Cryptographers Discover a New Foundation for Quantum Secrecy

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Article</title><path fill="currentColor" d="M2.1 0h45.8v50L25.5 37.5 2.1 50V0z"></path></svg> <div class='h6t uppercase kern ml1 mv0 theme__text'> Read Later </div> </button> <div class='q-tooltip hidden force-mobile-placement w-32 ml-n16 -top-10'> <div class='q-tooltip-content'> <div class='q-tooltip-arrow -bottom-3'></div> <div class='q-tooltip-inner py-1 pl-1' role='tooltip'> <div class='h6t relative z1 uppercase kern--w mx025'> <span class='small no-wrap'>Read Later</span> </div> </div> </div> </div> </div> </li> </ul> <div class='nav__local__progress absolute fit-b fit-l fit-r z1 theme__accent'> <span class='block' style='transform: translateX(-100%);' data-role='content-progress-bar'></span> </div> </div> </div> <div id='postBody' class='theme__background-background theme__text'> <section class='post__title__wrapper relative '> <section class='outer fill-h relative outer--content '> <div class='mha container--s'> <div class='header-spacer'></div> <div class='post__title pv1 scale1 mha'> <div class='scale0'> <div class='mb1 pb025 mt0 h6t post__title__kicker '> <a class="kicker theme__accent theme__text-hover uppercase" href="/tag/quantum-cryptography/">quantum cryptography</a> </div> <h1 class='post__title__title mv025 noe theme__text' >Cryptographers Discover a New Foundation for Quantum Secrecy</h1> <div class='post__title__author-date h5 mt1'> <div class='byline relative flex flex-items-start merriweather mv025 mr1 gray3 h6t theme__text-hover'> <em class='byline__by gray4 mr075'>By </em> <a href='https://www.quantamagazine.org/authors/brubaker_ben/'> <span class='byline__author uppercase kern light small'>Ben Brubaker</span> </a> </div> <p class="h6 mv1 pv025 o6"><em>June 3, 2024</em></p> </div> <div class='post__title__meta flex flex-wrap flex-items-start'> <div class='post__title__excerpt wysiwyg p italic mb1 mt025 pr2 o4 theme__text ' > Researchers have proved that secure quantum encryption is possible in a world without hard problems. </div> <div 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<section class='py-0 px-12 s:p-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:flex-row l:max-w-mod-large justify-end s:mt-4 s:mb-4'> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h text-left w-auto before:block l:before:hidden l:w-half-minus-17 l:text-right l:pl-24'> <p>Eliot Wyatt for <em>Quanta Magazine</em></p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <h2 class='screen-reader-text'>Introduction</h2> <div class='post__wrapper scale0 show-dropcap'> <div class='mha container--m'> <div class='post__content relative flex flex-items-start flex-justify-between'> <aside class='post__sidebar hide flex flex-justify-center '> <div class='post__sidebar__content'> <div class='post__sidebar__content__inner'> <div class='align-c mb075'> <div class='sidebar__author'> <a class='theme__accent-hover transition--color ' 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<span class='theme__text theme__accent-hover transition--color relative'>computational complexity</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/computer-science'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>computer science</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/cryptography'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>cryptography</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/quanta-podcast'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>Quanta Podcast</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' 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topics</span> <svg class='icon ml05' viewbox='0 0 50 50' enable-background='new 0 0 50 50'><path fill='currentColor' d='M50 25l-17.4-8.7v6.5H0v4.4h32.6v6.5'></path></svg> </a> </div> </div> <div class='sidebar__poster'> <a href='https://www.youtube.com/c/QuantaScienceChannel' title='' target='_blank' class=''> <img width="320" height="550" src="https://www.quantamagazine.org/wp-content/uploads/2021/05/Youtube_Article_160.gif" class="fill-h" alt="" decoding="async" /></a> </div> </div> </aside> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <p>Say you want to send a private message, cast a secret vote or sign a document securely. If you do any of these tasks on a computer, you’re relying on encryption to keep your data safe. That encryption needs to withstand attacks from codebreakers with their own computers, so modern encryption methods rely on assumptions about what mathematical problems are hard for computers to solve.</p> <p>But as cryptographers laid the mathematical foundations for this approach to information security in the 1980s, a few researchers discovered that computational hardness wasn’t the only way to safeguard secrets. Quantum theory, originally developed to understand the physics of atoms, turned out to have deep connections to information and cryptography. Researchers found ways to base the security of a few specific cryptographic tasks directly on the laws of physics. But these tasks were strange outliers — for all others, there seemed to be no alternative to the classical computational approach.