News
Quanta Magazine
In 1994, the computer scientist Peter Shor discovered that if quantum computers were ever invented, they would decimate much of the infrastructure used to protect information shared online. That frightening possibility has had researchers scrambling to produce new, “post-quantum” encryption schemes, to save as much information as they could from falling into the hands of quantum hackers.
Earlier this year, the National Institute of Standards and Technology revealed four finalists in its search for a post-quantum cryptography standard. Three of them use “lattice cryptography” — a scheme inspired by lattices, regular arrangements of dots in space.
Lattice cryptography and other post-quantum possibilities differ from current standards in crucial ways. But they all rely on mathematical asymmetry. The security of many current cryptography systems is based on multiplication and factoring: Any computer can quickly multiply two numbers, but it could take centuries to factor a cryptographically large number into its prime constituents. That asymmetry makes secrets easy to encode but hard to decode.
What Shor revealed in his 1994 algorithm was that a quirk of factoring makes it vulnerable to attack by quantum computers. “It’s a very specific, special thing that the quantum computer can do,” said Katherine Stange, a mathematician at the University of Colorado, Boulder. So after Shor, cryptographers had a new job: Find a novel set of mathematical operations that are easy to do but nearly impossible to undo.
Lattice cryptography is one of the most successful attempts so far. Originally developed in the 1990s, it relies on the difficulty of reverse-engineering sums of points.
Here’s one way to describe lattice cryptography: Imagine your friend has a lattice, which is just a bunch of points in a regular, repeating pattern all over the plane. Your friend wants you to name 10 of these points. But he’s being difficult, and he won’t draw the whole lattice. Instead, he lists just two points — the first with an x-value of 101 and a y-value of 19, the other with coordinates [235, 44].
Luckily, it’s easy to find new points on a lattice, because when you add and subtract any two points on a lattice, you get a third point in the same lattice. So all you have to do is add up the points your friend gave you, or multiply them by integers and then add them up, or some combination of the two. Do this eight different ways, and you’ll be able to answer your friend’s question.
But your friend still isn’t satisfied. He gives you the same two starting points, and then asks you if the point [2, 1] is on the same lattice. To answer this question correctly, you have to find the combination of [101, 19] and [235, 44] that produces [2, 1]. This problem is much harder than the first one, and you’ll probably end up just guessing and checking to get the answer.* That asymmetry is what underlies lattice cryptography.
If you actually want to use lattice cryptography to share information, you’d do the following. Imagine that a friend (a nicer one!) wants to send you a secure message. You start with a square grid of numbers. Say it has two rows and two columns, and looks like this:
Now you come up with a private “key” that only you know. In this example, let’s say your private key is just two secret numbers: 3 and −2. You multiply the numbers in the first column by 3, and the ones in the second column by −2. Add up the results in each row to get a third column with two entries.
Stick the new column onto the end of your grid. This new three-column grid is your public key. Share it freely!
(A real-world scenario will be a bit more complicated. To keep hackers from decoding your private key, you have to add a bit of random noise into your final column. But here we’re going to ignore that step for simplicity’s sake.)
Now your friend will use the public key to send you a message. She thinks of two secret numbers of her own: 2 and 0. She multiplies the numbers in the first row by 2, and the ones in the second row by 0. She then adds up the results in each column to get a third row.
She now attaches the new row to the bottom of the grid and sends it back to you. (Again, in a real system, she’d need to add some noise to her row.)
Now you’ll read the message. To do this, you check to see if your friend’s last row is correct. Apply your own private key to the first two entries of her row. The result should match the last entry.
Your friend can also choose to send you a row with a wrong number in the last column. She knows that this number won’t match your calculations.
If your friend sends a row where the last number is correct, you’ll interpret this as a 0. If she sends a row where the number is incorrect, you’ll interpret it as a 1. The row, therefore, encodes a single bit: either 0 or 1.
Note that an outside attacker won’t have access to either your private key or your friend’s. Without those, the attacker will have no idea if the final number is correct or not.
In practice, you’d like to send messages that are longer than one bit long. So people who want to receive, say, a 100-bit message will generate 100 new columns instead of just one. Then the sender of the message will create a single new row, modifying the last 100 entries to encode either a 0 or a 1 for each entry.
If lattice cryptography is actually implemented, it will have countless nuances not covered in this scenario. For instance, if you want the message to be truly safe from prying eyes, the matrix needs to have an unthinkable number of entries, making the whole thing so unwieldy that it’s not worth using. To get around this, researchers use matrices with useful symmetries that can cut down on the number of parameters. Beyond that, there is a whole suite of tweaks that can be applied to the problem itself, to the way errors are incorporated, and more.
Of course, it’s always possible that someone will find a fatal flaw in lattice cryptography, just as Shor did for factoring. There’s no assurance that a particular cryptographic scheme will work in the face of any possible attack. Cryptography works until it’s cracked. Indeed, earlier this summer one promising post-quantum cryptography scheme was cracked using not a quantum computer, but an ordinary laptop. To Stange, the entire project creates an uncomfortable paradox: “What I find so amazing about cryptography is that we’ve built this infrastructure for the human race on the firm belief that our ability as humans is limited,” she said. “It’s so backward.”
*: The answer, if you’re curious, is 7 × [101, 19] – 3 × [235, 44] = [2, 1]. [back to article]
\r\n // Define dataLayer and the gtag function.\r\n window.dataLayer = window.dataLayer || [];\r\n function gtag(){dataLayer.push(arguments);}\r\n\r\n // Default ad_storage to ‘denied’.\r\n gtag(‘consent’, ‘default’, {\r\n ‘ad_storage’: ‘denied’\r\n });\r\n\u003c\/script>\r\n\u003c\!– Google Tag Manager –>\r\n\u003cscript>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({‘gtm.start’:\r\nnew Date().getTime(),event:’gtm.js’});var f=d.getElementsByTagName(s)[0],\r\nj=d.createElement(s),dl=l!=’dataLayer’?’&l=”+l:”‘;j.async=true;j.src=\r\n’ End Google Tag Manager –>\r\n\u003c\!– Google Tag Manager (noscript) –>\r\n\u003cnoscript>\u003ciframe src=\” width=\”0\” style=\”display:none;visibility:hidden\”>\u003c/iframe>\u003c/noscript>\r\n\u003c\!– End Google Tag Manager (noscript) –>\r\n\u003cscript>\r\nfunction getCookie(name) {\r\n let value = \”; \” + document.cookie;\r\n var parts = value.split(\”; \” + name + \”=\”);\r\n if (parts.length === 2) return parts.pop().split(\”;\”).shift();\r\n}\r\n\r\nif(getCookie(‘acceptedPolicy’)) {\r\n// google analytics\r\n(function(i,s,o,g,r,a,m){i[‘GoogleAnalyticsObject’]=r;i[r]=i[r]||function(){\r\n(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),\r\nm=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)\r\n})(window,document,’script’,’ ‘UA-8526335-13’, ‘auto’);\r\nga(‘set’, ‘forceSSL’, true);\r\nga(‘require’, ‘displayfeatures’);\r\nga(‘send’,’pageview’);\r\n\r\n// facebook pixel\r\n!function(f,b,e,v,n,t,s)\r\n{if(f.fbq)return;n=f.fbq=function()\r\n{n.callMethod? n.callMethod.apply(n,arguments):n.queue.push(arguments)}\r\n;\r\nif(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version=’2.0′;\r\nn.queue=[];t=b.createElement(e);t.async=!0;\r\nt.src=v;s=b.getElementsByTagName(e)[0];\r\ns.parentNode.insertBefore(t,s)}(window,document,’script’,\r\n’ ‘190747804793608’); \r\nfbq(‘track’, ‘PageView’);\r\n\r\n// chartbeat\r\nvar _sf_async_config = { uid: 65564, domain: ‘quantamagazine.org’, useCanonical: true };(function() {function loadChartbeat(){ window._sf_endpt = (new Date()).getTime(); var e = document.createElement(‘script’); e.setAttribute(‘language’, ‘javascript’); e.setAttribute(‘type’, ‘text/javascript’); e.setAttribute(‘src’,’//static.chartbeat.com/js/chartbeat.js’); document.body.appendChild(e); };var oldonload = window.onload;window.onload = (typeof window.onload != ‘function’) ?loadChartbeat : function(){ oldonload(); loadChartbeat(); };})();\r\n\r\n// parsley\r\nconst head = document.getElementsByTagName(‘head’)[0];\r\nconst parsleyScript = document.createElement(\”script\”);\r\nparsleyScript.type = \”text/javascript\”;\r\nparsleyScript.src = \”//cdn.parsely.com/keys/quantamagazine.org/p.js\”;\r\nparsleyScript.id = \”parsley-cfg\”;\r\n// end parsley\r\n\r\n//smartlook\r\n window.smartlook||(function(d) {\r\n var o=smartlook=function(){ o.api.push(arguments)},h=d.getElementsByTagName(‘head’)[0];\r\n var c=d.createElement(‘script’);o.api=new Array();c.async=true;c.type=”text/javascript”;\r\n c.charset=”utf-8″;c.src=” })(document);\r\n smartlook(‘init’, ‘3bac9c73fbc7f7f1c527d035a117e2b66f7c3e30’);\r\n\r\n// Google Ads conversions\r\n window.dataLayer = window.dataLayer || [];\r\n function gtag(){dataLayer.push(arguments);}\r\n gtag(‘js’, new Date());\r\n\r\n gtag(‘config’, ‘AW-10788252298’);\r\n\r\n} else {\r\n(function(i,s,o,g,r,a,m){i[‘GoogleAnalyticsObject’]=r;i[r]=i[r]||function(){\r\n(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),\r\nm=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)\r\n})(window,document,’script’,’ ‘UA-8526335-13’, { storage: ‘none’ });\r\nga(‘set’, ‘anonymizeIp’, true);\r\nga(‘set’, ‘forceSSL’, true);\r\nga(‘require’, ‘displayfeatures’);\r\nga(‘send’,’pageview’);\r\n}\r\n\u003c\/script>\r\n”,”google_analytics”:null,”tracking_scripts_no_cookie”:null,”google_analytics_no_cookie”:null,”popular_searches”:[{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.popular_searches.0″,”typename”:”PopularSearch”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.popular_searches.1″,”typename”:”PopularSearch”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.popular_searches.2″,”typename”:”PopularSearch”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.popular_searches.3″,”typename”:”PopularSearch”}],”search_topics”:[{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.0″,”typename”:”SearchTopic”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.1″,”typename”:”SearchTopic”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.2″,”typename”:”SearchTopic”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.3″,”typename”:”SearchTopic”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.4″,”typename”:”SearchTopic”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.5″,”typename”:”SearchTopic”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.6″,”typename”:”SearchTopic”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.7″,”typename”:”SearchTopic”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.8″,”typename”:”SearchTopic”}],”search_sections”:[{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_sections.0″,”typename”:”Term”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_sections.1″,”typename”:”Term”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_sections.2″,”typename”:”Term”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_sections.3″,”typename”:”Term”}],”search_authors”:[{“type”:”id”,”generated”:false,”id”:”AuthorList:38171″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:28087″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:29794″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:39302″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:56″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:47249″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:29458″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:73″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:39164″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:59″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:8728″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:11648″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:42689″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:95″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:15493″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:450″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:36490″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:16315″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:2752″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:15492″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:68″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:62″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:13684″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:13691″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:50″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:15142″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:8084″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:742″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:11543″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:57″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:7262″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:70″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:19918″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:13695″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:32676″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:13724″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:26310″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:30207″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:19266″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:13251″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:17000″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:17149″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:5279″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:58″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:32612″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:27534″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:25173″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:64″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:47″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:14784″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:98″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:5830″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:6793″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:75″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:52″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:69″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:77″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:19092″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:20557″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:66″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:46418″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:85″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:37141″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:44758″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:12170″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:32″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:51″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:44787″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:72″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:16475″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:91″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:10351″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:31716″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:1241″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:8463″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:49″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:16815″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:67″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:37462″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:87″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:36139″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:20556″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:90″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:39551″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:27374″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:40″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:45758″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:38413″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:12570″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:38699″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:23451″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:79″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:38″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:47180″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:60″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:2333″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:3569″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:414″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:20495″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:17147″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:30953″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:32437″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:38705″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:40613″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:7186″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:14093″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:34″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:23″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:74″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:19093″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:1472″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:6476″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:42264″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:10″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:37605″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:43298″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:37428″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:19962″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:24″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:1816″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:46889″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:84″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:55″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:31″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:24011″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:100″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:2784″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:26114″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:9412″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:820″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:1666″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:20950″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:48″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:80″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:15681″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:24577″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:78″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:23845″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:83″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:35441″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:76″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:15680″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:7239″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:44197″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:65″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:5944″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:61″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:63″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:26311″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:71″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:17148″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:13356″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:17150″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:39768″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:2960″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:14785″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:3″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:54″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:88″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:12964″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:53″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:86″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:3244″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:89″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:15913″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:42263″,”typename”:”AuthorList”},{“type”:”id”,”generated”:false,”id”:”AuthorList:45757″,”typename”:”AuthorList”}],”address_to_editor”:[{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.0″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.1″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.2″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.3″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.4″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.5″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.6″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.7″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.8″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.9″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.10″,”typename”:”Editor”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.address_to_editor.11″,”typename”:”Editor”}]},”$ROOT_QUERY.options”:{“acf”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf”,”typename”:”ThemeOptions”},”__typename”:”Options”},”$ROOT_QUERY.getPostPageArchive({\”slug\”:\”cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\”,\”type\”:\”\”}).data.0.acf”:{“custom_page_colors”:””,”page_accent_color”:null,”page_text_color”:null,”page_background_color”:null,”header_type”:”default”,”header_gradient_color”:null,”header_gradient_opacity”:null,”header_solid_colors”:””,”header_solid_primary_color”:null,”header_solid_secondary_color”:null,”header_solid_hover_color”:null,”header_transparent_colors”:null,”header_transparent_primary_color”:null,”header_transparent_secondary_color”:null,”header_transparent_hover_color”:null,”__typename”:”ACFFields”},”$ROOT_QUERY.getPostPageArchive({\”slug\”:\”cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\”,\”type\”:\”\”}).data.0″:{“acf”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.getPostPageArchive({\”slug\”:\”cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\”,\”type\”:\”\”}).data.0.acf”,”typename”:”ACFFields”},”__typename”:”Post”},”$ROOT_QUERY.getPostPageArchive({\”slug\”:\”cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\”,\”type\”:\”\”})”:{“data”:[{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.getPostPageArchive({\”slug\”:\”cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\”,\”type\”:\”\”}).data.0″,”typename”:”Post”}],”__typename”:”PostPageArchive”},”$ROOT_QUERY.getPageMeta({\”slug\”:\”cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\”,\”type\”:\”\”})”:{“redirect_path”:null,”meta”:”\u003cmeta name=\”description\” content=\”Lattice cryptography promises to protect secrets from the attacks of far-future quantum computers.\” />\n\u003cmeta property=\”og:image\” content=\” />\n\u003cmeta property=\”og:image:width\” content=\”1200\” />\n\u003cmeta property=\”og:image:height\” content=\”630\” />\n\u003cmeta property=\”og:image:alt\” content=\”A purple key drawn on a lattice of points.\” />\n\u003cmeta property=\”og:locale\” content=\”en_US\” />\n\u003cmeta property=\”og:type\” content=\”article\” />\n\u003cmeta property=\”og:title\” content=\”Cryptography’s Future Will Be Quantum-Safe. Here’s How It Will Work. | Quanta Magazine\” />\n\u003cmeta property=\”og:description\” content=\”Lattice cryptography promises to protect secrets from the attacks of far-future quantum computers.\” />\n\u003cmeta property=\”og:url\” content=\” />\n\u003cmeta property=\”og:site_name\” content=\”Quanta Magazine\” />\n\u003cmeta property=\”og:updated_time\” content=\”2022-11-09T15:04+00:00\” />\n\u003cmeta property=\”article:publisher\” content=\” />\n\u003cmeta property=\”fb:app_id\” content=\”533309373681765\” />\n\u003cmeta property=\”article:published_time\” content=\”2022-11-09T15:04+00:00\” />\n\u003cmeta property=\”article:modified_time\” content=\”2022-11-09T15:04+00:00\” />\n\u003cmeta name=\”twitter:card\” content=\”summary_large_image\” />\n\u003cmeta name=\”twitter:site\” content=\”@QuantaMagazine\” />\n\u003cmeta name=\”twitter:title\” content=\”Cryptography’s Future Will Be Quantum-Safe. Here’s How It Will Work. | Quanta Magazine\” />\n\u003cmeta name=\”twitter:description\” content=\”Lattice cryptography promises to protect secrets from the attacks of far-future quantum computers.\” />\n\u003cmeta name=\”twitter:image\” content=\” />\n\u003cmeta name=\”twitter:image:width\” content=\”1200\” />\n\u003cmeta name=\”twitter:image:height\” content=\”630\” />\n\u003cmeta name=\”twitter:image:alt\” content=\”A purple key drawn on a lattice of points.\” />\n\u003clink rel=\”canonical\” href=\” />\n\u003cscript type=\”application/ld+json\”>{\”@context\”:\”https://schema.org\”,\”@type\”:\”BreadcrumbList\”,\”itemListElement\”:[{\”@type\”:\”ListItem\”,\”position\”:1,\”item\”:{\”@id\”:\”https://www.quantamagazine.org/\”,\”name\”:\”Quanta Magazine | Science and Math News\”}},{\”@type\”:\”ListItem\”,\”position\”:2,\”item\”:{\”@id\”:\” blog\”}},{\”@type\”:\”ListItem\”,\”position\”:3,\”item\”:{\”@id\”:\”,\”name\”:\”Cryptography\\u2019s Future Will Be Quantum-Safe. Here\\u2019s How It Will Work.