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ID 49321
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Author
Sumo, Taichi
Abstract
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.
Keywords
pairing–friendly curve
torsion point
group structure
rank
Published Date
2013-01
Publication Title
Memoirs of the Faculty of Engineering, Okayama University
Publication Title Alternative
岡山大学工学部紀要
Volume
volume47
Publisher
Faculty of Engineering, Okayama University
Start Page
19
End Page
24
ISSN
1349-6115
NCID
AA12014085
Content Type
Departmental Bulletin Paper
language
英語
Copyright Holders
Copyright © by the authors
File Version
publisher
Refereed
False
Eprints Journal Name
mfe