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<?xml version="1.0" encoding="UTF-8"?>
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draw:textarea-vertical-align="middle" draw:auto-grow-height="false" fo:min-height="0.908cm" fo:min-width="3.373cm" style:run-through="foreground"/></style:style></office:automatic-styles><office:body><office:text text:use-soft-page-breaks="true"><office:forms form:automatic-focus="false" form:apply-design-mode="false"/><text:sequence-decls><text:sequence-decl text:display-outline-level="0" text:name="Illustration"/><text:sequence-decl text:display-outline-level="0" text:name="Table"/><text:sequence-decl text:display-outline-level="0" text:name="Text"/><text:sequence-decl text:display-outline-level="0" text:name="Drawing"/><text:sequence-decl text:display-outline-level="0" text:name="Figure"/></text:sequence-decls><draw:frame text:anchor-type="page" text:anchor-page-number="1" draw:z-index="30" draw:style-name="gr2" draw:text-style-name="P133" svg:width="16.59cm" svg:height="3.585cm" svg:x="2.207cm" svg:y="23.061cm"><draw:text-box><text:p text:style-name="P129"><text:span text:style-name="T4">Dieses Werk ist unter einem </text:span><text:span text:style-name="T228">Creative</text:span><text:span text:style-name="T4"> </text:span><text:span text:style-name="T228">Commons 3.0 Deutschland Lizenzvertrag</text:span><text:span text:style-name="T4"> lizenziert:</text:span></text:p><text:p text:style-name="P130"><text:span text:style-name="T4"><text:s/></text:span><text:span text:style-name="T4">- Namensnennung</text:span></text:p><text:p><text:span text:style-name="T4"><text:s/></text:span><text:span text:style-name="T4">- Keine kommerzielle Nutzung</text:span></text:p><text:p><text:span text:style-name="T4"><text:s/></text:span><text:span text:style-name="T4">- Weitergabe unter gleichen Bedingungen</text:span></text:p><text:p text:style-name="P131"><text:span text:style-name="T4">Um die Lizenz anzusehen, gehen Sie bitte zu http://creativecommons.org/licenses/by-nc-sa/3.0/de oder schicken Sie einen Brief an Creative Commons, 171 Second Street, Suite 300, San Francisco, California 94105, USA. </text:span></text:p><text:p text:style-name="P132"><text:span text:style-name="T229">Miriam Klein – E-Mail: miriam.klein@lmg-bzk.de – Januar 2020</text:span></text:p></draw:text-box></draw:frame><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="P2">Informationsgesellschaft und Datensicherheit:</text:p><text:p text:style-name="ZPG_5f_Titel"/><text:p text:style-name="P3">Asymmetrische Verschlüsselung</text:p><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="P6"/><text:table-of-content text:style-name="Sect1" text:protected="true" text:name="Inhaltsverzeichnis1"><text:table-of-content-source text:outline-level="10"><text:index-title-template text:style-name="ZPG_5f_Überschrift">Inhaltsverzeichnis</text:index-title-template><text:table-of-content-entry-template text:outline-level="1" text:style-name="ZPG_5f_Inhaltsverz"><text:index-entry-chapter/><text:index-entry-text/><text:index-entry-tab-stop style:type="right" style:leader-char="."/><text:index-entry-page-number/></text:table-of-content-entry-template><text:table-of-content-entry-template text:outline-level="2" text:style-name="ZPG_5f_Inhaltsverz2"><text:index-entry-chapter/><text:index-entry-text/><text:index-entry-tab-stop style:type="right" style:leader-char="."/><text:index-entry-page-number/></text:table-of-content-entry-template><text:table-of-content-entry-template text:outline-level="3" text:style-name="Contents_20_3"><text:index-entry-chapter/><text:index-entry-text/><text:index-entry-tab-stop style:type="right" style:leader-char="."/><text:index-entry-page-number/></text:table-of-content-entry-template><text:table-of-content-entry-template text:outline-level="4" text:style-name="Contents_20_4"><text:index-entry-chapter/><text:index-entry-text/><text:index-entry-tab-stop style:type="right" style:leader-char="."/><text:index-entry-page-number/></text:table-of-content-entry-template><text:table-of-content-entry-template text:outline-level="5" text:style-name="Contents_20_5"><text:index-entry-chapter/><text:index-entry-text/><text:index-entry-tab-stop style:type="right" style:leader-char="."/><text:index-entry-page-number/></text:table-of-content-entry-template><text:table-of-content-entry-template text:outline-level="6" text:style-name="Contents_20_6"><text:index-entry-chapter/><text:index-entry-text/><text:index-entry-tab-stop style:type="right" style:leader-char="."/><text:index-entry-page-number/></text:table-of-content-entry-template><text:table-of-content-entry-template text:outline-level="7" text:style-name="Contents_20_7"><text:index-entry-chapter/><text:index-entry-text/><text:index-entry-tab-stop style:type="right" style:leader-char="."/><text:index-entry-page-number/></text:table-of-content-entry-template><text:table-of-content-entry-template text:outline-level="8" text:style-name="Contents_20_8"><text:index-entry-chapter/><text:index-entry-text/><text:index-entry-tab-stop style:type="right" style:leader-char="."/><text:index-entry-page-number/></text:table-of-content-entry-template><text:table-of-content-entry-template text:outline-level="9" text:style-name="Contents_20_9"><text:index-entry-chapter/><text:index-entry-text/><text:index-entry-tab-stop style:type="right" style:leader-char="."/><text:index-entry-page-number/></text:table-of-content-entry-template><text:table-of-content-entry-template text:outline-level="10" text:style-name="Contents_20_10"><text:index-entry-chapter/><text:index-entry-text/><text:index-entry-tab-stop style:type="right" style:leader-char="."/><text:index-entry-page-number/></text:table-of-content-entry-template></text:table-of-content-source><text:index-body><text:index-title text:style-name="Sect1" text:name="Inhaltsverzeichnis1_Head"><text:p text:style-name="ZPG_5f_Überschrift">Inhaltsverzeichnis</text:p></text:index-title><text:p text:style-name="P126">Wiederholung Kryptologie Klasse 8<text:tab/>3</text:p><text:p text:style-name="P126">Asymmetrische Verschlüsselung<text:tab/>4</text:p><text:p text:style-name="P126">Man-in-the-middle-Angriff<text:tab/>7</text:p><text:p text:style-name="P126">Zertifikate<text:tab/>9</text:p><text:p text:style-name="P126">Digitale Signatur<text:tab/>10</text:p><text:p text:style-name="P126">Vergleich der Verfahren<text:tab/>15</text:p></text:index-body></text:table-of-content><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="ZPG_5f_Standard"/><text:p text:style-name="P7"/><text:p text:style-name="P27">Hinweis zur Verzahnung mit Mathematik: </text:p><text:p text:style-name="P19">Das Konzept der <text:span text:style-name="T148">a</text:span>symmetrischen Verschlüsselung ist Basis sowohl für den Informatik Unterricht <text:span text:style-name="T49">Informationsgesellschaft und Datensicherheit</text:span> <text:s/>als auch für den Mathematikunterricht <text:span text:style-name="T49">mathematische Grundlagen der Kryptologie</text:span>. <text:span text:style-name="T222">Eine enge Abstimmung mit dem Kollegen, der IMP-Mathematik unterrichtet, ist notwendig.</text:span></text:p><text:p text:style-name="P20"><text:span text:style-name="T103">Fall 1 : Im Mathematikunterricht wurde noch nicht mit </text:span><text:span text:style-name="T49">mathematische Grundlagen der Kryptologie </text:span><text:span text:style-name="T107">begonnen</text:span><text:span text:style-name="T104">: </text:span><text:span text:style-name="T107">Dann wird im Informatikunterricht diese Einheit ‚normal‘ am Stück unterrichtet.</text:span></text:p><text:p text:style-name="P24"><text:span text:style-name="T104">Fall 2: Der Mathematikunterricht beginnt mit <text:s/></text:span><text:span text:style-name="T51">mathematische</text:span><text:span text:style-name="T55">n</text:span><text:span text:style-name="T51"> Grundlagen der Kryptologie</text:span><text:span text:style-name="T105"> </text:span><text:span text:style-name="T116">bevor</text:span><text:span text:style-name="T104"> der Informatikunterricht mit <text:s/></text:span><text:span text:style-name="T51">Informationsgesellschaft und Datensicherheit </text:span><text:span text:style-name="T49">(IuD)</text:span><text:span text:style-name="T51"> </text:span><text:span text:style-name="T104">beginnt: Dann werden die beiden Kapitel </text:span></text:p><text:p text:style-name="P24"><text:span text:style-name="T106"><text:tab/></text:span><text:span text:style-name="T49">I</text:span><text:span text:style-name="T50">uD </text:span><text:span text:style-name="T51">- </text:span><text:span text:style-name="T52">Wiederholung </text:span><text:span text:style-name="T50">Kryptologie </text:span><text:span text:style-name="T52">Klasse 8 </text:span><text:span text:style-name="T104">und</text:span><text:span text:style-name="T49"> </text:span></text:p><text:p text:style-name="P23"><text:span text:style-name="T52"><text:tab/></text:span><text:span text:style-name="T51">I</text:span><text:span text:style-name="T49">uD</text:span><text:span text:style-name="T51"> - </text:span><text:span text:style-name="T49">Asymmetrische Verschlüsselung </text:span></text:p><text:p text:style-name="P23"><text:span text:style-name="T107">im Mathematikunterricht als Einstieg unterrichtet und später im Informatikunterricht wegge-lassen. Der Informatikunterricht beginnt dann mit dem Kapitel </text:span><text:span text:style-name="T53">Man-in-the-middle</text:span><text:span text:style-name="T107">.</text:span></text:p><text:p text:style-name="P44"><text:span text:style-name="T107">Das Thema </text:span><text:span text:style-name="T53">(9) die behandelten Verschlüsselungsverfahren vergleichend beurteilen</text:span><text:span text:style-name="T107"> des Bil-dungsplans Mathematik (Mathem. Grundl. der Kryptologie) wurde in den Bereich Informatik übernommen, weil es thematisch sehr gut im Anschluss an die Asymmetrische Verschlüsselung unterrichtet werden kann. (</text:span><text:span text:style-name="T53">06_iud_ab_vergleich_verfahren.odt</text:span><text:span text:style-name="T107">)</text:span></text:p><text:p text:style-name="P41"><text:span text:style-name="T42">Ergänzung</text:span>: Mit dem Arbeitsblatt 0e<text:span text:style-name="T49">_iud_ab_Caesar-mod.odt</text:span> kann eine Verknüpfung zwischen der (neuen) Modulo-Rechnung und dem (bekannten) Cäsarverfahren hergestellt werden – sofern das noch nicht in Mathematik erfolgt ist.</text:p><text:p text:style-name="P12"><text:toc-mark-start text:id="IMark2177830384872" text:outline-level="1"/>Wiederholung <text:span text:style-name="T102">Kryptologie </text:span>Klasse 8<text:toc-mark-end text:id="IMark2177830384872"/></text:p><text:p text:style-name="P57"><text:span text:style-name="T46">Material</text:span><text:span text:style-name="T176">: <text:s/><text:tab/></text:span><text:span text:style-name="T59">0</text:span><text:span text:style-name="T60">1</text:span><text:span text:style-name="T59">_iud_ab_</text:span><text:span text:style-name="T60">wdh</text:span><text:span text:style-name="T59">.