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Bernstein</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 18 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-18" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">18 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%A7%D9%86%D9%8A%D9%8A%D9%84_%D9%8A%D9%88%D9%84%D9%8A%D9%88%D8%B3_%D8%A8%D9%8A%D8%B1%D9%86%D8%B4%D8%AA%D8%A7%D9%8A%D9%86" title="دانييل يوليوس بيرنشتاين – Arabic" lang="ar" hreflang="ar" data-title="دانييل يوليوس بيرنشتاين" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AF%D9%86%DB%8C%D9%84_%D8%A8%D8%B1%D9%86%D8%B4%D8%AA%D8%A7%DB%8C%D9%86" title="دنیل برنشتاین – South Azerbaijani" lang="azb" hreflang="azb" data-title="دنیل برنشتاین" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Daniel_J._Bernstein" title="Daniel J. Bernstein – Danish" lang="da" hreflang="da" data-title="Daniel J. Bernstein" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Daniel_J._Bernstein" title="Daniel J. Bernstein – German" lang="de" hreflang="de" data-title="Daniel J. Bernstein" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Daniel_J._Bernstein" title="Daniel J. Bernstein – Spanish" lang="es" hreflang="es" data-title="Daniel J. Bernstein" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D9%86%DB%8C%D9%84_%D8%A8%D8%B1%D9%86%D8%B4%D8%AA%D8%A7%DB%8C%D9%86" title="دنیل برنشتاین – Persian" lang="fa" hreflang="fa" data-title="دنیل برنشتاین" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Daniel_J._Bernstein" title="Daniel J. Bernstein – French" lang="fr" hreflang="fr" data-title="Daniel J. Bernstein" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8C%80%EB%8B%88%EC%96%BC_J._%EB%B2%88%EC%8A%A4%ED%83%80%EC%9D%B8" title="대니얼 J. 번스타인 – Korean" lang="ko" hreflang="ko" data-title="대니얼 J. 번스타인" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Daniel_J._Bernstein" title="Daniel J. Bernstein – Italian" lang="it" hreflang="it" data-title="Daniel J. Bernstein" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Daniel_Bernstein" title="Daniel Bernstein – Haitian Creole" lang="ht" hreflang="ht" data-title="Daniel Bernstein" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AF%D8%A7%D9%86%D9%8A%D9%8A%D9%84_%D9%8A%D9%88%D9%84%D9%8A%D9%88%D8%B3_%D8%A8%D9%8A%D8%B1%D9%86%D8%B4%D8%AA%D8%A7%D9%8A%D9%86" title="دانييل يوليوس بيرنشتاين – Egyptian Arabic" lang="arz" hreflang="arz" data-title="دانييل يوليوس بيرنشتاين" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Daniel_J._Bernstein" title="Daniel J. Bernstein – Dutch" lang="nl" hreflang="nl" data-title="Daniel J. Bernstein" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%80%E3%83%8B%E3%82%A8%E3%83%AB%E3%83%BB%E3%83%90%E3%83%BC%E3%83%B3%E3%82%B9%E3%82%BF%E3%82%A4%E3%83%B3" title="ダニエル・バーンスタイン – Japanese" lang="ja" hreflang="ja" data-title="ダニエル・バーンスタイン" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Daniel_J._Bernstein" title="Daniel J. Bernstein – Uzbek" lang="uz" hreflang="uz" data-title="Daniel J. Bernstein" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Daniel_J._Bernstein" title="Daniel J. Bernstein – Polish" lang="pl" hreflang="pl" data-title="Daniel J. Bernstein" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Daniel_J._Bernstein" title="Daniel J. Bernstein – Swedish" lang="sv" hreflang="sv" data-title="Daniel J. Bernstein" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B0%D0%BD%D1%96%D0%B5%D0%BB%D1%8C_%D0%94%D0%B6%D1%83%D0%BB%D1%96%D1%83%D1%81_%D0%91%D0%B5%D1%80%D0%BD%D1%88%D1%82%D0%B0%D0%B9%D0%BD" title="Даніель Джуліус Бернштайн – Ukrainian" lang="uk" hreflang="uk" data-title="Даніель Джуліус Бернштайн" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%B8%B9%E5%B0%BC%E5%B0%94%C2%B7J%C2%B7%E4%BC%AF%E6%81%A9%E6%96%AF%E5%9D%A6" title="丹尼尔·J·伯恩斯坦 – Chinese" lang="zh" hreflang="zh" data-title="丹尼尔·J·伯恩斯坦" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">American mathematician, cryptologist and computer scientist (born 1971)</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the American businessman and activist, see <a href="/wiki/Daniel_J._Bernstein_(businessman)" title="Daniel J. Bernstein (businessman)">Daniel J. Bernstein (businessman)</a>.</div><style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Daniel J. Bernstein</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Dan_Bernstein_27C3.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Dan_Bernstein_27C3.jpg/220px-Dan_Bernstein_27C3.jpg" decoding="async" width="220" height="330" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Dan_Bernstein_27C3.jpg/330px-Dan_Bernstein_27C3.