Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing

Yumi Sakemi, Shoichi Takeuchi, Yasuyuki Nogami, Yoshitaka Morikawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

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 . On the other hand, the twisted Ate pairing requires 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 proposal 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 attained by the most efficient Ate pairings.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages47-64
Number of pages18
Volume5984 LNCS
DOIs
Publication statusPublished - 2010
Event12th International Conference on Information Security and Cryptology, ICISC 2009 - Seoul, Korea, Republic of
Duration: Dec 2 2009Dec 4 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5984 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other12th International Conference on Information Security and Cryptology, ICISC 2009
CountryKorea, Republic of
CitySeoul
Period12/2/0912/4/09

Fingerprint

Scalar multiplication
Frobenius
Pairing
Iteration
Curve

Keywords

  • Frobenius map
  • Miller's algorithm
  • multi-pairing
  • thread computing
  • twisted Ate pairing

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Sakemi, Y., Takeuchi, S., Nogami, Y., & Morikawa, Y. (2010). Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5984 LNCS, pp. 47-64). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5984 LNCS). https://doi.org/10.1007/978-3-642-14423-3_4

Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing. / Sakemi, Yumi; Takeuchi, Shoichi; Nogami, Yasuyuki; Morikawa, Yoshitaka.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5984 LNCS 2010. p. 47-64 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5984 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sakemi, Y, Takeuchi, S, Nogami, Y & Morikawa, Y 2010, Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 5984 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5984 LNCS, pp. 47-64, 12th International Conference on Information Security and Cryptology, ICISC 2009, Seoul, Korea, Republic of, 12/2/09. https://doi.org/10.1007/978-3-642-14423-3_4
Sakemi Y, Takeuchi S, Nogami Y, Morikawa Y. Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5984 LNCS. 2010. p. 47-64. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-14423-3_4
Sakemi, Yumi ; Takeuchi, Shoichi ; Nogami, Yasuyuki ; Morikawa, Yoshitaka. / Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5984 LNCS 2010. pp. 47-64 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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