{"id":9705,"date":"2024-02-11T16:20:48","date_gmt":"2024-02-11T16:20:48","guid":{"rendered":"https:\/\/topat10.com\/?p=9705"},"modified":"2024-02-11T16:20:48","modified_gmt":"2024-02-11T16:20:48","slug":"a-celebrated-cryptography-breaking-algorithm-just-got-an-upgrade","status":"publish","type":"post","link":"https:\/\/topat10.com\/?p=9705","title":{"rendered":"A Celebrated Cryptography-Breaking Algorithm Just Got an Upgrade"},"content":{"rendered":"<p> <br \/>\n<\/p>\n<div>\n<p class=\"paywall\">This is a job for LLL: Give it (or its brethren) a basis of a multidimensional lattice, and it\u2019ll spit out a better one. This process is known as lattice basis reduction.<\/p>\n<p class=\"paywall\">What does this all have to do with cryptography? It turns out that the task of breaking a cryptographic system can, in some cases, be recast as another problem: finding a relatively short vector in a lattice. And sometimes, that vector can be plucked from the reduced basis generated by an LLL-style algorithm. This strategy has helped researchers topple systems that, on the surface, appear to have little to do with lattices.<\/p>\n<p class=\"paywall\">In a theoretical sense, the original LLL algorithm runs quickly: The time it takes to run doesn\u2019t scale exponentially with the size of the input\u2014that is, the dimension of the lattice and the size (in bits) of the numbers in the basis vectors. But it does increase as a polynomial function, and \u201cif you actually want to do it, polynomial time is not always so feasible,\u201d said L\u00e9o Ducas, a cryptographer at the national research institute CWI in the Netherlands.<\/p>\n<div class=\"GenericCalloutWrapper-tojWn iYblVH callout--has-top-border\" data-testid=\"GenericCallout\">\n<figure class=\"AssetEmbedWrapper-eVDQiB byBkf asset-embed\">\n<div class=\"AssetEmbedAssetContainer-eJxoAx dBHGoQ asset-embed__asset-container\"><span class=\"SpanWrapper-umhxW kGxnNB responsive-asset AssetEmbedResponsiveAsset-cXBNxi eCxVQK asset-embed__responsive-asset\"><picture class=\"ResponsiveImagePicture-cWuUZO dUOtEa AssetEmbedResponsiveAsset-cXBNxi eCxVQK asset-embed__responsive-asset responsive-image\"><noscript><img decoding=\"async\" alt=\"tile\" class=\"ResponsiveImageContainer-eybHBd fptoWY responsive-image__image lazyload\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/media.wired.com\/photos\/65c66a3b9669718859322a45\/master\/w_1600%2Cc_limit\/Quanta-tile-detail-03-smaller.jpg\" data-sizes=\"auto\" data-srcset=\"https:\/\/media.wired.com\/photos\/65c66a3b9669718859322a45\/master\/w_120,c_limit\/Quanta-tile-detail-03-smaller.jpg 120w, https:\/\/media.wired.com\/photos\/65c66a3b9669718859322a45\/master\/w_240,c_limit\/Quanta-tile-detail-03-smaller.jpg 240w, https:\/\/media.wired.com\/photos\/65c66a3b9669718859322a45\/master\/w_320,c_limit\/Quanta-tile-detail-03-smaller.jpg 320w, https:\/\/media.wired.com\/photos\/65c66a3b9669718859322a45\/master\/w_640,c_limit\/Quanta-tile-detail-03-smaller.jpg 640w, https:\/\/media.wired.com\/photos\/65c66a3b9669718859322a45\/master\/w_960,c_limit\/Quanta-tile-detail-03-smaller.jpg 960w, https:\/\/media.wired.com\/photos\/65c66a3b9669718859322a45\/master\/w_1280,c_limit\/Quanta-tile-detail-03-smaller.jpg 1280w, https:\/\/media.wired.com\/photos\/65c66a3b9669718859322a45\/master\/w_1600,c_limit\/Quanta-tile-detail-03-smaller.jpg 1600w\" sizes=\"100vw\"\/><\/noscript><\/picture><\/span><\/div>\n<\/figure>\n<\/div>\n<p class=\"paywall\">In practice, this means that the original LLL algorithm can\u2019t handle inputs that are too large. \u201cMathematicians and cryptographers wanted the ability to do more,\u201d said <a data-offer-url=\"https:\/\/www.semanticscholar.org\/author\/Keegan-Ryan\/30512433\" class=\"external-link\" data-event-click=\"{&quot;element&quot;:&quot;ExternalLink&quot;,&quot;outgoingURL&quot;:&quot;https:\/\/www.semanticscholar.org\/author\/Keegan-Ryan\/30512433&quot;}\" href=\"https:\/\/www.semanticscholar.org\/author\/Keegan-Ryan\/30512433\" rel=\"noopener\" target=\"_blank\">Keegan Ryan<\/a>, a doctoral student at the University of California, San Diego. Researchers worked to optimize LLL-style algorithms to accommodate bigger inputs, often achieving good performance. Still, some tasks have remained stubbornly out of reach.<\/p>\n<p class=\"paywall\">The new paper, authored by Ryan and his adviser, <a data-offer-url=\"https:\/\/cseweb.ucsd.edu\/~nadiah\/\" class=\"external-link\" data-event-click=\"{&quot;element&quot;:&quot;ExternalLink&quot;,&quot;outgoingURL&quot;:&quot;https:\/\/cseweb.ucsd.edu\/~nadiah\/&quot;}\" href=\"https:\/\/cseweb.ucsd.edu\/~nadiah\/\" rel=\"noopener\" target=\"_blank\">Nadia Heninger<\/a>, combines multiple strategies to improve the efficiency of its LLL-style algorithm. For one thing, the technique uses a recursive structure that breaks the task down into smaller chunks. For another, the algorithm carefully manages the precision of the numbers involved, finding a balance between speed and a correct result. The new work makes it feasible for researchers to reduce the bases of lattices with thousands of dimensions.