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Dan_Bernstein_27C3.jpg/440px-Dan_Bernstein_27C3.jpg 2x" data-file-width="2856" data-file-height="4288" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none"> (<span class="bday">1971-10-29</span>) </span>October 29, 1971<span class="noprint ForceAgeToShow"> (age 53)</span><br /><div style="display:inline" class="birthplace"><a href="/wiki/East_Patchogue,_New_York" title="East Patchogue, New York">East Patchogue, New York</a><sup id="cite_ref-cv_1-0" class="reference"><a href="#cite_note-cv-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></div></td></tr><tr><th scope="row" class="infobox-label">Citizenship</th><td class="infobox-data category"><a href="/wiki/Americans" title="Americans">American</a>, <a href="/wiki/Germans" title="Germans">German</a><sup id="cite_ref-cv_1-1" class="reference"><a href="#cite_note-cv-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/University_of_California,_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a> (<a href="/wiki/PhD" class="mw-redirect" title="PhD">PhD</a>)<br /><a href="/wiki/New_York_University" title="New York University">New York University</a> (<a href="/wiki/Bachelor_of_Arts" title="Bachelor of Arts">BA</a>)</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Qmail" title="Qmail">qmail</a>, <a href="/wiki/Djbdns" title="Djbdns">djbdns</a>, <a href="/wiki/Salsa20" title="Salsa20">Salsa20</a>, <a href="/wiki/ChaCha20" class="mw-redirect" title="ChaCha20">ChaCha20</a>, <a href="/wiki/Poly1305" title="Poly1305">Poly1305</a>, <a href="/wiki/Curve25519" title="Curve25519">Curve25519</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a>, <a href="/wiki/Cryptography" title="Cryptography">Cryptography</a>,<br /><a href="/wiki/Computer_Security" class="mw-redirect" title="Computer Security">Computer Security</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/University_of_Illinois_at_Chicago" class="mw-redirect" title="University of Illinois at Chicago">University of Illinois at Chicago</a>, <a href="/wiki/Eindhoven_University_of_Technology" title="Eindhoven University of Technology">Eindhoven University of Technology</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Hendrik_Lenstra" title="Hendrik Lenstra">Hendrik Lenstra</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th scope="row" class="infobox-label">Website</th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="https://cr.yp.to/djb.html">cr<wbr />.yp<wbr />.to<wbr />/djb<wbr />.html</a></span></td></tr></tbody></table> <p><b>Daniel Julius Bernstein</b> (sometimes known as <b>djb</b>; born October 29, 1971) is an American <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>, <a href="/wiki/Cryptologist" class="mw-redirect" title="Cryptologist">cryptologist</a>, and <a href="/wiki/Computer_scientist" title="Computer scientist">computer scientist</a>. He was a <a href="/wiki/Visiting_professor" class="mw-redirect" title="Visiting professor">visiting professor</a> at CASA<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> at <a href="/wiki/Ruhr_University_Bochum" title="Ruhr University Bochum">Ruhr University Bochum</a> until 2024<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>, as well as a <a href="/wiki/Research_professor" class="mw-redirect" title="Research professor">research professor</a> of Computer Science at the <a href="/wiki/University_of_Illinois_at_Chicago" class="mw-redirect" title="University of Illinois at Chicago">University of Illinois at Chicago</a>. Before this, he was a visiting professor in the department of mathematics and computer science at the <a href="/wiki/Eindhoven_University_of_Technology" title="Eindhoven University of Technology">Eindhoven University of Technology</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2023)">citation needed</span></a></i>]</sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Early_life">Early life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Daniel_J._Bernstein&action=edit&section=1" title="Edit section: Early life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bernstein attended <a href="/wiki/Bellport_High_School" title="Bellport High School">Bellport High School</a>, a public high school on <a href="/wiki/Long_Island" title="Long Island">Long Island</a>, graduating in 1987 at the age of 15.