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Efficient Software Implementation of GMT6-672 and GMT8-542 Pairing-Friendly Curves for a 128-Bit Security Level

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Applied Cryptography and Network Security Workshops (ACNS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13285))

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Abstract

A Bilinear pairing on an elliptic curve defined over a finite field provides an attractive prospect for designing cryptographic schemes with various functionalities. An elliptic curve over which a computationally efficient bilinear pairing can be defined is called a “pairing-friendly curve”. Finding families of pairing-friendly curves with sufficient anticipated bit security has attracted significant research attention. For example, the Barreto-Neahrig (BN) and Barreto-Lynn-Scott (BLS) curves, are existing curves of this type. However, there is a need for alternatives to back up these already evaluated curves. In 2020 Guillevic, Masson, and Thomé (GMT) proposed pairing-friendly curves with embedding degrees 5 to 8 range. GMTk denotes curves with an embedding degree k. A composite k is preferred from the efficiency viewpoint. However, to the best of the GMT6 and GMT8 curves have been reported in the literature. In this paper, novel field-towering methods using two types of extension method and constructions are developed. These methods are applied to efficiently implement and analyze the bilinear pairings based on the GMT6 curve over a 672-bit prime field and the GMT8 curve over a 542-bit prime field. The pairing-computation times of our developed software evaluated using an Intel Core i7-8700 (@4.3 GHz Turbo Boost on) is computer are 0.987 ms and 1.12 ms for GMT6-672 and GMT8-542, respectively indicating the practicality of these curves.

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Acknowledgments

A part of this work was supported by the Cabinet Office (CAO), Cross-ministerial Strategic Innovation Promotion Program (SIP), “Cyber Physical Security for IoT Society”, JPNP18015 (Funding agency: NEDO). The authors thank Tadanori Teruya of CPSEC, AIST, for his assistance with the towering construction, and Yuki Nanjo of Okayama University for her comments on improving the manuscript.

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Authors and Affiliations

  1. Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan

    Zihao Song, Junichi Sakamoto, Naoki Yoshida, Riku Anzai & Tsutomu Matsumoto

  2. National Institute of Advanced Industrial Science and Technology, 2-3-26 Aomi, Koto-ku, Tokyo, 135-0064, Japan

    Junichi Sakamoto

  3. Cybozu Labs, Inc, Tokyo Nihombashi Tower 27F, 2-7-1 Nihombashi, Chuo-ku, Tokyo, 103-6028, Japan

    Shigeo Mitsunari

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  1. Zihao Song
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  2. Junichi Sakamoto
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  3. Shigeo Mitsunari
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  4. Naoki Yoshida
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  5. Riku Anzai
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  6. Tsutomu Matsumoto
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Correspondence to Tsutomu Matsumoto .

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Editors and Affiliations

  1. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

  2. University of Bristol, Bristol, UK

    Sridhar Adepu

  3. University of Malaga, Malaga, Spain

    Cristina Alcaraz

  4. Radboud University Nijmegen, Málaga, The Netherlands

    Lejla Batina

  5. Sapienza University of Rome, Rome, Roma, Italy

    Emiliano Casalicchio

  6. Singapore University of Technology and Design, Singapore, Singapore

    Sudipta Chattopadhyay

  7. Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

    Chenglu Jin

  8. University of Science and Technology of China, Hefei, China

    Jingqiang Lin

  9. University of Padua, Padua, Italy

    Eleonora Losiouk

  10. Concordia University, Montreal, QC, Canada

    Suryadipta Majumdar

  11. Technical University Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

  12. Delft University of Technology, Delft, The Netherlands

    Stjepan Picek

  13. Zhejiang Gongshang University, Hangzhou, China

    Jun Shao

  14. University of Aizu, Aizu-Wakamatsu, Japan

    Chunhua Su

  15. City University of Hong Kong, Hong Kong, Hong Kong

    Cong Wang

  16. Delft University of Technology, Delft, The Netherlands

    Yury Zhauniarovich

  17. Rutgers University, Piscataway, NJ, USA

    Saman Zonouz

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Song, Z., Sakamoto, J., Mitsunari, S., Yoshida, N., Anzai, R., Matsumoto, T. (2022). Efficient Software Implementation of GMT6-672 and GMT8-542 Pairing-Friendly Curves for a 128-Bit Security Level. In: Zhou, J., et al. Applied Cryptography and Network Security Workshops. ACNS 2022. Lecture Notes in Computer Science, vol 13285. Springer, Cham. https://doi.org/10.1007/978-3-031-16815-4_25

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  • DOI: https://doi.org/10.1007/978-3-031-16815-4_25

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