{"created":"2022-10-24T23:55:21.378450+00:00","id":2001207,"links":{},"metadata":{"_buckets":{"deposit":"8ed58166-f348-4172-b84c-bae3ff3136af"},"_deposit":{"id":"2001207","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"2001207"},"status":"published"},"_oai":{"id":"oai:soar-ir.repo.nii.ac.jp:02001207","sets":["1221:1222"]},"author_link":[],"control_number":"2001207","item_1628147817048":{"attribute_name":"出版タイプ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_6_biblio_info_6":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2019-05-16","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicPageEnd":"91","bibliographicPageStart":"87","bibliographicVolumeNumber":"27","bibliographic_titles":[{"bibliographic_title":"FORMALIZED MATHEMATICS"}]}]},"item_6_description_20":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"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.","subitem_description_type":"Abstract"}]},"item_6_description_30":{"attribute_name":"資源タイプ（コンテンツの種類）","attribute_value_mlt":[{"subitem_description":"Article","subitem_description_type":"Other"}]},"item_6_description_5":{"attribute_name":"引用","attribute_value_mlt":[{"subitem_description":"FORMALIZED MATHEMATICS 27(1) : 87-91(2019)","subitem_description_type":"Other"}]},"item_6_link_3":{"attribute_name":"信州大学研究者総覧へのリンク","attribute_value_mlt":[{"subitem_link_text":"岡﨑, 裕之","subitem_link_url":"https://soar-rd.shinshu-u.ac.jp/profile/ja.geDNbpkh.html"}]},"item_6_publisher_4":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"SCIENDO"}]},"item_6_relation_48":{"attribute_name":"DOI","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"10.2478/forma-2019-0009"}],"subitem_relation_type":"isIdenticalTo","subitem_relation_type_id":{"subitem_relation_type_id_text":"https://doi.org/10.2478/forma-2019-0009","subitem_relation_type_select":"DOI"}}]},"item_6_rights_62":{"attribute_name":"権利","attribute_value_mlt":[{"subitem_rights":"© 2019 Hiroyuki Okazaki et al., published by SciendoThis work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License."}]},"item_6_source_id_35":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"1898-9934","subitem_source_identifier_type":"EISSN"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Okazaki, Hiroyuki","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Nagao, Koh-ichi","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Futa, Yuichi","creatorNameLang":"en"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2022-10-25"}],"filename":"17K00182_1.pdf","format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"17K00182_1.pdf","url":"https://soar-ir.repo.nii.ac.jp/record/2001207/files/17K00182_1.pdf"},"version_id":"42a32f18-8840-4c37-b72b-3226ecaecae5"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"algorithms","subitem_subject_scheme":"Other"},{"subitem_subject":"power residues","subitem_subject_scheme":"Other"},{"subitem_subject":"Euclidean algorithm","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"journal article","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Maximum Number of Steps Taken by Modular Exponentiation and Euclidean Algorithm","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Maximum Number of Steps Taken by Modular Exponentiation and Euclidean Algorithm","subitem_title_language":"en"}]},"item_type_id":"6","owner":"1","path":["1222"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2022-10-25"},"publish_date":"2022-10-25","publish_status":"0","recid":"2001207","relation_version_is_last":true,"title":["Maximum Number of Steps Taken by Modular Exponentiation and Euclidean Algorithm"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-12-14T04:15:09.732186+00:00"}