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On the Reduced Testing of a Primitive Element in ${\\mathbb Z}_n^\\times$
https://doi.org/10.15029/00000534
https://doi.org/10.15029/00000534d7655fbd-3dca-447c-959e-18d62366f4e0
名前 / ファイル | ライセンス | アクション |
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KJ00009952199 (1.4 MB)
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TUIS
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Item type | 紀要論文(ELS) / Departmental Bulletin Paper(1) | |||||||
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公開日 | 2015-09-30 | |||||||
タイトル | ||||||||
言語 | en | |||||||
タイトル | On the Reduced Testing of a Primitive Element in ${\\mathbb Z}_n^\\times$ | |||||||
タイトル | ||||||||
言語 | ja | |||||||
タイトル | On the Reduced Testing of a Primitive Element in ${\\mathbb Z}_n^\\times$ | |||||||
言語 | ||||||||
言語 | eng | |||||||
キーワード | ||||||||
主題 | primitive element modulo a composite, primitive root, universal exponent | |||||||
資源タイプ | ||||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
資源タイプ | departmental bulletin paper | |||||||
ID登録 | ||||||||
ID登録 | 10.15029/00000534 | |||||||
ID登録タイプ | JaLC | |||||||
ページ属性 | ||||||||
内容記述タイプ | Other | |||||||
内容記述 | P(論文) | |||||||
著者名(日) |
鈴木, 英男
× 鈴木, 英男× Suzuki, Hideo
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著者所属(日) | ||||||||
ja | ||||||||
東京情報大学総合情報学部 | ||||||||
著者所属(英) | ||||||||
en | ||||||||
Tokyo University of Information Sciences, Faculty of Informatics | ||||||||
抄録(日) | ||||||||
内容記述タイプ | Other | |||||||
内容記述 | The primitive roots in ${\mathbb Z}_n^\times$ are defined and exist iff $n = 2, 4, p^{\alpha}, 2p^{\alpha}$. Knuth gave the definition of the primitive roots in ${\mathbb Z}_{p^\alpha}^\times$, and showed the necessary and sufficient condition for testing a primitive root in ${\mathbb Z}_{p^\alpha}^\times$. In this paper we define the primitive elements in ${\mathbb Z}_n^\times$, which is a generalization of primitive roots, as elements that take the maximum multiplicative order.And we give two theorems for the reduced testing of a primitive element in ${\mathbb Z}_n^\times$ for any composite $n$. It is shown that the two theorems, using a technique of a lemma, for testing a primitive element allow us an effective reduction in testing processes and in computing time cost as a consequence. | |||||||
抄録(英) | ||||||||
内容記述タイプ | Other | |||||||
内容記述 | The primitive roots in ${\mathbb Z}_n^\times$ are defined and exist iff $n = 2, 4, p^{\alpha}, 2p^{\alpha}$. Knuth gave the definition of the primitive roots in ${\mathbb Z}_{p^\alpha}^\times$, and showed the necessary and sufficient condition for testing a primitive root in ${\mathbb Z}_{p^\alpha}^\times$. In this paper we define the primitive elements in ${\mathbb Z}_n^\times$, which is a generalization of primitive roots, as elements that take the maximum multiplicative order.And we give two theorems for the reduced testing of a primitive element in ${\mathbb Z}_n^\times$ for any composite $n$. It is shown that the two theorems, using a technique of a lemma, for testing a primitive element allow us an effective reduction in testing processes and in computing time cost as a consequence. | |||||||
言語 | en | |||||||
雑誌書誌ID | ||||||||
収録物識別子タイプ | NCID | |||||||
収録物識別子 | AA11155514 | |||||||
書誌情報 |
ja : 東京情報大学研究論集 巻 19, 号 1, p. 41-47, 発行日 2015-09-30 |
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出版者 | ||||||||
言語 | ja | |||||||
出版者 | 東京情報大学 |