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International Workshop on Security

IWSEC 2016: Advances in Information and Computer Security pp 319–334Cite as

Faster Explicit Formulae for Computing Pairings via Elliptic Nets and Their Parallel Computation

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9836))

Abstract

In this paper, we discuss computations of optimal pairings over some pairing-friendly curves and a symmetric pairing over supersingular curves via elliptic nets. We show that optimal pairings can be computed more efficiently if we use twists of elliptic curves and give formulae for computing optimal pairings via elliptic nets of these twist curves. Furthermore, we propose parallel algorithms for these pairings and estimate the costs of these algorithms in certain reasonable assumptions.

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References

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Acknowledgments

We would like to thank the anonymous referees for valuable suggestions. This work was supported by a research grant from the KDDI Foundation A study on improvement of pairing-based cryptography, a Grant-in-Aid for Scientific Research(C) (24540135) and a research grant from NTT Secure Platform Laboratories.

Author information

Authors and Affiliations

  1. Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo, 192-0372, Japan

    Hiroshi Onuki & Shigenori Uchiyama

  2. National Institute of Advanced Industrial Science and Technology, 2-4-7 Aomi, Koto-ku, Tokyo, 135-0064, Japan

    Tadanori Teruya

  3. University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Naoki Kanayama

Authors
  1. Hiroshi Onuki
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  2. Tadanori Teruya
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  3. Naoki Kanayama
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  4. Shigenori Uchiyama
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Corresponding author

Correspondence to Hiroshi Onuki .

Editor information

Editors and Affiliations

  1. Japan Broadcasting Corporation, Tokyo, Japan

    Kazuto Ogawa

  2. Yokohama National University, Yokohama, Japan

    Katsunari Yoshioka

A Parallel Algorithms

A Parallel Algorithms

We give parallel algorithms and estimations of these costs for each \(d = 2, 3, 4, 6\). We use notations in Algorithm 1 in the following. In the following tables, “proc.” and “sync.” means processor and synchronization of each processor respectively (Tables 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15).

Table 4. Parallel algorithm for 4 processors (\(d=2\))
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Table 5. Parallel algorithm for 8 processors (\(d=2\))
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Table 6. Parallel algorithm for 16 processor (\(d=2\))
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Table 7. Parallel algorithm for 4 processors (\(d=3\))
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Table 8. Parallel algorithm 8 processors (\(d=3\))
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Table 9. Parallel algorithm for 12 processors (\(d=3\))
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Table 10. Parallel algorithm for 4 processors (\(d=4\))
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Table 11. Parallel algorithm for 8 processors (\(d=4\))
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Table 12. Parallel algorithm for 12 processor (\(d=4\))
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Table 13. Parallel algorithm for 4 processors (\(d=6\))
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Table 14. Parallel algorithm for 8 processors (\(d=6\))
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Table 15. Parallel algorithm for 10 processors (\(d=6\))
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© 2016 Springer International Publishing Switzerland

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Onuki, H., Teruya, T., Kanayama, N., Uchiyama, S. (2016). Faster Explicit Formulae for Computing Pairings via Elliptic Nets and Their Parallel Computation. In: Ogawa, K., Yoshioka, K. (eds) Advances in Information and Computer Security. IWSEC 2016. Lecture Notes in Computer Science(), vol 9836. Springer, Cham. https://doi.org/10.1007/978-3-319-44524-3_19

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  • DOI: https://doi.org/10.1007/978-3-319-44524-3_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44523-6

  • Online ISBN: 978-3-319-44524-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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