</text:span><text:span text:style-name="T183">odt</text:span></text:p><text:p text:style-name="P71"><text:span text:style-name="T183"><text:tab/><text:tab/></text:span><text:span text:style-name="T184">00_iud_krypto.odp (Folie </text:span><text:span text:style-name="T186">3</text:span><text:span text:style-name="T184">-</text:span><text:span text:style-name="T186">1</text:span><text:span text:style-name="T185">0</text:span><text:span text:style-name="T184">)</text:span></text:p><text:p text:style-name="P13">Aus Klasse 7 und 8 kennen die SuS bereits Tra<text:span text:style-name="T87">n</text:span>spositions- sowie Substitutionsverfahren (Cäsar, Vigenère, One-Time-Pad) und wissen, dass moderne symmetrische Verschlüsselungs-verfahren auf elementaren Verschlüsselungsverfahren basieren und ein<text:span text:style-name="T148">en</text:span> Kompromiss zwischen Sicherheit und Praktikabilität sind.</text:p><text:p text:style-name="P14"><text:span text:style-name="T87">Auf dem ersten Arbeitsblatt werden d</text:span>ie V<text:span text:style-name="T87">erschlüsselungsv</text:span>erfahren mit ihren Vor-und Nachteilen werden wiederholt. <text:span text:style-name="T87">Es werden die Gefahren bei einer Kommunikation über einen unsicheren Kanal sowie die daraus resultierenden Kryptoziele Vertraulichkeit, Integrität, Authentizität und Verbindlichkeit behandelt. Auf Verbindlichkeit wird im Folgenden nicht weiter eingegangen.</text:span></text:p><text:p text:style-name="ZPG_5f_Standard"><text:span text:style-name="T82">Der </text:span><text:span text:style-name="T81">Schlüsseltausch </text:span><text:span text:style-name="T82">ist bei symmetrischen Verfahren ein zentrales Problem, das</text:span><text:span text:style-name="T83"> </text:span><text:span text:style-name="T82">nur mit einem persönlichen Treffen gelöst werden kann. </text:span><text:span text:style-name="T83">Allerdings gibt ein interessantes Verfahren, Merkles Puzzle, bei dem dieses Problem auch ohne persönliches Treffen gelöst wird</text:span><text:span text:style-name="T83"><text:note text:id="ftn1" text:note-class="footnote"><text:note-citation>1</text:note-citation><text:note-body><text:p text:style-name="P35"><text:a xlink:type="simple" xlink:href="https://de.wikipedia.org/wiki/Merkles_Puzzle" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T149">https://de.wikipedia.org/wiki/M</text:span></text:a><text:a xlink:type="simple" xlink:href="https://de.wikipedia.org/wiki/Merkles_Puzzle" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link">erkles_Puzzle</text:a><text:span text:style-name="T150"> </text:span><text:span text:style-name="T151">(abgerufen 27.4.20)</text:span></text:p></text:note-body></text:note></text:span><text:span text:style-name="T83">. Das geht aber weit über den Bildungsplan hinaus und sei hier als Hintergrundinformation erwähnt.</text:span></text:p><text:p text:style-name="P55"><text:toc-mark-start text:id="IMark2177830380744" text:outline-level="1"/>Asymmetrische Verschlüsselung<text:toc-mark-end text:id="IMark2177830380744"/></text:p><text:p text:style-name="P56"><text:span text:style-name="T46">Material</text:span><text:span text:style-name="T176">: <text:s/><text:tab/></text:span><text:span text:style-name="T59">02_iud_ab_asym.</text:span><text:span text:style-name="T183">odt</text:span></text:p><text:p text:style-name="P72"><text:span text:style-name="T183"><text:tab/><text:tab/>0</text:span><text:span text:style-name="T185">2</text:span><text:span text:style-name="T183">_iud_</text:span><text:span text:style-name="T185">mat</text:span><text:span text:style-name="T183">_</text:span><text:span text:style-name="T185">schluessel</text:span><text:span text:style-name="T183">.odt</text:span></text:p><text:p text:style-name="P70"><text:span text:style-name="T183"><text:tab/><text:tab/></text:span><text:span text:style-name="T184">00_iud_krypto.odp (Folie </text:span><text:span text:style-name="T185">12</text:span><text:span text:style-name="T184">-2</text:span><text:span text:style-name="T185">0</text:span><text:span text:style-name="T184">)</text:span></text:p><text:p text:style-name="P33"><draw:frame draw:style-name="fr4" draw:name="Bild1" text:anchor-type="paragraph" svg:x="11.654cm" svg:y="0.131cm" svg:width="5.188cm" svg:height="1.572cm" draw:z-index="37"><draw:image xlink:href="Pictures/1000000000000C7A000004764CDF1C04A85DAFE8.png" xlink:type="simple" xlink:show="embed" xlink:actuate="onLoad" loext:mime-type="image/png"/></draw:frame><text:span text:style-name="T148">Als erste Idee, dass das Schlüsselproblem gelöst werden könnte eignet sich </text:span>folgende Analogie: </text:p><text:p text:style-name="P31"><draw:frame draw:style-name="fr5" draw:name="Bild6" text:anchor-type="paragraph" svg:x="11.654cm" svg:y="0.607cm" svg:width="5.161cm" svg:height="1.538cm" draw:z-index="38"><draw:image xlink:href="Pictures/1000000000000CC100000476DC5458E6774319C1.png" xlink:type="simple" xlink:show="embed" xlink:actuate="onLoad" loext:mime-type="image/png"/></draw:frame><draw:frame draw:style-name="fr6" draw:name="Bild7" text:anchor-type="paragraph" svg:x="11.654cm" svg:y="2.261cm" svg:width="5.17cm" svg:height="1.767cm" draw:z-index="39"><draw:image xlink:href="Pictures/1000000000000C230000045BCEF17D50535ABA9B.png" xlink:type="simple" xlink:show="embed" xlink:actuate="onLoad" loext:mime-type="image/png"/></draw:frame><text:span text:style-name="T6">Alice verschlüsselt die </text:span><text:span text:style-name="T14">Nachricht mit ihren Schloss und schickt sie zu Bob </text:span><text:span text:style-name="T15">(Bild 1)</text:span><text:span text:style-name="T14">. Bob verschlüsselt die Nachricht zusätzlich mit seinem Schloss und schickt sie zurück zu Alice </text:span><text:span text:style-name="T15">(Bild 2)</text:span><text:span text:style-name="T14">. Alice entfernt ihr Schloss </text:span><text:span text:style-name="T15">(Bild 3)</text:span><text:span text:style-name="T14">. Nun kann Bob sein Schloss entfernen und die Nachricht lesen </text:span><text:span text:style-name="T15">(Bild 4)</text:span><text:span text:style-name="T14">. </text:span></text:p><text:p text:style-name="P84"><draw:frame draw:style-name="fr7" draw:name="Bild8" text:anchor-type="paragraph" svg:x="11.636cm" svg:y="0.377cm" svg:width="5.188cm" svg:height="1.612cm" draw:z-index="40"><draw:image xlink:href="Pictures/1000000000000BD2000003ACF406BE4B0FB2854C.png" xlink:type="simple" xlink:show="embed" xlink:actuate="onLoad" loext:mime-type="image/png"/></draw:frame>D<text:span text:style-name="T133">iese Veranschaulichung ist für die</text:span> SuS sofort verständlich: <text:span text:style-name="T88">Das Schloss als Einwegfunktion ist sehr einleuchtend. Um allerdings eine korrekte Analogie zu öffentlichem und privatem Schlüssel zu erhalten, müsste Alice eher ein geöffnetes Schloss verschicken, das Bob zu „klickt“ und damit seine Nachricht an Alice verschlüsselt. Nur Alice hat den Schlüssel zum Öffnen des Schlosses. Weiterhin</text:span> hinkt der Vergleich <text:span text:style-name="T130">(</text:span>Schloss = privater Schlüssel, Schlüssel = öffentlicher Schlüssel<text:span text:style-name="T130">)</text:span> beim Signieren von Nachrichten. Trotzdem kann man das Prinzip den SuS vorstellen, um <text:span text:style-name="T153">grundsätzlich zur </text:span><text:span text:style-name="T47">Idee</text:span><text:span text:style-name="T153"> der asymmetrischen Verschlüsselung zu gelangen. </text:span></text:p><text:p text:style-name="P40"><text:s/></text:p><text:p text:style-name="ZPG_5f_Standard"><draw:g text:anchor-type="paragraph" draw:z-index="35" draw:style-name="gr29"><draw:g draw:name="Form2" draw:style-name="gr4"><draw:g draw:style-name="gr4"><draw:custom-shape draw:name="Form6" draw:style-name="gr30" draw:text-style-name="P145" svg:width="0.147cm" svg:height="0.608cm" svg:x="14.028cm" svg:y="1.238cm"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:type="rectangle" draw:enhanced-path="M 0 0 L 21600 0 21600 21600 0 21600 0 0 Z N"/></draw:custom-shape><draw:custom-shape draw:name="Form4" draw:style-name="gr31" draw:text-style-name="P146" svg:width="0.643cm" svg:height="0.424cm" draw:transform="skewX 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3200 18400 18400" draw:type="round-callout" draw:modifiers="20183.606557377 26726.4" draw:enhanced-path="W 0 0 21600 21600 ?f22 ?f23 ?f18 ?f19 L ?f14 ?f15 Z N"><draw:equation draw:name="f0" draw:formula="$0 -10800"/><draw:equation draw:name="f1" draw:formula="$1 -10800"/><draw:equation draw:name="f2" draw:formula="?f0 *?f0 "/><draw:equation draw:name="f3" draw:formula="?f1 *?f1 "/><draw:equation draw:name="f4" draw:formula="?f2 +?f3 "/><draw:equation draw:name="f5" draw:formula="sqrt(?f4 )"/><draw:equation draw:name="f6" draw:formula="?f5 -10800"/><draw:equation draw:name="f7" draw:formula="atan2(?f1 ,?f0 )/(pi/180)"/><draw:equation draw:name="f8" draw:formula="?f7 -10"/><draw:equation draw:name="f9" draw:formula="?f7 +10"/><draw:equation draw:name="f10" draw:formula="10800*cos(?f7 *(pi/180))"/><draw:equation draw:name="f11" draw:formula="10800*sin(?f7 *(pi/180))"/><draw:equation draw:name="f12" draw:formula="?f10 +10800"/><draw:equation draw:name="f13" draw:formula="?f11 +10800"/><draw:equation draw:name="f14" draw:formula="if(?f6 ,$0 ,?f12 )"/><draw:equation draw:name="f15" draw:formula="if(?f6 ,$1 ,?f13 )"/><draw:equation draw:name="f16" draw:formula="10800*cos(?f8 *(pi/180))"/><draw:equation draw:name="f17" draw:formula="10800*sin(?f8 *(pi/180))"/><draw:equation draw:name="f18" draw:formula="?f16 +10800"/><draw:equation draw:name="f19" draw:formula="?f17 +10800"/><draw:equation draw:name="f20" draw:formula="10800*cos(?f9 *(pi/180))"/><draw:equation draw:name="f21" draw:formula="10800*sin(?f9 *(pi/180))"/><draw:equation draw:name="f22" draw:formula="?f20 +10800"/><draw:equation draw:name="f23" draw:formula="?f21 +10800"/><draw:handle draw:handle-position="$0 $1"/></draw:enhanced-geometry></draw:custom-shape><draw:custom-shape draw:name="Form19" draw:style-name="gr39" draw:text-style-name="P149" svg:width="1.872cm" svg:height="0.66cm" svg:x="15.113cm" svg:y="0.284cm"><text:p text:style-name="P135">öffentlich</text:p><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:glue-points="10800 0 3160 3160 0 10800 3160 18440 10800 21600 18440 18440 21600 10800 18440 3160 ?f14 ?f15" draw:text-areas="3200 3200 18400 18400" draw:type="round-callout" draw:modifiers="1952.54237288136 28684.8" draw:enhanced-path="W 0 0 21600 21600 ?f22 ?f23 ?f18 ?f19 L ?f14 ?f15 Z N"><draw:equation draw:name="f0" draw:formula="$0 -10800"/><draw:equation draw:name="f1" draw:formula="$1 -10800"/><draw:equation draw:name="f2" draw:formula="?f0 *?f0 "/><draw:equation draw:name="f3" draw:formula="?f1 *?f1 "/><draw:equation draw:name="f4" draw:formula="?f2 +?f3 "/><draw:equation draw:name="f5" draw:formula="sqrt(?f4 )"/><draw:equation draw:name="f6" draw:formula="?f5 -10800"/><draw:equation draw:name="f7" draw:formula="atan2(?f1 ,?f0 )/(pi/180)"/><draw:equation draw:name="f8" draw:formula="?f7 -10"/><draw:equation draw:name="f9" draw:formula="?f7 +10"/><draw:equation draw:name="f10" draw:formula="10800*cos(?f7 *(pi/180))"/><draw:equation draw:name="f11" draw:formula="10800*sin(?f7 *(pi/180))"/><draw:equation draw:name="f12" draw:formula="?f10 +10800"/><draw:equation draw:name="f13" draw:formula="?f11 +10800"/><draw:equation draw:name="f14" draw:formula="if(?f6 ,$0 ,?f12 )"/><draw:equation draw:name="f15" draw:formula="if(?f6 ,$1 ,?f13 )"/><draw:equation draw:name="f16" draw:formula="10800*cos(?f8 *(pi/180))"/><draw:equation draw:name="f17" draw:formula="10800*sin(?f8 *(pi/180))"/><draw:equation draw:name="f18" draw:formula="?f16 +10800"/><draw:equation draw:name="f19" draw:formula="?f17 +10800"/><draw:equation draw:name="f20" draw:formula="10800*cos(?f9 *(pi/180))"/><draw:equation draw:name="f21" draw:formula="10800*sin(?f9 *(pi/180))"/><draw:equation draw:name="f22" draw:formula="?f20 +10800"/><draw:equation draw:name="f23" draw:formula="?f21 +10800"/><draw:handle draw:handle-position="$0 $1"/></draw:enhanced-geometry></draw:custom-shape></draw:g>Verschlüsselungsverfahren, bei denen <text:span text:style-name="T202">Sender</text:span> und <text:span text:style-name="T202">Empfänger einer verschlüsselten Nachricht</text:span> <text:span text:style-name="T81">verschiedene</text:span> Schlüssel haben, nennt man <text:span text:style-name="T44">asymmetrische</text:span> Verfahren. <text:span text:style-name="T89">Hierbei wird ein </text:span><text:span text:style-name="T67">Schlüsselpaar</text:span><text:span text:style-name="T41"> erzeugt. Den privaten Schlüssel <text:s/>behält man, den öffentlichen Schlüssel kopiert man und verteilt ihn an jeden, der mit einem kommunizieren möchte.