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

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• 关键词：Optimal pairing ; Symmetric pairing ; Tate pairing ; Elliptic net ; Parallel computation
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9836
• 期：1
• 页码：319-334
• 全文大小：873 KB
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  3.Hess, F., Smart, N., Vercauteren, F.: The eta pairing revisited. IEEE Trans. Inf. Theory 52, 4595–4602 (2006)MathSciNet CrossRef MATH
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  5.Ogura, N., Kanayama, N., Uchiyama, S., Okamoto, E.: Cryptographic pairings based on elliptic nets. In: Iwata, T., Nishigaki, M. (eds.) IWSEC 2011. LNCS, vol. 7038, pp. 65–78. Springer, Heidelberg (2011)CrossRef
  6.Onuki, H., Teruya, T., Kanayama, N., Uchiyama, S.: The optimal ate pairing over the Barreto-Naehrig curve via parallelizing elliptic nets. JSIAM Lett. 8, 9–12 (2016)MathSciNet CrossRef
  7.Silverman, J.H.: The Arithmetic of Elliptic Curves. Springer, New York (1992)
  8.Stange, K.E.: The tate pairing via elliptic nets. In: Takagi, T., Okamoto, E., Okamoto, T., Okamoto, T. (eds.) Pairing 2007. LNCS, vol. 4575, pp. 329–348. Springer, Heidelberg (2007)CrossRef
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• 作者单位：Hiroshi Onuki (15)
  Tadanori Teruya (16)
  Naoki Kanayama (17)
  Shigenori Uchiyama (15)
  
  15. Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo, 192-0372, Japan
  16. National Institute of Advanced Industrial Science and Technology, 2-4-7 Aomi, Koto-ku, Tokyo, 135-0064, Japan
  17. University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan
  
• 丛书名：Advances in Information and Computer Security
• ISBN：978-3-319-44524-3
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9836

文摘

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.