\”}}]}\u003c\/script>\n”,”__typename”:”PageMeta”},”$ROOT_QUERY.options.acf.social_media_links.0″:{“type”:”facebook”,”label”:”Facebook”,”url”:” Joy of Why”,”slug”:”the-joy-of-why”,”description”:”The mathematician and author Steven Strogatz interviews leading researchers about the great scientific and mathematical questions of our time.”,”featured_image”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.channels.0.featured_image”,”typename”:”Image”},”square_image”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.channels.0.square_image”,”typename”:”Image”},”subscribe_itunes_link”:” Science Podcast”,”slug”:”quanta-podcast”,”description”:”Susan Valot narrates in-depth news episodes based on \u003ci>Quanta Magazine\u003c/i>’s articles about mathematics, physics, biology and computer science. “,”featured_image”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.channels.1.featured_image”,”typename”:”Image”},”square_image”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.channels.1.square_image”,”typename”:”Image”},”subscribe_itunes_link”:” of a neuron showing aggregations of tau protein.”,”caption”:””,”url”:” Joy of x”,”slug”:”the-joy-of-x”,”description”:”The acclaimed mathematician and author Steven Strogatz interviews some of the world’s leading scientists about their lives and work.”,”featured_image”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.channels.2.featured_image”,”typename”:”Image”},”square_image”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.channels.2.square_image”,”typename”:”Image”},”subscribe_itunes_link”:” holes”,”label”:”Black Holes”,”__typename”:”PopularSearch”},”$ROOT_QUERY.options.acf.popular_searches.3″:{“term”:”evolution”,”label”:”Evolution”,”__typename”:”PopularSearch”},”$ROOT_QUERY.options.acf.search_topics.0″:{“type”:”Tag”,”label”:”Podcasts”,”tag”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.0.tag”,”typename”:”Term”},”category”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.0.category”,”typename”:”Term”},”__typename”:”SearchTopic”},”$ROOT_QUERY.options.acf.search_topics.0.tag”:{“name”:”Quanta Podcast”,”slug”:”quanta-podcast”,”term_id”:”552″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.0.category”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.1″:{“type”:”Tag”,”label”:”Columns”,”tag”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.1.tag”,”typename”:”Term”},”category”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.1.category”,”typename”:”Term”},”__typename”:”SearchTopic”},”$ROOT_QUERY.options.acf.search_topics.1.tag”:{“name”:”Quantized Columns”,”slug”:”quantized”,”term_id”:”551″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.1.category”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.2″:{“type”:”Series”,”label”:”Series”,”tag”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.2.tag”,”typename”:”Term”},”category”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.2.category”,”typename”:”Term”},”__typename”:”SearchTopic”},”$ROOT_QUERY.options.acf.search_topics.2.tag”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.2.category”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.3″:{“type”:”Category”,”label”:”Interviews”,”tag”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.3.tag”,”typename”:”Term”},”category”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.3.category”,”typename”:”Term”},”__typename”:”SearchTopic”},”$ROOT_QUERY.options.acf.search_topics.3.tag”:{“name”:”Q&A”,”slug”:”qa”,”term_id”:”567″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.3.category”:{“name”:”Q&A”,”slug”:”qa”,”term_id”:”176″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.4″:{“type”:”Category”,”label”:”Multimedia”,”tag”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.4.tag”,”typename”:”Term”},”category”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.4.category”,”typename”:”Term”},”__typename”:”SearchTopic”},”$ROOT_QUERY.options.acf.search_topics.4.tag”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.4.category”:{“name”:”Multimedia”,”slug”:”multimedia”,”term_id”:”43″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.5″:{“type”:”Category”,”label”:”Puzzles”,”tag”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.5.tag”,”typename”:”Term”},”category”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.5.category”,”typename”:”Term”},”__typename”:”SearchTopic”},”$ROOT_QUERY.options.acf.search_topics.5.tag”:{“name”:”puzzles”,”slug”:”puzzles”,”term_id”:”542″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.5.category”:{“name”:”Puzzles”,”slug”:”puzzles”,”term_id”:”546″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.6″:{“type”:”Category”,”label”:”Blog Posts”,”tag”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.6.tag”,”typename”:”Term”},”category”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.6.category”,”typename”:”Term”},”__typename”:”SearchTopic”},”$ROOT_QUERY.options.acf.search_topics.6.tag”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.6.category”:{“name”:”Abstractions blog”,”slug”:”abstractions”,”term_id”:”619″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.7″:{“type”:”news”,”label”:”News Articles”,”tag”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.7.tag”,”typename”:”Term”},”category”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.7.category”,”typename”:”Term”},”__typename”:”SearchTopic”},”$ROOT_QUERY.options.acf.search_topics.7.tag”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.7.category”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.8″:{“type”:”videos”,”label”:”Videos”,”tag”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.8.tag”,”typename”:”Term”},”category”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.options.acf.search_topics.8.category”,”typename”:”Term”},”__typename”:”SearchTopic”},”$ROOT_QUERY.options.acf.search_topics.8.tag”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_topics.8.category”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_sections.0″:{“name”:”Mathematics”,”slug”:”mathematics”,”term_id”:”188″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_sections.1″:{“name”:”Physics”,”slug”:”physics”,”term_id”:”189″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_sections.2″:{“name”:”Biology”,”slug”:”biology”,”term_id”:”191″,”__typename”:”Term”},”$ROOT_QUERY.options.acf.search_sections.3″:{“name”:”Computer Science”,”slug”:”computer-science”,”term_id”:”190″,”__typename”:”Term”},”AuthorList:38171″:{“id”:”38171″,”name”:”Adam Becker”,”__typename”:”AuthorList”},”AuthorList:28087″:{“id”:”28087″,”name”:”Adam Mann”,”__typename”:”AuthorList”},”AuthorList:29794″:{“id”:”29794″,”name”:”Alex Kontorovich”,”__typename”:”AuthorList”},”AuthorList:39302″:{“id”:”39302″,”name”:”Alexander Hellemans”,”__typename”:”AuthorList”},”AuthorList:56″:{“id”:”56″,”name”:”Alla Katsnelson”,”__typename”:”AuthorList”},”AuthorList:47249″:{“id”:”47249″,”name”:”Allison Parshall”,”__typename”:”AuthorList”},”AuthorList:29458″:{“id”:”29458″,”name”:”Allison Whitten”,”__typename”:”AuthorList”},”AuthorList:73″:{“id”:”73″,”name”:”Amanda Gefter”,”__typename”:”AuthorList”},”AuthorList:39164″:{“id”:”39164″,”name”:”Ana Kova”,”__typename”:”AuthorList”},”AuthorList:59″:{“id”:”59″,”name”:”Andreas von Bubnoff”,”__typename”:”AuthorList”},”AuthorList:8728″:{“id”:”8728″,”name”:”Anil Ananthaswamy”,”__typename”:”AuthorList”},”AuthorList:11648″:{“id”:”11648″,”name”:”Ann Finkbeiner”,”__typename”:”AuthorList”},”AuthorList:42689″:{“id”:”42689″,”name”:”Annie Melchor”,”__typename”:”AuthorList”},”AuthorList:95″:{“id”:”95″,”name”:”Ariel Bleicher”,”__typename”:”AuthorList”},”AuthorList:15493″:{“id”:”15493″,”name”:”Ashley Smart”,”__typename”:”AuthorList”},”AuthorList:450″:{“id”:”450″,”name”:”Ashley Yeager”,”__typename”:”AuthorList”},”AuthorList:36490″:{“id”:”36490″,”name”:”Ben Brubaker”,”__typename”:”AuthorList”},”AuthorList:16315″:{“id”:”16315″,”name”:”Bill Andrews”,”__typename”:”AuthorList”},”AuthorList:2752″:{“id”:”2752″,”name”:”Bob Henderson”,”__typename”:”AuthorList”},”AuthorList:15492″:{“id”:”15492″,”name”:”Brendan Z. Foster”,”__typename”:”AuthorList”},”AuthorList:68″:{“id”:”68″,”name”:”Brooke Borel”,”__typename”:”AuthorList”},”AuthorList:62″:{“id”:”62″,”name”:”Carl Zimmer”,”__typename”:”AuthorList”},”AuthorList:13684″:{“id”:”13684″,”name”:”Caroline Lee”,”__typename”:”AuthorList”},”AuthorList:13691″:{“id”:”13691″,”name”:”Caroline Lee”,”__typename”:”AuthorList”},”AuthorList:50″:{“id”:”50″,”name”:”Carrie Arnold”,”__typename”:”AuthorList”},”AuthorList:15142″:{“id”:”15142″,”name”:”Chanda Prescod-Weinstein”,”__typename”:”AuthorList”},”AuthorList:8084″:{“id”:”8084″,”name”:”Charlie Wood”,”__typename”:”AuthorList”},”AuthorList:742″:{“id”:”742″,”name”:”Christie Wilcox”,”__typename”:”AuthorList”},”AuthorList:11543″:{“id”:”11543″,”name”:”Claudia Dreifus”,”__typename”:”AuthorList”},”AuthorList:57″:{“id”:”57″,”name”:”Courtney Humphries”,”__typename”:”AuthorList”},”AuthorList:7262″:{“id”:”7262″,”name”:”Dalmeet Singh Chawla”,”__typename”:”AuthorList”},”AuthorList:70″:{“id”:”70″,”name”:”Dan Falk”,”__typename”:”AuthorList”},”AuthorList:19918″:{“id”:”19918″,”name”:”Dana Najjar”,”__typename”:”AuthorList”},”AuthorList:13695″:{“id”:”13695″,”name”:”Daniel Garisto”,”__typename”:”AuthorList”},”AuthorList:32676″:{“id”:”32676″,”name”:”Daniel S. Freed”,”__typename”:”AuthorList”},”AuthorList:13724″:{“id”:”13724″,”name”:”David H. Freedman”,”__typename”:”AuthorList”},”AuthorList:26310″:{“id”:”26310″,”name”:”David S. Richeson”,”__typename”:”AuthorList”},”AuthorList:30207″:{“id”:”30207″,”name”:”David Tse”,”__typename”:”AuthorList”},”AuthorList:19266″:{“id”:”19266″,”name”:”Devin Powell”,”__typename”:”AuthorList”},”AuthorList:13251″:{“id”:”13251″,”name”:”Diana Kwon”,”__typename”:”AuthorList”},”AuthorList:17000″:{“id”:”17000″,”name”:”Elena Renken”,”__typename”:”AuthorList”},”AuthorList:17149″:{“id”:”17149″,”name”:”Elizabeth Landau”,”__typename”:”AuthorList”},”AuthorList:5279″:{“id”:”5279″,”name”:”Elizabeth Preston”,”__typename”:”AuthorList”},”AuthorList:58″:{“id”:”58″,”name”:”Elizabeth Svoboda”,”__typename”:”AuthorList”},”AuthorList:32612″:{“id”:”32612″,”name”:”Ellen Horne”,”__typename”:”AuthorList”},”AuthorList:27534″:{“id”:”27534″,”name”:”Emily Buder”,”__typename”:”AuthorList”},”AuthorList:25173″:{“id”:”25173″,”name”:”Emily Levesque”,”__typename”:”AuthorList”},”AuthorList:64″:{“id”:”64″,”name”:”Emily Singer”,”__typename”:”AuthorList”},”AuthorList:47″:{“id”:”47″,”name”:”Erica Klarreich”,”__typename”:”AuthorList”},”AuthorList:14784″:{“id”:”14784″,”name”:”Erika K. Carlson”,”__typename”:”AuthorList”},”AuthorList:98″:{“id”:”98″,”name”:”Esther Landhuis”,”__typename”:”AuthorList”},”AuthorList:5830″:{“id”:”5830″,”name”:”Eva Silverstein”,”__typename”:”AuthorList”},”AuthorList:6793″:{“id”:”6793″,”name”:”Evelyn Lamb”,”__typename”:”AuthorList”},”AuthorList:75″:{“id”:”75″,”name”:”Ferris Jabr”,”__typename”:”AuthorList”},”AuthorList:52″:{“id”:”52″,”name”:”Frank Wilczek”,”__typename”:”AuthorList”},”AuthorList:69″:{“id”:”69″,”name”:”Gabriel Popkin”,”__typename”:”AuthorList”},”AuthorList:77″:{“id”:”77″,”name”:”George Musser”,”__typename”:”AuthorList”},”AuthorList:19092″:{“id”:”19092″,”name”:”Grant Sanderson”,”__typename”:”AuthorList”},”AuthorList:20557″:{“id”:”20557″,”name”:”Howard Lee”,”__typename”:”AuthorList”},”AuthorList:66″:{“id”:”66″,”name”:”Ingrid Daubechies”,”__typename”:”AuthorList”},”AuthorList:46418″:{“id”:”46418″,”name”:”Ingrid Wickelgren”,”__typename”:”AuthorList”},”AuthorList:85″:{“id”:”85″,”name”:”Ivan Amato”,”__typename”:”AuthorList”},”AuthorList:37141″:{“id”:”37141″,”name”:”Jake Buehler”,”__typename”:”AuthorList”},”AuthorList:44758″:{“id”:”44758″,”name”:”James Dinneen”,”__typename”:”AuthorList”},”AuthorList:12170″:{“id”:”12170″,”name”:”Janna Levin”,”__typename”:”AuthorList”},”AuthorList:32″:{“id”:”32″,”name”:”Jeanette Kazmierczak”,”__typename”:”AuthorList”},”AuthorList:51″:{“id”:”51″,”name”:”Jennifer Ouellette”,”__typename”:”AuthorList”},”AuthorList:44787″:{“id”:”44787″,”name”:”Joanna Thompson”,”__typename”:”AuthorList”},”AuthorList:72″:{“id”:”72″,”name”:”John Pavlus”,”__typename”:”AuthorList”},”AuthorList:16475″:{“id”:”16475″,”name”:”John Preskill”,”__typename”:”AuthorList”},”AuthorList:91″:{“id”:”91″,”name”:”John Rennie”,”__typename”:”AuthorList”},”AuthorList:10351″:{“id”:”10351″,”name”:”Jonathan Lambert”,”__typename”:”AuthorList”},”AuthorList:31716″:{“id”:”31716″,”name”:”Jonathan O’Callaghan”,”__typename”:”AuthorList”},”AuthorList:1241″:{“id”:”1241″,”name”:”Jordana Cepelewicz”,”__typename”:”AuthorList”},”AuthorList:8463″:{“id”:”8463″,”name”:”Joshua Roebke”,”__typename”:”AuthorList”},”AuthorList:49″:{“id”:”49″,”name”:”Joshua Sokol”,”__typename”:”AuthorList”},”AuthorList:16815″:{“id”:”16815″,”name”:”jye”,”__typename”:”AuthorList”},”AuthorList:67″:{“id”:”67″,”name”:”K.C. Cole”,”__typename”:”AuthorList”},”AuthorList:37462″:{“id”:”37462″,”name”:”Karmela Padavic-Callaghan”,”__typename”:”AuthorList”},”AuthorList:87″:{“id”:”87″,”name”:”Kat McGowan”,”__typename”:”AuthorList”},”AuthorList:36139″:{“id”:”36139″,”name”:”Katarina Zimmer”,”__typename”:”AuthorList”},”AuthorList:20556″:{“id”:”20556″,”name”:”Katherine