Ultimately customized multiplication algorithm in the extension field for Xate and R-ate Pairing with Freeman curve

Kenta Nekado; Yasuyuki Nogami; Yoshitaka Morikawa

doi:10.1109/TENCON.2010.5686591

Ultimately customized multiplication algorithm in the extension field for Xate and R-ate Pairing with Freeman curve

Kenta Nekado, Yasuyuki Nogami, Yoshitaka Morikawa

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

Abstract

Recently, pairing-based cryptographies such as ID-based cryptography and group signature have been studied. For their implementations, pairings such as Xate pairing and R-ate pairing are efficient. In order to make pairing calculations faster, it is important to make not only pairing algorithms but also arithmetic operations in the definition field efficient. Thus, in several kinds of ordinary pairing-friendly curves, this paper focuses on Freeman curve that enables fast pairing-based cryptographies. This paper proposes ultimately an customized multiplication algorithm in the extension field for Freeman curve, and then shows some implementation results of Xate pairing and R-ate pairing with Freeman curve.

Original language	English
Title of host publication	TENCON 2010 - 2010 IEEE Region 10 Conference
Pages	773-778
Number of pages	6
DOIs	https://doi.org/10.1109/TENCON.2010.5686591
Publication status	Published - 2010
Event	2010 IEEE Region 10 Conference, TENCON 2010 - Fukuoka, Japan Duration: Nov 21 2010 → Nov 24 2010

Publication series

Name	IEEE Region 10 Annual International Conference, Proceedings/TENCON

Other

Other	2010 IEEE Region 10 Conference, TENCON 2010
Country/Territory	Japan
City	Fukuoka
Period	11/21/10 → 11/24/10

ASJC Scopus subject areas

Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TENCON.2010.5686591

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Ultimately customized multiplication algorithm in the extension field for Xate and R-ate Pairing with Freeman curve. / Nekado, Kenta; Nogami, Yasuyuki; Morikawa, Yoshitaka.

TENCON 2010 - 2010 IEEE Region 10 Conference. 2010. p. 773-778 5686591 (IEEE Region 10 Annual International Conference, Proceedings/TENCON).

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

Nekado, K, Nogami, Y & Morikawa, Y 2010, Ultimately customized multiplication algorithm in the extension field for Xate and R-ate Pairing with Freeman curve. in TENCON 2010 - 2010 IEEE Region 10 Conference., 5686591, IEEE Region 10 Annual International Conference, Proceedings/TENCON, pp. 773-778, 2010 IEEE Region 10 Conference, TENCON 2010, Fukuoka, Japan, 11/21/10. https://doi.org/10.1109/TENCON.2010.5686591

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abstract = "Recently, pairing-based cryptographies such as ID-based cryptography and group signature have been studied. For their implementations, pairings such as Xate pairing and R-ate pairing are efficient. In order to make pairing calculations faster, it is important to make not only pairing algorithms but also arithmetic operations in the definition field efficient. Thus, in several kinds of ordinary pairing-friendly curves, this paper focuses on Freeman curve that enables fast pairing-based cryptographies. This paper proposes ultimately an customized multiplication algorithm in the extension field for Freeman curve, and then shows some implementation results of Xate pairing and R-ate pairing with Freeman curve.",

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N2 - Recently, pairing-based cryptographies such as ID-based cryptography and group signature have been studied. For their implementations, pairings such as Xate pairing and R-ate pairing are efficient. In order to make pairing calculations faster, it is important to make not only pairing algorithms but also arithmetic operations in the definition field efficient. Thus, in several kinds of ordinary pairing-friendly curves, this paper focuses on Freeman curve that enables fast pairing-based cryptographies. This paper proposes ultimately an customized multiplication algorithm in the extension field for Freeman curve, and then shows some implementation results of Xate pairing and R-ate pairing with Freeman curve.

AB - Recently, pairing-based cryptographies such as ID-based cryptography and group signature have been studied. For their implementations, pairings such as Xate pairing and R-ate pairing are efficient. In order to make pairing calculations faster, it is important to make not only pairing algorithms but also arithmetic operations in the definition field efficient. Thus, in several kinds of ordinary pairing-friendly curves, this paper focuses on Freeman curve that enables fast pairing-based cryptographies. This paper proposes ultimately an customized multiplication algorithm in the extension field for Freeman curve, and then shows some implementation results of Xate pairing and R-ate pairing with Freeman curve.

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Ultimately customized multiplication algorithm in the extension field for Xate and R-ate Pairing with Freeman curve

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