</p> <p>By the end of the millennium, quantum cryptography researchers thought that was the end of the story. But in just the past few years, the field has undergone another seismic shift.</p> <aside class="post__aside mb2 relative print-text-border post__aside--right post__aside--divider hide-on-print"> <div class="post__aside__content theme__anchors--solid wysiwyg h6 "> <div class="post__content wysiwyg p theme__anchors--underline"><h4 class="large"><span class="pangram theme__accent">Quanta Science Podcast</span></h4> <p class="large"><span class="gray4"><span class="pangram">The problem of distinguishing two quantum states is not just hard, but almost inconceivably hard. That’s great news for cryptography.<br /> </span></span></p> <hr /> <aside class="post__aside mb2 relative post__aside--inline hide-on-print"><div class='podcast scale0 '> <a href='/tag/quanta-podcast' class='h6 pangram uppercase kern mt0 xbold mbr1 decoration--none no--shadow block align-r'> <span class='theme__text'>All episodes <svg class="icon-s theme__accent" x="0px" y="0px" viewBox="0 0 50 50" enable-background="new 0 0 50 50" xml:space="preserve"><path fill="currentColor" d="M14.7,48.4l-2.2-2.2c-1.1-1.1-1.1-2.8,0-3.9L29.7,25L12.5,7.7c-1.1-1.1-1.1-2.8,0-3.9l2.2-2.2 c1.1-1.1,2.8-1.1,3.9,0L40,23c1.1,1.1,1.1,2.8,0,3.9L18.6,48.4C17.5,49.5,15.7,49.5,14.7,48.4z"></path></svg></span> </a> <audio preload='none' data-role='podcast' data-name='podcast-138291'> <source src='https://chrt.fm/track/C9B4G7/www.quantamagazine.org/wp-content/uploads/2024/06/quanta-253_v1.mp3' type='audio/mpeg'> Your browser does not support the audio element. </audio> <div class='flex flex-items-center fill-h 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c1.6-0.7,4.3-2.6,6-4.3c2.9-2.9,5-6.6,6-10.5c0.6-2.4,0.5-7.9-0.1-10.4c-2.2-8-8.7-14.2-16.7-15.9c-2.3-0.5-6.6-0.5-8.9,0 C12.5,5.4,5.8,11.9,3.7,20.2c-0.5,2.2-0.5,7.7,0,9.9c1.4,5.4,4.9,10.4,9.5,13.4c0.9,0.6,2,1.2,2.4,1.4c1,0.4,1.2,0.8,1.4,2.5 c0.1,1.1,0.1,1.4-0.2,1.4c-0.2,0-1.4-0.5-2.7-1.1L14.1,47.6z M14.2,37.9c-2.5-2-4.7-5.5-5.6-8.9c-0.5-2.1-0.5-6,0-8.1 C10.2,15.3,14.3,11,20,9c1.9-0.7,6.3-0.8,8.7-0.3c8.3,1.8,14.1,10.1,13,18.3c-0.5,3.3-1.6,6-3.6,8.6c-1,1.3-3.4,3.4-3.9,3.4 c-0.1,0-0.1-0.8-0.1-1.8v-1.8l1.2-1.5c4.7-5.6,4.3-13.4-0.8-18.5c-2-2-4.3-3.2-7.2-3.7c-1.9-0.4-2.3-0.4-4.3,0 c-3,0.5-5.4,1.7-7.5,3.7c-5.1,5.1-5.4,12.9-0.8,18.5l1.2,1.5v1.8c0,1-0.1,1.8-0.2,1.8C15.8,39,15.1,38.5,14.2,37.9L14.2,37.9z M22.5,28.2c-2.1-1-3.3-2.8-3.3-5.3c0-2.2,1.2-4.1,3.3-5.2c1.3-0.7,3.7-0.7,5,0c1.5,0.8,2.6,2.2,3.1,3.7C32,26.2,27,30.3,22.5,28.2 L22.5,28.2z"></path></svg></div> <div class='h6 kern--s pangram uppercase bold gray3 pl05'> APPLE </div> </a> <a href='https://open.spotify.com/show/7oKXOpbHzbICFUcJNbZ5wF?si=jdnj9sTHSD2bj4hDMFLKEA' target='_blank' class='flex flex-items-center pr1 three--ms-max mb1-ms-max'> <div class='icon-button inline-block relative pointer '> <div class='absolute fit-x mxa o2 theme__accent-hover hover:opacity-100 theme__text'> </div> <svg class="icon absolute fit-x mxa theme__accent" viewbox="0 0 50 50" enable-background="new 0 0 50 50"><path fill="currentColor" d="M25,0C11.2,0,0,11.2,0,25c0,13.8,11.2,25,25,25c13.8,0,25-11.2,25-25C50,11.2,38.8,0,25,0L25,0L25,0z M36.5,36.1c-0.4,0.7-1.4,1-2.1,0.5c-5.9-3.6-13.3-4.4-22-2.4c-0.8,0.2-1.7-0.3-1.9-1.2c-0.2-0.8,0.3-1.7,1.2-1.9 c9.5-2.2,17.7-1.2,24.3,2.8C36.7,34.4,36.9,35.3,36.5,36.1L36.5,36.1z M39.5,29.2c-0.6,0.9-1.8,1.2-2.7,0.6 c-6.7-4.1-17-5.3-24.9-2.9c-1,0.3-2.1-0.3-2.4-1.3c-0.3-1,0.3-2.1,1.3-2.4c9.1-2.8,20.4-1.4,28.1,3.3C39.8,27.1,40.1,28.3,39.5,29.2 L39.5,29.2L39.5,29.2z M39.8,22.2c-8.1-4.8-21.3-5.2-29-2.9c-1.2,0.4-2.5-0.3-2.9-1.6c-0.4-1.2,0.3-2.5,1.6-2.9 c8.8-2.7,23.5-2.2,32.8,3.3c1.1,0.7,1.5,2.1,0.8,3.2C42.3,22.5,40.9,22.8,39.8,22.2L39.8,22.2L39.8,22.2z"></path></svg></div> <div class='h6 kern--s pangram uppercase bold gray3 pl05'> SPOTIFY </div> </a> <a href='https://chrt.fm/track/C9B4G7/www.quantamagazine.org/wp-content/uploads/2024/06/quanta-253_v1.mp3' target='_blank' class='flex-align-self-start mla'> <div class='icon-button inline-block relative pointer bg-gray1 circ'> <div class='absolute fit-x mxa o2 white theme__accent-hover hover:opacity-100'> </div> <svg class="icon-s absolute fit-x mxa theme__accent" viewbox="0 0 50 50" enable-background="new 0 0 50 50"><path fill="currentColor" d="M38.6 27l-3.2-4-8.4 6.8V0h-5v29.8L13.6 23l-3.2 4 14.1 11.2M2 45h45v5H2z"></path></svg></div> </a> </div> </div> </aside> </div> </div> </aside> <p>“There’s been this rearrangement of what we believe is possible with quantum cryptography,” said <a href="https://www.engineering.columbia.edu/faculty/henry-yuen">Henry Yuen</a>, a quantum information theorist at Columbia University.