</text:span></text:p><text:p text:style-name="P85"><text:span text:style-name="T89">Wird eine Text mit dem </text:span>private<text:span text:style-name="T89">n</text:span> Schlüssel <text:span text:style-name="T89">v</text:span>erschlüssel<text:span text:style-name="T89">t, kann man ihn nur</text:span> mit <text:span text:style-name="T84">dem </text:span>öffentliche<text:span text:style-name="T89">n</text:span> Schlüssel <text:span text:style-name="T129">e</text:span>ntschlüsseln. <text:span text:style-name="T89">Wird ein Text </text:span>mit <text:span text:style-name="T89">dem </text:span>öffentliche<text:span text:style-name="T89">n</text:span> Schlüssel <text:span text:style-name="T89">v</text:span>erschlüssel<text:span text:style-name="T89">t,</text:span> <text:span text:style-name="T89">kann man ihn nur </text:span>mit <text:span text:style-name="T84">dem </text:span>privatem Schlüssel <text:span text:style-name="T89">e</text:span>ntschlüsseln.</text:p><text:p text:style-name="P32"><text:span text:style-name="T6">Zur schematischen Darstellung: Im Folgenden wird ein Schlüsselpaar immer in derselben Farbe dargestellt. Der Schlüssel mit dem </text:span><text:span text:style-name="T7">Ö</text:span><text:span text:style-name="T6"> im Ring ist der öffentliche, der Schlüssel ohne ein </text:span><text:span text:style-name="T7">Ö</text:span><text:span text:style-name="T6"> ist der private.</text:span></text:p><text:p text:style-name="P86">Die SuS spielen <text:span text:style-name="T131">auf dem AB </text:span><text:span text:style-name="T54">02_iud_ab_asym_</text:span><text:span text:style-name="T56">rsa</text:span><text:span text:style-name="T54">.odt </text:span>das Ver- und Entschlüsseln <text:span text:style-name="T202">händisch </text:span>mit de<text:span text:style-name="T202">n Schlüsselpaaren des </text:span>Material<text:span text:style-name="T202">s</text:span><text:span text:style-name="T190"> </text:span>du<text:span text:style-name="T85">r</text:span>ch <text:span text:style-name="T85">(Aufgabe 2-3).</text:span></text:p><text:p text:style-name="P92"><text:span text:style-name="T42">Vorbereitung</text:span>: Die bunten Schlüssel <text:span text:style-name="T202">(</text:span><text:span text:style-name="T188">0</text:span><text:span text:style-name="T189">2</text:span><text:span text:style-name="T188">_iud_</text:span><text:span text:style-name="T189">mat</text:span><text:span text:style-name="T188">_</text:span><text:span text:style-name="T189">schluessel</text:span><text:span text:style-name="T188">.odt</text:span><text:span text:style-name="T190">) </text:span>werden ausgeschnitten und laminiert. Für jede Gruppe wird <text:s/><text:span text:style-name="T131">ein privater Schlüssel und zwei bis drei öffentliche Schlüssel</text:span> benötigt. <text:span text:style-name="T132">(Das Material kann wiederverwendet werden, jedoch ist die Herstellung aufwendiger.)</text:span></text:p><text:p text:style-name="P113"><draw:frame draw:style-name="fr9" draw:name="Bild5" text:anchor-type="paragraph" svg:x="11.76cm" svg:y="0.337cm" svg:width="4.937cm" svg:height="2.166cm" draw:z-index="32"><draw:image xlink:href="Pictures/1000000000000D2B0000062DD61C593CD5E03D03.png" xlink:type="simple" xlink:show="embed" xlink:actuate="onLoad" loext:mime-type="image/png"/></draw:frame><text:span text:style-name="T91">Einfache Variante </text:span><text:span text:style-name="T92">(ohne Wiederverwendung)</text:span><text:span text:style-name="T91">: </text:span></text:p><text:p text:style-name="P109"><draw:frame draw:style-name="fr8" draw:name="Bild2" text:anchor-type="paragraph" svg:x="7.041cm" svg:y="0.097cm" svg:width="4.498cm" svg:height="1.461cm" draw:z-index="31"><draw:image xlink:href="Pictures/1000000000000D610000034D2585658908975084.png" xlink:type="simple" xlink:show="embed" xlink:actuate="onLoad" loext:mime-type="image/png"/></draw:frame><text:span text:style-name="T91">Die schwarzweiße Seite wird kopiert und in Streifen geschnitten. </text:span><text:span text:style-name="T92">Zusätzlich </text:span><text:span text:style-name="T93">schne</text:span><text:span text:style-name="T94">i</text:span><text:span text:style-name="T93">det man </text:span><text:span text:style-name="T92">so viele </text:span><text:soft-page-break/><text:span text:style-name="T92">leere Streifen, wie Gruppen </text:span><text:span text:style-name="T96">vorhanden sind</text:span><text:span text:style-name="T92">. J</text:span><text:span text:style-name="T91">ede Gruppe erhält ein Schlüsselpaar, welches </text:span><text:span text:style-name="T92">von den SuS </text:span><text:span text:style-name="T91">noch auseinander geschnitten werden muss. Weiterhin muss </text:span><text:span text:style-name="T97">jede</text:span><text:span text:style-name="T91"> Gruppe </text:span><text:span text:style-name="T97">aus</text:span><text:span text:style-name="T92"> dem leeren Streifen 1-2</text:span><text:span text:style-name="T91"> Kopie</text:span><text:span text:style-name="T92">n</text:span><text:span text:style-name="T91"> des öffentlichen Schlüssels anfertigen.</text:span></text:p><text:p text:style-name="P87"><draw:frame draw:style-name="fr10" draw:name="Bild10" text:anchor-type="paragraph" svg:x="13.226cm" svg:y="0.864cm" svg:width="4.553cm" svg:height="2.63cm" draw:z-index="42" draw:transform="translate (-15.5025cm -2.179cm) rotate (1.5707963267949) translate (15.5025cm 2.179cm)"><draw:image xlink:href="Pictures/1000000000000900000006C0257D4362688B52A3.jpg" xlink:type="simple" xlink:show="embed" xlink:actuate="onLoad" loext:mime-type="image/jpeg"/></draw:frame><draw:frame draw:style-name="fr11" draw:name="Bild9" text:anchor-type="paragraph" svg:x="10.178cm" svg:y="0.88cm" svg:width="4.553cm" svg:height="2.596cm" draw:z-index="41" draw:transform="translate (-12.4545cm -2.178cm) rotate (1.5707963267949) translate (12.4545cm 2.178cm)"><draw:image xlink:href="Pictures/1000000000000D8000000A204142659383FC5CB2.jpg" xlink:type="simple" xlink:show="embed" xlink:actuate="onLoad" loext:mime-type="image/jpeg"/></draw:frame><text:span text:style-name="T45">Durchführung</text:span><text:span text:style-name="T90">: </text:span>Die SuS teilen sich in <text:span text:style-name="T171">D</text:span>reier- <text:span text:style-name="T131">oder Vierer-g</text:span>ruppen auf. Alice erhält ein Schlüsselpaar, sowie <text:span text:style-name="T131">die</text:span> Kopie<text:span text:style-name="T131">n</text:span> ihres öffentlichen Schlüssels. Die öffentlichen Schlüssel gibt sie ihren beiden Freunden Bob und Charlie. Will man eine Nachricht verschlüsseln, <text:span text:style-name="T90">so schreibt man die Nachricht auf einen DIN-A-6-Blatt, faltet ihn in der Mitte, legt den öffentlichen Schlüssel des Empfängers darauf und zeichnet die Schnittlinie ab. Der Empfänger legt seinen privaten Schlüssel an die Schnittlinie. Passt er, kann er die Nachricht entschlüsseln und darf den Zettel öffnen und lesen.</text:span></text:p><text:p text:style-name="P86"><text:span text:style-name="T85">Die SuS</text:span> erkennen <text:span text:style-name="T89">folgende Zusammenhänge: </text:span></text:p><text:p text:style-name="P86">Wird mit dem öffentlichen Schlüssel <text:span text:style-name="T42">ver</text:span>schlüsselt und mit dem privaten Schlüsselt <text:span text:style-name="T42">ent</text:span>schlüsselt, dann kann die Nachricht nicht mitgelesen werden (Kryptoziel: Vertraulichkeit).</text:p><text:p text:style-name="P89">Wird <text:span text:style-name="T204">mit </text:span>de<text:span text:style-name="T204">m</text:span> private<text:span text:style-name="T205">n</text:span> Schlüssel <text:span text:style-name="T42">ver</text:span>schlüsselt und mit dem öffentlichen Schlüsselt <text:span text:style-name="T42">ent</text:span>schlüsselt, dann ist die Nachricht nicht vertraulich, <text:span text:style-name="T154">weil jeder den öffentlichen Schlüssel zum Entschlüsseln <text:s/>haben und anwenden kann. A</text:span>ber es ist gesichert, dass <text:span text:style-name="T84">d</text:span>ie Nachricht tatsächlich vom Absender stammt. <text:span text:style-name="T80">Die Verschlüsselung mit dem privaten Schlüssel ist vergleichbar mit einer Unterschrift, die unter ein Dokument gesetzt wird. Gemäß dieser Parallele nennt man das Anwenden des privaten Schlüssels </text:span><text:span text:style-name="T63">signier</text:span><text:span text:style-name="T64">en </text:span><text:span text:style-name="T80">und das darauffolgende Anwenden des öffentlichen Schlüssels </text:span><text:span text:style-name="T62">verifizieren</text:span><text:span text:style-name="T80">. </text:span>(Kryptoziel: Authentizität) </text:p><text:p text:style-name="P90"><text:span text:style-name="T205">Beim eigentlichen Verfahren der „digitalen Signatur“</text:span><text:span text:style-name="T209"> wird aus </text:span><text:span text:style-name="T211">einem</text:span><text:span text:style-name="T209"> Text ein Hashwert (Fingerprint) generiert und nur auf diesen wird der private Schlüssel angewendet. Die eigentliche Nachricht wird nicht notwendigerweise verschlüsselt. </text:span><text:span text:style-name="T210">Die digitale Signatur wird erst später betrachtet. </text:span></text:p><text:p text:style-name="P110"><text:span text:style-name="T48">Anmerkung</text:span>: Im Zusammenhang mit <text:span text:style-name="T116">Vertraulichkeit</text:span> werden die Begriffe <text:span text:style-name="T49">verschlüsseln</text:span> und <text:span text:style-name="T49">entschlüsseln</text:span> verwendet. Im Zusammenhang mit <text:span text:style-name="T42">Authentizität</text:span> hingegen werden die Begriffe s<text:span text:style-name="T49">ignieren</text:span> und v<text:span text:style-name="T49">erifizieren</text:span> verwendet. Das Verfahren ist in beiden Fällen das Gleiche: Der Schlüssel wird <text:span text:style-name="T49">angewendet:</text:span></text:p><text:list xml:id="list1724917271" text:style-name="L2"><text:list-item><text:p text:style-name="P112">Verschlüsseln: <text:span text:style-name="T203">D</text:span>er öffentliche Schlüssel wird auf einen Text angewendet, um Vertraulichkeit sicherzustellen. Durch Entschlüsseln (mit dem privaten Schlüssel) wird der Klartext wieder hergestellt.