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<!doctype html>
<html>
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
<title>ECDSA</title>
<link rel="stylesheet" href="css/reveal.css">
<link rel="stylesheet" href="css/theme/simple.css">
<!-- Theme used for syntax highlighting of code -->
<link rel="stylesheet" href="lib/css/xcode.css">
<!-- Theme override for teachbitcoin -->
<link rel="stylesheet" href="css/teachbitcoin.css">
<!-- Google Font Roboto -->
<link href="https://fonts.googleapis.com/css?family=Open+Sans:300,400,400i,600" rel="stylesheet">
<link href="https://fonts.googleapis.com/css?family=Roboto+Mono" rel="stylesheet">
</head>
<body>
<div class="reveal">
<div class="slides">
<!-- *********** Begin: Pedersenn Commitment *********** -->
<section class = "box">
<div class = "title">
<span class = "title weight">Pedersen 承诺(commiment)</span>
</div>
<!-- Derivation Graphic -->
<img src="images/ecdsa/commitment0.svg" class = "image" style = "z-index: -1;">
<img src="images/ecdsa/commitment1.svg" class = "fragment image" style = "z-index: -1;">
<img src="images/ecdsa/commitment2.svg" class = "fragment image" style = "z-index: -1;">
<!-- 2 column container -->
<!-- 45% div for formula and curve--><!-- 45% text & bulletpoint -->
<div class = "multi_text_box_container" style = "padding: 0px 0 0 0; width: 1350px;">
<!-- 45% div for formula and curve-->
<div class = "" style = "width: 40%; font-size: 22px;">
<div style ="text-align: center;">
</div>
</div>
<!-- 45% text & bulletpoint -->
<div class = "text_box"
style = "width: 50%; font-size: 22px; margin: 60px 0 0 0">
<ul style = "margin: 0; padding: 0px; list-style-type: none;">
<li style = "font-weight: bold;">只有一个值能产生（计算出）对应的承诺：<br>这就是”绑定(binding)“</li>
<ul>
<li>一旦 <span class="inline_code">u</span> 被揭示，承诺 <span class="inline_code">C</span> 就可以被验证。</li>
<li>绑定: 对于给定的秘密 <span class="inline_code">u</span>，<span class="inline_code">C</span> 也固定。</li>
<li>信息泄漏：两个相同的值拥有相同的承诺。</li>
</ul>
<hr style = "height: 5px; visibility: hidden;">
<li style = "font-weight: bold;">随机的因素(factor)使承诺得以”隐藏(hiding)“。</li>
<ul>
<li>无论 <span class="inline_code">u</span> 的值如何，拥有不同的承诺。</li>
<li>假设不知道点 <span class="inline_code">H</span> 的生成元(generator)。</li>
</ul>
<hr style = "height: 5px; visibility: hidden;">
<li style = "font-weight: bold;">被破坏的承诺概形(commitment scheme):</li>
<ul>
<li>点 <span class="inline_code">H</span> 的生成元 <span class="inline_code">e</span> 被知道了。</li>
<li><span class="inline_code">u</span> 得值可被修改，承诺仍然不变。</li>
</ul>
</div>
</div><!-- End of 2 column container -->
</section>
<!-- *********** END: Pedersen Commitment *********** -->
<!-- *********** Begin: ecdsa *********** -->
<section class = "box">
<div class = "title">
<span class = "title weight">椭圆曲线数字签名算法(ECDSA)</span>
</div>
<!-- Derivation Graphic -->
<img src="images/ecdsa/ecdsa0.svg" class = "image" style = "z-index: -1;">
<img src="images/ecdsa/ecdsa1.svg" class = "fragment image" style = "z-index: -1;">
<!-- 2 column container -->
<!-- 45% div for formula and curve--><!-- 45% text & bulletpoint -->
<div class = "multi_text_box_container" style = "padding: 0px 0 0 0; width: 1350px;">
<!-- 45% div for formula and curve-->
<div class = "" style = "width: 40%; font-size: 22px;">
<div style ="text-align: center;">
</div>
</div>
<!-- 45% text & bulletpoint -->
<div class = "text_box"
style = "width: 50%; font-size: 22px; margin: 60px 0 0 0">
<ul style = "margin: 0; padding: 0px; list-style-type: none;">
<li style = "font-weight: bold;">ECDSA 可以看作一个只能被秘密`e`的拥有者“破坏”的承诺概形。</li>
<hr style = "height: 5px; visibility: hidden;">
<li style = "font-weight: bold;">R 点:</li>
<ul>
<li>随机点 (盲化blinding).</li>
