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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
<meta name="viewport" content="width=1024, user-scalable=no">
<title>Diffie-Hellmann for Everyone</title>
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</style>
</head>
<body>
<div class="deck-container">
<!-- <img class="logo" src="resources/img/logo.png" /> -->
<div class="deck-loading-splash" style="background: green; font-size: 30px; font-family: Arial;">
Securing The Cyber...
</div>
<section class="slide">
<h1>Das "S" in HTTPS</h1>
<a href="resources/img/DH-Form.odt" style="float: right;">(Die Formulare)</a>
</section>
<section class="slide intro">
<canvas class="content"></canvas>
</section>
<section class="slide">
<h2>Ausgangs-Situation</h2>
<ul>
<li>Der gemeinsame Schlüssel darf nicht über die Leitung gehen <span class="idee__plain">weil HTTP ein Plaintext-Protokoll ist</span>
</li>
<div class="anim-show slide" data-what=".idee__plain"></div>
<li class="slide"><img src="resources/img/wireshark-plaintext.png"/></li>
<li class="slide">es reicht, wenn ebay und ich uns auf den gleichen Schlüssel einigen</li>
<li class="slide">auch wenn wir auf verschiedenen Wegen zum selben Ziel kommen</li>
<li class="slide">Das Ziel ist ein sicherer Kanal, nicht die Authentifizierung von ebay oder mir - dazu
werden
Zertifikate benutzt
</li>
</ul>
</section>
<section class="slide">
<h2>Grundidee von Diffie-Hellmann</h2>
<blockquote cite="http://example.org">
<p>Wir benutzen einfach eine Funktion, die zwei Sachen kann:</p>
<ol>
<li class="slide">In die eine Richtung ist sie einfach, in die andere Richtung sehr, sehr schwer
(Einweg-Funktion)
</li>
<li class="slide">Wer von uns sie zuerst ausführt ist egal, solange beide sie ausführen (kommutativ)
</li>
</ol>
<p><cite>Whitfield Diffie und Martin Hellmann 1976</cite></p>
</blockquote>
</section>
<section class="slide">
<h1>$$f(a) = g^a\:mod\:p$$</h1>
</section>
<section class="slide">
<h2>Einwegfunktion: Potenzrechnung mit Modulo</h2>
<h3>Modulo: Teilen mit Rest</h3>
<div class="slide">$$4\:mod\:3 = 1$$</div>
<div class="slide">$$5\:mod\:3 = 2$$</div>
<div class="slide">$$6\:mod\:3 = 0$$</div>
<div class="slide">$$7\:mod\:3 = 1$$</div>
<div class="slide">$$8\:mod\:3 = 2$$</div>
</section>
<section class="slide">
<h2>Einwegfunktion: Potenzrechnung mit Modulo</h2>
<h3>Modulo: Teilen mit Rest</h3>
<div class="modulo_11">
<div class="centered">$\mathbb Z_{/ 11}$</div>
<div class="mod deg0">2</div>
<div class="mod deg32">3</div>
<div class="mod deg64">4</div>
<div class="mod deg96">5</div>
<div class="mod deg128">6</div>
<div class="mod deg160">7</div>
<div class="mod deg192">8</div>
<div class="mod deg224">9</div>
<div class="mod deg256">10</div>
<div class="mod deg288">0</div>
<div class="mod deg320">1</div>
</div>
<div class="anim-addclass slide" data-what=".deg160" data-class="highlight"></div>
<div class="anim-removeclass slide anim-continue" data-what=".deg160" data-class="highlight"></div>
<div class="anim-addclass slide" data-what=".deg192" data-class="highlight"></div>
<div class="anim-removeclass slide anim-continue" data-what=".deg192" data-class="highlight"></div>
<div class="anim-addclass slide" data-what=".deg224" data-class="highlight"></div>
<div class="anim-removeclass slide anim-continue" data-what=".deg224" data-class="highlight"></div>
<div class="anim-addclass slide" data-what=".deg256" data-class="highlight"></div>
<div class="anim-removeclass slide anim-continue" data-what=".deg256" data-class="highlight"></div>
<div class="anim-addclass slide" data-what=".deg288" data-class="highlight"></div>
<div class="anim-removeclass slide anim-continue" data-what=".deg288" data-class="highlight"></div>
<div class="anim-addclass slide" data-what=".deg320" data-class="highlight"></div>
</section>
<section class="slide exponential">
<canvas class="content"></canvas>
</section>
<section class="slide">
<h1>$$f(a) = g^a\:mod\:p$$</h1>
</section>
<section class="slide">
<h2>Potenzrechnung</h2>
<div class="slide">$$8^2\:=\:8\:*\:8$$</div>
<div class="slide">$$8^3\:=\:8\:*\:8\:*\:8$$</div>
<div class="slide">$$8^4\:=\:8\:*\:8\:*\:8\:*\:8$$</div>
</section>
<section class="slide kommutativ">
<h2>Kommutativ</h2>
<div class="slide">$$8^{2^4}\:=$$</div>
<div class="slide">$$8^2\:*\:8^2\:*\:8^2\:*\:8^2\:=$$</div>
<div class="slide">$$(8*8)\:*\:(8*8)\:*\:(8*8)\:*\:(8*8)\:=$$</div>
<div class="slide">$$8*8\:*\:8*8\:*\:8*8\:*\:8*8\:=$$</div>
<div class="slide">$$(8*8*8*8)\:*\:(8*8*8*8)\:=$$</div>
<div class="slide">$$8^4\:*\:8^4\:=$$</div>
<div class="slide">$$8^{4^2}$$</div>
</section>
<section class="slide kommutativ">
<h2>Kommutativ</h2>
<h3 class="kommutativ_formula">$ 3^{\color{blue} 4\color{black}^{\color{green}5}}\color{black}$