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The same year, he ranked fifth in the <a href="/wiki/Westinghouse_Science_Talent_Search" class="mw-redirect" title="Westinghouse Science Talent Search">Westinghouse Science Talent Search</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In 1987 (at the age of 16), he achieved a Top 10 ranking in the <a href="/wiki/William_Lowell_Putnam_Mathematical_Competition" title="William Lowell Putnam Mathematical Competition">William Lowell Putnam Mathematical Competition</a>,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> and was a member of the second-place team from <a href="/wiki/Princeton_University" title="Princeton University">Princeton University</a> the following year.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Bernstein earned a B.A. in mathematics from <a href="/wiki/New_York_University" title="New York University">New York University</a> (1991) and a Ph.D. in mathematics from the <a href="/wiki/University_of_California,_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a> (1995), where he studied under <a href="/wiki/Hendrik_Lenstra" title="Hendrik Lenstra">Hendrik Lenstra</a>.<sup id="cite_ref-cv_1-2" class="reference"><a href="#cite_note-cv-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Bernstein_v._United_States"><i><a href="/wiki/Bernstein_v._United_States" title="Bernstein v. United States">Bernstein v. United States</a></i></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Daniel_J._Bernstein&action=edit&section=2" title="Edit section: Bernstein v. United States"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Export_of_cryptography_from_the_United_States" title="Export of cryptography from the United States">export of cryptography from the United States</a> was controlled as a <a href="/wiki/Munition" class="mw-redirect" title="Munition">munition</a> starting from the <a href="/wiki/Cold_War" title="Cold War">Cold War</a> until recategorization in 1996, with further relaxation in the late 1990s.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> In 1995, Bernstein brought the court case <i><a href="/wiki/Bernstein_v._United_States" title="Bernstein v. United States">Bernstein v. United States</a></i>. The ruling in the case declared that software was <a href="/wiki/Protected_speech" class="mw-redirect" title="Protected speech">protected speech</a> under the <a href="/wiki/First_Amendment_to_the_United_States_Constitution" title="First Amendment to the United States Constitution">First Amendment</a>, which contributed to regulatory changes reducing controls on encryption.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Bernstein was originally represented by the <a href="/wiki/Electronic_Frontier_Foundation" title="Electronic Frontier Foundation">Electronic Frontier Foundation</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> He later <a href="/wiki/Pro_se_legal_representation_in_the_United_States" title="Pro se legal representation in the United States">represented himself</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Cryptography">Cryptography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Daniel_J._Bernstein&action=edit&section=3" title="Edit section: Cryptography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bernstein designed the <a href="/wiki/Salsa20" title="Salsa20">Salsa20</a> <a href="/wiki/Stream_cipher" title="Stream cipher">stream cipher</a> in 2005 and submitted it to <a href="/wiki/ESTREAM" title="ESTREAM">eSTREAM</a> for review and possible standardization. He later published the <a href="/wiki/ChaCha20" class="mw-redirect" title="ChaCha20">ChaCha20</a> variant of Salsa in 2008. In 2005, he proposed the <a href="/wiki/Elliptic-curve_cryptography" title="Elliptic-curve cryptography">elliptic curve</a> <a href="/wiki/Curve25519" title="Curve25519">Curve25519</a> as a basis for <a href="/wiki/Public-key_cryptography" title="Public-key cryptography">public-key</a> schemes. He worked as the lead researcher on the <a href="/wiki/Ed25519" class="mw-redirect" title="Ed25519">Ed25519</a> version of <a href="/wiki/EdDSA" title="EdDSA">EdDSA</a>. The algorithms made their way into popular software. For example, since 2014, when <a href="/wiki/OpenSSH" title="OpenSSH">OpenSSH</a> is compiled without <a href="/wiki/OpenSSL" title="OpenSSL">OpenSSL</a> they power most of its operations, and <a href="/wiki/OpenBSD" title="OpenBSD">OpenBSD</a> package <a href="/wiki/Digital_signature" title="Digital signature">signing</a> is based on Ed25519.