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Succinct LWE Sampling, Random Polynomials, and Obfuscation
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We then present a candidate LWE sampler whose security is related to the hardness of solving systems of polynomial equations. Our construction improves on the recent iO candidate of Wee and Wichs (Eurocrypt 2021) in two ways: first, we show that a much weaker and simpler notion of LWE sampling suffices for iO; and secondly, our candidate LWE sampler is secure based on a compactly specified and falsifiable assumption about random polynomials, with a simple error distribution that facilitates cryptanalysis." /> <meta property="article:section" content="" /> <meta property="article:modified_time" content="2021-10-18T17:22:00+00:00" /> <meta property="article:published_time" content="2021-09-20T10:56:36+00:00" /> <meta property="article:tag" content="Indistinguishability Obfuscation" /> <meta property="article:tag" content="Learning with Errors" /> <meta property="article:tag" content="LWE sampling" /> </head> <body> <noscript> <h1 class="text-center">What a lovely hat</h1> <h4 class="text-center">Is it made out of <a href="https://iacr.org/tinfoil.html">tin foil</a>?</h4> </noscript> <div class="fixed-top" 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class="col-md-7 col-lg-8 pe-md-5"> <h4>Paper 2021/1226</h4> <h3 class="mb-3">Succinct LWE Sampling, Random Polynomials, and Obfuscation</h3> <p class="fst-italic mb-3"> Lalita Devadas, Willy Quach, Vinod Vaikuntanathan, Hoeteck Wee, and Daniel Wichs </p> <h5 class="mt-3">Abstract</h5> <p style="white-space: pre-wrap;">We present a construction of indistinguishability obfuscation (iO) that relies on the learning with errors (LWE) assumption together with a new notion of succinctly sampling pseudo-random LWE samples. We then present a candidate LWE sampler whose security is related to the hardness of solving systems of polynomial equations. Our construction improves on the recent iO candidate of Wee and Wichs (Eurocrypt 2021) in two ways: first, we show that a much weaker and simpler notion of LWE sampling suffices for iO; and secondly, our candidate LWE sampler is secure based on a compactly specified and falsifiable assumption about random polynomials, with a simple error distribution that facilitates cryptanalysis.</p> </div> <div id="metadata" class="col-md-5 col-lg-4 ps-md-5 mt-4 mt-md-0"> <h5>Metadata</h5> <dl> <dt> Available format(s) </dt> <dd> <a class="btn btn-sm btn-outline-dark" href="/2021/1226.pdf"> <img class="icon" src="/img/file-pdf.svg">PDF</a> </dd> <dt>Publication info</dt> <dd>A major revision of an IACR publication in TCC 2021</dd> <dt>Keywords</dt> <dd class="keywords"><a href="/search?q=Indistinguishability%20Obfuscation" class="me-2 badge bg-secondary keyword">Indistinguishability Obfuscation</a><a href="/search?q=Learning%20with%20Errors" class="me-2 badge bg-secondary keyword">Learning with Errors</a><a href="/search?q=LWE%20sampling" class="me-2 badge bg-secondary keyword">LWE sampling</a></dd> <dt>Contact author(s)</dt> <dd><span class="font-monospace"> lali<span class="obfuscate"> @ </span>mit edu<br>quach w<span class="obfuscate"> @ </span>northeastern edu<br>vinodv<span class="obfuscate"> @ </span>mit edu<br>hoeteck<span class="obfuscate"> @ </span>alum mit edu<br>wichs<span class="obfuscate"> @ </span>ccs neu edu </span> </dd> <dt>History</dt> <dd>2021-10-18: revised</dd> <dd>2021-09-20: received</dd> <dd><a rel="nofollow" href="/archive/versions/2021/1226">See all versions</a></dd> <dt>Short URL</dt> <dd><a href="https://ia.cr/2021/1226">https://ia.cr/2021/1226</a></dd> <dt>License</dt> <dd><a rel="license" target="_blank" href="https://creativecommons.org/licenses/by/4.0/"> <img class="licenseImg" src="/img/license/CC_BY.svg" alt="Creative Commons Attribution" title="Creative Commons Attribution"><br> <small>CC BY</small> </a> </dd> </dl> </div> </div> <p class="mt-4"><strong>BibTeX</strong> <button id="bibcopy" class="ms-2 btn btn-sm btn-outline-dark" aria-label="Copy to clipboard" onclick="copyBibtex()"> <img src="/img/copy-outline.svg" class="icon">Copy to clipboard</button></p> <pre id="bibtex"> @misc{cryptoeprint:2021/1226, author = {Lalita Devadas and Willy Quach and Vinod Vaikuntanathan and Hoeteck Wee and Daniel Wichs}, title = {Succinct {LWE} Sampling, Random Polynomials, and Obfuscation}, howpublished = {Cryptology {ePrint} Archive, Paper 2021/1226}, year = {2021}, url = {https://eprint.iacr.org/2021/1226} } </pre> <script> var bibcopy; function triggerTooltip() { console.log('setting tooltip'); } window.onload = triggerTooltip; function copyBibtex() { let range = document.createRange(); range.selectNode(document.getElementById('bibtex')); window.getSelection().removeAllRanges(); window.getSelection().addRange(range); document.execCommand('copy'); window.getSelection().removeAllRanges(); let bibcopy = document.getElementById('bibcopy'); let copyTooltip = new bootstrap.Tooltip(bibcopy, {trigger: 'manual', title: 'Copied!'}); copyTooltip.show(); setTimeout(function() { copyTooltip.dispose(); }, 2000); } </script> </main> <div class="container-fluid mt-auto" id="eprintFooter"> <a href="https://iacr.org/"> <img id="iacrlogo" src="/img/iacrlogo_small.png" class="img-fluid d-block mx-auto" alt="IACR Logo"> </a> <div class="colorDiv"></div> <div class="alert alert-success w-75 mx-auto"> Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content. </div> </div> <script src="/css/bootstrap/js/bootstrap.bundle.min.js"></script> <script> var topNavbar = document.getElementById('topNavbar'); if (topNavbar) { document.addEventListener('scroll', function(e) { if (window.scrollY > 100) { topNavbar.classList.add('scrolled'); } else { topNavbar.classList.remove('scrolled'); } }) } </script> </body> </html>