</p> <p>In a string of recent papers, researchers have shown that most cryptographic tasks could still be accomplished securely even in hypothetical worlds where practically all computation is easy. All that matters is the difficulty of a special computational problem about quantum theory itself.</p> <p>“The assumptions you need can be way, way, way weaker,” said <a href="https://simons.berkeley.edu/people/fermi-ma">Fermi Ma</a>, a quantum cryptographer at the Simons Institute for the Theory of Computing in Berkeley, California. “This is giving us new insights into computational hardness itself.”</p> <h2><strong>This Message Will Self-Destruct</strong></h2> <p>The story begins in the late 1960s, when a physics graduate student named Stephen Wiesner started thinking about the destructive nature of measurement in quantum theory. Measure any system governed by the rules of quantum physics, and you’ll alter the quantum state that mathematically describes its configuration. This quantum measurement disturbance was a hindrance for most physicists. Wiesner, who took an unorthodox information-centric view of quantum theory, wondered whether it could be made useful. Perhaps it could serve as a form of built-in tamper protection for sensitive data.</p> <p>But Wiesner’s ideas were too far ahead of their time, and he left academia after graduate school. Fortunately, he’d discussed his ideas with his friend and fellow physicist Charles Bennett, who unsuccessfully tried to interest others in the subject for a decade. Finally, in 1979, Bennett met the computer scientist Gilles Brassard while swimming off the coast of Puerto Rico during a conference. Together, they wrote a <a href="https://arxiv.org/abs/2003.06557">groundbreaking paper</a> describing a new approach to an important cryptographic task. Their protocol was based on quantum measurement disturbance, and needed no assumptions about the difficulty of any computational problems.</p> <p>“The very nature of quantum information seems somewhat cryptographic,” Ma said.</p> </div> </div> </div> </section> <aside class='post__sidebar hide flex flex-justify-center theme__anchors--solid '> <div class='post__sidebar__content'> <div class='post__sidebar__content__inner'> <div class='h3t mt0'> Share this article </div> <div data-id='social-links'> <div class='social-links social-links--share flex flex-justify-between'> <a href='http://www.facebook.com/sharer.php?u=https://www.quantamagazine.org/cryptographers-discover-a-new-foundation-for-quantum-secrecy-20240603/' class='social-links__link flex flex-items-center relative' target="_blank" > <div class='icon-button inline-block relative pointer theme__accent-hover-child'> <div class='absolute fit-x mxa o2 hover--opaque theme__text'> </div> <svg class="absolute fit-x mxa theme__text" 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items-center justify-center flex-col max-w-img-regular py-0 px-0 l:px-0 '> <div class='w-full flex justify-center max-w-mod-regular m:max-w-unset image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1'> <img width="1120" height="1549" src="https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf-MOBILE.webp" class="w-full m:hidden l:hidden mb-6 w-full s:mb-4" alt="Charles Bennett in a striped shirt in front of molecular structures. Gilles Brassard in an orange shirt indoors with a blurry background." decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf-MOBILE.webp 1120w, https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf-MOBILE-376x520.webp 376w, https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf-MOBILE-768x1062.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf-MOBILE-1111x1536.webp 1111w" sizes="(max-width: 1120px) 100vw, 1120px" /><img width="2242" height="818" src="https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf.webp" class="mb-6 w-full s:mb-4 s:hidden" alt="Charles Bennett in a striped shirt in front of molecular structures. Gilles Brassard in an orange shirt indoors with a blurry background." decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf.webp 2242w, https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf-1720x628.webp 1720w, https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf-520x190.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf-768x280.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf-1536x560.webp 1536w, https://www.quantamagazine.org/wp-content/uploads/2024/06/CharlesBennett-crBBVAFoundation-GillesBrassard-crLeaKimChateauneuf-2048x747.webp 2048w" sizes="(max-width: 2242px) 100vw, 2242px" /><figcaption class='block my-0 mx-auto w-full m:hidden l:hidden w-full l:max-w-mod-inline'> <section class='p-0 m:py-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:m-0 l:p-0 max-w-mod-inline s:mb-8'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h '> <p>In the 1980s, Charles Bennett (top) and Gilles Brassard pioneered a new approach to cryptography based on quantum physics.