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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>reveal.js</title>
<link rel="stylesheet" href="css/reset.css">
<link rel="stylesheet" href="css/reveal.css">
<link rel="stylesheet" href="css/theme/black.css">
<!-- Theme used for syntax highlighting of code -->
<link rel="stylesheet" href="lib/css/monokai.css">
<!-- Printing and PDF exports -->
<script>
var link = document.createElement( 'link' );
link.rel = 'stylesheet';
link.type = 'text/css';
link.href = window.location.search.match( /print-pdf/gi ) ? 'css/print/pdf.css' : 'css/print/paper.css';
document.getElementsByTagName( 'head' )[0].appendChild( link );
</script>
</head>
<body>
<div class="reveal">
<div class="slides">
<section>
<section>
<p>How to Share a Secret</p>
<p>Adi Shamir</p>
</section>
<section>
<img data-src="./abstract.png"/>
</section>
<section>
<img data-src="./rsa.png"/>
<!-- this construction occurred shortly after publishing the rsa cryptosystem in 1977 -->
</section>
<section>
<img data-src="./adi-shamir.jpg"/>
<!-- mathematician by training -->
</section>
</section>
<section>
<section>
Threshold Scheme
</section>
<section>
<img data-src="./our-goal.png"/>
</section>
<section>
<img data-src="./cooperation.png"/>
</section>
</section>
<section>
<section>
<img height="319" width="453" data-src="./c-l-liu.png"/>
<img data-src="./eleven-scientists.png"/>
</section>
<section>
<img data-src="./3-2-key-lock-scheme.png"/>
</section>
<section>
<img data-src="./5-3-key-lock-scheme.png"/>
</section>
<section>
<img data-src="./locks-keys-formula.png"/>
</section>
<section>
<img data-src="./locks-keys-formula-example.png"/>
</section>
</section>
<section>
<section>
<img data-src="./our-scheme.png"/>
</section>
<section>
<p>k = 2</p>
</section>
<section>
<img data-src="./linear.png"/>
<p>Secret: -3</p>
</section>
<section>
<p>(1, -1)</p>
<p>(3, 3)</p>
<p>(2, 1)</p>
</section>
</section>
<section>
<section>
<img data-src="./k-1-degree-polynomial.png"/>
</section>
<section>
<p>k = 3</p>
</section>
<section>
<img data-src="./infinite-field-plot.png"/>
<p>Secret: +1</p>
</section>
<section>
<p>(2, 0)</p>
<p>(2, -3)</p>
<p>(-3, -5)</p>
<p>(3, -2)</p>
<p>(4, -5)</p>
</section>
</section>
<section>
<section>
Solving:
</section>
<section>
2 Methods:</br>Gaussian Elimination</br>Largrange Interpolation
</section>
<section>
<img data-src="./efficient-interpolation-algs.png"/>
</section>
</section>
<section>
<section>
<img data-src="./more-precisely.png"/>
</section>
<section>
<img data-src="./infinite-field-plot.png"/>
</section>
<section>
<img data-src="./pick-a-prime.png"/>
</section>
<section>
<img data-src="./finite-field-plot.png"/>
</section>
</section>
<section>
<section>
Mulitparty Computation
</section>
<section>
<img data-src="./summing-polynomials-video.png"/>
</section>
</section>
<section>
<section>
Secret Sharing vs. Multi-Signature Schemes
</section>
<section>
In MultiSig, threshold is k signatures from n distinct private keys
</section>
<section>
<p>Schnorr, 1991</p>
<img data-src="./schnorr-patent.png"/>
</section>
<section>
<p>Boneh, Lynn, Shacham (BLS), 2003</p>
<img data-src="./bls-paper.png"/>
</section>
<section>
Avoids reconstructing a single private key
</section>
<section>
Safer to use in multiple signing rounds
</section>
<section>
<p>Shamir Secret Sharing is suited for one-time key reconstruction</p>
</section>
</section>
<section>
Thanks!
</section>
</div>
</div>
<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 },
{ src: 'plugin/highlight/highlight.js', async: true }
]
});
</script>
</body>
</html>