Harmon Courage”,”__typename”:”AuthorList”},”AuthorList:90″:{“id”:”90″,”name”:”Katia Moskvitch”,”__typename”:”AuthorList”},”AuthorList:39551″:{“id”:”39551″,”name”:”Katie McCormick”,”__typename”:”AuthorList”},”AuthorList:27374″:{“id”:”27374″,”name”:”Kelsey Houston-Edwards”,”__typename”:”AuthorList”},”AuthorList:40″:{“id”:”40″,”name”:”Kevin Hartnett”,”__typename”:”AuthorList”},”AuthorList:45758″:{“id”:”45758″,”name”:”Kristina Armitage”,”__typename”:”AuthorList”},”AuthorList:38413″:{“id”:”38413″,”name”:”Lakshmi Chandrasekaran”,”__typename”:”AuthorList”},”AuthorList:12570″:{“id”:”12570″,”name”:”Laura Poppick”,”__typename”:”AuthorList”},”AuthorList:38699″:{“id”:”38699″,”name”:”Leila Sloman”,”__typename”:”AuthorList”},”AuthorList:23451″:{“id”:”23451″,”name”:”Liam Drew”,”__typename”:”AuthorList”},”AuthorList:79″:{“id”:”79″,”name”:”Liz Kruesi”,”__typename”:”AuthorList”},”AuthorList:38″:{“id”:”38″,”name”:”Lucy Reading-Ikkanda”,”__typename”:”AuthorList”},”AuthorList:47180″:{“id”:”47180″,”name”:”Lyndie Chiou”,”__typename”:”AuthorList”},”AuthorList:60″:{“id”:”60″,”name”:”Maggie McKee”,”__typename”:”AuthorList”},”AuthorList:2333″:{“id”:”2333″,”name”:”Mallory Locklear”,”__typename”:”AuthorList”},”AuthorList:3569″:{“id”:”3569″,”name”:”Marcus Woo”,”__typename”:”AuthorList”},”AuthorList:414″:{“id”:”414″,”name”:”Mark Kim-Mulgrew”,”__typename”:”AuthorList”},”AuthorList:20495″:{“id”:”20495″,”name”:”Matt Carlstrom”,”__typename”:”AuthorList”},”AuthorList:17147″:{“id”:”17147″,”name”:”Matthew Hutson”,”__typename”:”AuthorList”},”AuthorList:30953″:{“id”:”30953″,”name”:”Max G. Levy”,”__typename”:”AuthorList”},”AuthorList:32437″:{“id”:”32437″,”name”:”Max Kozlov”,”__typename”:”AuthorList”},”AuthorList:38705″:{“id”:”38705″,”name”:”mcho”,”__typename”:”AuthorList”},”AuthorList:40613″:{“id”:”40613″,”name”:”Melanie Mitchell”,”__typename”:”AuthorList”},”AuthorList:7186″:{“id”:”7186″,”name”:”Melinda Wenner Moyer”,”__typename”:”AuthorList”},”AuthorList:14093″:{“id”:”14093″,”name”:”Michael Harris”,”__typename”:”AuthorList”},”AuthorList:34″:{“id”:”34″,”name”:”Michael Kranz”,”__typename”:”AuthorList”},”AuthorList:23″:{“id”:”23″,”name”:”Michael Moyer”,”__typename”:”AuthorList”},”AuthorList:74″:{“id”:”74″,”name”:”Michael Nielsen”,”__typename”:”AuthorList”},”AuthorList:19093″:{“id”:”19093″,”name”:”Michele Bannister”,”__typename”:”AuthorList”},”AuthorList:1472″:{“id”:”1472″,”name”:”Moira Chas”,”__typename”:”AuthorList”},”AuthorList:6476″:{“id”:”6476″,”name”:”Monique Brouillette”,”__typename”:”AuthorList”},”AuthorList:42264″:{“id”:”42264″,”name”:”Mordechai Rorvig”,”__typename”:”AuthorList”},”AuthorList:10″:{“id”:”10″,”name”:”Natalie Wolchover”,”__typename”:”AuthorList”},”AuthorList:37605″:{“id”:”37605″,”name”:”Nick Thieme”,”__typename”:”AuthorList”},”AuthorList:43298″:{“id”:”43298″,”name”:”Nicole Yunger Halpern”,”__typename”:”AuthorList”},”AuthorList:37428″:{“id”:”37428″,”name”:”Nima Arkani-Hamed”,”__typename”:”AuthorList”},”AuthorList:19962″:{“id”:”19962″,”name”:”Nola Taylor Redd”,”__typename”:”AuthorList”},”AuthorList:24″:{“id”:”24″,”name”:”Olena Shmahalo”,”__typename”:”AuthorList”},”AuthorList:1816″:{“id”:”1816″,”name”:”Patrick Honner”,”__typename”:”AuthorList”},”AuthorList:46889″:{“id”:”46889″,”name”:”Paul Chaikin”,”__typename”:”AuthorList”},”AuthorList:84″:{“id”:”84″,”name”:”Peter Byrne”,”__typename”:”AuthorList”},”AuthorList:55″:{“id”:”55″,”name”:”Philip Ball”,”__typename”:”AuthorList”},”AuthorList:31″:{“id”:”31″,”name”:”Pradeep Mutalik”,”__typename”:”AuthorList”},”AuthorList:24011″:{“id”:”24011″,”name”:”Puja Changoiwala”,”__typename”:”AuthorList”},”AuthorList:100″:{“id”:”100″,”name”:”Quanta Magazine”,”__typename”:”AuthorList”},”AuthorList:2784″:{“id”:”2784″,”name”:”R. Douglas Fields”,”__typename”:”AuthorList”},”AuthorList:26114″:{“id”:”26114″,”name”:”Rachel Crowell”,”__typename”:”AuthorList”},”AuthorList:9412″:{“id”:”9412″,”name”:”Raleigh McElvery”,”__typename”:”AuthorList”},”AuthorList:820″:{“id”:”820″,”name”:”Ramin Skibba”,”__typename”:”AuthorList”},”AuthorList:1666″:{“id”:”1666″,”name”:”Rebecca Boyle”,”__typename”:”AuthorList”},”AuthorList:20950″:{“id”:”20950″,”name”:”Richard Masland”,”__typename”:”AuthorList”},”AuthorList:48″:{“id”:”48″,”name”:”Robbert Dijkgraaf”,”__typename”:”AuthorList”},”AuthorList:80″:{“id”:”80″,”name”:”Roberta Kwok”,”__typename”:”AuthorList”},”AuthorList:15681″:{“id”:”15681″,”name”:”Robin George Andrews”,”__typename”:”AuthorList”},”AuthorList:24577″:{“id”:”24577″,”name”:”Rodrigo Pérez Ortega”,”__typename”:”AuthorList”},”AuthorList:78″:{“id”:”78″,”name”:”Sabine Hossenfelder”,”__typename”:”AuthorList”},”AuthorList:23845″:{“id”:”23845″,”name”:”Samuel Velasco”,”__typename”:”AuthorList”},”AuthorList:83″:{“id”:”83″,”name”:”Sarah Lewin”,”__typename”:”AuthorList”},”AuthorList:35441″:{“id”:”35441″,”name”:”Scott Aaronson”,”__typename”:”AuthorList”},”AuthorList:76″:{“id”:”76″,”name”:”Sean B. Carroll”,”__typename”:”AuthorList”},”AuthorList:15680″:{“id”:”15680″,”name”:”Sean Carroll”,”__typename”:”AuthorList”},”AuthorList:7239″:{“id”:”7239″,”name”:”Shannon Hall”,”__typename”:”AuthorList”},”AuthorList:44197″:{“id”:”44197″,”name”:”Sheon Han”,”__typename”:”AuthorList”},”AuthorList:65″:{“id”:”65″,”name”:”Siobhan Roberts”,”__typename”:”AuthorList”},”AuthorList:5944″:{“id”:”5944″,”name”:”Sophia Chen”,”__typename”:”AuthorList”},”AuthorList:61″:{“id”:”61″,”name”:”Steph Yin”,”__typename”:”AuthorList”},”AuthorList:63″:{“id”:”63″,”name”:”Stephanie Bucklin”,”__typename”:”AuthorList”},”AuthorList:26311″:{“id”:”26311″,”name”:”Stephanie DeMarco”,”__typename”:”AuthorList”},”AuthorList:71″:{“id”:”71″,”name”:”Stephen Ornes”,”__typename”:”AuthorList”},”AuthorList:17148″:{“id”:”17148″,”name”:”Steve Nadis”,”__typename”:”AuthorList”},”AuthorList:13356″:{“id”:”13356″,”name”:”Steven Strogatz”,”__typename”:”AuthorList”},”AuthorList:17150″:{“id”:”17150″,”name”:”Susan D’Agostino”,”__typename”:”AuthorList”},”AuthorList:39768″:{“id”:”39768″,”name”:”Tamar Lichter Blanks”,”__typename”:”AuthorList”},”AuthorList:2960″:{“id”:”2960″,”name”:”Tara C. Smith”,”__typename”:”AuthorList”},”AuthorList:14785″:{“id”:”14785″,”name”:”Thomas Lewton”,”__typename”:”AuthorList”},”AuthorList:3″:{“id”:”3″,”name”:”Thomas Lin”,”__typename”:”AuthorList”},”AuthorList:54″:{“id”:”54″,”name”:”Tim Vernimmen”,”__typename”:”AuthorList”},”AuthorList:88″:{“id”:”88″,”name”:”Tom Siegfried”,”__typename”:”AuthorList”},”AuthorList:12964″:{“id”:”12964″,”name”:”Vanessa Schipani”,”__typename”:”AuthorList”},”AuthorList:53″:{“id”:”53″,”name”:”Veronique Greenwood”,”__typename”:”AuthorList”},”AuthorList:86″:{“id”:”86″,”name”:”Virginia Hughes”,”__typename”:”AuthorList”},”AuthorList:3244″:{“id”:”3244″,”name”:”Viviane Callier”,”__typename”:”AuthorList”},”AuthorList:89″:{“id”:”89″,”name”:”Wynne Parry”,”__typename”:”AuthorList”},”AuthorList:15913″:{“id”:”15913″,”name”:”XiaoZhi Lim”,”__typename”:”AuthorList”},”AuthorList:42263″:{“id”:”42263″,”name”:”Yasemin Saplakoglu”,”__typename”:”AuthorList”},”AuthorList:45757″:{“id”:”45757″,”name”:”Zack Savitsky”,”__typename”:”AuthorList”},”$ROOT_QUERY.options.acf.address_to_editor.0″:{“name”:”Bill Andrews – Senior CS Editor”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.1″:{“name”:”Ben Brubaker – Staff CS Writer”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.2″:{“name”:”Matt Carlstrom – Senior Engagement Editor”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.3″:{“name”:”Jordana Cepelewicz – Senior Math Writer”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.4″:{“name”:”Konstantin Kakaes – Senior Math Editor”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.5″:{“name”:”Thomas Lin – Editor in Chief”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.6″:{“name”:”Michael Moyer – Deputy Editor, Physics, Math, CS”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.7″:{“name”:”John Rennie – Deputy Editor, Biology, Podcasts”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.8″:{“name”:”Yasemin Saplakoglu – Staff Biology Writer”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.9″:{“name”:”Samuel Velasco – Art Director”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.10″:{“name”:”Natalie Wolchover – Senior Physics Editor”,”__typename”:”Editor”},”$ROOT_QUERY.options.acf.address_to_editor.11″:{“name”:”Charlie Wood – Staff Physics Writer”,”__typename”:”Editor”},”$ROOT_QUERY.menu({\”slug\”:\”footer\”}).items.0″:{“title”:”About Quanta”,”url”:” Us”,”url”:” & Conditions”,”url”:” Policy”,”url”:” Foundation”,”url”:”http://www.simonsfoundation.org”,”order”:6,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”footer\”})”:{“items”:[{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”footer\”}).items.0″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”footer\”}).items.1″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”footer\”}).items.2″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”footer\”}).items.3″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”footer\”}).items.4″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”footer\”}).items.5″,”typename”:”MenuItem”}],”__typename”:”Menu”},”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.0″:{“title”:”Physics”,”url”:”https://www.quantamagazine.org/physics/”,”order”:1,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.1″:{“title”:”Mathematics”,”url”:”https://www.quantamagazine.org/mathematics/”,”order”:2,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.2″:{“title”:”Biology”,”url”:”https://www.quantamagazine.org/biology/”,”order”:3,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.3″:{“title”:”Computer Science”,”url”:”https://www.quantamagazine.org/computer-science/”,”order”:4,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.4″:{“title”:”Topics”,”url”:”https://www.quantamagazine.org/topics”,”order”:5,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.5″:{“title”:”Archive”,”url”:”https://www.quantamagazine.org/archive/”,”order”:6,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”})”:{“items”:[{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.0″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.1″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.2″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.3″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.4″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”main-menu\”}).items.5″,”typename”:”MenuItem”}],”__typename”:”Menu”},”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.0″:{“title”:”Blog”,”url”:”https://www.quantamagazine.org/abstractions/”,”order”:1,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.1″:{“title”:”Q&A”,”url”:”https://www.quantamagazine.org/qa/”,”order”:2,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.2″:{“title”:”Columns”,”url”:”/tag/quantized”,”order”:3,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.3″:{“title”:”Puzzles”,”url”:”https://www.quantamagazine.org/puzzles/”,”order”:4,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.4″:{“title”:”Podcasts”,”url”:”/podcasts/”,”order”:5,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.5″:{“title”:”Videos”,”url”:”/videos”,”order”:6,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.6″:{“title”:”Multimedia”,”url”:”https://www.quantamagazine.org/multimedia/”,”order”:7,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.7″:{“title”:”About Quanta”,”url”:”https://www.quantamagazine.org/about/”,”order”:8,”__typename”:”MenuItem”},”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”})”:{“items”:[{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.0″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.1″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.2″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.3″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.4″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.5″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.6″,”typename”:”MenuItem”},{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.menu({\”slug\”:\”secondary-menu\”}).items.7″,”typename”:”MenuItem”}],”__typename”:”Menu”},”$ROOT_QUERY.getPostPageArchive({\”slug\”:\”cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\”})”:{“type”:”post”,”meta”:{“type”:”id”,”generated”:true,”id”:”$ROOT_QUERY.getPostPageArchive({\”slug\”:\”cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\”}).meta”,”typename”:”PageData”},”data”:[{“type”:”id”,”generated”:false,”id”:”Post:120459″,”typename”:”Post”}],”__typename”:”PostPageArchive”},”$ROOT_QUERY.getPostPageArchive({\”slug\”:\”cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\”}).meta”:{“title”:”Cryptography’s Future Will Be Quantum-Safe. Here’s How It Will Work. | Quanta Magazine”,”max_num_pages”:0,”found_posts”:0,”extra_term”:””,”author”:{“type”:”id”,”generated”:false,”id”:”Author:null”,”typename”:”Author”},”tag”:{“type”:”id”,”generated”:false,”id”:”Term:null”,”typename”:”Term”},”category”:{“type”:”id”,”generated”:false,”id”:”Term:null”,”typename”:”Term”},”__typename”:”PageData”},”Author:null”:{“id”:null,”name”:null,”link”:null,”description”:null,”url”:null,”public_email”:null,”facebook”:null,”twitter”:null,”instagram”:null,”acf”:null,”__typename”:”Author”},”Term:null”:{“id”:null,”slug”:null,”name”:null,”link”:null,”description”:null,”image”:””,”__typename”:”Term”},”Post:120459″:{“id”:”120459″,”title”:”Cryptography’s Future