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Nearly a decade later, <a href="/wiki/Edward_Snowden" title="Edward Snowden">Edward Snowden</a> <a href="/wiki/Global_surveillance_disclosures_(2013%E2%80%93present)" class="mw-redirect" title="Global surveillance disclosures (2013–present)">disclosed mass surveillance</a> by the <a href="/wiki/National_Security_Agency" title="National Security Agency">National Security Agency</a>, and researchers discovered a <a href="/wiki/Backdoor_(computing)" title="Backdoor (computing)">backdoor</a> in the Agency's <a href="/wiki/Dual_EC_DRBG" title="Dual EC DRBG">Dual EC DRBG</a> algorithm. These events raised suspicions of the elliptic curve parameters proposed by NSA and standardized by <a href="/wiki/National_Institute_of_Standards_and_Technology" title="National Institute of Standards and Technology">NIST</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Many researchers feared<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> that the NSA had chosen curves that gave them a <a href="/wiki/Cryptanalysis" title="Cryptanalysis">cryptanalytic</a> advantage.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Google" title="Google">Google</a> selected ChaCha20 along with Bernstein's <a href="/wiki/Poly1305" title="Poly1305">Poly1305</a> <a href="/wiki/Message_authentication_code" title="Message authentication code">message authentication code</a> for use in <a href="/wiki/Transport_Layer_Security" title="Transport Layer Security">TLS</a>, which is widely used for Internet security.<sup id="cite_ref-chacha20poly1305_18-0" class="reference"><a href="#cite_note-chacha20poly1305-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Many protocols based on his works have been adopted by various <a href="/wiki/Standards_organization" title="Standards organization">standards organizations</a> and are <a href="/wiki/Curve25519#Applications" title="Curve25519">used in a variety of applications</a>, such as <a href="/wiki/Apple_iOS" class="mw-redirect" title="Apple iOS">Apple iOS</a>,<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> the <a href="/wiki/Linux" title="Linux">Linux</a> kernel,<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> <a href="/wiki/OpenSSH" title="OpenSSH">OpenSSH</a>,<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Tor_(anonymity_network)" class="mw-redirect" title="Tor (anonymity network)">Tor</a>.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>In spring 2005, Bernstein taught a course on "high speed cryptography."<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> He introduced new <a href="/wiki/Side-channel_attacks" class="mw-redirect" title="Side-channel attacks">cache attacks</a> against implementations of <a href="/wiki/Advanced_Encryption_Standard" title="Advanced Encryption Standard">AES</a> in the same time period.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>In April 2008,<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Bernstein's <a href="/wiki/Stream_cipher" title="Stream cipher">stream cipher</a> "<a href="/wiki/Salsa20" title="Salsa20">Salsa20</a>" was selected as a member of the final portfolio of the <a href="/wiki/ESTREAM" title="ESTREAM">eSTREAM</a> project, part of a <a href="/wiki/European_Union" title="European Union">European Union</a> research directive. </p><p>In 2011, Bernstein published RFSB, a variant of the <a href="/wiki/Fast_Syndrome_Based_Hash" class="mw-redirect" title="Fast Syndrome Based Hash">Fast Syndrome Based Hash</a> function. </p><p>He is one of the editors of the 2009 book <i>Post-Quantum Cryptography</i>.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Software">Software</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Daniel_J._Bernstein&action=edit&section=4" title="Edit section: Software"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Starting in the mid-1990s, Bernstein wrote a number of security-aware programs, including <a href="/wiki/Qmail" title="Qmail">qmail</a>, <a href="/wiki/Ezmlm" title="Ezmlm">ezmlm</a>, <a href="/wiki/Djbdns" title="Djbdns">djbdns</a>, <a href="/wiki/Ucspi-tcp" title="Ucspi-tcp">ucspi-tcp</a>, <a href="/wiki/Daemontools" title="Daemontools">daemontools</a>, and <code>publicfile</code>. </p><p>Bernstein criticized the leading <a href="/wiki/Domain_Name_System" title="Domain Name System">DNS</a> package at the time, <a href="/wiki/BIND" title="BIND">BIND</a>, and wrote djbdns as a DNS package with security as a primary goal.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> Bernstein offers "security guarantees" for qmail and djbdns in the form of monetary rewards for the identification of flaws.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> A purported exploit targeting qmail running on <a href="/wiki/64-bit_computing" title="64-bit computing">64-bit platforms</a> was published in 2005,<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> but Bernstein believes that the exploit does not fall within the parameters of his qmail security guarantee. In March 2009, Bernstein awarded $1000 to Matthew Dempsky for finding a security flaw in <a href="/wiki/Djbdns" title="Djbdns">djbdns</a>.