Integer variable x-based ate pairing

Yasuyuki Nogami; Masataka Akane; Yumi Sakemi; Hidehiro Kato; Yoshitaka Morikawa

doi:10.1007/978-3-540-85538-5_13

Integer variable x-based ate pairing

Yasuyuki Nogami, Masataka Akane, Yumi Sakemi, Hidehiro Kato, Yoshitaka Morikawa

研究成果

60 被引用数 (Scopus)

抄録

In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log₂ r/Φ(k), where Φ(•) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from [log ₂r] to[log₂(t - 1)]. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ". For the curve, this paper gives integer variable χ -based Ate pairing that achieves the lower bound by reducing it to [log₂X].

本文言語	English
ホスト出版物のタイトル	Pairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings
ページ	178-191
ページ数	14
DOI	https://doi.org/10.1007/978-3-540-85538-5_13
出版ステータス	Published - 2008
イベント	2nd International Conference on Pairing-Based Cryptography, Pairing 2008 - Egham 継続期間: 9月 1 2008 → 9月 3 2008

出版物シリーズ

名前	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
巻	5209 LNCS
ISSN（印刷版）	0302-9743
ISSN（電子版）	1611-3349

Other

Other	2nd International Conference on Pairing-Based Cryptography, Pairing 2008
国/地域	United Kingdom
City	Egham
Period	9/1/08 → 9/3/08

ASJC Scopus subject areas

理論的コンピュータサイエンス
コンピュータサイエンス（全般）

文献へのアクセス

10.1007/978-3-540-85538-5_13

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引用スタイル

Nogami, Y., Akane, M., Sakemi, Y., Kato, H., & Morikawa, Y. (2008). Integer variable x-based ate pairing. In Pairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings (pp. 178-191). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5209 LNCS). https://doi.org/10.1007/978-3-540-85538-5_13

Nogami, Y, Akane, M, Sakemi, Y, Kato, H & Morikawa, Y 2008, Integer variable x-based ate pairing. in Pairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5209 LNCS, pp. 178-191, 2nd International Conference on Pairing-Based Cryptography, Pairing 2008, Egham, United Kingdom, 9/1/08. https://doi.org/10.1007/978-3-540-85538-5_13

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title = "Integer variable x-based ate pairing",

abstract = "In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log2 r/Φ(k), where Φ(•) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from [log 2r] to[log2(t - 1)]. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable {"}χ{"}. For the curve, this paper gives integer variable χ -based Ate pairing that achieves the lower bound by reducing it to [log2X].",

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author = "Yasuyuki Nogami and Masataka Akane and Yumi Sakemi and Hidehiro Kato and Yoshitaka Morikawa",

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T1 - Integer variable x-based ate pairing

AU - Nogami, Yasuyuki

AU - Akane, Masataka

AU - Sakemi, Yumi

AU - Kato, Hidehiro

AU - Morikawa, Yoshitaka

PY - 2008

Y1 - 2008

N2 - In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log2 r/Φ(k), where Φ(•) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from [log 2r] to[log2(t - 1)]. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ". For the curve, this paper gives integer variable χ -based Ate pairing that achieves the lower bound by reducing it to [log2X].

AB - In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log2 r/Φ(k), where Φ(•) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from [log 2r] to[log2(t - 1)]. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ". For the curve, this paper gives integer variable χ -based Ate pairing that achieves the lower bound by reducing it to [log2X].

KW - Ate pairing

KW - Miller's algorithm

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DO - 10.1007/978-3-540-85538-5_13

M3 - Conference contribution

AN - SCOPUS:52449098485

SN - 3540855033

SN - 9783540855033

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 178

EP - 191

BT - Pairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings

T2 - 2nd International Conference on Pairing-Based Cryptography, Pairing 2008

Y2 - 1 September 2008 through 3 September 2008

ER -

Integer variable x-based ate pairing

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