</p> </div> </div> </section> </figcaption> </div> </div> <figcaption class='block my-0 mx-auto w-full l:max-w-mod-inline'> <section class='p-0 m:py-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:m-0 l:p-0 max-w-mod-inline s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h s:hidden'> <p>In the 1980s, Charles Bennett (left) and Gilles Brassard pioneered a new approach to cryptography based on quantum physics.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h s:mt-n1'> <p>BBVA Foundation; Lëa-Kim Châteauneuf</p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <p>Bennett and Brassard’s breakthrough made researchers optimistic that similar quantum tricks could yield perfect security for other cryptographic tasks. Researchers focused mainly on a task called bit commitment, which is useful on its own and is also a key component of most advanced cryptographic protocols.</p> <p>To understand the basic idea behind bit commitment, imagine a two-player game in which you must make a secret decision that later gets revealed. One way to do this is to write the decision down on a slip of paper and put it in a sealed envelope. That way, you can’t change your decision later on, and your opponent can’t prematurely peek at the result.</p> <p>Now imagine you’re playing the same game online. To make cheating impossible, you need to seal the decision in a sort of digital envelope that neither player can open alone. That’s where cryptography comes in. In 1981, the pioneering computer scientist Manuel Blum <a href="https://dl.acm.org/doi/10.1145/1008908.1008911">constructed</a> the first bit commitment protocol — a way to build effectively unhackable envelopes out of hard computational problems.</p> <p>But how hard is hard? Researchers in the field of computational complexity theory study <a href="https://www.quantamagazine.org/a-short-guide-to-hard-problems-20180716/">many different kinds</a> of hard problems, and not all of them are useful for cryptographers. Bit commitment and all other cryptographic protocols rely on problems in a class that complexity theorists call “NP,” whose defining feature is that it’s easy to check whether a candidate solution is correct.</p> <p>Unfortunately, researchers haven’t been able to prove that any NP problems are truly hard. There could still be some clever undiscovered procedure, or algorithm, for solving even the ones that seem hardest. If there is, then all of classical cryptography would break.</p> <p>Such considerations animated the search for quantum-based security guarantees. But in 1997, <a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.78.3414">two</a> <a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.78.3410">papers</a> proved that bit commitment schemes could never be completely secure if they were based solely on the laws of quantum physics. The papers implied that some kind of computational hardness would be necessary for almost all cryptographic tasks.</p> </div> </div> </div> </section> </div> <figure class='leading-0 w-full my-0 mx-auto flex items-center justify-center flex-col max-w-img-inline py-0 px-16 s:px-0 l:px-16 '> <div class='w-full flex justify-center max-w-mod-inline image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1 s:px-5'> <img width="1300" height="885" src="https://www.quantamagazine.org/wp-content/uploads/2024/06/WilliamKretschmer-crJustinDuRant.webp" class="mb-6 w-full s:mb-4" alt="William Kretschmer standing outside in a black sweater." decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/06/WilliamKretschmer-crJustinDuRant.webp 1300w, https://www.quantamagazine.org/wp-content/uploads/2024/06/WilliamKretschmer-crJustinDuRant-520x354.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2024/06/WilliamKretschmer-crJustinDuRant-768x523.webp 768w" sizes="(max-width: 1300px) 100vw, 1300px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full'> <section class='s:pt-0 s:px-5 s:pb-6 s:w-full-minus-25'> <div class='w-full my-0 mx-auto max-w-mod-inline s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h '> <p>William Kretschmer’s work on distinguishing certain quantum states led researchers to rethink the foundations of quantum cryptography.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h '> <p>Justin DuRant</p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <p>That was the last word on the theoretical foundations of quantum bit commitments for nearly 25 years. Then, in 2021, <a href="https://arxiv.org/abs/2103.09320">a paper</a> by a graduate student named <a href="https://simons.berkeley.edu/people/william-kretschmer">William Kretschmer</a> prompted researchers to confront a question that nobody had thought to ask. Computational hardness was clearly necessary for bit commitments and most other forms of cryptography, but precisely what kind of hardness?