Efficient squaring algorithm in 2-nd tower field available for various pairing-based cryptographies

Kenta Nekado; Tatsuya Yuasa; Yasuyuki Nogami; Yoshitaka Morikawa

doi:10.1109/NBiS.2010.93

Efficient squaring algorithm in 2-nd tower field available for various pairing-based cryptographies

Kenta Nekado, Tatsuya Yuasa, Yasuyuki Nogami, Yoshitaka Morikawa

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

Abstract

Many public-key cryptographers have recently focused on cryptographic schemes based on pairing, which is a bilinear map from two elliptic curve groups to a group in an extension field. In order to provide efficient pairings, several kinds of pairing-friendly curves have been proposed. Since most of the pairing-friendly curves are defined over a certain extension field, arithmetic operations in extension field should be carried out efficiently. Especially for final exponentiation included in pairing calculation, squaring is more important than multiplication. This paper proposes an efficient squaring algorithm in 2-nd tower field available for various pairingfriendly curves.

Original language	English
Title of host publication	Proceedings - 13th International Conference on Network-Based Information Systems, NBiS 2010
Pages	569-574
Number of pages	6
DOIs	https://doi.org/10.1109/NBiS.2010.93
Publication status	Published - Dec 28 2010
Event	13th International Conference on Network-Based Information Systems, NBiS 2010 - Gifu, Japan Duration: Sept 14 2010 → Sept 16 2010

Publication series

Name	Proceedings - 13th International Conference on Network-Based Information Systems, NBiS 2010

Other

Other	13th International Conference on Network-Based Information Systems, NBiS 2010
Country/Territory	Japan
City	Gifu
Period	9/14/10 → 9/16/10

Keywords

All one polynomial field
Barreto-naehrig curve
Cyclic vecoter multiplication algorithm
Freeman curve
Miyaji-nakabayashi-takano curve

ASJC Scopus subject areas

Computer Networks and Communications
Information Systems

Access to Document

10.1109/NBiS.2010.93

Cite this

Nekado, K., Yuasa, T., Nogami, Y., & Morikawa, Y. (2010). Efficient squaring algorithm in 2-nd tower field available for various pairing-based cryptographies. In Proceedings - 13th International Conference on Network-Based Information Systems, NBiS 2010 (pp. 569-574). Article 5635542 (Proceedings - 13th International Conference on Network-Based Information Systems, NBiS 2010). https://doi.org/10.1109/NBiS.2010.93

Efficient squaring algorithm in 2-nd tower field available for various pairing-based cryptographies. / Nekado, Kenta; Yuasa, Tatsuya; Nogami, Yasuyuki et al.
Proceedings - 13th International Conference on Network-Based Information Systems, NBiS 2010. 2010. p. 569-574 5635542 (Proceedings - 13th International Conference on Network-Based Information Systems, NBiS 2010).

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

Nekado, K, Yuasa, T, Nogami, Y & Morikawa, Y 2010, Efficient squaring algorithm in 2-nd tower field available for various pairing-based cryptographies. in Proceedings - 13th International Conference on Network-Based Information Systems, NBiS 2010., 5635542, Proceedings - 13th International Conference on Network-Based Information Systems, NBiS 2010, pp. 569-574, 13th International Conference on Network-Based Information Systems, NBiS 2010, Gifu, Japan, 9/14/10. https://doi.org/10.1109/NBiS.2010.93

Nekado K, Yuasa T, Nogami Y, Morikawa Y. Efficient squaring algorithm in 2-nd tower field available for various pairing-based cryptographies. In Proceedings - 13th International Conference on Network-Based Information Systems, NBiS 2010. 2010. p. 569-574. 5635542. (Proceedings - 13th International Conference on Network-Based Information Systems, NBiS 2010). doi: 10.1109/NBiS.2010.93

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abstract = "Many public-key cryptographers have recently focused on cryptographic schemes based on pairing, which is a bilinear map from two elliptic curve groups to a group in an extension field. In order to provide efficient pairings, several kinds of pairing-friendly curves have been proposed. Since most of the pairing-friendly curves are defined over a certain extension field, arithmetic operations in extension field should be carried out efficiently. Especially for final exponentiation included in pairing calculation, squaring is more important than multiplication. This paper proposes an efficient squaring algorithm in 2-nd tower field available for various pairingfriendly curves.",

keywords = "All one polynomial field, Barreto-naehrig curve, Cyclic vecoter multiplication algorithm, Freeman curve, Miyaji-nakabayashi-takano curve",

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Efficient squaring algorithm in 2-nd tower field available for various pairing-based cryptographies

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Keywords

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