An improvement of twisted ate pairing efficient for multi-pairing and thread computing

Yumi Sakemi, Yasuyuki Nogami, Shoichi Takeuchi, Yoshitaka Morikawa

Research output: Contribution to journalArticlepeer-review


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)⌊log2 r⌋. On the other hand, the twisted Ate pairing requires (3/4)⌊log2 r⌋ 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 Miller's algorithm calculation into several independent parts, for which multi-pairing techniques apply efficiently. The maximum number of loop iterations in Miller's algorithm for the proposed twisted Ate pairing is equal to the (1/4)⌊log2 r⌋ attained by the most efficient Ate pairings.

Original languageEnglish
Pages (from-to)1356-1367
Number of pages12
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number6
Publication statusPublished - Jun 2011


  • Frobenius map
  • Miller's algorithm
  • Multipairing
  • Thread computing
  • Twisted Ate pairing

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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