Some efficient algorithms for the final exponentiation of ηT pairing

Masaaki Shirase; Tsuyoshi Takagi; Eiji Okamoto

doi:10.1007/978-3-540-72163-5_20

Some efficient algorithms for the final exponentiation of η_T pairing

Masaaki Shirase, Tsuyoshi Takagi, Eiji Okamoto

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

Abstract

Recently Tate pairing and its variations are attracted in cryptography. Their operations consist of a main iteration loop and a final exponentiation. The final exponentiation is necessary for generating a unique value of the bilinear pairing in the extension fields. The speed of the main loop has become fast by the recent improvements, e.g., the Duursma-Lee algorithm and η_T pairing. In this paper we discuss how to enhance the speed of the final exponentiation of the η_T pairing in the extension field double struk F sign₃6n. Indeed, we propose some efficient algorithms using the torus T2(double struk F sign₃3n) that can efficiently compute an inversion and a powering by 3ⁿ + 1. Consequently, the total processing cost of computing the η_T pairing can be reduced by 16% for n = 97.

Original language	English
Title of host publication	Information Security Practice and Experience - Third International Conference, ISPEC 2007, Proceedings
Publisher	Springer Verlag
Pages	254-268
Number of pages	15
ISBN (Print)	3540721592, 9783540721598
DOIs	https://doi.org/10.1007/978-3-540-72163-5_20
Publication status	Published - 2007
Externally published	Yes
Event	3rd International Conference on Information Security Practice and Experience, ISPEC 2007 - Hong Kong, Hong Kong Duration: May 7 2007 → May 9 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4464 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	3rd International Conference on Information Security Practice and Experience, ISPEC 2007
Country/Territory	Hong Kong
City	Hong Kong
Period	5/7/07 → 5/9/07

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-540-72163-5_20

Cite this

Shirase, M., Takagi, T., & Okamoto, E. (2007). Some efficient algorithms for the final exponentiation of η_T pairing. In Information Security Practice and Experience - Third International Conference, ISPEC 2007, Proceedings (pp. 254-268). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4464 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-72163-5_20

Some efficient algorithms for the final exponentiation of η_T pairing. / Shirase, Masaaki; Takagi, Tsuyoshi; Okamoto, Eiji.
Information Security Practice and Experience - Third International Conference, ISPEC 2007, Proceedings. Springer Verlag, 2007. p. 254-268 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4464 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Shirase, M, Takagi, T & Okamoto, E 2007, Some efficient algorithms for the final exponentiation of η_T pairing. in Information Security Practice and Experience - Third International Conference, ISPEC 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4464 LNCS, Springer Verlag, pp. 254-268, 3rd International Conference on Information Security Practice and Experience, ISPEC 2007, Hong Kong, Hong Kong, 5/7/07. https://doi.org/10.1007/978-3-540-72163-5_20

Shirase M, Takagi T, Okamoto E. Some efficient algorithms for the final exponentiation of η_T pairing. In Information Security Practice and Experience - Third International Conference, ISPEC 2007, Proceedings. Springer Verlag. 2007. p. 254-268. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-72163-5_20

Shirase, Masaaki ; Takagi, Tsuyoshi ; Okamoto, Eiji. / Some efficient algorithms for the final exponentiation of η_T pairing. Information Security Practice and Experience - Third International Conference, ISPEC 2007, Proceedings. Springer Verlag, 2007. pp. 254-268 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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