<li><span class="inline_code">R</span> 点的 x-坐标在等式左&右边的都有被表现。</li>
<li>只对于秘密 <span class="inline_code">e</span>等式才能达到平衡。</li>
</ul>
<hr style = "height: 5px; visibility: hidden;">
<li style = "font-weight: bold;">已签名的消息 z:</li>
<ul>
<li>对于一个给定的随机点 <span class="inline_code">R</span>，<span class="inline_code">z</span> 向等式的左边承诺。</li>
</ul>
<hr style = "height: 5px; visibility: hidden;">
<li style = "font-weight: bold;">ECDSA 验证：</li>
<ul>
<li>需要 <span class="inline_code">z</span>, <span class="inline_code">r_x</span>, <span class="inline_code">s</span> 和公钥 <span class="inline_code">P</span> 来验证签名。</li>
</ul>
</div>
</div><!-- End of 2 column container -->
</section>
<!-- *********** END: ecdsa *********** -->
<!-- *********** Begin: DER encoding *********** -->
<section class = "box">
<div class = "title">
<span class = "title weight">DER 编码</span>
</div>
<!-- Derivation Graphic -->
<img src="images/ecdsa/der_encoding.svg" class = "image" style = "z-index: -1;">
<!-- 2 column container -->
<!-- 45% div for formula and curve--><!-- 45% text & bulletpoint -->
<div class = "multi_text_box_container" style = "padding: 0px 0 0 0; width: 1350px;">
<!-- 45% div for formula and curve-->
<div class = "" style = "width: 40%; font-size: 22px;">
<div style ="text-align: center;">
</div>
</div>
<!-- 45% text & bulletpoint -->
<div class = "text_box"
style = "width: 50%; font-size: 22px; margin: 60px 0 0 0">
<ul style = "margin: 0; padding: 0px; list-style-type: none;">
<li style = "font-weight: bold;">libsecp256k1 代替 OpenSSL</li>
<ul>
<li>OpenSSL 的问题在于不同系统间编码可能不同。</li>
<li>libsecp256k1 解决了这个系统依赖性的问题。</li>
</ul>
<hr style = "height: 5px; visibility: hidden;">
<li style = "font-weight: bold;">严格的编码 (BIP66)</li>
<ul>
<li>移除了编码的可变性：共识层强制执行的编码标准。</li>
<li>移除了 ECDSA 的可变性：强制使用较小的 s 的值。</li>
</ul>
<hr style = "height: 5px; visibility: hidden;">
<li style = "font-weight: bold;">DER 签名大小为 70-72 字节。</li>
<ul>
<li>r_x 的长度: 32/33 字节</li>
<ul>
<li>有符号 256-位，无前导空位。</li>
</ul>
<li>s 的长度: 31/32 字节</li>
<ul>
<li>强制使用较小的 s，无前导空位。</li>
</ul>
</ul>
</div>
</div><!-- End of 2 column container -->
</section>
<!-- *********** END: ecdsa *********** -->
</div><!-- END: Lecture Materials Div -->
</div><!-- END: Reveal Div -->
<script src="lib/js/head.min.js"></script>
<script src="js/reveal.js"></script>
<script>
// More info about config & dependencies:
// - https://github.com/hakimel/reveal.js#configuration
// - https://github.com/hakimel/reveal.js#dependencies
Reveal.initialize({
dependencies: [
{ src: 'plugin/markdown/marked.js' },
{ src: 'plugin/markdown/markdown.js' },
{ src: 'plugin/notes/notes.js', async: true },
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// { src: 'plugin/math/math.js', async: true }
],
// math: {
// mathjax: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js',
// config: 'TeX-AMS_HTML-full' // See http://docs.mathjax.org/en/latest/config-files.html
// },
previewLinks: false,
// Push each slide change to the browser history
history: true,
// Enable keyboard shortcuts for navigation
keyboard: true,
// Enables touch navigation on devices with touch input
overview: false,
touch: false,
// The "normal" size of the presentation, aspect ratio will be preserved
// when the presentation is scaled to fit different resolutions. Can be
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width: 1366,
height: 768,
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margin: 0.05,
// Bounds for smallest/largest possible scale to apply to content
minScale: 0.2,
maxScale: 1.5
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Reveal.configure({ slideNumber: false });
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</body>
</html>