Efficient ate-based pairing over the attractive classes of BN curves

Yuki Nanjo; Md Al Amin Khandaker; Masaaki Shirase; Takuya Kusaka; Yasuyuki Nogami

doi:10.1007/978-3-030-17982-3_5

Efficient ate-based pairing over the attractive classes of BN curves

Yuki Nanjo, Md Al Amin Khandaker, Masaaki Shirase, Takuya Kusaka, Yasuyuki Nogami

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

1 Citation (Scopus)

Abstract

This paper proposes two attractive classes of Barreto-Naehrig curve for ate-based pairing by imposing certain condition χ ≡ 7, 11 (mod 12) on the integer χ that parameterizes the curve settings. The restriction results in an unparalleled way to determine a BN curve, its twisted curve coefficients, and obvious generator points. The proposed χ ≡ 11 (mod 12) are found to be more efficient than χ ≡ 7 (mod 12) together with pseudo 8-sparse multiplication in Miller's algorithm. The authors also provide comparative implementations for the proposal.

Original language	English
Title of host publication	Information Security Applications - 19th International Conference, WISA 2018, Revised Selected Papers
Editors	Brent ByungHoon Kang, JinSoo Jang
Publisher	Springer Verlag
Pages	55-67
Number of pages	13
ISBN (Print)	9783030179816
DOIs	https://doi.org/10.1007/978-3-030-17982-3_5
Publication status	Published - 2019
Event	19th World International Conference on Information Security and Application, WISA 2018 - Jeju Island, Korea, Republic of Duration: Aug 23 2018 → Aug 25 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11402 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	19th World International Conference on Information Security and Application, WISA 2018
Country/Territory	Korea, Republic of
City	Jeju Island
Period	8/23/18 → 8/25/18

Keywords

Barreto-naehrig curve
Pairing
Tower of extension field

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-030-17982-3_5

Cite this

Nanjo, Y., Khandaker, M. A. A., Shirase, M., Kusaka, T., & Nogami, Y. (2019). Efficient ate-based pairing over the attractive classes of BN curves. In B. B. Kang, & J. Jang (Eds.), Information Security Applications - 19th International Conference, WISA 2018, Revised Selected Papers (pp. 55-67). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11402 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-17982-3_5

Efficient ate-based pairing over the attractive classes of BN curves. / Nanjo, Yuki; Khandaker, Md Al Amin; Shirase, Masaaki; Kusaka, Takuya ; Nogami, Yasuyuki.

Information Security Applications - 19th International Conference, WISA 2018, Revised Selected Papers. ed. / Brent ByungHoon Kang; JinSoo Jang. Springer Verlag, 2019. p. 55-67 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11402 LNCS).

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

Nanjo, Y, Khandaker, MAA, Shirase, M, Kusaka, T & Nogami, Y 2019, Efficient ate-based pairing over the attractive classes of BN curves. in BB Kang & J Jang (eds), Information Security Applications - 19th International Conference, WISA 2018, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11402 LNCS, Springer Verlag, pp. 55-67, 19th World International Conference on Information Security and Application, WISA 2018, Jeju Island, Korea, Republic of, 8/23/18. https://doi.org/10.1007/978-3-030-17982-3_5

Nanjo Y, Khandaker MAA, Shirase M, Kusaka T , Nogami Y. Efficient ate-based pairing over the attractive classes of BN curves. In Kang BB, Jang J, editors, Information Security Applications - 19th International Conference, WISA 2018, Revised Selected Papers. Springer Verlag. 2019. p. 55-67. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-17982-3_5

Nanjo, Yuki ; Khandaker, Md Al Amin ; Shirase, Masaaki ; Kusaka, Takuya ; Nogami, Yasuyuki. / Efficient ate-based pairing over the attractive classes of BN curves. Information Security Applications - 19th International Conference, WISA 2018, Revised Selected Papers. editor / Brent ByungHoon Kang ; JinSoo Jang. Springer Verlag, 2019. pp. 55-67 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "This paper proposes two attractive classes of Barreto-Naehrig curve for ate-based pairing by imposing certain condition χ ≡ 7, 11 (mod 12) on the integer χ that parameterizes the curve settings. The restriction results in an unparalleled way to determine a BN curve, its twisted curve coefficients, and obvious generator points. The proposed χ ≡ 11 (mod 12) are found to be more efficient than χ ≡ 7 (mod 12) together with pseudo 8-sparse multiplication in Miller's algorithm. The authors also provide comparative implementations for the proposal.",

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note = "Funding Information: Acknowledgement. This work was supported by the Strategic Information and Communications R&D Promotion Programme (SCOPE) of Ministry of Internal Affairs and Communications, Japan. Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.; 19th World International Conference on Information Security and Application, WISA 2018 ; Conference date: 23-08-2018 Through 25-08-2018",

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N1 - Funding Information: Acknowledgement. This work was supported by the Strategic Information and Communications R&D Promotion Programme (SCOPE) of Ministry of Internal Affairs and Communications, Japan. Publisher Copyright: © Springer Nature Switzerland AG 2019.

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N2 - This paper proposes two attractive classes of Barreto-Naehrig curve for ate-based pairing by imposing certain condition χ ≡ 7, 11 (mod 12) on the integer χ that parameterizes the curve settings. The restriction results in an unparalleled way to determine a BN curve, its twisted curve coefficients, and obvious generator points. The proposed χ ≡ 11 (mod 12) are found to be more efficient than χ ≡ 7 (mod 12) together with pseudo 8-sparse multiplication in Miller's algorithm. The authors also provide comparative implementations for the proposal.

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Efficient ate-based pairing over the attractive classes of BN curves

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Keywords

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