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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/reveal.css">
<link rel="stylesheet" href="css/theme/black.css">
<!-- Theme used for syntax highlighting of code -->
<link rel="stylesheet" href="lib/css/zenburn.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>
<p>On Data Banks and Privacy Homomorphisms</p>
<p>Ronald L Rivest</p>
<p>Len Adleman</p>
<p>Michael L. Dertouzos</p>
</section>
<section>
<section>
<img src='rsa.png'/>
<!-- source: http://techdrag.blogspot.com/2010/05/famous-cryptographers-who-proposed-rsa.html -->
<small>A Method for Obtaining Digital Signatures and Public-Key Cryptosystems (ACM '78)</small>
</br>
<small>Rivest, Shamir, Adleman</small>
<aside class="notes">
While they have the ear of the entire security community,
they publish a speculative paper that outlines the basics of a technology
that still hasn't seen wide use 40 years later.
</aside>
</section>
<section>
<p>And Dertouzos!</p>
<img src="dertouzos.jpg"/>
<aside class="notes">
Berners-Lee said, "If it hadn't been for Michael, there would not probably have been a World Wide Web Consortium.
</aside>
</section>
</section>
<section>
<section>
<p>End-to-end Encryption</p>
<img src='figure1.png'/>
<p>e.g. LastPass, Apple HealthKit</p>
</section>
<section>
<q>... an information system working with encrypted data can at most
store or retrieve the data for the user</q>
</section>
</section>
<section>
<section>
Glove-box Analogy
<img src='diamond-worker.jpg'>
</section>
<section>
<span>
<img height="395" width="333" src='diamond-glove-box-with-key.png'>
<br/>
<ol>
<li class='fragment'>Alice locks diamonds in the box</li>
<li class='fragment'>Eve refines diamonds with gloves</li>
<li class='fragment'>Alice unlocks refined diamonds</li>
</ol>
</span>
</section>
</section>
<section>
<section>
Applications
</section>
<section>
Database as a Service
</section>
<section>
Machine Translation
</section>
<section>
Medical Diagnosis
</section>
<section>
<p>Secure Voting</p>
<img src='rivest-youtube.png'/>
</section>
<section>
Crowd Sourced Hedge Funds
<img src='numerai.png'/>
</sections>
</section>
</section>
<section>
<section>
<p>Homomorphic</p>
<p class='fragment'>"same shape"</p>
</section>
<section>
<pre>
<math>
f(x * y) = f(x) *' f(y)
</math>
</pre>
<p class='fragment'>f is the encryption function</p>
<p class='fragment'>* is some useful computation</p>
</section>
<section>
<img src='./commutative-diagram.png'/>
</section>
</section>
<section>
<section>
<p>RSA</p>
</section>
<section>
<!-- source: https://medium.com/oxbridge-inspire/public-key-cryptography-answers-ad3733ec4b21 -->
<img src="./pubkey.png"/>
</section>
<section>
<p>Encryption:</p>
<p>
$$c\equiv m^e \pmod n$$
</p>
<p>Decryption:</p>
<p>
$$c^d\equiv (m^e)^d\equiv m\pmod n$$
</p>
</section>
<section>
<p>RSA Homomorphism:</p>
<p>
$$(m_1 * m_2)^e = m_1^e * m_2^e$$
</p>
</section>
</section>
<section>
<section>
<p>Security Considerations</p>
</section>
<section>
<p>Binary Search with ≤</p>
<p>"most severe restriction"</p>
<img height="186" width="1158" src='fact1.png'/>
</section>
<section>
<p>Given:</p>
<p>$$Enc(x) = (-2)x$$</p>
<p>$$Enc(pt) = -8$$</p>
<p class='fragment'>$$Enc(0) ≤' Enc(pt) = 0 ≤' -8 = false$$</p>
<p class='fragment'>$$Enc(10) ≤' Enc(pt) = -20 ≤' -8 = true$$</p>
<p class='fragment'>$$Enc(5) ≤' Enc(pt) = -10 ≤' -8 = true$$</p>
<p class='fragment'>$$Enc(3) ≤' Enc(pt) = -6 ≤' -8 = false$$</p>
<p class='fragment'>∎</p>
</section>
<section>
<p>Choosen Plaintext Attack</p>
<img src="M_O_Rabin.png"/>
<img style='background:none; border:none; box-shadow:none;' src='rabin-cpa-dialogue.png'>
</section>
<section>
<p>Choosen Plaintext Attack</p>
<img src='rivest-dialogue.png'>
</section>
<section>
<p>Semantic Security</p>
<ul>
<li>Formal yet practical definition of security</li>
<li>Goldwasser, Micali (1982)</li>
<li>Measure security as computational complexity of decryption task</li>
</ul>
</section>
<section>
<ul>
<li>Textbook RSA is not semantically secure</li>
<li>Deterministic encryption schemes in general are not semantically secure</li>
</ul>
</section>
</section>
<section>
<section>
<img height="78" width="770" src='open-question.png'/>
</section>
<section>
<p>Semantically Secure Fully Homomorphic Encryption scheme</p>
<p>"Efficiently" compute any function on ciphertext</p>
<p>Gentry (2009)</p>
</section>
<section>
<h3>Limitations</h3>
<ul>
<li>Lack of Choosen Ciphertext Security</li>
<li>No Random Access</li>
<li>len(Ciphertext) >> len(Plaintext)</li>
<li>Noise growth during computation</li>
</ul>
</section>
</section>
<section>
<section>
Thanks!
</section>
<section>
<p>See Also:</p>
<ul>
<li><a href="https://www.youtube.com/watch?v=wXB-V_Keiu8">Public Key Cryptography, Art of the Problem</a></li>
<li><a href="https://crypto.stackexchange.com/questions/47512/why-plain-rsa-encryption-does-not-achieve-cpa-security">Why plain RSA encryption does not achieve CPA-security?</a></li>
<li><a href="https://crypto.stanford.edu/craig/easy-fhe.pdf">Computing Arbitrary Functions of Encrypted Data</a></li>
<li><a href="https://www.youtube.com/watch?v=xlcb_G1_rzk">Fully Homomorphic Encryption I, Shai Helevi</a></li>
</ul>
</section>
</section>
</div>
</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/math/math.js' },
{ src: 'plugin/markdown/markdown.js' },
{ src: 'plugin/notes/notes.js', async: true },
{ src: 'plugin/highlight/highlight.js', async: true, callback: function() { hljs.initHighlightingOnLoad(); } }
]
});
</script>
</body>
</html>