</p> <p>The answer would turn out to be weirder than anybody had anticipated.</p> <h2><strong>Consulting Oracles</strong></h2> <p>The 2021 paper came out of Kretschmer’s struggle to understand a <a href="http://arxiv.org/abs/1711.00385">specific version</a> of a problem that sounds conceptually straightforward: How hard is it to distinguish, or discriminate between, two quantum states that look superficially similar? Kretschmer, who’s now a postdoctoral researcher at the Simons Institute, was initially interested in the problem for reasons that had nothing to do with bit commitment.</p> <p>“Cryptography was not even on my radar,” he said.</p> <p>The discrimination problem was interesting in part because it wasn’t even clear how to describe it using familiar mathematical language. Complexity theorists traditionally study problems with different possible inputs represented by strings of bits, or 0s and 1s. For the problem of decomposing large numbers into their prime factors, for instance, this string represents the number to be factored.</p> <p>Even after researchers started studying how quantum physics might be harnessed for computation, they continued to focus on such “classical-input” problems. Typical quantum algorithms start with an ordinary classical bit string and then process it using quantum trickery. But in “quantum-input” problems like Kretschmer’s, the inputs aren’t bit strings — they’re quantum states that are as easily disrupted by computation as by measurement.</p> <aside class="post__aside mb2 relative post__aside--right post__aside--medium hide-on-print"> <div class='card clearfix mv05 pv1 theme__anchors--none is-grid-variant is-shortcode border-grey-o25'> <div class='card__image mr1 mb1' data-toggle-hover='card'> <a href='https://www.quantamagazine.org/graduate-student-solves-quantum-verification-problem-20181008/' class='relative'> <span class='screen-reader-text'>Graduate Student Solves Quantum Verification Problem</span> <div class='image mx0 relative image--standard'> <div class='image__inner absolute fit-x is-loaded'> <img width="520" height="292" src="https://www.quantamagazine.org/wp-content/uploads/2018/10/UrmilaMahadev_520x292.jpg" class="absolute fit-x fill-h fill-v mxa" alt="Photo of Urmila Mahadev" decoding="async" /> </div> </div> </a> </div> <div class='card__content '> <div class='mb1 pb025 mt0 h6t card__kicker'> <a class="kicker theme__accent theme__text-hover uppercase" href="/tag/quantum-computing/">quantum computing</a> </div> <a href='https://www.quantamagazine.org/graduate-student-solves-quantum-verification-problem-20181008/' data-toggle-hover='card'> <h3 class='card__title noe mv0 theme__accent-hover transition--color h2t'> Graduate Student Solves Quantum Verification Problem </h3> </a> <div class='card__meta mb0 mt025 flex flex-items-center flex-wrap'> <div class='card-date h6 flex flex-items-center mv05'> <div class='uppercase mr1 kern small gray3'>October 8, 2018</div> <span class='o-divider o-divider--vertical mr1 relative'></span> </div> <div class='card__actions h6 flex flex-items-center mv05'> <div class='comments-button mr05 flex flex-items-center theme__accent-hover ' data-name='comment-bubble' > <a href='https://www.quantamagazine.org/graduate-student-solves-quantum-verification-problem-20181008/#comments' class='flex flex-items-center pangram'> <svg viewbox='0 0 50 50' enable-background='new 0 0 50 50' xmlns='http://www.w3.org/2000/svg' class='o2'><title>Comment</title><path fill='currentColor' d='M9.4 4.2h31.2c8.6 0 9.4 7 9.4 15.6s-.7 15.6-9.4 15.6h-2.2l-.9 9.4-18.8-9.4H9.4c-8.6 0-9.4-7-9.4-15.6S.7 4.2 9.4 4.2z'></path></svg> </a> </div> <span class='o-divider mh075 relative'></span> <div class='relative'> <button class='bookmark-button mh05 flex flex-items-center theme__accent-hover ' data-toggle-hover='tooltip' data-id='63838' data-active-class='' aria-expanded='false'> <svg class="icon" viewbox="0 0 50 50" enable-background="new 0 0 50 50" xmlns="http://www.w3.org/2000/svg"><title>Save Article</title><path fill="currentColor" d="M2.1 0h45.8v50L25.5 37.5 2.1 50V0z"></path></svg> </button> <div class='q-tooltip hidden force-mobile-placement w-32 ml-n16 -top-10'> <div class='q-tooltip-content'> <div class='q-tooltip-arrow -bottom-3'></div> <div class='q-tooltip-inner py-1 pl-1' role='tooltip'> <div class='h6t relative z1 uppercase kern--w mx025'> <span class='small no-wrap'>Read Later</span> </div> </div> </div> </div> </div> </div> </div> <div class='card__excerpt h5 pangram o6 mb4 mt025'> </div> </div> </div> </aside> <p>“The language with which we’ve described quantum computations in traditional complexity theory can’t directly talk about these problems,” Yuen said.</p> <p>At first, Kretschmer thought he just needed to translate the problem into more standard language, but he couldn’t figure out how. So he did what complexity theorists often do when they’re desperate: He turned to an oracle.