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p><p>In August 2008, Bernstein announced<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> <a href="/wiki/DNSCurve" title="DNSCurve">DNSCurve</a>, a proposal to secure the <a href="/wiki/Domain_Name_System" title="Domain Name System">Domain Name System</a>. DNSCurve applies techniques from <a href="/wiki/Elliptic_curve_cryptography" class="mw-redirect" title="Elliptic curve cryptography">elliptic curve cryptography</a> with the goal of providing a vast increase in performance over the <a href="/wiki/RSA_(algorithm)" class="mw-redirect" title="RSA (algorithm)">RSA</a> public-key algorithm used by <a href="/wiki/DNSSEC" class="mw-redirect" title="DNSSEC">DNSSEC</a>. It uses the existing DNS hierarchy to propagate trust by embedding public keys into specially formatted, <a href="/wiki/Backward_compatibility" title="Backward compatibility">backward-compatible</a> DNS records. </p><p>Bernstein proposed <a href="/wiki/Internet_Mail_2000" title="Internet Mail 2000">Internet Mail 2000</a>, an alternative system for electronic mail, which he intended to replace the <a href="/wiki/Simple_Mail_Transfer_Protocol" title="Simple Mail Transfer Protocol">Simple Mail Transfer Protocol</a> (SMTP), the <a href="/wiki/Post_Office_Protocol" title="Post Office Protocol">Post Office Protocol</a> (POP3) and the <a href="/wiki/Internet_Message_Access_Protocol" title="Internet Message Access Protocol">Internet Message Access Protocol</a> (IMAP).<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p><p>Bernstein is also known for his <a href="/wiki/Universal_hashing#Hashing_strings" title="Universal hashing">string hashing function</a> <i>djb2</i><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> and the <a href="/wiki/Cdb_(software)" title="Cdb (software)">cdb</a> database library.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematics">Mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Daniel_J._Bernstein&action=edit&section=5" title="Edit section: Mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bernstein has published a number of papers on <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> and <a href="/wiki/Computation" title="Computation">computation</a>. Many of his papers deal with <a href="/wiki/Algorithm" title="Algorithm">algorithms</a> or implementations. </p><p>In 2001, Bernstein circulated "Circuits for <a href="/wiki/Integer_factorization" title="Integer factorization">integer factorization</a>: a proposal,"<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> which suggested that, if physical hardware implementations could be brought close to their theoretical efficiency, the then-popular estimates of adequate security parameters might be off by a factor of three. Since 512-bit <a href="/wiki/RSA_(algorithm)" class="mw-redirect" title="RSA (algorithm)">RSA</a> was breakable at the time, so might be 1536-bit RSA. Bernstein was careful not to make any actual predictions, and emphasized the importance of correctly interpreting <a href="/wiki/Asymptotic_analysis" title="Asymptotic analysis">asymptotic</a> expressions. Several prominent researchers (among them <a href="/wiki/Arjen_Lenstra" title="Arjen Lenstra">Arjen Lenstra</a>, <a href="/wiki/Adi_Shamir" title="Adi Shamir">Adi Shamir</a>, Jim Tomlinson, and <a href="/wiki/Eran_Tromer" title="Eran Tromer">Eran Tromer</a>) disagreed strongly with Bernstein's conclusions.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> Bernstein has received funding to investigate whether this potential can be realized.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2023)">citation needed</span></a></i>]</sup> </p><p>Bernstein is also the author of the mathematical <a href="/wiki/Library_(computing)" title="Library (computing)">libraries</a> DJBFFT, a fast <a href="/wiki/Software_portability" title="Software portability">portable</a> <a href="/wiki/Fast_Fourier_transform" title="Fast Fourier transform">FFT</a> library, and <code>primegen</code>, an asymptotically fast small prime <a href="/wiki/Sieve_theory" title="Sieve theory">sieve</a> with low <a href="/wiki/Memory_footprint" title="Memory footprint">memory footprint</a> based on the <a href="/wiki/Sieve_of_Atkin" title="Sieve of Atkin">sieve of Atkin</a> (rather than the more usual <a href="/wiki/Sieve_of_Eratosthenes" title="Sieve of Eratosthenes">sieve of Eratosthenes</a>). Both have been used effectively in the search for large <a href="/wiki/Prime_number" title="Prime number">prime