ID | 49321 |
JaLCDOI | |
Sort Key | 3
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FullText URL | |
Author |
Sumo, Taichi
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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.
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Keywords | pairing–friendly curve
torsion point
group structure
rank
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Publication Title |
Memoirs of the Faculty of Engineering, Okayama University
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Published Date | 2013-01
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Volume | volume47
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Publisher | Faculty of Engineering, Okayama University
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Start Page | 19
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End Page | 24
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ISSN | 1349-6115
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NCID | AA12014085
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Content Type |
Departmental Bulletin Paper
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OAI-PMH Set |
岡山大学
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language |
English
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Copyright Holders | Copyright © by the authors
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File Version | publisher
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NAID | |
Eprints Journal Name | mfe
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