</text:p></text:list-item><text:list-item><text:p text:style-name="P111">Signieren: <text:span text:style-name="T203">D</text:span>er private Schlüssel wird auf einen Text angewendet, um Authentizität sicherzustellen, <text:span text:style-name="T206">der Text wird signiert</text:span>. <text:span text:style-name="T203">D</text:span>ie Authentizität <text:span text:style-name="T203">wird </text:span>geprüft, indem der öffentliche Schlüssel angewendet wird <text:span text:style-name="T203">(=</text:span> <text:span text:style-name="T206">v</text:span>erifizieren<text:span text:style-name="T203">)</text:span>. </text:p></text:list-item></text:list><text:p text:style-name="P93"><text:span text:style-name="T208">Bis Klasse 10 wurden die Begriffe „einen Schlüssel </text:span><text:span text:style-name="T61">anwenden</text:span><text:span text:style-name="T203">“ und „</text:span><text:span text:style-name="T61">ver-</text:span><text:span text:style-name="T203"> bzw. </text:span><text:span text:style-name="T61">entschlüsseln“ </text:span><text:span text:style-name="T114">im Unterricht</text:span><text:span text:style-name="T115"> </text:span><text:span text:style-name="T114">synonym verwendet</text:span><text:span text:style-name="T115">. </text:span><text:span text:style-name="T203">Nachdem an dieser Stelle die neue Möglichkeit des Signierens eingeführt wird, sollte darauf geachtet werden, im Zusammenhang mit Authentizität nicht die Begriffe </text:span><text:span text:style-name="T61">ver</text:span><text:span text:style-name="T203">- und </text:span><text:span text:style-name="T61">entschlüsseln</text:span><text:span text:style-name="T203"> zu verwenden, sondern „einen Schlüssel </text:span><text:span text:style-name="T61">anwenden</text:span><text:span text:style-name="T115">“. </text:span><text:span text:style-name="T114">Damit wird unterstrichen, dass es hierbei nicht um Geheimhaltung geht.</text:span></text:p><text:p text:style-name="P88"/><text:p text:style-name="ZPG_5f_Standard">In Aufgabe 5 wird das Erlernte eingeübt - diesmal nicht händisch, sondern mit einem <text:span text:style-name="T129">Chat-</text:span>Tool. <text:span text:style-name="T129">Dazu bilden die SuS Dreiergruppen. Je Gruppe wird ein Server gestartet und jeder Schüler startet einen Client und meldet sich am Server an. (siehe Aufgabe)</text:span></text:p><text:p text:style-name="P91"><text:soft-page-break/>In Aufgabe 4 werden symmetrische und asymmetrische Verfahren verglichen hinsichtlich der benötigten Anzahl an Schlüsseln.</text:p><text:p text:style-name="P116"><text:span text:style-name="T209">Nachteil asymmetrischer Verschlüsselung;</text:span></text:p><text:p text:style-name="P91"><text:span text:style-name="T209">In der praktischen Anwendung eigne</text:span><text:span text:style-name="T212">n</text:span><text:span text:style-name="T209"> sich </text:span><text:span text:style-name="T212">asymmetrische Verfahren, wie </text:span><text:span text:style-name="T209">das RSA-Verfahren nicht zur Verschlüsselung längerer Texte. Je länger der zu verschlüsselnde Text, desto länger der Schlüssel und desto länger dauert das Verschlüsseln. Das erkennt man auch im Chat-Tool, wo zwischen verschieden langen Schlüsselpaaren gewählt werden kann. (Auspobieren!) Eine Verschlüsselung mit RSA dauert ca. 100 mal so lang wie mit dem symmetrischen AES-Verfahren.</text:span></text:p><text:p text:style-name="P91"><text:span text:style-name="T209"/></text:p><text:p text:style-name="P21"><text:span text:style-name="T42">Hinweis:</text:span> <text:span text:style-name="T133">Falls</text:span> dieser Einstig <text:span text:style-name="T133">innerhalb</text:span> IMP-Mathematik unterrichtet w<text:span text:style-name="T207">i</text:span>rd, geht es an dieser Stelle weiter mit den mathematischen Grundlagen der Kryptologie. Der <text:span text:style-name="T133">IMP-</text:span>Informatikunterricht beginnt in diesem Fall erst an dieser Stelle.</text:p><text:p text:style-name="P22"/><table:table table:name="Tabelle4" table:style-name="Tabelle4"><table:table-column table:style-name="Tabelle4.A"/><table:table-column table:style-name="Tabelle4.B"/><table:table-row><table:table-cell table:style-name="Tabelle4.A1" office:value-type="string"><text:p text:style-name="P69">Aufgabe <text:span text:style-name="T164">auf dem AB</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle4.B1" office:value-type="string"><text:p text:style-name="P69">zugehörige <text:span text:style-name="T163">Folie in der </text:span>Präsentation</text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle4.A2" office:value-type="string"><text:p text:style-name="P61">Nr. <text:span text:style-name="T195">2</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle4.B2" office:value-type="string"><text:p text:style-name="P65">15 - 16</text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle4.A2" office:value-type="string"><text:p text:style-name="P61">Nr. <text:span text:style-name="T195">3</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle4.B2" office:value-type="string"><text:p text:style-name="P65">17</text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle4.A2" office:value-type="string"><text:p text:style-name="P61">Nr. <text:span text:style-name="T195">4</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle4.B2" office:value-type="string"><text:p text:style-name="P65">18 - 19</text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle4.A2" office:value-type="string"><text:p text:style-name="P62">Nr. <text:span text:style-name="T195">5</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle4.B2" office:value-type="string"><text:p text:style-name="P65">20</text:p></table:table-cell></table:table-row></table:table><text:p text:style-name="P10"><text:toc-mark-start text:id="IMark2177830384296" text:outline-level="1"/>Man-in-the-middle-Angriff<text:toc-mark-end text:id="IMark2177830384296"/></text:p><text:p text:style-name="P56"><text:span text:style-name="T46">Material</text:span><text:span text:style-name="T176">: <text:s/><text:tab/>03_iud_ab_man-in-the-middle.</text:span><text:span text:style-name="T183">odt</text:span></text:p><text:p text:style-name="P70"><text:span text:style-name="T183"><text:tab/><text:tab/></text:span><text:span text:style-name="T184">00_iud_krypto.odp (Folie 21-29)</text:span></text:p><text:p text:style-name="P25">Nachdem die SuS das Prinzip der asymmetrischen Verschlüsselung verstanden haben, wird die Frage aufgeworfen, ob es bei dieser Art der Kommunikation wirklich keinen Angriffspunkt gibt.</text:p><text:p text:style-name="ZPG_5f_Standard">Beim symmetrischen Verfahren ist der Schlüsseltausch das zentrale Problem. Das Verteilen des öffentlichen Schlüssels sollte beim <text:span text:style-name="T99">a</text:span>symmetrischen Verfahren kein Problem darstellen, da der öffentliche Schlüssel <text:span text:style-name="T171">(wie der Name schon sagt)</text:span> kein Geheimnis darstellt. Dennoch gibt es <text:span text:style-name="T99">genau hier </text:span>eine <text:span text:style-name="T86">Schwachstelle, </text:span>die die SuS finden sollen.</text:p><text:p text:style-name="ZPG_5f_Standard"><text:span text:style-name="T134">Die SuS spielen in Aufgabe 1 das Szenario durch, das beginnt, </text:span><text:span text:style-name="T43">bevor</text:span><text:span text:style-name="T74"> Alice ihren öffentlichen Schlüssel verteilt hat und erstellen dazu das Sequenzdiagramm.</text:span></text:p><text:p text:style-name="P26">Gearbeitet wird wieder in Dreiergruppen. Jede <text:span text:style-name="T158">Dreierg</text:span>ruppe <text:span text:style-name="T159">erhält</text:span> <text:span text:style-name="T158">drei Schlüsselpaare (für Alice, Bob, Mal). <text:s/></text:span>Alternativ kann man <text:span text:style-name="T158">zuerst nur Alice ein Schlüsselpaar (</text:span>mit zwei öffentlichen Schlüsseln<text:span text:style-name="T158">)</text:span> <text:span text:style-name="T158">geben. Das zusätzliche Schlüsselpaar für Mal erhält die Gruppe erst wenn die SuS die Notwendigkeit erkennen, dass Mal auch ein eigenes</text:span> Schlüsselpaar <text:span text:style-name="T159">benötigt. Oder sie erhalten Mals Schlüsselpaar bei Bedarf als Tipp.</text:span></text:p><text:p text:style-name="P36">Für Mal ist es leicht, d<text:span text:style-name="T155">i</text:span><text:span text:style-name="T156">e Nachricht mit dem öffentlichen</text:span> Schlüssel von Alice <text:span text:style-name="T155">z</text:span><text:span text:style-name="T156">u lesen und eine Kopie des öffentlichen Schlüssels für sich zu erstellen</text:span>. Allerdings stellt das kein Problem da, da Alice Schlüssel ohnehin öffentlich ist. <text:span text:style-name="T155">P</text:span><text:span text:style-name="T157">roblematisch ist allerdings, wenn Mal die Nachricht </text:span>abfängt, <text:span text:style-name="T155">d</text:span><text:span text:style-name="T157">en</text:span> Schlüssel von Alice entfernt und durch seinen eigenen <text:span text:style-name="T100">öffentlichen Schlüssel </text:span>ersetzt. Bob erhält scheinbar eine Nachricht von Alice mit einem Schlüssel. Er geht davon aus, dass dies Alice Schlüssel ist und verschlüsselt damit vertrauliche Nachrichten an Alice. Diese kann Mal lesen, <text:span text:style-name="T100">w</text:span>eil er ja den passenden privaten Schlüssel hat. <text:span text:style-name="T100">Leitet er die Nachricht weiter an Alice (unverändert oder manipuliert) verschlüsselt er sie zuvor mit Alice öffentlichem Schlüssel. Alice denkt nun, die verschlüsselte Nachricht käme von Bob.</text:span></text:p><text:p text:style-name="P100">Das zentrale Problem <text:span text:style-name="T161">(siehe Aufgabe 2) ist</text:span> also, <text:span text:style-name="T158">dass nicht sichergestellt werden kann, </text:span>ob der erhaltene öffentliche Schlüssel tatsächlich vom scheinbaren Absender stammt. Die Lösung könnte in einem persönlichen Treffen liegen oder in einer <text:span text:style-name="T122">P</text:span>erson, <text:span text:style-name="T134">d</text:span>er beide Kommunikationspartner vertrauen und <text:span text:style-name="T158">deren öffentlichen </text:span>Schlüssel <text:span text:style-name="T158">sie bereits auf sicherem Weg erhalten</text:span> haben. Sie wird im Folgenden CAty genannt, von <text:span text:style-name="T42">C</text:span>ertification <text:span text:style-name="T42">A</text:span>uthori<text:span text:style-name="T42">ty</text:span>. <text:span text:style-name="T162">Zentraler Punkt ist, dass Alice und Bob Caty vertrauen, es ist hingegen nicht notwendig, dass Caty jemandem <text:s/>vertraut.</text:span></text:p><text:p text:style-name="P101">Auf dem Arbeitsblatt wird in Aufgabe <text:span text:style-name="T222">3 die man-in-the-middle-Problematik</text:span> mit dem bereits bekannten Chat-Tool praktisch umgesetzt.