numbers</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2023)">citation needed</span></a></i>]</sup> </p><p>In 2007, Bernstein proposed the use of a <a href="/wiki/Twisted_Edwards_curve" title="Twisted Edwards curve">(twisted) Edwards curve</a>, <a href="/wiki/Curve25519" title="Curve25519">Curve25519</a>, as a basis for <a href="/wiki/Elliptic_curve_cryptography" class="mw-redirect" title="Elliptic curve cryptography">elliptic curve cryptography</a>; it is employed in Ed25519 implementation of <a href="/wiki/EdDSA" title="EdDSA">EdDSA</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2023)">citation needed</span></a></i>]</sup> </p><p>In February 2015, Bernstein and others published a paper on a stateless <a href="/wiki/Post-quantum_cryptography" title="Post-quantum cryptography">post-quantum</a> <a href="/wiki/Hash-based_cryptography" title="Hash-based cryptography">hash-based signature scheme</a> called SPHINCS.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> In July 2022, SPHINCS+, a signature scheme adapted from SPHINCS by Bernstein and others, was one of four algorithms selected as winners of the <a href="/wiki/NIST_Post-Quantum_Cryptography_Standardization" title="NIST Post-Quantum Cryptography Standardization">NIST Post-Quantum Cryptography Standardization</a> competition. It was the only hash-based algorithm of the four winners.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p><p>In April 2017, Bernstein and others published a paper on Post-Quantum RSA that includes an integer factorization algorithm claimed to be "often much faster than <a href="/wiki/Shor%27s_algorithm" title="Shor's algorithm">Shor's</a>".<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Teaching">Teaching</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Daniel_J._Bernstein&action=edit&section=6" title="Edit section: Teaching"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 2004, Bernstein taught a course on <a href="/wiki/Application_security" title="Application security">computer software security</a> where he assigned each student to find ten <a href="/wiki/Vulnerability_(computing)" class="mw-redirect" title="Vulnerability (computing)">vulnerabilities</a> in published software.<sup id="cite_ref-:0_45-0" class="reference"><a href="#cite_note-:0-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> The 25 students discovered 44 vulnerabilities, and the class published <a href="/wiki/Vulnerability_(computing)" class="mw-redirect" title="Vulnerability (computing)">security advisories</a> about the issues.<sup id="cite_ref-:0_45-1" class="reference"><a href="#cite_note-:0-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Daniel_J._Bernstein&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/CubeHash" title="CubeHash">CubeHash</a>, Bernstein's submission to the <a href="/wiki/NIST_hash_function_competition" title="NIST hash function competition">NIST hash function competition</a></li> <li><a href="/wiki/SipHash" title="SipHash">SipHash</a></li> <li><a href="/wiki/NaCl_(software)" title="NaCl (software)">NaCl (Software), a Networking and Cryptography library</a></li> <li><a href="/wiki/Quick_Mail_Queuing_Protocol" class="mw-redirect" title="Quick Mail Queuing Protocol">Quick Mail Queuing Protocol</a> (QMQP)</li> <li><a href="/wiki/Quick_Mail_Transport_Protocol" class="mw-redirect" title="Quick Mail Transport Protocol">Quick Mail Transport Protocol</a> (QMTP)</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Daniel_J._Bernstein&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-cv-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-cv_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-cv_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-cv_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBernstein" class="citation web cs1">Bernstein, Daniel J. <a rel="nofollow" class="external text" href="https://cr.yp.to/cv/cv-20080915.pdf">"Curriculum vitae"</a> <span class="cs1-format">(PDF)</span>. <i>cr.yp.to</i><span class="reference-accessdate">. Retrieved <span class="nowrap">20 March</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=cr.yp.to&rft.atitle=Curriculum+vitae&rft.aulast=Bernstein&rft.aufirst=Daniel+J.&rft_id=https%3A%2F%2Fcr.yp.to%2Fcv%2Fcv-20080915.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADaniel+J.+Bernstein" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20231218203136/https://casa.rub.de/ueber-casa/team">"CASA team list with Bernstein being a part of it"</a>. <i>web.archive.org</i>. 