Will Be Quantum-Safe. Here’s How It Will Work.”,”excerpt”:”\u003cp>Lattice cryptography promises to protect secrets from the attacks of far-future quantum computers. \u003c/p>\n”,”link”:” https://www.quantamagazine.org/?p=120459″,”date”:”2022-11-09T10:04:37″,”featured_media_image”:null,”authors”:[{“type”:”id”,”generated”:true,”id”:”Post:120459.authors.0″,”typename”:”Author”}],”tags”:[{“type”:”id”,”generated”:true,”id”:”Post:120459.tags.0″,”typename”:”Term”},{“type”:”id”,”generated”:true,”id”:”Post:120459.tags.1″,”typename”:”Term”},{“type”:”id”,”generated”:true,”id”:”Post:120459.tags.2″,”typename”:”Term”},{“type”:”id”,”generated”:true,”id”:”Post:120459.tags.3″,”typename”:”Term”},{“type”:”id”,”generated”:true,”id”:”Post:120459.tags.4″,”typename”:”Term”},{“type”:”id”,”generated”:true,”id”:”Post:120459.tags.5″,”typename”:”Term”},{“type”:”id”,”generated”:true,”id”:”Post:120459.tags.6″,”typename”:”Term”}],”podcast”:null,”acf”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf”,”typename”:”ACFFields”},”__typename”:”Post”,”status”:”publish”,”content”:””,”categories”:[{“type”:”id”,”generated”:false,”id”:”Term:619″,”typename”:”Term”},{“type”:”id”,”generated”:false,”id”:”Term:188″,”typename”:”Term”}],”attachments”:null,”series_prev”:null,”series_next”:null,”next”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.next”,”typename”:”PostPageArchive”}},”Post:120459.authors.0″:{“name”:”Leila Sloman”,”link”:” blog”,”link”:” science”,”link”:” security”,”link”:” computing”,”link”:” Cryptography’s Quantum-Safe Future Will Work”,”kicker”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.kicker”,”typename”:”Term”},”featured_image_default”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.featured_image_default”,”typename”:”Image”},”featured_image_square”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.featured_image_square”,”typename”:”Image”},”featured_image_full_width”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.featured_image_full_width”,”typename”:”Image”},”featured_image_gif”:false,”featured_video”:”false”,”full_page_interactive”:false,”podcast_publish_date”:””,”__typename”:”ACFFields”,”interactive_type”:null,”iframe_url”:null,”return_cursor”:null,”exclude_blurb”:null,”interactive_html”:null,”interactive_css”:null,”interactive_js”:null,”interactive_blurb”:null,”related_article”:null,”modules”:[{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.modules.0″,”typename”:”ACFImageComponent”},{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.modules.1″,”typename”:”ACFContent”}],”template”:”article”,”subtitle”:”Lattice cryptography promises to protect secrets from the attacks of far-future quantum computers. “,”title_layout”:”default”,”title_background_type”:null,”title_background_image”:null,”title_background_video”:null,”title_background_attribution”:null,”title_background_image_gif”:null,”title_overlay_enable”:null,”title_overlay_color”:null,”title_overlay_opacity”:null,”title_text_color”:null,”featured_image_attribution”:”\u003cp>Kristina Armitage/Quanta Magazine\u003c/p>\n”,”featured_overlay_enable”:”false”,”featured_overlay_color”:null,”featured_overlay_opacity”:null,”series”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.series”,”typename”:”Term”},”intro_content”:null,”make_image_full_width”:null,”hide_ad_on_post”:false},”$Post:120459.acf.kicker”:{“name”:”explainers”,”link”:” purple key drawn on a lattice of points.”,”caption”:””,”url”:” purple key drawn on a lattice of points.”,”caption”:””,”url”:” purple key drawn on a lattice of points.”,”caption”:””,”url”:” blog”,”slug”:”abstractions”,”link”:” Writer”,”avatar”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.authors.0.acf.avatar”,”typename”:”Image”},”__typename”:”AuthorACF”},”$Post:120459.authors.0.acf.avatar”:{“alt”:””,”caption”:””,”url”:” Armitage/Quanta Magazine\u003c/p>\n”,”caption”:”\u003cp>Lattice cryptography relies on mathematical lattices — arrangements of dots in space.\u003c/p>\n”,”mobile_comp_caption”:””,”mobile_comp_attribution”:””,”sets”:[{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.modules.0.sets.0″,”typename”:”ImageSet”}],”__typename”:”ACFImageComponent”},”$Post:120459.acf.modules.0.sets.0″:{“settings”:””,”image”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.modules.0.sets.0.image”,”typename”:”Image”},”mobile_image”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.modules.0.sets.0.mobile_image”,”typename”:”Image”},”mobile_side_margins”:false,”mobile_width_constraint”:””,”mobile_caption”:””,”mobile_attribution”:””,”zoom_image”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.modules.0.sets.0.zoom_image”,”typename”:”Image”},”zoom_caption”:””,”zoom_attribution”:””,”mobile_zoom_image”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.acf.modules.0.sets.0.mobile_zoom_image”,”typename”:”Image”},”mobile_zoom_caption”:””,”mobile_zoom_attribution”:””,”external_link”:””,”__typename”:”ImageSet”},”$Post:120459.acf.modules.0.sets.0.image”:{“alt”:”A purple key drawn on a lattice of points.”,”caption”:””,”url”:” 1994, the computer scientist Peter Shor \u003ca href=\” that if quantum computers were ever invented, they would decimate much of the infrastructure used to protect information shared online. That frightening possibility has had researchers scrambling to produce new, “post-quantum” encryption schemes, to save as much information as they could from falling into the hands of quantum hackers.\u003c/p>\n\u003cp>Earlier this year, the National Institute of Standards and Technology \u003ca href=\” four finalists in its search for a post-quantum cryptography standard. Three of them use “lattice cryptography” — a scheme inspired by lattices, regular arrangements of dots in space.\u003c/p>\n\u003cp>Lattice cryptography and other post-quantum possibilities differ from current standards in crucial ways. But they all rely on mathematical asymmetry. The security of many current cryptography systems is based on multiplication and factoring: Any computer can quickly multiply two numbers, but it could take centuries to factor a cryptographically large number into its prime constituents. That asymmetry makes secrets easy to encode but hard to decode.\u003c/p>\n\u003cdiv id=’component-636bc1a03cb16′ class=””>\u003cscript type=\”text/template\”>{\”type\”:\”CategoryDetails\”,\”id\”:\”component-636bc1a03cb16\”,\”data\”:{\”type\”:\”category\”,\”id\”:619,\”title\”:\”Abstractions blog\”,\”description\”:\”\u003cem>Abstractions\u003c\\/em> navigates promising ideas in science and mathematics. Journey with us and join the conversation.\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/abstractions\\/\”,\”image\”:{\”ID\”:41194,\”id\”:41194,\”title\”:\”Abstractions\”,\”filename\”:\”Abstractions.png\”,\”filesize\”:17245,\”url\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2017\\/04\\/Abstractions.png\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/new-algorithm-solves-cake-cutting-problem-20161006\\/abstractions\\/\”,\”alt\”:\”Abstractions logo\”,\”author\”:\”24\”,\”description\”:\”\”,\”caption\”:\”Abstractions\\u200b navigates promising ideas in science and mathematics. Journey with us and join the conversation.\”,\”name\”:\”abstractions\”,\”status\”:\”inherit\”,\”uploaded_to\”:30685,\”date\”:\”2017-04-19 21:19:01\”,\”modified\”:\”2017-04-28 15:40:02\”,\”menu_order\”:0,\”mime_type\”:\”image\\/png\”,\”type\”:\”image\”,\”subtype\”:\”png\”,\”icon\”:\”https:\\/\\/api.quantamagazine.org\\/wp-includes\\/images\\/media\\/default.png\”,\”width\”:600,\”height\”:520,\”sizes\”:{\”thumbnail\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2017\\/04\\/Abstractions-520×451.png\”,\”thumbnail-width\”:520,\”thumbnail-height\”:451,\”medium\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2017\\/04\\/Abstractions.png\”,\”medium-width\”:600,\”medium-height\”:520,\”medium_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2017\\/04\\/Abstractions.png\”,\”medium_large-width\”:600,\”medium_large-height\”:520,\”large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2017\\/04\\/Abstractions.png\”,\”large-width\”:600,\”large-height\”:520,\”1536×1536\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2017\\/04\\/Abstractions.png\”,\”1536×1536-width\”:600,\”1536×1536-height\”:520,\”2048×2048\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2017\\/04\\/Abstractions.png\”,\”2048×2048-width\”:600,\”2048×2048-height\”:520,\”square_small\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2017\\/04\\/Abstractions-160×160.png\”,\”square_small-width\”:160,\”square_small-height\”:160,\”square_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2017\\/04\\/Abstractions-520×520.png\”,\”square_large-width\”:520,\”square_large-height\”:520}}}}\u003c\/script>\u003c/div>\n\u003cp>What Shor revealed in his 1994 algorithm was that a quirk of factoring makes it vulnerable to attack by quantum computers. “It’s a very specific, special thing that the quantum computer can do,” said \u003ca href=\” Stange\u003c/a>, a mathematician at the University of Colorado, Boulder. So after Shor, cryptographers had a new job: Find a novel set of mathematical operations that are easy to do but nearly impossible to undo.\u003c/p>\n\u003cp>Lattice cryptography is one of the most successful attempts so far. Originally developed in the 1990s, it relies on the difficulty of reverse-engineering sums of points.\u003c/p>\n\u003cp>Here’s one way to describe lattice cryptography: Imagine your friend has a lattice, which is just a bunch of points in a regular, repeating pattern all over the plane. Your friend wants you to name 10 of these points. But he’s being difficult, and he won’t draw the whole lattice. Instead, he lists just two points — the first with an \u003cem>x\u003c/em>-value of 101 and a \u003cem>y\u003c/em>-value of 19, the other with coordinates [235, 44].\u003c/p>\n\u003cp>Luckily, it’s easy to find new points on a lattice, because when you add and subtract any two points on a lattice, you get a third point in the same lattice. So all you have to do is add up the points your friend gave you, or multiply them by integers and then add them up, or some combination of the two. Do this eight different ways, and you’ll be able to answer your friend’s question.\u003c/p>\n\u003cp>\u003ca id=\”backtotop\”>\u003c/a>But your friend still isn’t satisfied. He gives you the same two starting points, and then asks you if the point [2, 1] is on the same lattice. To answer this question correctly, you have to find the combination of [101, 19] and [235, 44] that produces [2, 1]. This problem is much harder than the first one, and you’ll probably end up just guessing and checking to get the answer.\u003ca href=\”#asterisk\”>*\u003c/a> That asymmetry is what underlies lattice cryptography.\u003c/p>\n\u003cp>If you actually want to use lattice cryptography to share information, you’d do the following. Imagine that a friend (a nicer one!) wants to send you a secure message. You start with a square grid of numbers. Say it has two rows and two columns, and looks like this:\u003c/p>\n\u003cdiv id=’component-636bc1a04270d’ class=””>\u003cscript type=\”text/template\”>{\”type\”:\”Image\”,\”id\”:\”component-636bc1a04270d\”,\”data\”:{\”id\”:120495,\”src\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”alt\”:\”\”,\”class\”:\”\”,\”width\”:0,\”height\”:0,\”mobileSrc\”:false,\”zoomSrc\”:false,\”mobileZoomSrc\”:false,\”align\”:\”align=\\\”inline\\\”\”,\”wrapper_width\”:\”\”,\”caption\”:\”\”,\”attribution\”:\”\”,\”variant\”:\”shortcode\”,\”size\”:\”wide\”,\”disableZoom\”:true,\”disableMobileZoom\”:false,\”srcImage\”:{\”ID\”:120495,\”id\”:120495,\”title\”:\”LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman(2)\”,\”filename\”:\”LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”filesize\”:3475,\”url\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\\/lattice_cryptography_fig1-cr-merrillsherman2\\/\”,\”alt\”:\”\”,\”author\”:\”42689\”,\”description\”:\”\”,\”caption\”:\”\”,\”name\”:\”lattice_cryptography_fig1-cr-merrillsherman2\”,\”status\”:\”inherit\”,\”uploaded_to\”:120459,\”date\”:\”2022-11-09 14:35:26\”,\”modified\”:\”2022-11-09 14:35:26\”,\”menu_order\”:0,\”mime_type\”:\”image\\/svg+xml\”,\”type\”:\”image\”,\”subtype\”:\”svg+xml\”,\”icon\”:\”https:\\/\\/api.quantamagazine.org\\/wp-includes\\/images\\/media\\/default.png\”,\”width\”:0,\”height\”:0,\”sizes\”:{\”thumbnail\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”thumbnail-width\”:1,\”thumbnail-height\”:1,\”medium\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”medium-width\”:1,\”medium-height\”:1,\”medium_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”medium_large-width\”:1,\”medium_large-height\”:1,\”large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”large-width\”:1,\”large-height\”:1,\”1536×1536\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”1536×1536-width\”:1,\”1536×1536-height\”:1,\”2048×2048\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”2048×2048-width\”:1,\”2048×2048-height\”:1,\”square_small\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”square_small-width\”:1,\”square_small-height\”:1,\”square_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig1-cr.MerrillSherman2.svg\”,\”square_large-width\”:1,\”square_large-height\”:1}},\”largeForPrint\”:true,\”externalLink\”:\”\”,\”original_resolution\”:false}}\u003c\/script>\u003c/div>\n\u003cp>Now you come up with a private “key” that only you know. In this example, let’s say your private key is just two secret numbers: 3 and −2. You multiply the numbers in the first column by 3, and the ones in the second column by −2. Add up the results in each row to get a third column with two entries.\u003c/p>\n\u003cdiv id=’component-636bc1a045ff4′ class=””>\u003cscript type=\”text/template\”>{\”type\”:\”Image\”,\”id\”:\”component-636bc1a045ff4\”,\”data\”:{\”id\”:120473,\”src\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”alt\”:\”\”,\”class\”:\”\”,\”width\”:0,\”height\”:0,\”mobileSrc\”:false,\”zoomSrc\”:false,\”mobileZoomSrc\”:false,\”align\”:\”align=\\\”inline\\\”\”,\”wrapper_width\”:\”\”,\”caption\”:\”\”,\”attribution\”:\”\”,\”variant\”:\”shortcode\”,\”size\”:\”wide\”,\”disableZoom\”:true,\”disableMobileZoom\”:false,\”srcImage\”:{\”ID\”:120473,\”id\”:120473,\”title\”:\”LATTICE_CRYPTOGRAPHY_Fig2\”,\”filename\”:\”LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”filesize\”:20724,\”url\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\\/lattice_cryptography_fig2\\/\”,\”alt\”:\”\”,\”author\”:\”42689\”,\”description\”:\”\”,\”caption\”:\”\”,\”name\”:\”lattice_cryptography_fig2\”,\”status\”:\”inherit\”,\”uploaded_to\”:120459,\”date\”:\”2022-11-08 19:24:34\”,\”modified\”:\”2022-11-08 19:24:34\”,\”menu_order\”:0,\”mime_type\”:\”image\\/svg+xml\”,\”type\”:\”image\”,\”subtype\”:\”svg+xml\”,\”icon\”:\”https:\\/\\/api.quantamagazine.org\\/wp-includes\\/images\\/media\\/default.png\”,\”width\”:0,\”height\”:0,\”sizes\”:{\”thumbnail\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”thumbnail-width\”:1,\”thumbnail-height\”:1,\”medium\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”medium-width\”:1,\”medium-height\”:1,\”medium_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”medium_large-width\”:1,\”medium_large-height\”:1,\”large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”large-width\”:1,\”large-height\”:1,\”1536×1536\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”1536×1536-width\”:1,\”1536×1536-height\”:1,\”2048×2048\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”2048×2048-width\”:1,\”2048×2048-height\”:1,\”square_small\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”square_small-width\”:1,\”square_small-height\”:1,\”square_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig2.svg\”,\”square_large-width\”:1,\”square_large-height\”:1}},\”largeForPrint\”:false,\”externalLink\”:\”\”,\”original_resolution\”:false}}\u003c\/script>\u003c/div>\n\u003cp>Stick the new column onto the end of your grid. This new three-column grid is your public key. Share it freely!\u003c/p>\n\u003cdiv id=’component-636bc1a0469fb’ class=””>\u003cscript type=\”text/template\”>{\”type\”:\”Image\”,\”id\”:\”component-636bc1a0469fb\”,\”data\”:{\”id\”:120472,\”src\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”alt\”:\”\”,\”class\”:\”\”,\”width\”:0,\”height\”:0,\”mobileSrc\”:false,\”zoomSrc\”:false,\”mobileZoomSrc\”:false,\”align\”:\”align=\\\”inline\\\”\”,\”wrapper_width\”:\”\”,\”caption\”:\”\”,\”attribution\”:\”\”,\”variant\”:\”shortcode\”,\”size\”:\”default\”,\”disableZoom\”:true,\”disableMobileZoom\”:false,\”srcImage\”:{\”ID\”:120472,\”id\”:120472,\”title\”:\”LATTICE_CRYPTOGRAPHY_Fig3\”,\”filename\”:\”LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”filesize\”:4401,\”url\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\\/lattice_cryptography_fig3\\/\”,\”alt\”:\”\”,\”author\”:\”42689\”,\”description\”:\”\”,\”caption\”:\”\”,\”name\”:\”lattice_cryptography_fig3\”,\”status\”:\”inherit\”,\”uploaded_to\”:120459,\”date\”:\”2022-11-08 19:24:33\”,\”modified\”:\”2022-11-08 19:24:33\”,\”menu_order\”:0,\”mime_type\”:\”image\\/svg+xml\”,\”type\”:\”image\”,\”subtype\”:\”svg+xml\”,\”icon\”:\”https:\\/\\/api.quantamagazine.org\\/wp-includes\\/images\\/media\\/default.png\”,\”width\”:0,\”height\”:0,\”sizes\”:{\”thumbnail\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”thumbnail-width\”:1,\”thumbnail-height\”:1,\”medium\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”medium-width\”:1,\”medium-height\”:1,\”medium_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”medium_large-width\”:1,\”medium_large-height\”:1,\”large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”large-width\”:1,\”large-height\”:1,\”1536×1536\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”1536×1536-width\”:1,\”1536×1536-height\”:1,\”2048×2048\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”2048×2048-width\”:1,\”2048×2048-height\”:1,\”square_small\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”square_small-width\”:1,\”square_small-height\”:1,\”square_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig3.svg\”,\”square_large-width\”:1,\”square_large-height\”:1}},\”largeForPrint\”:false,\”externalLink\”:\”\”,\”original_resolution\”:false}}\u003c\/script>\u003c/div>\n\u003cp>(A real-world scenario will be a bit more complicated. To keep hackers from decoding your private key, you have to add a bit of random noise into your final column. But here we’re going to ignore that step for simplicity’s sake.)\u003c/p>\n\u003cp>Now your friend will use the public key to send you a message. She thinks of two secret numbers of her own: 2 and 0. She multiplies the numbers in the first row by 2, and the ones in the second row by 0. She then adds up the results in each column to get a third row.\u003c/p>\n\u003cdiv id=’component-636bc1a04a4fa’ class=””>\u003cscript type=\”text/template\”>{\”type\”:\”Image\”,\”id\”:\”component-636bc1a04a4fa\”,\”data\”:{\”id\”:120471,\”src\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”alt\”:\”\”,\”class\”:\”\”,\”width\”:0,\”height\”:0,\”mobileSrc\”:false,\”zoomSrc\”:false,\”mobileZoomSrc\”:false,\”align\”:\”align=\\\”inline\\\”\”,\”wrapper_width\”:\”\”,\”caption\”:\”\”,\”attribution\”:\”\”,\”variant\”:\”shortcode\”,\”size\”:\”default\”,\”disableZoom\”:true,\”disableMobileZoom\”:false,\”srcImage\”:{\”ID\”:120471,\”id\”:120471,\”title\”:\”LATTICE_CRYPTOGRAPHY_Fig4\”,\”filename\”:\”LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”filesize\”:14824,\”url\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\\/lattice_cryptography_fig4\\/\”,\”alt\”:\”\”,\”author\”:\”42689\”,\”description\”:\”\”,\”caption\”:\”\”,\”name\”:\”lattice_cryptography_fig4\”,\”status\”:\”inherit\”,\”uploaded_to\”:120459,\”date\”:\”2022-11-08 19:24:32\”,\”modified\”:\”2022-11-08 19:24:32\”,\”menu_order\”:0,\”mime_type\”:\”image\\/svg+xml\”,\”type\”:\”image\”,\”subtype\”:\”svg+xml\”,\”icon\”:\”https:\\/\\/api.quantamagazine.org\\/wp-includes\\/images\\/media\\/default.png\”,\”width\”:0,\”height\”:0,\”sizes\”:{\”thumbnail\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”thumbnail-width\”:1,\”thumbnail-height\”:1,\”medium\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”medium-width\”:1,\”medium-height\”:1,\”medium_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”medium_large-width\”:1,\”medium_large-height\”:1,\”large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”large-width\”:1,\”large-height\”:1,\”1536×1536\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”1536×1536-width\”:1,\”1536×1536-height\”:1,\”2048×2048\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”2048×2048-width\”:1,\”2048×2048-height\”:1,\”square_small\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”square_small-width\”:1,\”square_small-height\”:1,\”square_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig4.svg\”,\”square_large-width\”:1,\”square_large-height\”:1}},\”largeForPrint\”:false,\”externalLink\”:\”\”,\”original_resolution\”:false}}\u003c\/script>\u003c/div>\n\u003cp>She now attaches the new row to the bottom of the grid and sends it back to you. (Again, in a real system, she’d need to add some noise to her row.)\u003c/p>\n\u003cp>Now you’ll read the message. To do this, you check to see if your friend’s last row is correct. Apply your own private key to the first two entries of her row. The result should match the last entry.\u003c/p>\n\u003cdiv id=’component-636bc1a04e53a’ class=””>\u003cscript type=\”text/template\”>{\”type\”:\”Image\”,\”id\”:\”component-636bc1a04e53a\”,\”data\”:{\”id\”:120470,\”src\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”alt\”:\”\”,\”class\”:\”\”,\”width\”:0,\”height\”:0,\”mobileSrc\”:false,\”zoomSrc\”:false,\”mobileZoomSrc\”:false,\”align\”:\”align=\\\”inline\\\”\”,\”wrapper_width\”:\”\”,\”caption\”:\”\”,\”attribution\”:\”\”,\”variant\”:\”shortcode\”,\”size\”:\”default\”,\”disableZoom\”:true,\”disableMobileZoom\”:false,\”srcImage\”:{\”ID\”:120470,\”id\”:120470,\”title\”:\”LATTICE_CRYPTOGRAPHY_Fig5\”,\”filename\”:\”LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”filesize\”:11539,\”url\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\\/lattice_cryptography_fig5\\/\”,\”alt\”:\”\”,\”author\”:\”42689\”,\”description\”:\”\”,\”caption\”:\”\”,\”name\”:\”lattice_cryptography_fig5\”,\”status\”:\”inherit\”,\”uploaded_to\”:120459,\”date\”:\”2022-11-08 19:24:32\”,\”modified\”:\”2022-11-08 19:24:32\”,\”menu_order\”:0,\”mime_type\”:\”image\\/svg+xml\”,\”type\”:\”image\”,\”subtype\”:\”svg+xml\”,\”icon\”:\”https:\\/\\/api.quantamagazine.org\\/wp-includes\\/images\\/media\\/default.png\”,\”width\”:0,\”height\”:0,\”sizes\”:{\”thumbnail\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”thumbnail-width\”:1,\”thumbnail-height\”:1,\”medium\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”medium-width\”:1,\”medium-height\”:1,\”medium_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”medium_large-width\”:1,\”medium_large-height\”:1,\”large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”large-width\”:1,\”large-height\”:1,\”1536×1536\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”1536×1536-width\”:1,\”1536×1536-height\”:1,\”2048×2048\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”2048×2048-width\”:1,\”2048×2048-height\”:1,\”square_small\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”square_small-width\”:1,\”square_small-height\”:1,\”square_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig5.svg\”,\”square_large-width\”:1,\”square_large-height\”:1}},\”largeForPrint\”:false,\”externalLink\”:\”\”,\”original_resolution\”:false}}\u003c\/script>\u003c/div>\n\u003cp>Your friend can also choose to send you a row with a wrong number in the last column. She knows that this number won’t match your calculations.\u003c/p>\n\u003cdiv id=’component-636bc1a051d95′ class=””>\u003cscript type=\”text/template\”>{\”type\”:\”Image\”,\”id\”:\”component-636bc1a051d95\”,\”data\”:{\”id\”:120469,\”src\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”alt\”:\”\”,\”class\”:\”\”,\”width\”:0,\”height\”:0,\”mobileSrc\”:false,\”zoomSrc\”:false,\”mobileZoomSrc\”:false,\”align\”:\”align=\\\”inline\\\”\”,\”wrapper_width\”:\”\”,\”caption\”:\”\”,\”attribution\”:\”\”,\”variant\”:\”shortcode\”,\”size\”:\”default\”,\”disableZoom\”:false,\”disableMobileZoom\”:false,\”srcImage\”:{\”ID\”:120469,\”id\”:120469,\”title\”:\”LATTICE_CRYPTOGRAPHY_Fig6\”,\”filename\”:\”LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”filesize\”:15386,\”url\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\\/lattice_cryptography_fig6\\/\”,\”alt\”:\”\”,\”author\”:\”42689\”,\”description\”:\”\”,\”caption\”:\”\”,\”name\”:\”lattice_cryptography_fig6\”,\”status\”:\”inherit\”,\”uploaded_to\”:120459,\”date\”:\”2022-11-08 19:24:31\”,\”modified\”:\”2022-11-08 19:24:31\”,\”menu_order\”:0,\”mime_type\”:\”image\\/svg+xml\”,\”type\”:\”image\”,\”subtype\”:\”svg+xml\”,\”icon\”:\”https:\\/\\/api.quantamagazine.org\\/wp-includes\\/images\\/media\\/default.png\”,\”width\”:0,\”height\”:0,\”sizes\”:{\”thumbnail\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”thumbnail-width\”:1,\”thumbnail-height\”:1,\”medium\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”medium-width\”:1,\”medium-height\”:1,\”medium_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”medium_large-width\”:1,\”medium_large-height\”:1,\”large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”large-width\”:1,\”large-height\”:1,\”1536×1536\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”1536×1536-width\”:1,\”1536×1536-height\”:1,\”2048×2048\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”2048×2048-width\”:1,\”2048×2048-height\”:1,\”square_small\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”square_small-width\”:1,\”square_small-height\”:1,\”square_large\”:\”https:\\/\\/d2r55xnwy6nx47.cloudfront.net\\/uploads\\/2022\\/11\\/LATTICE_CRYPTOGRAPHY_Fig6.svg\”,\”square_large-width\”:1,\”square_large-height\”:1}},\”largeForPrint\”:false,\”externalLink\”:\”\”,\”original_resolution\”:false}}\u003c\/script>\u003c/div>\n\u003cp>If your friend sends a row where the last number is correct, you’ll interpret this as a 0. If she sends a row where the number is incorrect, you’ll interpret it as a 1. The row, therefore, encodes a single bit: either 0 or 1.\u003c/p>\n\u003cp>Note that an outside attacker won’t have access to either your private key or your friend’s. Without those, the attacker will have no idea if the final number is correct or not.