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On Constructing Prime Order Elliptic Curves Suitable for Pairing-Based Cryptography

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Blockchain and Trustworthy Systems (BlockSys 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1156))

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Abstract

Since Boneh and Franklin implemented the Identity Based Encryption in 2001, a number of novel schemes have been proposed based on bilinear pairings, which have been widely used in the scenario of blockchain. The elliptic curves with low embedding degree and large prime-order subgroup (a.k.a pairing-friendly elliptic curves) are the basic components for such schemes, where prime order elliptic curves are most frequently used in practice. In this paper, a systematic method is utilized to find all the possible prime order families, then it is shown that all the existing constructions can be explained via our method. We further give the evidence that it’s unlikely to produce extra families.

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Acknowledgments

The authors would like to thank the anonymous reviewers for insightful comments and helpful suggestions. Meng Zhang, Maozhi Xu and Jie Wang were partially supported by the National Key R&D Program of China, 2017YFB0802000 and Natural Science Foundation of China, 61672059. Xuehong Chen was partially supported by the National Key R&D Program of China, 2018YFB2100400.

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Authors and Affiliations

  1. School of Mathematical Sciences Peking University, Beijing, 100871, China

    Meng Zhang, Maozhi Xu & Jie Wang

  2. Aisino Corporation, Beijing, 100195, China

    Meng Zhang

  3. Industrial Control Systems Cyber Emergency Response Team, Beijing, 100040, China

    Xuehong Chen

Authors
  1. Meng Zhang
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  2. Xuehong Chen
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  3. Maozhi Xu
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  4. Jie Wang
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Corresponding author

Correspondence to Meng Zhang .

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Editors and Affiliations

  1. Sun Yat-sen University, Guangzhou, China

    Zibin Zheng

  2. Macau University of Science and Technology, Macau, China

    Hong-Ning Dai

  3. Guangdong University of Foreign Studies, Guangzhou, China

    Mingdong Tang

  4. Sun Yat-sen University, Guangzhou, China

    Xiangping Chen

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Zhang, M., Chen, X., Xu, M., Wang, J. (2020). On Constructing Prime Order Elliptic Curves Suitable for Pairing-Based Cryptography. In: Zheng, Z., Dai, HN., Tang, M., Chen, X. (eds) Blockchain and Trustworthy Systems. BlockSys 2019. Communications in Computer and Information Science, vol 1156. Springer, Singapore. https://doi.org/10.1007/978-981-15-2777-7_5

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  • DOI: https://doi.org/10.1007/978-981-15-2777-7_5

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-2776-0

  • Online ISBN: 978-981-15-2777-7

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