</p> <p>In complexity theory, the term “oracle” refers to a hypothetical device that can solve a specific problem instantly. A computer with access to an oracle might be able to solve other problems more easily by consulting the oracle as an intermediate step in an algorithm. Of course, oracles don’t actually exist in the real world, but studying them helps complexity theorists understand the relationships between the difficulty levels of different problems.</p> <p>Kretschmer wondered what kind of oracle could make it easy to distinguish two quantum states — the so-called state-discrimination problem. He decided to start with a special oracle that would boost the power of normal quantum algorithms, the ones that use quantum tricks to solve problems with classical bit string inputs. Such algorithms can solve some problems too hard for classical ones, <a href="https://www.quantamagazine.org/thirty-years-later-a-speed-boost-for-quantum-factoring-20231017/">like factoring large numbers</a>, but they’re not omnipotent — many other problems lie beyond their reach.</p> <p>Access to Kretschmer’s oracle would enable such algorithms to solve certain classical-input problems too hard for real quantum computers. Kretschmer assumed that it would be overkill, but to his surprise, he proved that the state-discrimination problem could still stump these souped-up quantum algorithms.</p> <p>“I was really fascinated by William’s paper,” said <a href="https://cs-people.bu.edu/luowenq/">Luowen Qian</a>, a graduate student studying cryptography at Boston University. “I actually thought it had to be wrong, because it’s so counterintuitive.”</p> </div> </div> </div> </section> </div> <figure class='leading-0 w-full my-0 mx-auto flex items-center justify-center flex-col max-w-img-medium py-0 px-0 l:px-0 '> <div class='w-full flex justify-center max-w-mod-medium m:max-w-unset image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1'> <img width="2560" height="682" src="https://www.quantamagazine.org/wp-content/uploads/2024/06/LuowenQian-crXichenLi-Triptych-scaled.webp" class="mb-6 w-full s:mb-4" alt="Luowen Qian standing outside in a gray shirt. Makrand Sinha standing outside in a light blue shirt. Avishay Tal standing in a blue shirt against a dark background." decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/06/LuowenQian-crXichenLi-Triptych-scaled.webp 2560w, https://www.quantamagazine.org/wp-content/uploads/2024/06/LuowenQian-crXichenLi-Triptych-1720x458.webp 1720w, https://www.quantamagazine.org/wp-content/uploads/2024/06/LuowenQian-crXichenLi-Triptych-520x138.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2024/06/LuowenQian-crXichenLi-Triptych-768x205.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2024/06/LuowenQian-crXichenLi-Triptych-1536x409.webp 1536w, https://www.quantamagazine.org/wp-content/uploads/2024/06/LuowenQian-crXichenLi-Triptych-2048x545.webp 2048w" sizes="(max-width: 2560px) 100vw, 2560px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full'> <section class='py-0 px-12 s:p-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:flex-row l:max-w-mod-medium justify-end s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h w-auto l:w-140'> <p>Luowen Qian (left), Avishay Tal (center) and Makrand Sinha teamed up with Kretschmer to prove that many quantum cryptography techniques could still be secure even if classical cryptography is impossible.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h text-left w-auto before:block l:before:hidden l:w-half-minus-17 l:text-right l:pl-24'> <p>Xichen Li; Herve Attia/TerrificShot Photography; Heather Coit/Grainger Engineering</p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <p>Qian, Yuen and others <a href="https://arxiv.org/abs/2112.10020">soon</a> <a href="https://arxiv.org/abs/2112.06369">proved</a> that if Kretschmer’s state discrimination problem really was hard, secure quantum bit commitment schemes would be possible. That would in turn imply security for a slew of more advanced cryptographic protocols. The scope of quantum cryptography was far broader than researchers in the 1990s had realized, and it all came down to the hardness of one problem.</p> <h2><strong>How Hard Could It Be?</strong></h2> <p>Kretschmer’s result came with one big caveat — to make the proof work, he had to rely on an unusual oracle that only quantum algorithms could consult. Perhaps a more familiar oracle would make his state discrimination problem easy, and therefore make secure quantum bit commitments impossible? In 2022, Kretschmer and Qian began working together to see what they could prove about an oracle everybody could understand: one that could solve any NP problem instantaneously. In a world with such oracles, all classical cryptography would be impossible.