\u003c/p>\n\u003cdiv id=’component-636bc1a0523e3′ class=”related-list”>\u003cscript type=\”text/template\”>{\”type\”:\”LinkList\”,\”id\”:\”component-636bc1a0523e3\”,\”data\”:{\”title\”:\”Related:\”,\”class\”:\”related-list\”,\”links\”:[{\”type\”:\”internal\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/researchers-identify-master-problem-underlying-all-cryptography-20220406\\/\”,\”title\”:\”Researchers Identify \\u2018Master Problem\\u2019 Underlying All Cryptography\”},{\”type\”:\”internal\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/post-quantum-cryptography-scheme-is-cracked-on-a-laptop-20220824\\/\”,\”title\”:\”\\u2018Post-Quantum\\u2019 Cryptography Scheme Is Cracked on a Laptop\”},{\”type\”:\”internal\”,\”link\”:\”https:\\/\\/www.quantamagazine.org\\/new-entanglement-results-hint-at-better-quantum-codes-20221024\\/\”,\”title\”:\”New Entanglement Results Hint at Better Quantum Codes\”}]}}\u003c\/script>\u003c/div>\n\u003cp>In practice, you’d like to send messages that are longer than one bit long. So people who want to receive, say, a 100-bit message will generate 100 new columns instead of just one. Then the sender of the message will create a single new row, modifying the last 100 entries to encode either a 0 or a 1 for each entry.\u003c/p>\n\u003cp>If lattice cryptography is actually implemented, it will have countless nuances not covered in this scenario. For instance, if you want the message to be truly safe from prying eyes, the matrix needs to have an unthinkable number of entries, making the whole thing so unwieldy that it’s not worth using. To get around this, researchers use matrices with useful symmetries that can cut down on the number of parameters. Beyond that, there is a whole suite of tweaks that can be applied to the problem itself, to the way errors are incorporated, and more.\u003c/p>\n\u003cp>Of course, it’s always possible that someone will find a fatal flaw in lattice cryptography, just as Shor did for factoring. There’s no assurance that a particular cryptographic scheme will work in the face of any possible attack. Cryptography works until it’s cracked. Indeed, earlier this summer \u003ca href=\” promising post-quantum cryptography scheme was cracked\u003c/a> using not a quantum computer, but an ordinary laptop. To Stange, the entire project creates an uncomfortable paradox: “What I find so amazing about cryptography is that we’ve built this infrastructure for the human race on the firm belief that our ability as humans is limited,” she said. “It’s so backward.”\u003c/p>\n\u003cp>\u003ca id=\”asterisk\”>\u003c/a>*: The answer, if you’re curious, is 7 × [101, 19] – 3 × [235, 44] = [2, 1]. [\u003ca href=\”#backtotop\”>\u003cem>back to article\u003c/em>\u003c/a>]\u003c/p>\n”,”fadein”:false,”__typename”:”ACFContent”},”$Post:120459.acf.series”:{“name”:null,”link”:null,”__typename”:”Term”},”$Post:120459.next.data.0″:{“title”:”How Supergenes Fuel Evolution Despite Harmful Mutations”,”link”:”https://www.quantamagazine.org/how-supergenes-fuel-evolution-despite-harmful-mutations-20221108/”,”categories”:[{“type”:”id”,”generated”:true,”id”:”$Post:120459.next.data.0.categories.0″,”typename”:”Term”}],”featured_media_image”:null,”acf”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.next.data.0.acf”,”typename”:”ACFFields”},”__typename”:”Post”},”$Post:120459.next.data.0.categories.0″:{“slug”:”biology”,”__typename”:”Term”},”$Post:120459.next.data.0.acf”:{“template”:”article”,”featured_block_title”:””,”featured_image_gif”:false,”featured_image_default”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.next.data.0.acf.featured_image_default”,”typename”:”Image”},”featured_image_full_width”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.next.data.0.acf.featured_image_full_width”,”typename”:”Image”},”__typename”:”ACFFields”},”$Post:120459.next.data.0.acf.featured_image_default”:{“alt”:”Illustration of butterflies with similar wing-color patterns holding bundles of DNA.”,”caption”:””,”url”:” of butterflies with similar wing-color patterns holding bundles of DNA.”,”caption”:””,”url”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/11/Supergenes_2880x1220_HP-scaled.webp”,”width”:2560,”height”:1084,”sizes”:{“type”:”id”,”generated”:true,”id”:”$Post:120459.next.data.0.acf.featured_image_full_width.sizes”,”typename”:”ImageSizes”},”__typename”:”Image”},”$Post:120459.next.data.0.acf.featured_image_full_width.sizes”:{“thumbnail”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/11/Supergenes_2880x1220_HP-520×220.webp”,”square_small”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/11/Supergenes_2880x1220_HP-160×160.webp”,”square_large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/11/Supergenes_2880x1220_HP-520×520.webp”,”medium”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/11/Supergenes_2880x1220_HP-1720×729.webp”,”medium_large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/11/Supergenes_2880x1220_HP-768×325.webp”,”large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/11/Supergenes_2880x1220_HP-scaled.webp”,”__typename”:”ImageSizes”},”$Post:120459.next”:{“data”:[{“type”:”id”,”generated”:true,”id”:”$Post:120459.next.data.0″,”typename”:”Post”}],”__typename”:”PostPageArchive”}}\n”,”settings”:{“socialLinks”:[{“type”:”facebook”,”label”:”Facebook”,”url”:”https://www.facebook.com/QuantaNews”,”__typename”:”SocialMediaLink”},{“type”:”twitter”,”label”:”Twitter”,”url”:”https://twitter.com/QuantaMagazine”,”__typename”:”SocialMediaLink”},{“type”:”youtube”,”label”:”YouTube”,”url”:”https://www.youtube.com/c/QuantaScienceChannel”,”__typename”:”SocialMediaLink”},{“type”:”instagram”,”label”:”Instagram”,”url”:”https://instagram.com/quantamag”,”__typename”:”SocialMediaLink”},{“type”:”rss”,”label”:”RSS”,”url”:”https://api.quantamagazine.org/feed/”,”__typename”:”SocialMediaLink”}],”newsletterAction”:”https://quantamagazine.us1.list-manage.com/subscribe/post?u=0d6ddf7dc1a0b7297c8e06618&id=f0cb61321c”,”newsletterUrl”:”http://us1.campaign-archive2.com/home/?u=0d6ddf7dc1a0b7297c8e06618&id=f0cb61321c”,”sfNotice”:”An editorially independent publication supported by the Simons Foundation.”,”commentsHeader”:”
\n”,”channels”:[{“title”:”The Joy of Why”,”slug”:”the-joy-of-why”,”description”:”The mathematician and author Steven Strogatz interviews leading researchers about the great scientific and mathematical questions of our time.”,”featured_image”:{“alt”:””,”caption”:””,”url”:” Science Podcast”,”slug”:”quanta-podcast”,”description”:”Susan Valot narrates in-depth news episodes based on Quanta Magazine‘s articles about mathematics, physics, biology and computer science. “,”featured_image”:{“alt”:”Micrograph of a neuron showing aggregations of tau protein.”,”caption”:””,”url”:” Joy of x”,”slug”:”the-joy-of-x”,”description”:”The acclaimed mathematician and author Steven Strogatz interviews some of the world’s leading scientists about their lives and work.”,”featured_image”:{“alt”:””,”caption”:””,”url”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1.jpg”,”width”:1920,”height”:1080,”sizes”:{“thumbnail”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1-520×293.jpg”,”square_small”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1-160×160.jpg”,”square_large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1-520×520.jpg”,”medium”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1-1720×968.jpg”,”medium_large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1-768×432.jpg”,”large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JoX_Spheres_1920x1080-1.jpg”,”__typename”:”ImageSizes”},”__typename”:”Image”},”square_image”:{“alt”:””,”caption”:””,”url”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600.jpg”,”width”:600,”height”:600,”sizes”:{“thumbnail”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600-520×520.jpg”,”square_small”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600-160×160.jpg”,”square_large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600-520×520.jpg”,”medium”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600.jpg”,”medium_large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600.jpg”,”large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2022/03/JofX_podcast_logo-NEW-600.jpg”,”__typename”:”ImageSizes”},”__typename”:”Image”},”subscribe_itunes_link”:”https://podcasts.apple.com/us/podcast/the-joy-of-x/id1495067186″,”subscribe_spotify_link”:”https://open.spotify.com/show/5HcCtKPH5gnOjRiMtTdC07?si=lFzCzat9QfuPU3hWuYibxQ”,”subscribe_android_link”:”https://podcasts.google.com/feed/aHR0cHM6Ly9hcGkucXVhbnRhbWFnYXppbmUub3JnL2ZlZWQvdGhlLWpveS1vZi14Lw”,”subscribe_stitcher_link”:”https://www.stitcher.com/podcast/the-joy-of-x”,”__typename”:”Channel”}],”editors”:[{“name”:”Bill Andrews – Senior CS Editor”,”__typename”:”Editor”},{“name”:”Ben Brubaker – Staff CS Writer”,”__typename”:”Editor”},{“name”:”Matt Carlstrom – Senior Engagement Editor”,”__typename”:”Editor”},{“name”:”Jordana Cepelewicz – Senior Math Writer”,”__typename”:”Editor”},{“name”:”Konstantin Kakaes – Senior Math Editor”,”__typename”:”Editor”},{“name”:”Thomas Lin – Editor in Chief”,”__typename”:”Editor”},{“name”:”Michael Moyer – Deputy Editor, Physics, Math, CS”,”__typename”:”Editor”},{“name”:”John Rennie – Deputy Editor, Biology, Podcasts”,”__typename”:”Editor”},{“name”:”Yasemin Saplakoglu – Staff Biology Writer”,”__typename”:”Editor”},{“name”:”Samuel Velasco – Art Director”,”__typename”:”Editor”},{“name”:”Natalie Wolchover – Senior Physics Editor”,”__typename”:”Editor”},{“name”:”Charlie Wood – Staff Physics Writer”,”__typename”:”Editor”}],”popularSearches”:[{“term”:”math”,”label”:”Mathematics”,”__typename”:”PopularSearch”},{“term”:”physics”,”label”:”Physics”,”__typename”:”PopularSearch”},{“term”:”black holes”,”label”:”Black Holes”,”__typename”:”PopularSearch”},{“term”:”evolution”,”label”:”Evolution”,”__typename”:”PopularSearch”}],”searchTopics”:[{“type”:”Tag”,”label”:”Podcasts”,”tag”:{“name”:”Quanta Podcast”,”slug”:”quanta-podcast”,”term_id”:”552″,”__typename”:”Term”},”category”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”__typename”:”SearchTopic”},{“type”:”Tag”,”label”:”Columns”,”tag”:{“name”:”Quantized Columns”,”slug”:”quantized”,”term_id”:”551″,”__typename”:”Term”},”category”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”__typename”:”SearchTopic”},{“type”:”Series”,”label”:”Series”,”tag”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”category”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”__typename”:”SearchTopic”},{“type”:”Category”,”label”:”Interviews”,”tag”:{“name”:”Q&A”,”slug”:”qa”,”term_id”:”567″,”__typename”:”Term”},”category”:{“name”:”Q&A”,”slug”:”qa”,”term_id”:”176″,”__typename”:”Term”},”__typename”:”SearchTopic”},{“type”:”Category”,”label”:”Multimedia”,”tag”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”category”:{“name”:”Multimedia”,”slug”:”multimedia”,”term_id”:”43″,”__typename”:”Term”},”__typename”:”SearchTopic”},{“type”:”Category”,”label”:”Puzzles”,”tag”:{“name”:”puzzles”,”slug”:”puzzles”,”term_id”:”542″,”__typename”:”Term”},”category”:{“name”:”Puzzles”,”slug”:”puzzles”,”term_id”:”546″,”__typename”:”Term”},”__typename”:”SearchTopic”},{“type”:”Category”,”label”:”Blog Posts”,”tag”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”category”:{“name”:”Abstractions blog”,”slug”:”abstractions”,”term_id”:”619″,”__typename”:”Term”},”__typename”:”SearchTopic”},{“type”:”news”,”label”:”News Articles”,”tag”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”category”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”__typename”:”SearchTopic”},{“type”:”videos”,”label”:”Videos”,”tag”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”category”:{“name”:null,”slug”:null,”term_id”:null,”__typename”:”Term”},”__typename”:”SearchTopic”}],”searchSections”:[{“name”:”Mathematics”,”slug”:”mathematics”,”term_id”:”188″,”__typename”:”Term”},{“name”:”Physics”,”slug”:”physics”,”term_id”:”189″,”__typename”:”Term”},{“name”:”Biology”,”slug”:”biology”,”term_id”:”191″,”__typename”:”Term”},{“name”:”Computer Science”,”slug”:”computer-science”,”term_id”:”190″,”__typename”:”Term”}],”searchAuthors”:[{“id”:”38171″,”name”:”Adam Becker”,”__typename”:”AuthorList”},{“id”:”28087″,”name”:”Adam Mann”,”__typename”:”AuthorList”},{“id”:”29794″,”name”:”Alex Kontorovich”,”__typename”:”AuthorList”},{“id”:”39302″,”name”:”Alexander Hellemans”,”__typename”:”AuthorList”},{“id”:”56″,”name”:”Alla Katsnelson”,”__typename”:”AuthorList”},{“id”:”47249″,”name”:”Allison Parshall”,”__typename”:”AuthorList”},{“id”:”29458″,”name”:”Allison Whitten”,”__typename”:”AuthorList”},{“id”:”73″,”name”:”Amanda Gefter”,”__typename”:”AuthorList”},{“id”:”39164″,”name”:”Ana Kova”,”__typename”:”AuthorList”},{“id”:”59″,”name”:”Andreas von Bubnoff”,”__typename”:”AuthorList”},{“id”:”8728″,”name”:”Anil Ananthaswamy”,”__typename”:”AuthorList”},{“id”:”11648″,”name”:”Ann Finkbeiner”,”__typename”:”AuthorList”},{“id”:”42689″,”name”:”Annie Melchor”,”__typename”:”AuthorList”},{“id”:”95″,”name”:”Ariel Bleicher”,”__typename”:”AuthorList”},{“id”:”15493″,”name”:”Ashley Smart”,”__typename”:”AuthorList”},{“id”:”450″,”name”:”Ashley Yeager”,”__typename”:”AuthorList”},{“id”:”36490″,”name”:”Ben Brubaker”,”__typename”:”AuthorList”},{“id”:”16315″,”name”:”Bill Andrews”,”__typename”:”AuthorList”},{“id”:”2752″,”name”:”Bob Henderson”,”__typename”:”AuthorList”},{“id”:”15492″,”name”:”Brendan Z. Foster”,”__typename”:”AuthorList”},{“id”:”68″,”name”:”Brooke