</text:p><text:p text:style-name="P96"><text:span text:style-name="T217">Aufgabe 4 führt hin zur Idee und Notwendigkeit eines Zertifikats. Diese Aufgabe ist nicht zwingend notwendig und man kann stattdessen auch gleich zu den Zertifikaten übergehen. Es soll nicht der Eindruck erweckt werden, dass CAty eine Art Schlüsseldatenbank ist, an die alle ihre Schlüsselanfragen stellen. Tatsächlich prüft die CA die Identität der Antragsteller und stellt ihnen das Zertifikat aus. Für die Verteilung sind die Zertifikat-Eigentümer selber verantwortlich. </text:span></text:p><text:p text:style-name="P96"><text:span text:style-name="T19">Bob fragt </text:span><text:span text:style-name="T24">in Aufgabe </text:span><text:span text:style-name="T25">4</text:span><text:span text:style-name="T24"> </text:span><text:span text:style-name="T19">Alice nach ihrem öffentlichen Schlüssel. Alice bittet CAty zu bestätigen, dass es sich um Alice Schlüssel handelt. CAty wendet auf die Nachricht mit Alice Schlüssel ihren eigenen privaten Schlüssel an und schickt sie zu Bob. Bob wendet Catys öffentlichen Schlüssel an, verifiziert also die Nachricht und hat Alice öffentlichen Schlüssel. </text:span><text:span text:style-name="T22">Mal kann Alice Nachricht </text:span><text:soft-page-break/><text:span text:style-name="T22">mit der Bitte um Bestätigung nicht lesen, </text:span><text:span text:style-name="T21">weil Alice sie mit CAtys öffentlichen Schlüssel verschlüsselt hat. </text:span><text:span text:style-name="T20">Die Vertraulichkeit der Nachricht ist sichergestellt. </text:span><text:span text:style-name="T22">D</text:span><text:span text:style-name="T18">ie Nachricht, die Alice Schlüssel beinhaltet, </text:span><text:span text:style-name="T23">kann Mal </text:span><text:span text:style-name="T18">lesen</text:span><text:span text:style-name="T19">, weil er CAtys öffentlichen Schlüssel hat. Das ist aber nicht problematisch, da es sich um den öffentlichen Schlüssel von Alice handelt, den jeder haben darf. </text:span><text:span text:style-name="T22">Weil </text:span><text:span text:style-name="T10">CAty</text:span><text:span text:style-name="T11"> auf</text:span><text:span text:style-name="T10"> die Nachricht, die Alice Schlüssel beinhaltet, ihrem eigenen privaten Schlüssel </text:span><text:span text:style-name="T11">anwendet</text:span><text:span text:style-name="T10">, </text:span><text:span text:style-name="T12">kann </text:span><text:span text:style-name="T13">Bob</text:span><text:span text:style-name="T12"> sicher sein, dass die Nachricht von CAty stammt.</text:span></text:p><text:p text:style-name="P95"><text:span text:style-name="T217">Eine Schwachstelle (siehe Aufgabe 4 d) liegt z.B.</text:span> <text:span text:style-name="T160">darin, dass Mal eine verschlüsselte Nachricht von Alice an CAty sieht und vermutet, dass dies eine Schlüsselanfrage sein könnte (weil CAty ja als vertrauenswürdige Person bekannt ist). Spätestens mit diesem Hinweis können die SuS erkennen, dass Mal Bobs Nachricht abfängt und statt dessen eine eigene Schlüsselanfrage nach seinem, Mals, Schlüssel an CAty schickt. CAty kennt Mals öffentlichen Schlüssel, wendet auf die Nachricht mit Mals Schlüssel ihrem eigenen privaten Schlüssel an (Authentifizierung) und schickt sie zurück. Mal braucht nichts weiter zu tun, als diese Nachricht an Bob weiterzuleiten. Da die Nachricht als Antwort auf seine Schlüsselanfrage kommt und zudem von CAty signiert ist, geht er fälschlicherweise davon aus, dass es sich um Alice Schlüssel handelt. Nun kann Mal Bobs Nachrichten an Alice lesen und ändern. 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10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape><draw:custom-shape draw:name="Form4" draw:style-name="gr16" draw:text-style-name="P139" svg:width="0.207cm" svg:height="0.13cm" draw:transform="rotate (1.56695660244051) translate (15.2629305555556cm 1.02305555555556cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape><draw:g draw:style-name="gr4"><draw:custom-shape draw:name="Form4" draw:style-name="gr17" draw:text-style-name="P139" svg:width="0.207cm" svg:height="0.13cm" draw:transform="rotate (1.56695660244051) translate (15.2629305555556cm 1.01952777777778cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:mirror-horizontal="false" draw:mirror-vertical="false" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape><draw:custom-shape draw:name="Form25" draw:style-name="gr18" draw:text-style-name="P143" svg:width="0.057cm" svg:height="0.084cm" draw:transform="rotate (1.5707963267949) translate (15.1535694444444cm 1.02481944444444cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape><draw:custom-shape draw:name="Form25" draw:style-name="gr18" draw:text-style-name="P143" svg:width="0.057cm" svg:height="0.084cm" draw:transform="rotate (1.5707963267949) translate (15.1535694444444cm 0.885472222222222cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape></draw:g></draw:g></draw:g>Die Lösung <text:span text:style-name="T123">dieses Dilemmas (siehe Aufgabe 4 e) </text:span>besteht darin, dass CAty nicht nur den Schlüssel von Alice <text:span text:style-name="T222">signiert</text:span>, sondern zusätzlich Alice Namen. Nun würde es sofort auffallen, wenn die Nachricht <text:span text:style-name="T123">nicht Alice sondern</text:span> Mals Schlüssel (und auch sein<text:span text:style-name="T123">en</text:span> Name<text:span text:style-name="T123">n</text:span>) beinhaltet. </text:p><text:p text:style-name="P81"/><table:table table:name="Tabelle1" table:style-name="Tabelle1"><table:table-column table:style-name="Tabelle1.A"/><table:table-column table:style-name="Tabelle1.B"/><table:table-row><table:table-cell table:style-name="Tabelle1.A1" office:value-type="string"><text:p text:style-name="P67">Aufgabe <text:span text:style-name="T164">auf dem AB</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle1.B1" office:value-type="string"><text:p text:style-name="P67">zugehörige <text:span text:style-name="T163">Folie in der </text:span>Präsentation</text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle1.A2" office:value-type="string"><text:p text:style-name="P59">Nr. 1</text:p></table:table-cell><table:table-cell table:style-name="Tabelle1.B2" office:value-type="string"><text:p text:style-name="P58"><text:span text:style-name="T163">21 </text:span>- <text:span text:style-name="T163">23</text:span></text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle1.A2" office:value-type="string"><text:p text:style-name="P59">Nr. 2</text:p></table:table-cell><table:table-cell table:style-name="Tabelle1.B2" office:value-type="string"><text:p text:style-name="P59">24 - 25</text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle1.A2" office:value-type="string"><text:p text:style-name="P59">Nr. <text:span text:style-name="T223">4</text:span> a-c, <text:span text:style-name="T199">d, e</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle1.B2" office:value-type="string"><text:p text:style-name="P59">2<text:span text:style-name="T173">6, 27, 28</text:span> (- <text:span text:style-name="T173">29</text:span>)</text:p></table:table-cell></table:table-row></table:table><text:p text:style-name="P37"/><text:p text:style-name="P39"><text:s/></text:p><text:p text:style-name="P8"><text:toc-mark-start text:id="IMark2177830381992" text:outline-level="1"/><text:span text:style-name="T143">Zertifikat</text:span><text:span text:style-name="T144">e</text:span><text:toc-mark-end text:id="IMark2177830381992"/></text:p><text:p text:style-name="P56"><text:span text:style-name="T46">Material</text:span><text:span text:style-name="T176">: <text:s/><text:tab/></text:span><text:span text:style-name="T183">0</text:span><text:span text:style-name="T184">4</text:span><text:span text:style-name="T183">_iud_ab_</text:span><text:span text:style-name="T184">zertifikat</text:span><text:span text:style-name="T183">.odt</text:span></text:p><text:p text:style-name="P70"><text:span text:style-name="T183"><text:tab/><text:tab/></text:span><text:span text:style-name="T184">00_iud_krypto.odp (Folie 29-</text:span><text:span text:style-name="T187">31</text:span><text:span text:style-name="T184">)</text:span></text:p><text:p text:style-name="P15"><draw:g text:anchor-type="paragraph" draw:z-index="34" draw:style-name="gr19"><draw:g draw:style-name="gr4"><draw:path draw:name="Form7" draw:style-name="gr20" draw:text-style-name="P144" svg:width="2.145cm" svg:height="1.306cm" draw:transform="skewX (0.251152879361984) rotate (2.66616496534654) translate (16.085958124688cm 2.00115932908808cm)" svg:viewBox="0 0 2146 1307" svg:d="M1052 1270c90 4 186-11 247-67 59-56 59-184 157-180 102 3 171-40 241-74 79-39 118-114 176-166 68-62 189 10 250-62 95-110-151-119-55-227 55-62 47-165-63-196-81-23-209-51-214-135-3-69-43-225-133-137-56 54-91 135-182 150-78 14-218-9-240 74-24 97-112 112-149 191-41 87-160 68-245 68-128 1-106 122-134 185-31 69-175 71-232-2-43-58-150-117-123-188 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(1.59348560707082) translate (15.4393194444444cm 1.0795cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:mirror-horizontal="false" draw:mirror-vertical="false" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape><draw:custom-shape draw:name="Form4" draw:style-name="gr25" draw:text-style-name="P139" svg:width="0.186cm" svg:height="0.115cm" draw:transform="rotate (1.56695660244051) translate (15.509875cm 0.973666666666667cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape><draw:g draw:style-name="gr4"><draw:custom-shape draw:name="Form4" draw:style-name="gr26" draw:text-style-name="P139" svg:width="0.184cm" svg:height="0.115cm" draw:transform="rotate (1.56695660244051) translate (15.509875cm 0.968375cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:mirror-horizontal="false" draw:mirror-vertical="false" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape><draw:custom-shape draw:name="Form25" draw:style-name="gr27" draw:text-style-name="P143" svg:width="0.052cm" svg:height="0.075cm" draw:transform="rotate (1.5707963267949) translate (15.4128611111111cm 0.970138888888889cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape><draw:custom-shape draw:name="Form25" draw:style-name="gr28" draw:text-style-name="P143" svg:width="0.05cm" svg:height="0.075cm" draw:transform="rotate (1.5707963267949) translate (15.4128611111111cm 0.848430555555555cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape></draw:g></draw:g></draw:g>Eine Einheit aus <text:span text:style-name="T135">dem </text:span>Name<text:span text:style-name="T135">n</text:span> und <text:span text:style-name="T135">dem </text:span>öffentlichem Schlüssel, die mit dem privaten Schlüssel einer Zertifizierungsinstanz (also einer vertrauenswürdige<text:span text:style-name="T165">n</text:span> CAty) verschlüsselt ist, nennt man <text:span text:style-name="T42">Zertifikat</text:span>. <text:span text:style-name="T101">Eine </text:span><text:span text:style-name="T42">Zertifizierungsinstanz</text:span> <text:span text:style-name="T124">(Zertifizierungsstelle, </text:span>Certification Authority (CA)<text:span text:style-name="T124">) ist </text:span>(wie CAty) <text:span text:style-name="T124">eine vertrauenswürdige Instanz, die die Zertifikate sicher verwaltet.</text:span> </text:p><text:p text:style-name="P18">Tatsächlich beantwortet die Zertifizierungsstelle nicht jede einzelne Schlüsselanfrage, sondern stellt für Alice ein Zertifikat aus, verschlüsselt dieses mit dem privaten Schlüssel der Zertifizierungsstelle und übergibt es Alice. Alice schickt dieses verschlüsselte Zertifikat an ihre Kunden. Um sicher zu sein, dass Alice wirklich Alice ist, muss Alice persönlich bei der Zertifizierungsstelle erscheinen und sich ausweisen.