Consideration of efficient pairing applying two construction methods of extension fields

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

doi:10.1109/CANDARW.2018.00087

Consideration of efficient pairing applying two construction methods of extension fields

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

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

Abstract

In recent years, many innovative cryptography protocols based on the pairing. Finding out an efficient extension field construction is one of the prerequisites for a practical pairing implementation. The author tries to find an elegant extension field construction which will result in efficient pairing over Barreto-Naehrig (BN) curve. In this paper, two construction methods are considered for extension field of degree 12, and one of them results in an efficient exponentiation and the other enables to compute faster Miller loop than the former one. Therefore, a method which uses a basis conversion matrix between the two extension field is proposed. In comparison to the performance of Aranha et al.'s towering, the proposed implementation results in the efficient exponentiation in a multiplicative group, although pairing cost is slightly increased.

Original language	English
Title of host publication	Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	445-451
Number of pages	7
ISBN (Electronic)	9781538691847
DOIs	https://doi.org/10.1109/CANDARW.2018.00087
Publication status	Published - Dec 26 2018
Event	6th International Symposium on Computing and Networking Workshops, CANDARW 2018 - Takayama, Japan Duration: Nov 27 2018 → Nov 30 2018

Publication series

Name	Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018

Conference

Conference	6th International Symposium on Computing and Networking Workshops, CANDARW 2018
Country/Territory	Japan
City	Takayama
Period	11/27/18 → 11/30/18

Keywords

Barreto-Naehrig Curve
Extension Field
Pairing

ASJC Scopus subject areas

Computer Networks and Communications
Hardware and Architecture
Statistics, Probability and Uncertainty
Computer Science Applications

Access to Document

10.1109/CANDARW.2018.00087

Cite this

Nanjo, Y., Khandaker, M. A. A., Kusaka, T., & Nogami, Y. (2018). Consideration of efficient pairing applying two construction methods of extension fields. In Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018 (pp. 445-451). [8590941] (Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CANDARW.2018.00087

Consideration of efficient pairing applying two construction methods of extension fields. / Nanjo, Yuki; Khandaker, Md Al Amin; Kusaka, Takuya ; Nogami, Yasuyuki.

Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 445-451 8590941 (Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018).

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

Nanjo, Y, Khandaker, MAA, Kusaka, T & Nogami, Y 2018, Consideration of efficient pairing applying two construction methods of extension fields. in Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018., 8590941, Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018, Institute of Electrical and Electronics Engineers Inc., pp. 445-451, 6th International Symposium on Computing and Networking Workshops, CANDARW 2018, Takayama, Japan, 11/27/18. https://doi.org/10.1109/CANDARW.2018.00087

Nanjo Y, Khandaker MAA, Kusaka T , Nogami Y. Consideration of efficient pairing applying two construction methods of extension fields. In Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 445-451. 8590941. (Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018). https://doi.org/10.1109/CANDARW.2018.00087

Nanjo, Yuki ; Khandaker, Md Al Amin ; Kusaka, Takuya ; Nogami, Yasuyuki. / Consideration of efficient pairing applying two construction methods of extension fields. Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 445-451 (Proceedings - 2018 6th International Symposium on Computing and Networking Workshops, CANDARW 2018).

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abstract = "In recent years, many innovative cryptography protocols based on the pairing. Finding out an efficient extension field construction is one of the prerequisites for a practical pairing implementation. The author tries to find an elegant extension field construction which will result in efficient pairing over Barreto-Naehrig (BN) curve. In this paper, two construction methods are considered for extension field of degree 12, and one of them results in an efficient exponentiation and the other enables to compute faster Miller loop than the former one. Therefore, a method which uses a basis conversion matrix between the two extension field is proposed. In comparison to the performance of Aranha et al.'s towering, the proposed implementation results in the efficient exponentiation in a multiplicative group, although pairing cost is slightly increased.",

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AB - In recent years, many innovative cryptography protocols based on the pairing. Finding out an efficient extension field construction is one of the prerequisites for a practical pairing implementation. The author tries to find an elegant extension field construction which will result in efficient pairing over Barreto-Naehrig (BN) curve. In this paper, two construction methods are considered for extension field of degree 12, and one of them results in an efficient exponentiation and the other enables to compute faster Miller loop than the former one. Therefore, a method which uses a basis conversion matrix between the two extension field is proposed. In comparison to the performance of Aranha et al.'s towering, the proposed implementation results in the efficient exponentiation in a multiplicative group, although pairing cost is slightly increased.

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Consideration of efficient pairing applying two construction methods of extension fields

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Keywords

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