Item type |
学術雑誌論文 / Journal Article(1) |
公開日 |
2022-10-25 |
タイトル |
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タイトル |
Maximum Number of Steps Taken by Modular Exponentiation and Euclidean Algorithm |
言語 |
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言語 |
eng |
DOI |
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関連タイプ |
isIdenticalTo |
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関連識別子 |
https://doi.org/10.2478/forma-2019-0009 |
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関連名称 |
10.2478/forma-2019-0009 |
キーワード |
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主題 |
algorithms, power residues, Euclidean algorithm |
資源タイプ |
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資源 |
http://purl.org/coar/resource_type/c_6501 |
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タイプ |
journal article |
著者 |
Okazaki, Hiroyuki
Nagao, Koh-ichi
Futa, Yuichi
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信州大学研究者総覧へのリンク |
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氏名 |
岡﨑, 裕之 |
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URL |
https://soar-rd.shinshu-u.ac.jp/profile/ja.geDNbpkh.html |
出版者 |
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出版者 |
SCIENDO |
引用 |
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内容記述 |
FORMALIZED MATHEMATICS 27(1) : 87-91(2019) |
書誌情報 |
FORMALIZED MATHEMATICS
巻 27,
号 1,
p. 87-91,
発行日 2019-05-16
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抄録 |
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内容記述 |
In this article we formalize in Mizar the maximum number of steps taken by some number theoretical algorithms, “right–to–left binary algorithm” for modular exponentiation and “Euclidean algorithm” For any natural numbers a, b, n, “right–to–left binary algorithm” can calculate the natural number, see (Def. 2), AlgoBPow(a, n,m) := ab mod n and for any integers a, b, “Euclidean algorithm” can calculate the non negative integer gcd(a, b). W have not formalized computational complexity of algorithms yet, though we had already formalize the “Euclidean algorithm” in. For “right-to-left binary algorithm”, we formalize the theorem, which says that the required number of the modular squares and modular products in this algorithms are 1+blog2 nc and for “Euclidean algorithm”, we formalize the Lam´e's theorem, which says the required number of the divisions in this algorithm is at most 5 log10 min(|a|, |b|). Our aim is to support the implementation of number theoretic tools and evaluating computational complexities of algorithms to prove the security of cryptographic systems. |
資源タイプ(コンテンツの種類) |
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内容記述 |
Article |
ISSN |
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収録物識別子タイプ |
EISSN |
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収録物識別子 |
1898-9934 |
権利 |
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権利情報 |
© 2019 Hiroyuki Okazaki et al., published by SciendoThis work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License. |
出版タイプ |
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出版タイプ |
VoR |
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出版タイプResource |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |