan

    Tadanori Teruya

  2. Internet Initiative Japan Inc., Jinbocho Mitsui Bldg., 1-105 Kanda Jinbo-cho, Chiyoda-ku, Tokyo, 101-0051, Japan

    Kazutaka Saito

  3. Faculty of Systems and Information Engineering, University of Tsukuba, 1-1-1, Ten-nohdai, Tsukuba-shi, Ibaraki-ken, 305-8573, Japan

    Naoki Kanayama & Eiji Okamoto

  4. NTT Secure Platform Laboratories, 3-9-11, Midori-cho, Musashino-shi, Tokyo, 180-8585, Japan

    Yuto Kawahara & Tetsutaro Kobayashi

Authors
  1. Tadanori Teruya
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  2. Kazutaka Saito
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  3. Naoki Kanayama
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  4. Yuto Kawahara
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  5. Tetsutaro Kobayashi
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  6. Eiji Okamoto
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Editor information

Editors and Affiliations

  1. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, No. 800, Dongchuan Road, 200240, Shanghai, China

    Zhenfu Cao

  2. School of Information Science and Technology, Sun Yat-sen University, No. 135, Xingang Xi Road, 510275, Guangzhou, China

    Fangguo Zhang

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Teruya, T., Saito, K., Kanayama, N., Kawahara, Y., Kobayashi, T., Okamoto, E. (2014). Constructing Symmetric Pairings over Supersingular Elliptic Curves with Embedding Degree Three. In: Cao, Z., Zhang, F. (eds) Pairing-Based Cryptography – Pairing 2013. Pairing 2013. Lecture Notes in Computer Science, vol 8365. Springer, Cham. https://doi.org/10.1007/978-3-319-04873-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-04873-4_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04872-7

  • Online ISBN: 978-3-319-04873-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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