2023-12-18<span class="reference-accessdate">. Retrieved <span class="nowrap">2024-11-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=web.archive.org&rft.atitle=CASA+team+list+with+Bernstein+being+a+part+of+it&rft.date=2023-12-18&rft_id=https%3A%2F%2Fweb.archive.org%2Fweb%2F20231218203136%2Fhttps%3A%2F%2Fcasa.rub.de%2Fueber-casa%2Fteam&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADaniel+J.+Bernstein" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://casa.rub.de/en/about/team">"Team CASA"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">16 November</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Team+CASA&rft_id=https%3A%2F%2Fcasa.rub.de%2Fen%2Fabout%2Fteam&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADaniel+J.+Bernstein" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.nytimes.com/1987/01/21/nyregion/new-yorkers-excel-in-contest.html">"New Yorkers Excel In Contest"</a>. <i>New York Times</i>. 1987-01-21<span class="reference-accessdate">. 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Lenstra</a>; <a href="/wiki/Adi_Shamir" title="Adi Shamir">Adi Shamir</a>; Jim Tomlinson; <a href="/wiki/Eran_Tromer" title="Eran Tromer">Eran Tromer</a> (2002). <a rel="nofollow" class="external text" href="http://www.wisdom.weizmann.ac.il/~tromer/papers/meshc/meshc.html">"Analysis of Bernstein's Factorization Circuit"</a>. <i>Proc. Asiacrypt</i>. LNCS 2501: 1–26.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Asiacrypt&rft.atitle=Analysis+of+Bernstein%27s+Factorization+Circuit&rft.volume=LNCS+2501&rft.pages=1-26&rft.date=2002&rft.au=Arjen+K.+Lenstra&rft.au=Adi+Shamir&rft.au=Jim+Tomlinson&rft.au=Eran+Tromer&rft_id=http%3A%2F%2Fwww.wisdom.weizmann.ac.il%2F~tromer%2Fpapers%2Fmeshc%2Fmeshc.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADaniel+J.+Bernstein" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external free" href="https://sphincs.cr.yp.to/">https://sphincs.cr.yp.to/</a> <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Bare_URLs" title="Wikipedia:Bare URLs"><span title="A full citation is required to prevent link rot. (August 2024)">bare URL</span></a></i>]</sup></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://www.nist.gov/news-events/news/2022/07/nist-announces-first-four-quantum-resistant-cryptographic-algorithms">"NIST Announces First Four Quantum-Resistant Cryptographic Algorithms"</a>. <i>NIST</i>. 2022-07-05.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=NIST&rft.atitle=NIST+Announces+First+Four+Quantum-Resistant+Cryptographic+Algorithms&rft.date=2022-07-05&rft_id=https%3A%2F%2Fwww.nist.gov%2Fnews-events%2Fnews%2F2022%2F07%2Fnist-announces-first-four-quantum-resistant-cryptographic-algorithms&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADaniel+J.+Bernstein" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFComputer_Security_Division2017" class="citation web cs1">Computer Security Division, Information Technology Laboratory (2017-01-03). <a rel="nofollow" class="external text" href="https://csrc.nist.gov/Projects/post-quantum-cryptography/selected-algorithms-2022">"Selected Algorithms 2022 - Post-Quantum Cryptography | CSRC | CSRC"</a>. <i>CSRC | NIST</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-03-27</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=CSRC+%7C+NIST&rft.atitle=Selected+Algorithms+2022+-+Post-Quantum+Cryptography+%7C+CSRC+%7C+CSRC&rft.date=2017-01-03&rft.aulast=Computer+Security+Division&rft.aufirst=Information+Technology+Laboratory&rft_id=https%3A%2F%2Fcsrc.nist.gov%2FProjects%2Fpost-quantum-cryptography%2Fselected-algorithms-2022&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADaniel+J.+Bernstein" class="Z3988"></span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://cr.yp.to/papers/pqrsa-20170419.pdf">"Post-quantam RSA"</a> <span class="cs1-format">(PDF)</span>. <i>cr.yp.to</i><span class="reference-accessdate">. Retrieved <span class="nowrap">June 11,</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=cr.yp.to&rft.atitle=Post-quantam+RSA&rft_id=https%3A%2F%2Fcr.yp.to%2Fpapers%2Fpqrsa-20170419.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADaniel+J.+Bernstein" class="Z3988"></span></span> </li> <li id="cite_note-:0-45"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_45-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_45-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLemos2004" class="citation web cs1">Lemos, Robert (2004-12-16). <a rel="nofollow" class="external text" href="https://www.cnet.com/news/students-uncover-dozens-of-unix-software-flaws/">"Students uncover dozens of Unix software flaws"</a>. <i>CNET</i><span class="reference-accessdate">. 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