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class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目次" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目次</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">非表示</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">ページ先頭</div> </a> </li> <li id="toc-歴史" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#歴史"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>歴史</span> </div> </a> <ul id="toc-歴史-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-鍵導出" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#鍵導出"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>鍵導出</span> </div> </a> <ul id="toc-鍵導出-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-パスワードハッシュ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#パスワードハッシュ"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>パスワードハッシュ</span> </div> </a> <ul id="toc-パスワードハッシュ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-脚注" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#脚注"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>脚注</span> </div> </a> <ul id="toc-脚注-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部リンク" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部リンク"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>外部リンク</span> </div> </a> <ul id="toc-外部リンク-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目次" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="目次の表示・非表示を切り替え" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">目次の表示・非表示を切り替え</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">鍵導出関数</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="特定の記事の別の言語版に移動します。利用可能な言語13件" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-13" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">13の言語版</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Funkce_pro_odvozen%C3%AD_kl%C3%AD%C4%8De" title="チェコ語: Funkce pro odvození klíče" lang="cs" hreflang="cs" data-title="Funkce pro odvození klíče" data-language-autonym="Čeština" data-language-local-name="チェコ語" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Schl%C3%BCsselableitung" title="ドイツ語: Schlüsselableitung" lang="de" hreflang="de" data-title="Schlüsselableitung" data-language-autonym="Deutsch" data-language-local-name="ドイツ語" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Key_derivation_function" title="英語: Key derivation function" lang="en" hreflang="en" data-title="Key derivation function" data-language-autonym="English" data-language-local-name="英語" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Funci%C3%B3n_de_derivaci%C3%B3n_de_clave" title="スペイン語: Función de derivación de clave" lang="es" hreflang="es" data-title="Función de derivación de clave" data-language-autonym="Español" data-language-local-name="スペイン語" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Fonction_de_d%C3%A9rivation_de_cl%C3%A9" title="フランス語: Fonction de dérivation de clé" lang="fr" hreflang="fr" data-title="Fonction de dérivation de clé" data-language-autonym="Français" data-language-local-name="フランス語" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Derivazione_di_una_chiave_crittografica" title="イタリア語: Derivazione di una chiave crittografica" lang="it" hreflang="it" data-title="Derivazione di una chiave crittografica" data-language-autonym="Italiano" data-language-local-name="イタリア語" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%82%A4_%EC%9C%A0%EB%8F%84_%ED%95%A8%EC%88%98" title="韓国語: 키 유도 함수" lang="ko" hreflang="ko" data-title="키 유도 함수" data-language-autonym="한국어" data-language-local-name="韓国語" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_%D1%84%D0%BE%D1%80%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D1%8F_%D0%BA%D0%BB%D1%8E%D1%87%D0%B0" title="ロシア語: Функция формирования ключа" lang="ru" hreflang="ru" data-title="Функция формирования ключа" data-language-autonym="Русский" data-language-local-name="ロシア語" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Key_derivation_function" title="シンプル英語: Key derivation function" lang="en-simple" hreflang="en-simple" data-title="Key derivation function" data-language-autonym="Simple English" data-language-local-name="シンプル英語" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9F%E0%B8%B1%E0%B8%87%E0%B8%81%E0%B9%8C%E0%B8%8A%E0%B8%B1%E0%B8%99%E0%B9%81%E0%B8%9B%E0%B8%A5%E0%B8%87%E0%B9%83%E0%B8%AB%E0%B9%89%E0%B9%80%E0%B8%9B%E0%B9%87%E0%B8%99%E0%B8%81%E0%B8%B8%E0%B8%8D%E0%B9%81%E0%B8%88" title="タイ語: ฟังก์ชันแปลงให้เป็นกุญแจ" lang="th" hreflang="th" data-title="ฟังก์ชันแปลงให้เป็นกุญแจ" data-language-autonym="ไทย" data-language-local-name="タイ語" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Anahtar_t%C3%BCretme_fonksiyonu" title="トルコ語: Anahtar türetme fonksiyonu" lang="tr" hreflang="tr" data-title="Anahtar türetme