</text:p><text:p text:style-name="P18">Damit nicht alle Kunden bei der Zertifizierungsstelle nach deren öffentlichem Schlüssel anfragen müssen, ist der öffentliche Schlüssel der Zertifizierungsstelle direkt im Browser eingetragen.</text:p><text:p text:style-name="P16">Es gibt nicht nur eine einzelne CA für die ganze Welt, sondern mehrere, die hierarchisch gegliedert sind und sich gegenseitig vertrauen. </text:p><text:p text:style-name="P34">Es sollte die Problematik thematisiert werden, dass Zertifizierung auf dem Vertrauen gegenüber der gesamten Hierarchie der Zertifizierungsstellen beruht. Ein Fehler bzw. Betrug bei einer der Instanzen hätte Folgen für jeden Nutzer des Zertifikats.</text:p><text:p text:style-name="P45">In Aufgabe 1 verwenden die SuS das Chat-Tool <text:span text:style-name="T175">unter Einbeziehung von</text:span> Zertifikaten.</text:p><text:p text:style-name="P38"/><text:p text:style-name="P9"><text:toc-mark-start text:id="IMark2177830381032" text:outline-level="1"/>Digitale Signatur<text:toc-mark-end text:id="IMark2177830381032"/></text:p><text:p text:style-name="P56"><text:span text:style-name="T46">Material</text:span><text:span text:style-name="T176">: <text:s/><text:tab/></text:span><text:span text:style-name="T183">05_iud_ab_digit_signatur.odt</text:span></text:p><text:p text:style-name="P70"><text:span text:style-name="T183"><text:tab/><text:tab/></text:span><text:span text:style-name="T184">00_iud_krypto.odp (Folie 3</text:span><text:span text:style-name="T187">2</text:span><text:span text:style-name="T184"> - 3</text:span><text:span text:style-name="T187">9</text:span><text:span text:style-name="T184">)</text:span></text:p><text:p text:style-name="P47">Mit einem Zertifikat kann man seinen öffentlichen Schlüssel ‚fälschungssicher‘ an Personen verteilen, die einem damit vertrauliche Nachrichten schicken können.</text:p><text:p text:style-name="P47">Ein Zertifikat bietet aber noch mehr Möglichkeiten:</text:p><text:p text:style-name="P48"><text:span text:style-name="T126">Immer, wenn eine elektronische Unterschrift eine Unterschrift auf Papier ersetzen soll, kann eine digitale Signatur eingesetzt werden. (</text:span><text:span text:style-name="T65">Anträge bei Behörden, </text:span><text:span text:style-name="T66">Steuererklärung beim </text:span><text:span text:style-name="T65">Finanzamt, </text:span><text:span text:style-name="T66">Firmen, die anderen Firmen Rechnungen stellen,…</text:span><text:span text:style-name="T68">)</text:span></text:p><text:p text:style-name="P48"><text:span text:style-name="T127">So verschlüsselt Frau Müller zum Beispiel ihre Steuererklärung mit dem öffentlichen Schlüssel des Finanzamts, dessen Zertifikat sie erhalten hat. Damit ist die Nachricht vertraulich und kann nicht mitgelesen werden. Aber w</text:span>ie kann <text:span text:style-name="T125">das Finanzamt sicher sein, dass die Steuererklärung tatsächlich von Frau Müller stammt?</text:span> <text:span text:style-name="T127">Dazu benötigt Frau Müller ein eigenes Zertifikat.</text:span></text:p><text:p text:style-name="P28"><text:span text:style-name="T145">A</text:span>blauf:</text:p><text:p text:style-name="P48"><draw:g text:anchor-type="paragraph" draw:z-index="47" draw:style-name="gr40"><draw:g draw:style-name="gr4"><draw:g draw:style-name="gr4"><draw:g draw:style-name="gr4"><draw:path draw:name="Form7" draw:style-name="gr20" draw:text-style-name="P144" svg:width="1.957cm" svg:height="1.271cm" draw:transform="skewX (0.141895268187139) rotate (2.6162485487395) translate (14.5624581554529cm 8.25649965821524cm)" svg:viewBox="0 0 1958 1272" svg:d="M960 1236c82 4 170-10 225-65 54-54 54-179 144-175 93 3 156-39 220-72 72-38 108-111 161-162 62-60 172 10 228-60 87-107-138-116-50-221 50-60 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(13.2926666666667cm 0.943680555555556cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:mirror-horizontal="false" draw:mirror-vertical="false" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape><draw:custom-shape draw:name="Form25" draw:style-name="gr18" draw:text-style-name="P143" svg:width="0.057cm" svg:height="0.084cm" draw:transform="rotate (1.5707963267949) translate (13.2926666666667cm 0.808861111111111cm)"><text:p/><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:mirror-horizontal="false" draw:mirror-vertical="false" draw:glue-points="10800 0 3163 3163 0 10800 3163 18437 10800 21600 18437 18437 21600 10800 18437 3163" draw:text-areas="3163 3163 18437 18437" draw:type="ellipse" draw:enhanced-path="U 10800 10800 10800 10800 0 360 Z N"/></draw:custom-shape></draw:g></draw:g></draw:g><draw:custom-shape draw:name="Form2" draw:style-name="gr67" draw:text-style-name="P155" svg:width="4.146cm" svg:height="1.128cm" svg:x="1.849cm" svg:y="0.203cm"><text:p text:style-name="P135"><text:span text:style-name="T234">Alice</text:span></text:p><text:p text:style-name="P135">Müller</text:p><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:type="rectangle" draw:enhanced-path="M 0 0 L 21600 0 21600 21600 0 21600 0 0 Z N"/></draw:custom-shape><draw:custom-shape draw:name="Form2" draw:style-name="gr68" draw:text-style-name="P155" svg:width="4.116cm" svg:height="1.128cm" svg:x="10.139cm" svg:y="0.217cm"><text:p text:style-name="P135"><text:span text:style-name="T234">Finanz-</text:span></text:p><text:p text:style-name="P135"><text:span text:style-name="T234">amt</text:span></text:p><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:type="rectangle" draw:enhanced-path="M 0 0 L 21600 0 21600 21600 0 21600 0 0 Z N"/></draw:custom-shape></draw:g></text:p><text:p text:style-name="P48"><text:span text:style-name="T128">Um Zeit zu sparen,</text:span><text:span text:style-name="T5"> wird nicht die komplette Nachricht signiert, sondern nur ein kleiner Teil, der Fingerabdruck der Nachricht. </text:span>Dazu wird mit einer Hash-Funktion ein Hash-Wert berechnet. Das ist der Fingerabdruck der Nachricht. Nur <text:span text:style-name="T216">auf </text:span>diese<text:span text:style-name="T216">n</text:span> (viel <text:span text:style-name="T76">k</text:span>leinere<text:span text:style-name="T216">n</text:span>) Hash-Wert wird <text:span text:style-name="T216">der</text:span> private Schlüssel <text:span text:style-name="T216">angewendet</text:span>. Das Ergebnis ist die Signatur. Die Signatur wird zusammen mit der Nachricht an den Empfänger geschickt. <text:span text:style-name="T77">Das Zertifikat ihres öffentlichen Schlüssels schickt Alice gleich mit. </text:span>Der Empfänger trennt die Nachricht von der Signatur. Auf die Nachricht wendet er die Hash-Funktion an und erzeugt den Fingerabdruck der Nachricht. Parallel dazu <text:span text:style-name="T216">wendet</text:span> er <text:span text:style-name="T216">den </text:span><text:soft-page-break/>öffentlichen Schlüssel <text:span text:style-name="T77">aus dem Zertifikat auf </text:span>die Signatur <text:span text:style-name="T216">an </text:span>und erhält den Fingerabdruck der Nachricht. Diese beiden Fingerabdrücke vergleicht er. <text:span text:style-name="T78">Sind sie gleich, stammt die Nachricht tatsächlich von Alice.</text:span></text:p><text:p text:style-name="P48">Die <text:span text:style-name="T42">Hashfunktion</text:span> erzeugt eine Art Fingerabdruck der eigentlichen Nachricht. <text:span text:style-name="T167">Also e</text:span>inen Text, der viel kürzer ist als die Nachricht und aus dem man die ursprüngliche Nachricht<text:span text:style-name="T75"> </text:span>nicht wieder herleiten kann. <text:span text:style-name="T16">Weiterhin ist </text:span><text:span text:style-name="T152">es nicht möglich, die Nachricht so zu verändern, dass der Hash wieder gleich ist. </text:span><text:span text:style-name="T17">(Diese Genauigkeit genügt in Klasse 10.)</text:span></text:p><text:p text:style-name="P46">In Aufgabe 1 analysieren die SuS den im Diagramm dargestellten Ablauf und bringen ihn <text:span text:style-name="T146">mit der Definition aus Wikipedia in Zusammenhang. In Teilaufgabe (d) wird das Szenario dahingehend erweitert, dass die eigentliche Nachricht zusätzlich verschlüsselt wird. Damit sind dann Authentizität und Vertraulichkeit gewährleistet.</text:span></text:p><text:p text:style-name="P50">In den Aufgaben 2-4 <text:s/>spielen die SuS die Szenarien des Signierens und <text:span text:style-name="T216">V</text:span>erschlüsselns mit den Chat-Tool durch. Zunächst ohne Zertifikat (Aufgabe 2-3), dann mit Zertifikat Aufgabe 4).</text:p><text:p text:style-name="P46"><text:span text:style-name="T146">In Aufgabe 5 wird eine</text:span><text:span text:style-name="T69"> </text:span><text:span text:style-name="T70">a</text:span><text:span text:style-name="T71">symmetrisch-symmetrisch</text:span><text:span text:style-name="T72">e </text:span><text:span text:style-name="T146">Browserkommunikation analysiert, bei der nur der Austausch eines (symmetrischen) Schlüssels asymmetrisch erfolgt (siehe Diagramm). </text:span><text:span text:style-name="T118">Alice </text:span><text:span text:style-name="T119">schickt</text:span><text:span text:style-name="T118"> </text:span><text:span text:style-name="T120">dazu </text:span><text:span text:style-name="T119">eine</text:span><text:span text:style-name="T118"> Anfrage an Bobs Internetseite, </text:span><text:span text:style-name="T120">und teilt mit, dass</text:span><text:span text:style-name="T118"> sie kommunizieren will. Bob sendet ihr sein Zertifikat. Alice Browser entschlüsselt das und merkt sich Bobs öffentlichen Schlüssel. Es wird eine Nachricht an Bob geschickt mit einem symmetrischen Schlüssel. </text:span><text:span text:style-name="T121">Die folgende Kommunikation findet mit diesem symmetrischen Schlüssel statt. Wenn die Seite verlassen wird, wird der Schlüssel wieder gelöscht.</text:span></text:p><text:p text:style-name="P115"><text:span text:style-name="T121">H</text:span><text:span text:style-name="T117">intergrund: </text:span><text:span text:style-name="T215">Hybride Verschlüsselung</text:span><text:span text:style-name="T213">:</text:span></text:p><text:p text:style-name="P108"><text:span text:style-name="T214">In der praktischen Anwendung wird das RSA-Verfahren verwendet, um einen symmetrischen Schlüssel sicher auszutauschen. Die eigentliche Verschlüsselung erfolgt dann mit einem symmetrischen Verfahren, z.B. AES.</text:span></text:p><text:p text:style-name="P106"><text:span text:style-name="T219">Solche </text:span><text:span text:style-name="T221">h</text:span>ybride Verschlüsselungsverfahren kombinieren symmetrische und asymmetrische Verschlüsselungsverfahren und nutzen so die jeweiligen Vorteile:</text:p><text:p text:style-name="P107"><text:span text:style-name="T220">Symmetrische Verschlüsselungsverfahren sind sehr schnell und eignen sich auch für große Datenmengen. Asymmetrische Verschlüsselungsverfahren sind hingegen sehr langsam und nur für kleine Datenmengen geeignet, also z.B. um einen <text:s/>Schlüssel für ein symmetrisches Verfahren zu verschlüsseln. Dafür </text:span><text:span text:style-name="T213">löst asymmetrische RSA-Verfahren das Problem des Schlüsseltauschs, das bei symmetrischen Verfahren ein Angriffspunkt ist. 