</p> <p>Kretschmer soon realized that the state discrimination problem was mathematically related to a <a href="https://www.quantamagazine.org/finally-a-problem-that-only-quantum-computers-will-ever-be-able-to-solve-20180621/">superficially different problem</a> in quantum complexity theory, and he enlisted the help of two experts in the area, the complexity theorists <a href="https://www2.eecs.berkeley.edu/Faculty/Homepages/atal.html">Avishay Tal</a> and <a href="https://cs.illinois.edu/about/people/department-faculty/msinha">Makrand Sinha</a>. “William was really like a manager, and we were contractors,” Tal said.</p> <p>Working together, the four researchers quickly <a href="http://arxiv.org/abs/2212.00879">proved</a> that Kretschmer’s state discrimination problem could still be intractable even for computers that could call on this NP oracle. That means that practically all of quantum cryptography could remain secure even if every problem underpinning classical cryptography turned out to be easy. Classical cryptography and quantum cryptography increasingly seemed like two entirely separate worlds.</p> <p>The result caught Ma’s attention, and he began to wonder just how far he could push the line of work that Kretschmer had initiated. Could quantum cryptography remain secure even with more outlandish oracles — ones that could instantly solve computational problems far harder than those in NP? “Problems in NP are not the hardest classical problems one can think about,” said <a href="https://cs.illinois.edu/about/people/faculty/dakshita">Dakshita Khurana</a>, a cryptographer at the University of Illinois, Urbana-Champaign. “There’s hardness beyond that.”</p> </div> </div> </div> </section> </div> <figure class='leading-0 w-full my-0 mx-auto flex items-center justify-center flex-col max-w-img-medium py-0 px-0 l:px-0 '> <div class='w-full flex justify-center max-w-mod-medium m:max-w-unset image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1'> <img width="1500" height="647" src="https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-MOBILE.webp" class="w-full m:hidden l:hidden mb-6 w-full s:mb-4" alt="Fermi Ma standing outside in a blue button-down shirt. Alex Lombardi standing outside in a blue polo shirt. John Wright standing inside in a gray shirt." decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-MOBILE.webp 1500w, https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-MOBILE-520x224.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-MOBILE-768x331.webp 768w" sizes="(max-width: 1500px) 100vw, 1500px" /><img width="2560" height="759" src="https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-scaled.webp" class="mb-6 w-full s:mb-4 s:hidden" alt="Fermi Ma standing outside in a blue button-down shirt. Alex Lombardi standing outside in a blue polo shirt. John Wright standing inside in a gray shirt." decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-scaled.webp 2560w, https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-1720x510.webp 1720w, https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-520x154.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-768x228.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-1536x455.webp 1536w, https://www.quantamagazine.org/wp-content/uploads/2024/06/JohnWright-crSoyaPark-Trirtych-2048x607.webp 2048w" sizes="(max-width: 2560px) 100vw, 2560px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full'> <section class='py-0 px-12 s:p-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:flex-row l:max-w-mod-medium justify-end s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h w-auto l:w-140'> <p>Fermi Ma (left), John Wright (center) and Alex Lombardi proved that quantum cryptography could still be secure even with an oracle that could instantly solve any computational problem that had classical inputs.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h text-left w-auto before:block l:before:hidden l:w-half-minus-17 l:text-right l:pl-24'> <p>Xinyu Tan; Soya Park; Jessica Xu</p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <p>Ma began brainstorming how best to approach that question, together with <a href="https://www.cs.princeton.edu/people/profile/al2201">Alex Lombardi</a>, a cryptographer at Princeton University, and <a href="https://www2.eecs.berkeley.edu/Faculty/Homepages/jswright.html">John Wright</a>, a quantum computing researcher at the University of California, Berkeley. “It was just so fascinating and so mind-bending that I was immediately hooked,” Wright said.</p> <p>After thinking about the question for a while and getting nowhere, Ma suggested that they consider the most extreme case possible: an oracle that could instantly solve any computational problem with classical inputs. That would include all the problems complexity theorists have traditionally studied, even those <a href="https://www.quantamagazine.org/alan-turing-and-the-power-of-negative-thinking-20230905/">known to be unsolvable</a> in the real world.</p> <p>“It sounded a little bit insane to me,” Lombardi said.