fonksiyonu" data-language-autonym="Türkçe" data-language-local-name="トルコ語" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%96%D1%8F_%D1%84%D0%BE%D1%80%D0%BC%D1%83%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F_%D0%BA%D0%BB%D1%8E%D1%87%D0%B0" title="ウクライナ語: Функція формування ключа" lang="uk" hreflang="uk" data-title="Функція формування ключа" data-language-autonym="Українська" data-language-local-name="ウクライナ語" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%AF%86%E9%92%A5%E6%B4%BE%E7%94%9F%E5%87%BD%E6%95%B0" title="中国語: 密钥派生函数" lang="zh" hreflang="zh" data-title="密钥派生函数" data-language-autonym="中文" data-language-local-name="中国語" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q3496793#sitelinks-wikipedia" title="言語間リンクを編集" class="wbc-editpage">リンクを編集</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="名前空間"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0" title="本文を閲覧 [c]" accesskey="c"><span>ページ</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E3%83%8E%E3%83%BC%E3%83%88:%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0&action=edit&redlink=1" rel="discussion" class="new" title="「本文ページについての議論」 (存在しないページ) [t]" accesskey="t"><span>ノート</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="別の言語に切り替える" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">日本語</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="表示"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0"><span>閲覧</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0&action=edit" title="このページのソースコードを編集する [e]" accesskey="e"><span>編集</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0&action=history" title="このページの過去の版 [h]" accesskey="h"><span>履歴表示</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="ページツール"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="ツール" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">ツール</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">ツール</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" 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data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">表示</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">非表示</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">出典: フリー百科事典『ウィキペディア（Wikipedia）』</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ja" dir="ltr"><p><a href="/wiki/%E6%9A%97%E5%8F%B7%E7%90%86%E8%AB%96" title="暗号理論">暗号理論</a>分野における<b>鍵導出関数</b>（かぎどうしゅつかんすう, key derivation function, KDF）は、一つのマスター鍵やパスワード、パスフレーズなどの秘密の値から、一つあるいは複数の秘密鍵を導出するために用いられる関数であり、pseudorandom function（PRF）<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>が利用される<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>。鍵導出関数は、鍵をより長い鍵に引き延ばしたり、必要なフォーマットを持つ鍵を得るために使うことができる。例えば、<a href="/wiki/%E3%83%87%E3%82%A3%E3%83%95%E3%82%A3%E3%83%BC%E3%83%BB%E3%83%98%E3%83%AB%E3%83%9E%E3%83%B3%E9%8D%B5%E5%85%B1%E6%9C%89" title="ディフィー・ヘルマン鍵共有">ディフィー・ヘルマン鍵共有</a>で共有される値は何らかの群の要素であるが、これを<a href="/wiki/Advanced_Encryption_Standard" title="Advanced Encryption Standard">AES</a>で用いる共通鍵へ変換する。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="歴史"><span id=".E6.AD.B4.E5.8F.B2"></span>歴史</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0&action=edit&section=1" title="節を編集: 歴史"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/1978%E5%B9%B4" title="1978年">1978年</a>に「crypt」というパスワードベースの鍵導出関数が登場したが、パスワードの文字数の上限が8文字であることや、saltが弱い<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>など問題があった。 <a href="/wiki/PBKDF2" title="PBKDF2">PBKDF2</a>などの現代的なパスワードベースの鍵導出関数は、より強いsaltを使い、動作も良い意味で遅い。ただし、GPUやFPGAなどを使った並列処理による総当たり攻撃が問題になってきており、これに対処するために、<a href="/wiki/Bcrypt" title="Bcrypt">bcrypt</a>や<a href="/wiki/Scrypt" title="Scrypt">scrypt</a>、より新しいものでは<a href="/wiki/Argon2" title="Argon2">argon2</a>などが登場している。 </p> <div class="mw-heading mw-heading2"><h2 id="鍵導出"><span id=".E9.8D.B5.E5.B0.8E.E5.87.BA"></span>鍵導出</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0&action=edit&section=2" title="節を編集: 鍵導出"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>鍵導出関数の提案された当初の利用目的は、秘密のパスワードやパスフレーズから鍵を得ることであったが、以下のように異なる目的のものがある。 </p> <ul><li>パスワードやパスフレーズから鍵を生成するもの。パスワードベース鍵導出関数、Key stretching。パスワードに対する<a href="/wiki/%E7%B7%8F%E5%BD%93%E3%81%9F%E3%82%8A%E6%94%BB%E6%92%83" title="総当たり攻撃">総当たり攻撃</a>を困難にするため、多数の反復計算をするなど、わざと計算に時間がかかるように設計される。例えば<a href="/wiki/PBKDF2" title="PBKDF2">PBKDF2</a>がある。</li> <li>一つの秘密の値から、秘密ではない値を組み合わせることで複数の鍵を生成するもの。これは「key diversification」とも呼ばれる。生成された一つの鍵を得た攻撃者が、元の秘密の値や、他の鍵についての有用な情報を得るのを阻止する。また、鍵導出関数によって生成された鍵は、特定の暗号システムにおける「弱鍵」を避けるなど、望ましい性質を持つことも保証される。</li> <li>鍵共有プロトコルの一要素として利用されるもの。例として、KDF1（IEEE Std 1363-2000て定義されている）や ANSI X9.42の同様の関数がある。</li> <li>ある鍵から、長さの異なる鍵を得るためのもの。HKDFはこの目的の鍵導出関数である。