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svg:x="9.192cm" svg:y="1.651cm"><draw:text-box><text:p><text:span text:style-name="T230"><text:s/></text:span><text:span text:style-name="T230">Gib mir deinen öff. 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text:style-name="P135"><text:span text:style-name="T230">Einfacher </text:span></text:p><text:p text:style-name="P135"><text:span text:style-name="T230">symmetrischer </text:span></text:p><text:p text:style-name="P135"><text:span text:style-name="T230">Schlüssel</text:span></text:p><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:text-areas="800 800 20800 20800" draw:type="round-rectangular-callout" draw:modifiers="3402.7397260274 -4661.87050359712" draw:enhanced-path="M 3590 0 X 0 3590 L ?f2 ?f3 0 8970 0 12630 ?f4 ?f5 0 18010 Y 3590 21600 L ?f6 ?f7 8970 21600 12630 21600 ?f8 ?f9 18010 21600 X 21600 18010 L ?f10 ?f11 21600 12630 21600 8970 ?f12 ?f13 21600 3590 Y 18010 0 L ?f14 ?f15 12630 0 8970 0 ?f16 ?f17 Z N"><draw:equation draw:name="f0" draw:formula="$0 -10800"/><draw:equation draw:name="f1" draw:formula="$1 -10800"/><draw:equation draw:name="f2" draw:formula="if(?f18 ,$0 ,0)"/><draw:equation draw:name="f3" draw:formula="if(?f18 ,$1 ,6280)"/><draw:equation draw:name="f4" 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draw:formula="if(?f1 ,-1,?f22 )"/><draw:equation draw:name="f36" draw:formula="if($1 ,-1,?f37 )"/><draw:equation draw:name="f37" draw:formula="if(?f0 ,?f28 ,-1)"/><draw:equation draw:name="f38" draw:formula="if($1 ,-1,?f39 )"/><draw:equation draw:name="f39" draw:formula="if(?f0 ,-1,?f28 )"/><draw:equation draw:name="f40" draw:formula="$0 "/><draw:equation draw:name="f41" draw:formula="$1 "/><draw:handle draw:handle-position="$0 $1"/></draw:enhanced-geometry></draw:custom-shape><draw:custom-shape draw:name="Form2" draw:style-name="gr89" draw:text-style-name="P155" svg:width="3.373cm" svg:height="0.909cm" svg:x="0.794cm" svg:y="0.352cm"><text:p text:style-name="P135"><text:span text:style-name="T234">Bob die Bank</text:span></text:p><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:type="rectangle" draw:enhanced-path="M 0 0 L 21600 0 21600 21600 0 21600 0 0 Z N"/></draw:custom-shape><draw:custom-shape draw:name="Form2" draw:style-name="gr89" draw:text-style-name="P155" svg:width="3.373cm" svg:height="0.909cm" svg:x="12.127cm" svg:y="0.288cm"><text:p text:style-name="P135"><text:span text:style-name="T234">Alice</text:span></text:p><draw:enhanced-geometry svg:viewBox="0 0 21600 21600" draw:type="rectangle" draw:enhanced-path="M 0 0 L 21600 0 21600 21600 0 21600 0 0 Z N"/></draw:custom-shape></draw:g>Asymmetrisch-symmetrische Browserkommunikation</text:p></draw:text-box></draw:frame><text:soft-page-break/><text:span text:style-name="T213"/></text:p><text:p text:style-name="P46"><text:span text:style-name="T101">In Aufgabe 6 informieren sich die SuS, wie ein echtes Zertifikat aussieht und recherchieren nach den einzelnen Bestandteilen. Dazu kann man sich i</text:span><text:span text:style-name="T109">m Browser</text:span><text:span text:style-name="T108"> </text:span><text:span text:style-name="T112">z.B. </text:span><text:span text:style-name="T110">Zertifikate</text:span><text:span text:style-name="T111"> </text:span><text:span text:style-name="T108">anzeigen lassen</text:span><text:span text:style-name="T111">, </text:span><text:span text:style-name="T112">die</text:span><text:span text:style-name="T111"> </text:span><text:span text:style-name="T109">der Browserhersteller</text:span><text:span text:style-name="T111"> direkt in den Browser integriert hat</text:span><text:span text:style-name="T112">. </text:span></text:p><table:table table:name="Tabelle2" table:style-name="Tabelle2"><table:table-column table:style-name="Tabelle2.A"/><table:table-column table:style-name="Tabelle2.B"/><table:table-column table:style-name="Tabelle2.C"/><table:table-row><table:table-cell table:style-name="Tabelle2.A1" office:value-type="string"><text:p text:style-name="P120"><text:span text:style-name="T95">F</text:span><text:span text:style-name="T91">irefox: </text:span></text:p><text:p text:style-name="P122">Einstellungen → Daten-schutz & Sicherheit → Sicherheit → Zertifikate → Zertifikate anzeigen.</text:p></table:table-cell><table:table-cell table:style-name="Tabelle2.A1" office:value-type="string"><text:p text:style-name="P121">Chrome: </text:p><text:p text:style-name="P124"><text:span text:style-name="T166">Je nach Version: </text:span><text:span text:style-name="T57">kleines grünes Schloss links der Adresszeile.</text:span><text:span text:style-name="T166"> Oder: </text:span><text:span text:style-name="T57">rechts der Adresszeile die drei Punkte anklicken → weitere Tools → Entwicklertools (oder F12) → </text:span><text:span text:style-name="T49">Sicherheit </text:span><text:span text:style-name="T57">→ </text:span><text:span text:style-name="T49">Zertifikat anzeigen →</text:span><text:span text:style-name="T57"> Details.</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle2.C1" office:value-type="string"><text:p text:style-name="P121">Internet Explorer: </text:p><text:p text:style-name="P123">Menü: Datei → Eigen-schaften → Zertifikate → Zertifizierungspfad → Zertifikat anzeigen → Details.</text:p></table:table-cell></table:table-row></table:table><text:p text:style-name="P42"/><text:p text:style-name="P43">Mögliche Probleme werden in Aufgabe <text:span text:style-name="T218">7</text:span> <text:span text:style-name="T174">und 8</text:span> betrachtet.</text:p><text:p text:style-name="P49">In Aufgabe <text:span text:style-name="T200">9</text:span> wird im Chat-Tool mit der Hashfunktion experimentiert <text:span text:style-name="T147">und die SuS gelangen zu folgenden Erkenntnissen:</text:span></text:p><text:list xml:id="list3163364438" text:style-name="L1"><text:list-item><text:p text:style-name="P77"><text:soft-page-break/>Der Hashwert ist immer gleich lang, unabhängig <text:span text:style-name="T147">von </text:span>der <text:span text:style-name="T147">Länge des</text:span> Ursprungstext<text:span text:style-name="T147">es</text:span>. (<text:span text:style-name="T147">B</text:span>ei der MD2(128 bits)-Variante ist er 128 Bit bzw. 16 HexZahlen lang)</text:p></text:list-item><text:list-item><text:p text:style-name="P77">Selbst wenn nur ein einzelnes Zeichen geändert wird, ändert sich der Hashwert wesentlich. (um <text:span text:style-name="T79">mindestens fast 50%)</text:span></text:p></text:list-item><text:list-item><text:p text:style-name="P119">Weil der Hashwert kürzer ist als der Ursprungstext, <text:span text:style-name="T168">muss</text:span> es zu einem Hashwert mehrere Ausgangstexte geben. </text:p></text:list-item><text:list-item><text:p text:style-name="P78">Es ist quasi unmöglich, zu einem Hashwert den Ausgangstext zu rekonstruieren.</text:p></text:list-item></text:list><text:p text:style-name="P98"><text:span text:style-name="T113"/></text:p><text:p text:style-name="ZPG_5f_Standard"><text:span text:style-name="T8">Ergänzung/</text:span><text:span text:style-name="T9">Differenzierung:</text:span></text:p><text:p text:style-name="P103"><text:span text:style-name="T170">Alternativ oder zur Differenzierung </text:span>können die SuS mit <text:span text:style-name="T170">C</text:span>ryptool experimentieren und Hashwerte erzeugen. <text:span text:style-name="T169">Eine Anleitung sowie Aufgaben findet man auf </text:span><text:span text:style-name="T113"><text:s/>inf-schule.de</text:span><text:span text:style-name="T113"><text:note text:id="ftn2" text:note-class="footnote"><text:note-citation>2</text:note-citation><text:note-body><text:p text:style-name="P102"><text:span text:style-name="T142"><text:s/></text:span><text:a xlink:type="simple" xlink:href="https://www.inf-schule.de/kommunikation/kryptologie/digitalesignatur/einstieg_hashfunktion/experimentecryptool" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T140">https://www.inf-schule.de/kommunikation/kryptologie/digitalesignatur/einstieg_hashfunktion/experimentecryptool</text:span></text:a><text:span text:style-name="T140"> </text:span><text:span text:style-name="T138">(abgerufen: 30.3.20)</text:span></text:p></text:note-body></text:note></text:span></text:p><text:p text:style-name="P99"><text:span text:style-name="T27">Ebenfalls als Differenzierung recherchieren die SuS in Aufgabe </text:span><text:span text:style-name="T30">9</text:span><text:span text:style-name="T27"> gängige Hashfunktionen und deren Algorithmen.</text:span></text:p><text:p text:style-name="ZPG_5f_Standard"><text:span text:style-name="T27">In Aufgabe </text:span><text:span text:style-name="T30">1</text:span><text:span text:style-name="T31">1</text:span><text:span text:style-name="T28"> und </text:span><text:span text:style-name="T30">1</text:span><text:span text:style-name="T31">2</text:span><text:span text:style-name="T27"> recherchieren die SuS </text:span><text:span text:style-name="T26">PGP-Systeme (pretty good privacy) </text:span><text:span text:style-name="T28">und </text:span><text:span text:style-name="T26">Web-of-Trust, das auf transitiven Vertrauensbeziehungen </text:span><text:span text:style-name="T27">der Teilnehmer </text:span><text:span text:style-name="T26">beruht. </text:span><text:span text:style-name="T29">Ausgehend davon können Vor- und Nachteile analysiert und diskutiert werden. </text:span></text:p><text:p text:style-name="P51"><text:span text:style-name="T38">Hintergrund</text:span><text:span text:style-name="T32">: </text:span></text:p><text:p text:style-name="P51"><draw:frame draw:style-name="fr2" draw:name="Rahmen2" text:anchor-type="paragraph" svg:x="6.181cm" svg:y="-0.152cm" svg:width="10.781cm" draw:z-index="43"><draw:text-box fo:min-height="11.232cm"><text:p text:style-name="P75"><draw:frame draw:style-name="fr12" draw:name="Bild3" text:anchor-type="as-char" svg:width="10.781cm" style:rel-width="100%" svg:height="11.232cm" style:rel-height="scale" draw:z-index="44"><draw:image xlink:href="Pictures/10000201000004000000042B908E839989E1431A.png" xlink:type="simple" xlink:show="embed" xlink:actuate="onLoad" loext:mime-type="image/png"/><svg:desc>gfdsgfds</svg:desc></draw:frame><text:span text:style-name="T196"><text:line-break/></text:span><text:a xlink:type="simple" xlink:href="https://commons.wikimedia.org/wiki/File:PGP_diagram_de.svg" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T139">https://commons.wikimedia.org/wiki/File:PGP_diagram_de.svg</text:span></text:a><text:span text:style-name="T139"> <text:s/></text:span><text:span text:style-name="T198"><text:s/>(16.5.20)</text:span></text:p><text:p text:style-name="P75"><text:span text:style-name="T139">Gregorerhardt / CC BY-SA (</text:span><text:a xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by-sa/4.0" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T139">https://creativecommons.org/licenses/by-sa/4.0</text:span></text:a><text:span text:style-name="T139">)</text:span></text:p><text:p text:style-name="P76"/></draw:text-box></draw:frame><text:span text:style-name="T38">Pretty Good Privacy </text:span><text:span text:style-name="T33">(PGP)</text:span></text:p><text:p text:style-name="P114"><text:span text:style-name="T180">Um Zeit und Rechenkapazität zu sparen, wird nicht die ganze Nachricht mit dem öffentlichen Schlüssel des Empfängers ver-schlüsselt. Vielmehr wird ein zufälliger symmetrischer Schlüssel erzeugt, womit die Nachricht verschlüsselt wird. Nur der symmetrische Schlüs-sel wird mit dem öffentlichen Schlüssel verschlüsselt. </text:span><text:span text:style-name="T181">Vorteile: </text:span></text:p><text:list xml:id="list194373526" text:style-name="L3"><text:list-item><text:p text:style-name="P118"><text:span text:style-name="T180">b</text:span><text:span text:style-name="T177">enötigt weniger Zeit</text:span></text:p></text:list-item><text:list-item><text:p text:style-name="P117"><text:span text:style-name="T180">weniger Rech</text:span><text:span text:style-name="T181">e</text:span><text:span text:style-name="T180">nkapazität</text:span></text:p></text:list-item><text:list-item><text:p text:style-name="P117"><text:span text:style-name="T180">geht dieselbe Nachricht an mehrere Empfänger, muss nur einmal verschlüsselt werden.