</p> <p>But the question turned out to be remarkably fruitful. After working on it for nearly a year, they finally published <a href="http://arxiv.org/abs/2310.08870">a striking result</a>. No algorithm allowed to consult that all-powerful oracle exactly once can distinguish the two quantum states, as is required to undermine a quantum bit commitment scheme.</p> <p>Limiting algorithms to a single query is less of a constraint than it may sound, because quantum algorithms can effectively ask the oracle to solve multiple problems simultaneously by exploiting the phenomenon called superposition. Algorithms that can make multiple queries sequentially could be more powerful, because they can use the oracle’s answers to previous queries to decide what to ask next. Whether these algorithms are similarly limited remains an open question.</p> <p>Ma, Lombardi and Wright’s paper was also significant for another reason. While the three researchers were wrestling with their problem, they realized it was closely linked to a <a href="http://arxiv.org/abs/quant-ph/0604056">major open problem</a> posed 16 years earlier by the complexity theorist Scott Aaronson and the mathematician Greg Kuperberg, about the difficulty of transforming one quantum state into another. The new paper was the first significant step toward settling that question.</p> <div class="related-list"> <aside class="post__aside mb2 relative hide-on-print post__aside--right"> <h2 class="mv0 h5 bold uppercase kern">Related:</h2> <hr class="mt1 o2"> <ol class="post__aside__list theme__anchors--none pt05"> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/finally-a-problem-that-only-quantum-computers-will-ever-be-able-to-solve-20180621/"> <span class="' . $span_class . '">Finally, a Problem That Only Quantum Computers Will Ever Be Able to Solve</span> </a> </h3> </li> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/quantum-computing-test-offers-boost-to-quantum-cryptography-20130821/"> <span class="' . $span_class . '">The Proof in the Quantum Pudding</span> </a> </h3> </li> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/thirty-years-later-a-speed-boost-for-quantum-factoring-20231017/"> <span class="' . $span_class . '">Thirty Years Later, a Speed Boost for Quantum Factoring</span> </a> </h3> </li> </ol> </aside> </div> <p>“It’s a very strong result and also a very surprising result,” said <a href="https://kdb.iimc.kyoto-u.ac.jp/profile/en.0345e7ff26dc30a7.html">Tomoyuki Morimae</a>, a quantum cryptography researcher at the Yukawa Institute for Theoretical Physics in Kyoto.</p> <p>The string of recent results suggests that the innocuous-sounding problem of distinguishing two quantum states is not just hard, but almost inconceivably hard — far beyond the reach of normal quantum algorithms and even more exotic ones. That’s good news for cryptography, but it also has broader implications for computational problems whose inputs are quantum states. Traditional complexity theory seems unable to address these problems. Truly understanding them might require a radically new theoretical framework.</p> <p>“It feels like there’s something fundamentally different about how quantum information behaves,” said <a href="https://www.andreacoladangelo.com/">Andrea Coladangelo</a>, a quantum cryptographer at the University of Washington. “It’s bound to have connections that are also beyond cryptography.”</p> <p><em>Editor’s note: Scott Aaronson is a member of </em>Quanta Magazine<em>’s </em><a href="https://www.quantamagazine.org/about/"><em>advisory board</em></a><em>. His work was mentioned in this article but he played no part in the editorial process. Further, the Simons Institute for the Theory of Computing was established with a grant from the Simons Foundation, which also funds this editorially independent publication. Simons Foundation funding decisions have no influence on our coverage.<br /> </em></p> </div> </div> </div> </section> </div> <div class='pv2'></div> <div class='post__footer'> <div class='mha container--m'> <div class='flex flex-wrap flex-items-stretch'> <div class='post__footer__col fill-h pv2 flex flex-items-center flex-justify-center'> <section class='outer'> <aside class='post__sidebar hide flex flex-justify-center post__sidebar--footer'> <div class='post__sidebar__content'> <div class='post__sidebar__content__inner'> <div class='align-c mb075'> <div class='sidebar__author'> <a class='theme__accent-hover transition--color ' href='https://www.quantamagazine.org/authors/brubaker_ben/'> <div class='sidebar__author__avatar mha mb1'> <div class='image mx0 relative image--circle '> <div class='image__inner absolute fit-x is-loaded'> <img width="1500" height="1500" src="https://www.quantamagazine.org/wp-content/uploads/2022/10/Ben_Brubaker.jpg" class="absolute fit-x fill-h fill-v mxa" 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Cryptographers Discover a New Foundation for Quantum Secrecy | Quanta Magazine