{"created":"2023-06-20T16:34:19.266688+00:00","id":3486,"links":{},"metadata":{"_buckets":{"deposit":"325bce1a-0bdc-4585-8534-9757a2c2fced"},"_deposit":{"created_by":3,"id":"3486","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"3486"},"status":"published"},"_oai":{"id":"oai:kindai.repo.nii.ac.jp:00003486","sets":["14:2667:2668:2987","21:2669:2670:2988"]},"author_link":["4147"],"item_8_alternative_title_3":{"attribute_name":"その他（別言語等）のタイトル","attribute_value_mlt":[{"subitem_alternative_title":"Researches of functions on finite fields coming regular affine planes"}]},"item_8_biblio_info_21":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2014-01-01","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"4","bibliographicPageStart":"1","bibliographic_titles":[{"bibliographic_title":"科学研究費助成事業研究成果報告書 (2014 )"}]}]},"item_8_description_33":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"研究成果の概要（和文): 暗号理論では有限体上の関数で非線形度が高いものが重要である. そのような関数の一つにAPN関数がある. これらをEA同値類にわけて考える. 当研究では2元体のn次線形群が作用するある置換群の可遷域の個数は非同値なquadratic APN関数の異なる同値類の総数に等しいことを示した. また, 有限体上のある線形方程式の解が丁度2個である時の必要十分条件をその係数の関係式で求め,その応用として３つのAPN関数を構成し, これらを置換群の視点から特徴付けた. 更にAPN関数の中で最重要なGold関数にEA同値な関数の表示を明確にした.          研究成果の概要（英文): In the cryptography theory,it is important to construct functions over finite fields which have hight non-linearities. Almost perfect nonlinear(APN) functions are one of them. APN functions are classified in EA-equivalent classes. In the study,I consider some permutation group (G, S)where G is the linear group of degree n over GF(2) and S is a set of subspaces of the alternative product　of a finite field F with some properties. I proved the number of G-orbits on S equals to the namber of EA equivalent classes of quadratic APN functions on F.I obtained some conditions that a special linear equation over a finite field has exactly two solutions and as a application of the results, I constructed three APN functions and decided subspaces corresponding to these functions up to EA-equivalence. Moreover I obtained an effective expression of APN functions which are equivalent to Gold functions which are most interesting ones among APN functions.","subitem_description_type":"Abstract"}]},"item_8_description_36":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究種目：基盤研究(C);  研究期間：2011～2014;   課題番号：23540035;   研究分野：代数学;   科研費の分科・細目：","subitem_description_type":"Other"}]},"item_8_description_37":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"Research Paper","subitem_description_type":"Other"}]},"item_8_description_41":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_8_publisher_14":{"attribute_name":"出版者 名前","attribute_value_mlt":[{"subitem_publisher":"近畿大学"}]},"item_8_relation_11":{"attribute_name":"著者 外部リンク","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/d/r/10088403.ja.html"}]}]},"item_8_text_10":{"attribute_name":"著者 役割","attribute_value_mlt":[{"subitem_text_value":"研究代表者"}]},"item_8_text_7":{"attribute_name":"著者(英)","attribute_value_mlt":[{"subitem_text_language":"en","subitem_text_value":"NAKAGAWA, Nobuo"}]},"item_8_text_8":{"attribute_name":"著者 所属","attribute_value_mlt":[{"subitem_text_value":"近畿大学理工学部; 研究員"}]},"item_8_text_9":{"attribute_name":"著者所属(翻訳)","attribute_value_mlt":[{"subitem_text_value":"Kinki University"}]},"item_8_version_type_12":{"attribute_name":"版","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"中川,  暢夫"},{"creatorName":"ナカガワ, ノブオ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"4147","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"10088403","nameIdentifierScheme":"研究者番号","nameIdentifierURI":" "}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-02-17"}],"displaytype":"detail","filename":"23540035seika.pdf","filesize":[{"value":"84.0 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"23540035seika.pdf","url":"https://kindai.repo.nii.ac.jp/record/3486/files/23540035seika.pdf"},"version_id":"b175a93c-07de-41cb-b25d-c5fb5d2d3521"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"APN functions","subitem_subject_scheme":"Other"},{"subitem_subject":"finite fields","subitem_subject_scheme":"Other"},{"subitem_subject":"permutation group","subitem_subject_scheme":"Other"},{"subitem_subject":"EA-equivalence","subitem_subject_scheme":"Other"},{"subitem_subject":"plnar functions","subitem_subject_scheme":"Other"},{"subitem_subject":"alternative product","subitem_subject_scheme":"Other"},{"subitem_subject":"cryptography","subitem_subject_scheme":"Other"},{"subitem_subject":"linear equations","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"正則アフィン平面から派生する有限体上の関数の研究","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"正則アフィン平面から派生する有限体上の関数の研究"}]},"item_type_id":"8","owner":"3","path":["2987","2988"],"pubdate":{"attribute_name":"公開日","attribute_value":"2015-11-18"},"publish_date":"2015-11-18","publish_status":"0","recid":"3486","relation_version_is_last":true,"title":["正則アフィン平面から派生する有限体上の関数の研究"],"weko_creator_id":"3","weko_shared_id":-1},"updated":"2023-06-21T01:33:55.162720+00:00"}