An Improvement of Twisted Ate Pairing Efficient for Multi-Pairing and Thread Computing

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概要

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• In the case of Barreto-Naehrig pairing-friendly curves of embedding degree 12 of order r, recent efficient Ate pairings such as R-ate, optimal, and Xate pairings achieve Miller loop lengths of (1/4)⌊log2r⌋. On the other hand, the twisted Ate pairing requires (3/4)⌊log2r⌋ loop iterations, and thus is usually slower than the recent efficient Ate pairings. This paper proposes an improved twisted Ate pairing using Frobenius maps and a small scalar multiplication. The proposed idea splits the Millers algorithm calculation into several independent parts, for which multi-pairing techniques apply efficiently. The maximum number of loop iterations in Millers algorithm for the proposed twisted Ate pairing is equal to the (1/4)⌊log2r⌋ attained by the most efficient Ate pairings.

• （社）電子情報通信学会の論文
• 2011-06-01

著者

• NOGAMI Yasuyuki

  Graduate School of Natural Science and Technology, Okayama University

• NOGAMI Yasuyuki

  Okayama University

• SAKEMI Yumi

  Okayama University

• Morikawa Yoshitaka

  Okayama Univ. Okayama‐shi Jpn

• Sakemi Yumi

  Communication Network Engineering Natural Science And Technology Okayama University

• Nogami Yasuyuki

  Graduate School Of Natural Science And Technology Okayama University

• TAKEUCHI Shoichi

  Okayama University

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