Borel”,”__typename”:”AuthorList”},{“id”:”62″,”name”:”Carl Zimmer”,”__typename”:”AuthorList”},{“id”:”13684″,”name”:”Caroline Lee”,”__typename”:”AuthorList”},{“id”:”13691″,”name”:”Caroline Lee”,”__typename”:”AuthorList”},{“id”:”50″,”name”:”Carrie Arnold”,”__typename”:”AuthorList”},{“id”:”15142″,”name”:”Chanda Prescod-Weinstein”,”__typename”:”AuthorList”},{“id”:”8084″,”name”:”Charlie Wood”,”__typename”:”AuthorList”},{“id”:”742″,”name”:”Christie Wilcox”,”__typename”:”AuthorList”},{“id”:”11543″,”name”:”Claudia Dreifus”,”__typename”:”AuthorList”},{“id”:”57″,”name”:”Courtney Humphries”,”__typename”:”AuthorList”},{“id”:”7262″,”name”:”Dalmeet Singh Chawla”,”__typename”:”AuthorList”},{“id”:”70″,”name”:”Dan Falk”,”__typename”:”AuthorList”},{“id”:”19918″,”name”:”Dana Najjar”,”__typename”:”AuthorList”},{“id”:”13695″,”name”:”Daniel Garisto”,”__typename”:”AuthorList”},{“id”:”32676″,”name”:”Daniel S. Freed”,”__typename”:”AuthorList”},{“id”:”13724″,”name”:”David H. Freedman”,”__typename”:”AuthorList”},{“id”:”26310″,”name”:”David S. Richeson”,”__typename”:”AuthorList”},{“id”:”30207″,”name”:”David Tse”,”__typename”:”AuthorList”},{“id”:”19266″,”name”:”Devin Powell”,”__typename”:”AuthorList”},{“id”:”13251″,”name”:”Diana Kwon”,”__typename”:”AuthorList”},{“id”:”17000″,”name”:”Elena Renken”,”__typename”:”AuthorList”},{“id”:”17149″,”name”:”Elizabeth Landau”,”__typename”:”AuthorList”},{“id”:”5279″,”name”:”Elizabeth Preston”,”__typename”:”AuthorList”},{“id”:”58″,”name”:”Elizabeth Svoboda”,”__typename”:”AuthorList”},{“id”:”32612″,”name”:”Ellen Horne”,”__typename”:”AuthorList”},{“id”:”27534″,”name”:”Emily Buder”,”__typename”:”AuthorList”},{“id”:”25173″,”name”:”Emily Levesque”,”__typename”:”AuthorList”},{“id”:”64″,”name”:”Emily Singer”,”__typename”:”AuthorList”},{“id”:”47″,”name”:”Erica Klarreich”,”__typename”:”AuthorList”},{“id”:”14784″,”name”:”Erika K. Carlson”,”__typename”:”AuthorList”},{“id”:”98″,”name”:”Esther Landhuis”,”__typename”:”AuthorList”},{“id”:”5830″,”name”:”Eva Silverstein”,”__typename”:”AuthorList”},{“id”:”6793″,”name”:”Evelyn Lamb”,”__typename”:”AuthorList”},{“id”:”75″,”name”:”Ferris Jabr”,”__typename”:”AuthorList”},{“id”:”52″,”name”:”Frank Wilczek”,”__typename”:”AuthorList”},{“id”:”69″,”name”:”Gabriel Popkin”,”__typename”:”AuthorList”},{“id”:”77″,”name”:”George Musser”,”__typename”:”AuthorList”},{“id”:”19092″,”name”:”Grant Sanderson”,”__typename”:”AuthorList”},{“id”:”20557″,”name”:”Howard Lee”,”__typename”:”AuthorList”},{“id”:”66″,”name”:”Ingrid Daubechies”,”__typename”:”AuthorList”},{“id”:”46418″,”name”:”Ingrid Wickelgren”,”__typename”:”AuthorList”},{“id”:”85″,”name”:”Ivan Amato”,”__typename”:”AuthorList”},{“id”:”37141″,”name”:”Jake Buehler”,”__typename”:”AuthorList”},{“id”:”44758″,”name”:”James Dinneen”,”__typename”:”AuthorList”},{“id”:”12170″,”name”:”Janna Levin”,”__typename”:”AuthorList”},{“id”:”32″,”name”:”Jeanette Kazmierczak”,”__typename”:”AuthorList”},{“id”:”51″,”name”:”Jennifer Ouellette”,”__typename”:”AuthorList”},{“id”:”44787″,”name”:”Joanna Thompson”,”__typename”:”AuthorList”},{“id”:”72″,”name”:”John Pavlus”,”__typename”:”AuthorList”},{“id”:”16475″,”name”:”John Preskill”,”__typename”:”AuthorList”},{“id”:”91″,”name”:”John Rennie”,”__typename”:”AuthorList”},{“id”:”10351″,”name”:”Jonathan Lambert”,”__typename”:”AuthorList”},{“id”:”31716″,”name”:”Jonathan O’Callaghan”,”__typename”:”AuthorList”},{“id”:”1241″,”name”:”Jordana Cepelewicz”,”__typename”:”AuthorList”},{“id”:”8463″,”name”:”Joshua Roebke”,”__typename”:”AuthorList”},{“id”:”49″,”name”:”Joshua Sokol”,”__typename”:”AuthorList”},{“id”:”16815″,”name”:”jye”,”__typename”:”AuthorList”},{“id”:”67″,”name”:”K.C. Cole”,”__typename”:”AuthorList”},{“id”:”37462″,”name”:”Karmela Padavic-Callaghan”,”__typename”:”AuthorList”},{“id”:”87″,”name”:”Kat McGowan”,”__typename”:”AuthorList”},{“id”:”36139″,”name”:”Katarina Zimmer”,”__typename”:”AuthorList”},{“id”:”20556″,”name”:”Katherine Harmon Courage”,”__typename”:”AuthorList”},{“id”:”90″,”name”:”Katia Moskvitch”,”__typename”:”AuthorList”},{“id”:”39551″,”name”:”Katie McCormick”,”__typename”:”AuthorList”},{“id”:”27374″,”name”:”Kelsey Houston-Edwards”,”__typename”:”AuthorList”},{“id”:”40″,”name”:”Kevin Hartnett”,”__typename”:”AuthorList”},{“id”:”45758″,”name”:”Kristina Armitage”,”__typename”:”AuthorList”},{“id”:”38413″,”name”:”Lakshmi Chandrasekaran”,”__typename”:”AuthorList”},{“id”:”12570″,”name”:”Laura Poppick”,”__typename”:”AuthorList”},{“id”:”38699″,”name”:”Leila Sloman”,”__typename”:”AuthorList”},{“id”:”23451″,”name”:”Liam Drew”,”__typename”:”AuthorList”},{“id”:”79″,”name”:”Liz Kruesi”,”__typename”:”AuthorList”},{“id”:”38″,”name”:”Lucy Reading-Ikkanda”,”__typename”:”AuthorList”},{“id”:”47180″,”name”:”Lyndie Chiou”,”__typename”:”AuthorList”},{“id”:”60″,”name”:”Maggie McKee”,”__typename”:”AuthorList”},{“id”:”2333″,”name”:”Mallory Locklear”,”__typename”:”AuthorList”},{“id”:”3569″,”name”:”Marcus Woo”,”__typename”:”AuthorList”},{“id”:”414″,”name”:”Mark Kim-Mulgrew”,”__typename”:”AuthorList”},{“id”:”20495″,”name”:”Matt Carlstrom”,”__typename”:”AuthorList”},{“id”:”17147″,”name”:”Matthew Hutson”,”__typename”:”AuthorList”},{“id”:”30953″,”name”:”Max G. Levy”,”__typename”:”AuthorList”},{“id”:”32437″,”name”:”Max Kozlov”,”__typename”:”AuthorList”},{“id”:”38705″,”name”:”mcho”,”__typename”:”AuthorList”},{“id”:”40613″,”name”:”Melanie Mitchell”,”__typename”:”AuthorList”},{“id”:”7186″,”name”:”Melinda Wenner Moyer”,”__typename”:”AuthorList”},{“id”:”14093″,”name”:”Michael Harris”,”__typename”:”AuthorList”},{“id”:”34″,”name”:”Michael Kranz”,”__typename”:”AuthorList”},{“id”:”23″,”name”:”Michael Moyer”,”__typename”:”AuthorList”},{“id”:”74″,”name”:”Michael Nielsen”,”__typename”:”AuthorList”},{“id”:”19093″,”name”:”Michele Bannister”,”__typename”:”AuthorList”},{“id”:”1472″,”name”:”Moira Chas”,”__typename”:”AuthorList”},{“id”:”6476″,”name”:”Monique Brouillette”,”__typename”:”AuthorList”},{“id”:”42264″,”name”:”Mordechai Rorvig”,”__typename”:”AuthorList”},{“id”:”10″,”name”:”Natalie Wolchover”,”__typename”:”AuthorList”},{“id”:”37605″,”name”:”Nick Thieme”,”__typename”:”AuthorList”},{“id”:”43298″,”name”:”Nicole Yunger Halpern”,”__typename”:”AuthorList”},{“id”:”37428″,”name”:”Nima Arkani-Hamed”,”__typename”:”AuthorList”},{“id”:”19962″,”name”:”Nola Taylor Redd”,”__typename”:”AuthorList”},{“id”:”24″,”name”:”Olena Shmahalo”,”__typename”:”AuthorList”},{“id”:”1816″,”name”:”Patrick Honner”,”__typename”:”AuthorList”},{“id”:”46889″,”name”:”Paul Chaikin”,”__typename”:”AuthorList”},{“id”:”84″,”name”:”Peter Byrne”,”__typename”:”AuthorList”},{“id”:”55″,”name”:”Philip Ball”,”__typename”:”AuthorList”},{“id”:”31″,”name”:”Pradeep Mutalik”,”__typename”:”AuthorList”},{“id”:”24011″,”name”:”Puja Changoiwala”,”__typename”:”AuthorList”},{“id”:”100″,”name”:”Quanta Magazine”,”__typename”:”AuthorList”},{“id”:”2784″,”name”:”R. Douglas Fields”,”__typename”:”AuthorList”},{“id”:”26114″,”name”:”Rachel Crowell”,”__typename”:”AuthorList”},{“id”:”9412″,”name”:”Raleigh McElvery”,”__typename”:”AuthorList”},{“id”:”820″,”name”:”Ramin Skibba”,”__typename”:”AuthorList”},{“id”:”1666″,”name”:”Rebecca Boyle”,”__typename”:”AuthorList”},{“id”:”20950″,”name”:”Richard Masland”,”__typename”:”AuthorList”},{“id”:”48″,”name”:”Robbert Dijkgraaf”,”__typename”:”AuthorList”},{“id”:”80″,”name”:”Roberta Kwok”,”__typename”:”AuthorList”},{“id”:”15681″,”name”:”Robin George Andrews”,”__typename”:”AuthorList”},{“id”:”24577″,”name”:”Rodrigo Pérez Ortega”,”__typename”:”AuthorList”},{“id”:”78″,”name”:”Sabine Hossenfelder”,”__typename”:”AuthorList”},{“id”:”23845″,”name”:”Samuel Velasco”,”__typename”:”AuthorList”},{“id”:”83″,”name”:”Sarah Lewin”,”__typename”:”AuthorList”},{“id”:”35441″,”name”:”Scott Aaronson”,”__typename”:”AuthorList”},{“id”:”76″,”name”:”Sean B. Carroll”,”__typename”:”AuthorList”},{“id”:”15680″,”name”:”Sean Carroll”,”__typename”:”AuthorList”},{“id”:”7239″,”name”:”Shannon Hall”,”__typename”:”AuthorList”},{“id”:”44197″,”name”:”Sheon Han”,”__typename”:”AuthorList”},{“id”:”65″,”name”:”Siobhan Roberts”,”__typename”:”AuthorList”},{“id”:”5944″,”name”:”Sophia Chen”,”__typename”:”AuthorList”},{“id”:”61″,”name”:”Steph Yin”,”__typename”:”AuthorList”},{“id”:”63″,”name”:”Stephanie Bucklin”,”__typename”:”AuthorList”},{“id”:”26311″,”name”:”Stephanie DeMarco”,”__typename”:”AuthorList”},{“id”:”71″,”name”:”Stephen Ornes”,”__typename”:”AuthorList”},{“id”:”17148″,”name”:”Steve Nadis”,”__typename”:”AuthorList”},{“id”:”13356″,”name”:”Steven Strogatz”,”__typename”:”AuthorList”},{“id”:”17150″,”name”:”Susan D’Agostino”,”__typename”:”AuthorList”},{“id”:”39768″,”name”:”Tamar Lichter Blanks”,”__typename”:”AuthorList”},{“id”:”2960″,”name”:”Tara C. Smith”,”__typename”:”AuthorList”},{“id”:”14785″,”name”:”Thomas Lewton”,”__typename”:”AuthorList”},{“id”:”3″,”name”:”Thomas Lin”,”__typename”:”AuthorList”},{“id”:”54″,”name”:”Tim Vernimmen”,”__typename”:”AuthorList”},{“id”:”88″,”name”:”Tom Siegfried”,”__typename”:”AuthorList”},{“id”:”12964″,”name”:”Vanessa Schipani”,”__typename”:”AuthorList”},{“id”:”53″,”name”:”Veronique Greenwood”,”__typename”:”AuthorList”},{“id”:”86″,”name”:”Virginia Hughes”,”__typename”:”AuthorList”},{“id”:”3244″,”name”:”Viviane Callier”,”__typename”:”AuthorList”},{“id”:”89″,”name”:”Wynne Parry”,”__typename”:”AuthorList”},{“id”:”15913″,”name”:”XiaoZhi Lim”,”__typename”:”AuthorList”},{“id”:”42263″,”name”:”Yasemin Saplakoglu”,”__typename”:”AuthorList”},{“id”:”45757″,”name”:”Zack Savitsky”,”__typename”:”AuthorList”}],”adBehavior”:”everywhere”,”adUrl”:” and Learn “,”adImageHome”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2021/05/Youtube_Web-Default_260.gif”,”adImageArticle”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2021/05/Youtube_Article_160.gif”,”adImageTablet”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2021/05/Youtube_Tablet_890_op.gif”,”adImageMobile”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2021/05/Youtube_Web-Default_260.gif”,”trackingScripts”:”\r\n<\!-- Google Tag Manager -->\r\n\r\n<\!-- End Google Tag Manager -->\r\n<\!-- Google Tag Manager (noscript) -->\r\n\r\n<\!-- End Google Tag Manager (noscript) -->\r\n\r\n”},”theme”:{“page”:{“accent”:”#ff8600″,”text”:”#1a1a1a”,”background”:”white”},”header”:{“type”:”default”,”gradient”:{“color”:”white”},”solid”:{“primary”:”#1a1a1a”,”secondary”:”#999999″,”hover”:”#ff8600″},”transparent”:{“primary”:”white”,”secondary”:”white”,”hover”:”#ff8600″}}},”redirect”:null,”fallbackImage”:{“alt”:””,”caption”:””,”url”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default.gif”,”width”:1200,”height”:600,”sizes”:{“thumbnail”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default-520×260.gif”,”square_small”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default-160×160.gif”,”square_large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default-520×520.gif”,”medium”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default.gif”,”medium_large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default-768×384.gif”,”large”:”https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default.gif”,”__typename”:”ImageSizes”},”__typename”:”Image”}},”modals”:{“loginModal”:false,”signUpModal”:false,”forgotPasswordModal”:false,”resetPasswordModal”:false,”lightboxModal”:false,”callback”:null,”props”:null},”podcast”:{“id”:null,”playing”:false,”duration”:0,”currentTime”:0},”user”:{“loggedIn”:false,”savedArticleIDs”:[],”userEmail”:””,”editor”:false},”comments”:{“open”:false},”cookies”:{“acceptedCookie”:false}},
env: {
APP_URL: ‘
NODE_ENV: ‘production’,
WP_URL: ‘
HAS_GOOGLE_ID: true,
HAS_FACEBOOK_ID: true,
},
}
4 Amazing Trips for Your Family
Choosing somewhere for a family vacation that would pique the attention of adults and kids alike can be a fun...
Customising Your Makeup with Blendable Blush Options
In cosmetics, one’s face is a canvas for self-expression and creativity. Among the myriad of products available, blush is a...
The Benefits of Regular Home Maintenance
Regular home maintenance is essential for maintaining and even raising the value of your house. A proactive approach to repairs...
Understanding the Importance of SEO in Adelaide
In the digital marketplace, Adelaide businesses are in a continuous contest to gain the attention of their target audiences. With...
Breaking Down the Numbers: Understanding the Average Traveling Nurses Pay
The open road, adventure, and the chance to heal – travel nursing promises an undeniable allure. But amidst the excitement,...
Dealing with Oily Skin in Summer: Tips and Tricks
As the temperature rises, those with oily skin often face an additional challenge—maintaining a clear and balanced complexion. Excess oil...
Mountain Wedding Ideas for 2024
A mountain wedding is a stunning choice for couples who cherish nature and desire a distinctive wedding experience. Whether you...
3 Of The Best Ways To Keep Your Salon Clean
It is of the utmost importance to ensure that a salon is kept scrupulously clean, not just for the sake...
3 Reasons You Should Get Blood Tests Every Year
Regular blood tests are essential for preserving general health and identifying potential problems early on. Medical professionals can evaluate your...
How to Make Your Next Crafts Project Pop
Crafting is a creative outlet that allows individuals to express themselves through various mediums such as paper crafts, sewing, painting,...