<\/p>\n<p class=\"paywall\">Past work has followed a similar approach: A <a href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-3-030-84245-1_26\" target=\"_blank\" rel=\"noopener\">2021 paper<\/a> also combines recursion and precision management to make quick work of large lattices, but it worked only for specific kinds of lattices, and not all the ones that are important in cryptography. The new algorithm behaves well on a much broader range. \u201cI\u2019m really happy someone did it,\u201d said <a data-offer-url=\"https:\/\/espitau.github.io\/\" class=\"external-link\" data-event-click=\"{&quot;element&quot;:&quot;ExternalLink&quot;,&quot;outgoingURL&quot;:&quot;https:\/\/espitau.github.io\/&quot;}\" href=\"https:\/\/espitau.github.io\/\" rel=\"noopener\" target=\"_blank\">Thomas Espitau<\/a>, a cryptography researcher at the company PQShield and an author of the 2021 version. His team\u2019s work offered a \u201cproof of concept,\u201d he said; the new result shows that \u201cyou can do very fast lattice reduction in a sound way.\u201d<\/p>\n<p class=\"paywall\">The new technique has already started to prove useful. <a data-offer-url=\"https:\/\/www.normalesup.org\/~page\/index-en.html\" class=\"external-link\" data-event-click=\"{&quot;element&quot;:&quot;ExternalLink&quot;,&quot;outgoingURL&quot;:&quot;https:\/\/www.normalesup.org\/~page\/index-en.html&quot;}\" href=\"https:\/\/www.normalesup.org\/~page\/index-en.html\" rel=\"noopener\" target=\"_blank\">Aurel Page<\/a>, a mathematician with the French national research institute Inria, said that he and his team have put an adaptation of the algorithm to work on some computational number theory tasks.<\/p>\n<p class=\"paywall\">LLL-style algorithms can also play a role in research related to lattice-based cryptography systems designed to <a href=\"https:\/\/www.quantamagazine.org\/cryptographys-future-will-be-quantum-safe-heres-how-it-will-work-20221109\/\">remain secure<\/a> even in a future with powerful quantum computers. They don\u2019t pose a threat to such systems, since taking them down requires finding shorter vectors than these algorithms can achieve. But the best attacks researchers know of use an LLL-style algorithm as a \u201cbasic building block,\u201d said <a data-offer-url=\"https:\/\/wesselvanwoerden.com\/\" class=\"external-link\" data-event-click=\"{&quot;element&quot;:&quot;ExternalLink&quot;,&quot;outgoingURL&quot;:&quot;https:\/\/wesselvanwoerden.com\/&quot;}\" href=\"https:\/\/wesselvanwoerden.com\/\" rel=\"noopener\" target=\"_blank\">Wessel van Woerden<\/a>, a cryptographer at the University of Bordeaux. In practical experiments to study these attacks, that building block can slow everything down. Using the new tool, researchers may be able to expand the range of experiments they can run on the attack algorithms, offering a clearer picture of how they perform.<\/p>\n<hr class=\"paywall\"\/>\n<p class=\"paywall\"><a href=\"https:\/\/www.quantamagazine.org\/celebrated-cryptography-algorithm-gets-an-upgrade-20231214\/\"><em>Original story<\/em><\/a> <em>reprinted with permission from<\/em> <a href=\"https:\/\/www.quantamagazine.org\">Quanta Magazine<\/a>, <em>an editorially independent publication of the<\/em> <a href=\"https:\/\/www.simonsfoundation.org\"><em>Simons Foundation<\/em><\/a> <em>whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.<\/em><\/p>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>This is a job for LLL: Give it (or its brethren) a basis of a multidimensional lattice, and it\u2019ll spit out a better one. This process is known as lattice basis reduction. What does this all have to do with cryptography? It turns out that the task of breaking a cryptographic system can, in some [&hellip;]<\/p>\n","protected":false},"author":294,"featured_media":9706,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[703],"tags":[1173,1331,914,890,921],"class_list":["post-9705","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-technology","tag-computing","tag-cryptography","tag-quanta-magazine","tag-science","tag-security"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>A Celebrated Cryptography-Breaking Algorithm Just Got an Upgrade | Unlock Informed Choices with Us<\/title>\n<meta name=\"description\" content=\"Two researchers have improved a well-known technique for lattice basis reduction, opening up new 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Goldberg","author_link":"https:\/\/topat10.com\/?author=294"},"uagb_comment_info":0,"uagb_excerpt":"This is a job for LLL: Give it (or its brethren) a basis of a multidimensional lattice, and it\u2019ll spit out a better one. This process is known as lattice basis reduction. What does this all have to do with cryptography? It turns out that the task of breaking a cryptographic system can, in some&hellip;","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/topat10.com\/index.php?rest_route=\/wp\/v2\/posts\/9705","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/topat10.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/topat10.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/topat10.com\/index.php?rest_route=\/wp\/v2\/users\/294"}],"replies":[{"embeddable":true,"href":"https:\/\/topat10.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9705"}],"version-history":[{"count":0,"href":"https:\/\/topat10.com\/index.php?rest_route=\/wp\/v2\/posts\/9705\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/topat10.com\/index.php?rest_route=\/wp\/v2\/media\/9706"}],"wp:attachment":[{"href":"https:\/\/topat10.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9705"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/topat10.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9705"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/topat10.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9705"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}