このエントリーをはてなブックマークに追加
ID 49321
フルテキストURL
著者
Nogami, Yasuyuki Graduate School of Natural Science and Technology, Okayama University
Sumo, Taichi Graduate School of Natural Science and Technology, Okayama University
抄録
Recent efficient pairings such as Ate pairing use two efficient rational point subgroups such that π(P) = P and π(Q) = [p]Q, where π, p, P, and Q are the Frobenius map for rational point, the characteristic of definition field, and torsion points for pairing, respectively. This relation accelerates not only pairing but also pairing–related operations such as scalar multiplications. It holds in the case that the embedding degree k divides r − 1, where r is the order of torsion rational points. Thus, such a case has been well studied. Alternatively, this paper focuses on the case that the degree divides r + 1 but does not divide r − 1. Then, this paper shows a multiplicative representation for r–torsion points based on the fact that the characteristic polynomial f(π) becomes irreducible over Fr for which π also plays a role of variable.
キーワード
pairing–friendly curve
torsion point
group structure
rank
発行日
2013-01
出版物タイトル
Memoirs of the Faculty of Engineering, Okayama University
出版物タイトル(別表記)
岡山大学工学部紀要
47巻
出版者
Faculty of Engineering, Okayama University
開始ページ
19
終了ページ
24
ISSN
1349-6115
NCID
AA12014085
資料タイプ
紀要論文
言語
English
著作権者
Copyright © by the authors
論文のバージョン
publisher
査読
無し
Eprints Journal Name
mfe