</text:span></text:p></text:list-item></text:list><text:p text:style-name="P94"><text:span text:style-name="T192">Mit PGP kann man eine Nachricht nur signieren, nur verschlüsseln oder sowohl signieren als auch verschlüsseln. </text:span></text:p><text:p text:style-name="P104"><text:soft-page-break/><text:span text:style-name="T180">PGP wurde 1991</text:span><text:span text:style-name="T193"> von </text:span><text:span text:style-name="T191">Phil Zimmermann </text:span><text:span text:style-name="T192">entwickelt </text:span><text:span text:style-name="T194">und</text:span><text:span text:style-name="T192"> basiert auf dem Web of Trust. </text:span><text:span text:style-name="T36"><text:s/></text:span></text:p><text:p text:style-name="P104"><text:span text:style-name="T36"/></text:p><text:p text:style-name="P80"><text:span text:style-name="T224">Web of Trust (WOT)</text:span></text:p><text:p text:style-name="P53"><draw:frame draw:style-name="fr1" draw:name="Rahmen3" text:anchor-type="paragraph" svg:x="2.058cm" svg:y="0.039cm" svg:width="13.624cm" draw:z-index="45"><draw:text-box fo:min-height="8.047cm"><text:p text:style-name="Caption"><draw:frame draw:style-name="fr12" draw:name="Bild4" text:anchor-type="as-char" svg:width="10.58cm" style:rel-width="100%" svg:height="5.29cm" style:rel-height="scale" draw:z-index="46"><draw:image xlink:href="Pictures/100002010000050000000280BFB9E052A1161708.png" xlink:type="simple" xlink:show="embed" xlink:actuate="onLoad" loext:mime-type="image/png"/></draw:frame><text:span text:style-name="T196"><text:line-break/></text:span><text:a xlink:type="simple" xlink:href="https://commons.wikimedia.org/wiki/File:Web_of_Trust_2.svghttps://" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T139">https://commons.wikimedia.org/wiki/File:Web_of_Trust_2.svghttps://</text:span></text:a><text:a xlink:type="simple" xlink:href="https://commons.wikimedia.org/wiki/File:Web_of_Trust_2.svghttps://upload.wikimedia.org/wikipedia/commons/4/49" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T139"> <text:s text:c="3"/></text:span></text:a><text:a xlink:type="simple" xlink:href="https://commons.wikimedia.org/wiki/File:Web_of_Trust_2.svghttps://upload.wikimedia.org/wikipedia/commons/4/49" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T141">u</text:span></text:a><text:a xlink:type="simple" xlink:href="https://commons.wikimedia.org/wiki/File:Web_of_Trust_2.svghttps://upload.wikimedia.org/wikipedia/commons/4/49" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T139">pload.wikimedia.org/wikipedia/commons/4/49</text:span></text:a><text:span text:style-name="T139"> <text:s text:c="3"/>Web_of_Trust_2.svgUser:Ogmios / CC BY-SA (</text:span><text:a xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by-sa/3.0" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T139">https://creativecommons.org/licenses/by-sa/3.0</text:span></text:a><text:span text:style-name="T139">) </text:span><text:span text:style-name="T197"><text:s/></text:span><text:span text:style-name="T198">(16.5.20)</text:span></text:p></draw:text-box></draw:frame></text:p><text:p text:style-name="P52"><text:span text:style-name="T73">D</text:span><text:span text:style-name="T65">as WOT ist eine Alternative zum Prinzip der hierarchisch gegliederten Zertifizierungs-instanzen. </text:span>Die Echtheit der Schlüssel wird durch ein Netz von gegenseitigen Vertrauens-beziehungen gewährleistet: Alice vertraut Bob, ich vertraue Alice, also vertraue ich auch Bob.</text:p><text:p text:style-name="P54"><text:span text:style-name="T35">S</text:span><text:span text:style-name="T34">iehe dazu auch </text:span><text:span text:style-name="T36">Wikipedia</text:span><text:span text:style-name="T34"> </text:span><text:span text:style-name="T34"><text:note text:id="ftn3" text:note-class="footnote"><text:note-citation>3</text:note-citation><text:note-body><text:p text:style-name="P73"><text:a xlink:type="simple" xlink:href="https://de.wikipedia.org/wiki/Pretty_Good_Privacy" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T136">https://de.wikipedia.org/wiki/Pretty_Good_Privacy</text:span></text:a><text:span text:style-name="T136"> </text:span><text:span text:style-name="T137">(28.3.20)</text:span></text:p></text:note-body></text:note></text:span><text:span text:style-name="T34"><text:s/></text:span><text:span text:style-name="T34"><text:note text:id="ftn4" text:note-class="footnote"><text:note-citation>4</text:note-citation><text:note-body><text:p text:style-name="P73"><text:a xlink:type="simple" xlink:href="https://de.wikipedia.org/wiki/Web_of_Trust" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T136">https://de.wikipedia.org/wiki/Web_of_Trust</text:span></text:a><text:span text:style-name="T136"> </text:span><text:span text:style-name="T137">(28.3.20)</text:span></text:p></text:note-body></text:note></text:span><text:span text:style-name="T34"><text:s/></text:span><text:span text:style-name="T37">sowie</text:span><text:span text:style-name="T34"> inf-schule.de</text:span><text:span text:style-name="T34"><text:note text:id="ftn5" text:note-class="footnote"><text:note-citation>5</text:note-citation><text:note-body><text:p text:style-name="P74"><text:a xlink:type="simple" xlink:href="https://www.inf-schule.de/kommunikation/kryptologie/sicherheitsinfrastruktur/konzept_weboftrust" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link">https://www.inf-schule.de/kommunikation/kryptologie/sicherheitsinfrastruktur/konzept_weboftrust</text:a><text:span text:style-name="T39"> </text:span><text:span text:style-name="T40">(28.3.20)</text:span></text:p></text:note-body></text:note></text:span></text:p><text:p text:style-name="ZPG_5f_Standard"/><table:table table:name="Tabelle3" table:style-name="Tabelle3"><table:table-column table:style-name="Tabelle3.A"/><table:table-column table:style-name="Tabelle3.B"/><table:table-row><table:table-cell table:style-name="Tabelle3.A1" office:value-type="string"><text:p text:style-name="P68">Aufgabe <text:span text:style-name="T164">auf dem AB</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle3.B1" office:value-type="string"><text:p text:style-name="P68">zugehörige <text:span text:style-name="T163">Folie in der </text:span>Präsentation</text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle3.A2" office:value-type="string"><text:p text:style-name="P60">Nr. 1 <text:s/><text:span text:style-name="T199">(1 d )</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle3.B2" office:value-type="string"><text:p text:style-name="P64">3<text:span text:style-name="T225">2, </text:span>3<text:span text:style-name="T225">3</text:span> <text:span text:style-name="T199">(34)</text:span></text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle3.A2" office:value-type="string"><text:p text:style-name="P125">5</text:p></table:table-cell><table:table-cell table:style-name="Tabelle3.B2" office:value-type="string"><text:p text:style-name="P63">3<text:span text:style-name="T225">5</text:span></text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle3.A2" office:value-type="string"><text:p text:style-name="P125">6</text:p></table:table-cell><table:table-cell table:style-name="Tabelle3.B2" office:value-type="string"><text:p text:style-name="P63">3<text:span text:style-name="T225">6</text:span></text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle3.A2" office:value-type="string"><text:p text:style-name="P125">9</text:p></table:table-cell><table:table-cell table:style-name="Tabelle3.B2" office:value-type="string"><text:p text:style-name="P63"><text:span text:style-name="T225">37</text:span></text:p></table:table-cell></table:table-row><table:table-row><table:table-cell table:style-name="Tabelle3.A2" office:value-type="string"><text:p text:style-name="P66"><text:span text:style-name="T199">11</text:span>, <text:span text:style-name="T199">12</text:span></text:p></table:table-cell><table:table-cell table:style-name="Tabelle3.B2" office:value-type="string"><text:p text:style-name="P66">3<text:span text:style-name="T225">8</text:span>, 3<text:span text:style-name="T225">9</text:span></text:p></table:table-cell></table:table-row></table:table><text:p text:style-name="P11"><text:toc-mark-start text:id="IMark2177830380936" text:outline-level="1"/>Vergleich der Verfahren <text:toc-mark-end text:id="IMark2177830380936"/></text:p><text:p text:style-name="P30"><text:span text:style-name="T46">Material</text:span><text:span text:style-name="T176">: <text:s/><text:tab/></text:span><text:span text:style-name="T183">06_iud_ab_vergleich_verfahren.odt, </text:span></text:p><text:p text:style-name="P70"><text:span text:style-name="T183"><text:tab/><text:tab/>00_iud_</text:span><text:span text:style-name="T184">k</text:span><text:span text:style-name="T183">rypto.odp (</text:span><text:span text:style-name="T178">Folie </text:span><text:span text:style-name="T179">40-</text:span><text:span text:style-name="T182">42</text:span><text:span text:style-name="T178">)</text:span></text:p><text:p text:style-name="P29">Hinweis: Das Thema ist im Bildungsplan Mathematik – Mathematische Grundlagen der Kryptologie enthalten, passt aber thematisch besser an diese Stelle.</text:p><text:p text:style-name="P82">Im AB <text:span text:style-name="T58">06_iud_ab_vergleich_verfahren.odt</text:span><text:span text:style-name="T172"> </text:span>werden alle bisher kennengelernten Verschlüs-selungsverfahren gegenübergestellt und bezüglich ihrer Sicherheit bewertet.</text:p><text:p text:style-name="P82"/><text:p text:style-name="P82"/><text:p text:style-name="P82"/><text:p text:style-name="P82"/><text:p text:style-name="P79">Weitere Hinweise: </text:p><text:p text:style-name="P105"><text:span text:style-name="T91">Ein Tool, mit dem</text:span><text:span text:style-name="T98"> Sequenzdiagramme erstellt werden können (auch von SuS): </text:span><text:a xlink:type="simple" xlink:href="http://www.umletino.com/" text:style-name="Internet_20_link" text:visited-style-name="Visited_20_Internet_20_Link"><text:span text:style-name="T98">http://www.umletino.com</text:span></text:a><text:span text:style-name="T98"> </text:span><text:span text:style-name="T98"><text:note text:id="ftn0" text:note-class="footnote"><text:note-citation>6</text:note-citation><text:note-body><text:p text:style-name="P83"><text:span text:style-name="T201"><text:s text:c="2"/>zuletzt abgerufen 3.6.20</text:span></text:p></text:note-body></text:note></text:span></text:p></office:text></office:body></office:document-content> |