</li></ul> <div class="mw-heading mw-heading2"><h2 id="パスワードハッシュ"><span id=".E3.83.91.E3.82.B9.E3.83.AF.E3.83.BC.E3.83.89.E3.83.8F.E3.83.83.E3.82.B7.E3.83.A5"></span>パスワードハッシュ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0&action=edit&section=3" title="節を編集: パスワードハッシュ"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>鍵導出関数は、本来の目的とは異なる利用方法として、パスワードを<a href="/wiki/Passwd" title="Passwd">パスワードファイル</a>やシャドウパスワードファイルに保管する際のハッシュ関数として使われることが多く、「パスワードハッシュ関数」とも呼ばれる。パスワードハッシュ関数は、<a href="/wiki/%E7%B7%8F%E5%BD%93%E3%81%9F%E3%82%8A%E6%94%BB%E6%92%83" title="総当たり攻撃">総当たり攻撃</a>や<a href="/wiki/%E8%BE%9E%E6%9B%B8%E6%94%BB%E6%92%83" title="辞書攻撃">辞書攻撃</a>への耐性のため、計算に比較的時間がかかる必要があり、key stretching用の鍵導出関数がこの目的にかなっている。入力にランダムに選ばれた秘密でない値（ソルト）を加えることで、辞書攻撃に強くなる<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="脚注"><span id=".E8.84.9A.E6.B3.A8"></span>脚注</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0&action=edit&section=4" title="節を編集: 脚注"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text">これは、一般的な「<a href="/wiki/%E6%93%AC%E4%BC%BC%E4%B9%B1%E6%95%B0" title="擬似乱数">擬似乱数</a>の関数」のことではなく、暗号学上の概念で pseudorandom function family（<a href="https://en.wikipedia.org/wiki/Pseudorandom_function_family" class="extiw" title="en:Pseudorandom function family">en:Pseudorandom function family</a>）と呼ばれる関数の族に含まれるような、<a href="/wiki/%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%82%AA%E3%83%A9%E3%82%AF%E3%83%AB" title="ランダムオラクル">ランダムオラクル</a>をエミュレートするefficiently-computableな関数、のこと。</span> </li> <li id="cite_note-2"><b><a href="#cite_ref-2">^</a></b> <span class="reference-text"><cite style="font-style:normal" class="citation book">Bezzi, Michele (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vYxzh3C6OPUC&pg=PA185">“Data privacy”</a>. In Camenisch, Jan. <i>Privacy and Identity Management for Life</i>. Springer. pp. 185–186. <style data-mw-deduplicate="TemplateStyles:r101121245">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation.cs-ja1 q,.mw-parser-output .citation.cs-ja2 q{quotes:"「""」""『""』"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:var(--color-success,#3a3);margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%E7%89%B9%E5%88%A5:%E6%96%87%E7%8C%AE%E8%B3%87%E6%96%99/9783642203176" title="特別:文献資料/9783642203176">9783642203176</a><span style="display:none;">. <a rel="nofollow" class="external free" href="https://books.google.com/books?id=vYxzh3C6OPUC&pg=PA185">https://books.google.com/books?id=vYxzh3C6OPUC&pg=PA185</a></span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.btitle=Data+privacy&rft.atitle=Privacy+and+Identity+Management+for+Life&rft.aulast=Bezzi%2C+Michele&rft.au=Bezzi%2C+Michele&rft.date=2011&rft.pages=pp.%26nbsp%3B185%E2%80%93186&rft.pub=Springer&rft.isbn=9783642203176&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DvYxzh3C6OPUC%26pg%3DPA185&rfr_id=info:sid/ja.wikipedia.org:%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-3"><b><a href="#cite_ref-3">^</a></b> <span class="reference-text"><cite class="citation web" style="font-style:normal">Kaliski, Burt. “<a rel="nofollow" class="external text" href="https://www.ietf.org/rfc/rfc2898.txt">RFC 2898 -- PKCS #5: Password-Based Cryptography Specification, Version 2.0</a>”. <i>IETF</i>. <span title="">19 March 2017</span>閲覧。</cite></span> </li> <li id="cite_note-4"><b><a href="#cite_ref-4">^</a></b> <span class="reference-text"><cite class="citation web" style="font-style:normal">“<a rel="nofollow" class="external text" href="http://cm.bell-labs.com/cm/cs/who/dmr/passwd.ps">Password Security: A Case History.</a>”. <i>Bell Laboratories</i> (1978年4月3日). <span title="">2011年5月9日</span>閲覧。</cite></span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text"><cite class="citation web" style="font-style:normal">“<a rel="nofollow" class="external text" href="https://crackstation.net/hashing-security.htm">Salted Password Hashing - Doing it Right</a>”. <i>CrackStation.net</i>. <span title="">29 January 2015</span>閲覧。</cite></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="外部リンク"><span id=".E5.A4.96.E9.83.A8.E3.83.AA.E3.83.B3.E3.82.AF"></span>外部リンク</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%8D%B5%E5%B0%8E%E5%87%BA%E9%96%A2%E6%95%B0&action=edit&section=5" title="節を編集: 外部リンク"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation web" style="font-style:normal">Percival, Colin (May 2009). “<a rel="nofollow" class="external text" href="http://www.tarsnap.com/scrypt/scrypt.pdf">Stronger Key Derivation via Sequential Memory-Hard Functions</a>” (PDF). <i>BSDCan'09 Presentation</i>. <span title="">2009年5月19日</span>閲覧。</cite></li></ul> <div class="navbox" aria-label="Navbox" style="border-collapse:collapse;padding:3px"><table class="nowraplinks navbox-inner" style="background:transparent;color:inherit;min-width:100%;border-spacing:0px;border-collapse:separate"><tbody><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div 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