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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.
収録刊行物
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- Memoirs of the Faculty of Engineering, Okayama University
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Memoirs of the Faculty of Engineering, Okayama University 47 19-24, 2013-01
Faculty of Engineering, Okayama University
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詳細情報 詳細情報について
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- CRID
- 1390290699799545728
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- NII論文ID
- 120005232373
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- NII書誌ID
- AA12014085
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- ISSN
- 13496115
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- DOI
- 10.18926/49321
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- NDL書誌ID
- 025619185
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- IRDB
- NDL
- CiNii Articles