<span class="kommutativ_2">$= 3^{\color{blue} 4\color{black}* \color{green}5}\color{black}$</span>
<span class="kommutativ_3">$==3^{\color{green}5\color{black}* \color{blue} 4}\color{black}$</span>
<span class="kommutativ_4">$= 3^{\color{green}5\color{black}^{\color{blue} 4}}\color{black}$</span>
</h3>
<div class="anim-show slide" data-what=".kommutativ_2"></div>
<div class="anim-show slide" data-what=".kommutativ_3"></div>
<div class="anim-show slide" data-what=".kommutativ_4"></div>
<div class="slide kommutativ_head">
<span class="left">ALICE (4)</span>
<span class="right">BOB (5)</span>
</div>
<div class="kommutativ_original">
<span class="alice left">$3^{\color{blue} 4}$</span>
<span class="bob right">$3^{\color{green}5}$</span>
<div class="anim-show slide" data-what=".alice"></div>
<div class="anim-show slide" data-what=".bob"></div>
</div>
<div class="kommutativ_double">
<span class="bob hidden right">$3^{\color{green} 5}$</span>
<span class="alice hidden left">$3^{\color{blue} 4}$</span>
<div class="anim-removeclass slide anim-continue" data-what=".kommutativ_double .alice"
data-class="hidden"></div>
<div class="anim-removeclass slide anim-continue" data-what=".kommutativ_double .alice"
data-class="left"></div>
<div class="anim-addclass slide anim-continue" data-what=".kommutativ_double .alice"
data-class="right"></div>
<div class="anim-removeclass slide anim-continue" data-what=".kommutativ_double .bob"
data-class="hidden"></div>
<div class="anim-removeclass slide anim-continue" data-what=".kommutativ_double .bob"
data-class="right"></div>
<div class="anim-addclass slide anim-continue" data-what=".kommutativ_double .bob" data-class="left"></div>
<div class="anim-addclass slide" data-what=".kommutativ_double" data-class="down"></div>
</div>
<div class="kommutativ_final">
<span class="bob hidden left">$3^{\color{green}5\color{black}^{\color{blue} 4}}\color{black}$</span>
<span class="equals hidden center">$==$</span>
<span class="alice hidden right">$3^{\color{blue} 4\color{black}^{\color{green}5}}\color{black}$</span>
<div class="anim-addclass slide anim-continue" data-what=".kommutativ_double .alice"
data-class="hidden"></div>
<div class="anim-addclass slide anim-continue" data-what=".kommutativ_double .bob"
data-class="hidden"></div>
<div class="anim-removeclass slide anim-continue" data-what=".kommutativ_final .alice"
data-class="hidden"></div>
<div class="anim-removeclass slide" data-what=".kommutativ_final .bob" data-class="hidden"></div>
<div class="anim-removeclass slide" data-what=".kommutativ_final .equals" data-class="hidden"></div>
</div>
</section>
<section class="slide">
<h1>$$f(a) = g^a\:mod\:p$$</h1>
</section>
<section class="slide">
<h2>Taschenrechner</h2>
<div class="theCalculator">
<p class="link">https://halfdane.github.io/diffie_hellman/calc.html</p>
<p class="link">https://tinyurl.com/y4mua3o8</p>
<p><img src="resources/img/qrcode.png"/></p>
</div>
</section>
<section class="slide">
<h2>Selber machen</h2>
<div class="formulare">
<img class="form left" src="resources/img/DH-Form.png">
<img class="form right" src="resources/img/DH-Form.png">
</div>
</section>
<section class="slide">
<h1>Elliptische Kurven</h1>
</section>
<section class="slide elliptic2">
<div class="jxgbox content"></div>
</section>
<section class="slide">
<h1>Danke</h1>
</section>
<section class="slide">
<h1>Fragen?</h1>
</section>
<section class="slide">
<h2>Lizenz</h2>
<a rel="license" href="http://creativecommons.org/licenses/by/4.0/">
<img alt="Creative Commons Lizenzvertrag"
style="border-width:0"
src="https://i.creativecommons.org/l/by/4.0/88x31.png"/></a>
<span>Dieses
Werk ist lizenziert unter einer <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">Creative
Commons Namensnennung 4.0 International Lizenz</a>.
Zuschreibung bitte durch einen Link auf <a href="https://github.com/halfdane/diffie_hellman">https://github.com/halfdane/diffie_hellman</a>.
</span>
<h2>Referenzen</h2>
<ul>
<li>Diese Präsentation
<ul>
<li>https://halfdane.github.io/diffie_hellman/</li>
<li>https://tinyurl.com/yyobmbo8</li>
</ul>
</li>
<li>Github Repo
<ul>
<li>https://github.com/halfdane/diffie_hellman</li>
<li>https://tinyurl.com/y6hxpvnv</li>
</ul>
</li>
<li>RFCs
<ul>
<li>2409: The Internet Key Exchange</li>
<li>3526: More Modular Exponential Diffie-Hellman groups</li>
</ul>
</li>
<li>Mehr
<ul>
<li>
https://arstechnica.com/information-technology/2013/10/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/
</li>
<li>
https://www.golem.de/news/dsa-diffie-hellman-primzahlen-koennen-hintertuer-enthalten-1610-123778.html
</li>
<li>https://jsxgraph.uni-bayreuth.de/wp/index.html</li>
</ul>
</li>
</ul>
</section>
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