{"id":47786,"date":"2022-08-02T13:46:34","date_gmt":"2022-08-02T13:46:34","guid":{"rendered":"https:\/\/packetstormsecurity.com\/news\/view\/33687\/Post-Quantum-Encryption-Contender-Is-Taken-Out-By-Single-Core-PC-And-1-Hour.html"},"modified":"2022-08-02T13:46:34","modified_gmt":"2022-08-02T13:46:34","slug":"post-quantum-encryption-contender-is-taken-out-by-single-core-pc-and-1-hour","status":"publish","type":"post","link":"https:\/\/www.threatshub.org\/blog\/post-quantum-encryption-contender-is-taken-out-by-single-core-pc-and-1-hour\/","title":{"rendered":"Post-Quantum Encryption Contender Is Taken Out By Single-Core PC And 1 Hour"},"content":{"rendered":"<figure class=\"intro-image intro-left\"> <img decoding=\"async\" src=\"https:\/\/cdn.arstechnica.net\/wp-content\/uploads\/2022\/08\/quantum-computing2-800x600.jpeg\" alt=\"Post-quantum encryption contender is taken out by single-core PC and 1 hour\"><figcaption class=\"caption\">\n<div class=\"caption-credit\">Getty Images<\/div>\n<\/figcaption><\/figure>\n<aside id=\"social-left\" class=\"social-left\" aria-label=\"Read the comments or share this article\"> <a title=\"79 posters participating\" class=\"comment-count icon-comment-bubble-down\" href=\"https:\/\/arstechnica.com\/information-technology\/2022\/08\/sike-once-a-post-quantum-encryption-contender-is-koed-in-nist-smackdown\/?comments=1\"> <\/p>\n<h4 class=\"comment-count-before\">reader comments<\/h4>\n<p> <span class=\"comment-count-number\">113<\/span> <span class=\"visually-hidden\"> with 79 posters participating<\/span> <\/a> <\/p>\n<div class=\"share-links\">\n<h4>Share this story<\/h4>\n<\/p><\/div>\n<\/aside>\n<p> <!-- cache hit 58:single\/related:f9d3afa6e854bf80316831a1e15fec48 --><!-- empty --><\/p>\n<p>In the US government&#8217;s ongoing campaign to protect data in the age of quantum computers, a new and powerful attack that used a single traditional computer to completely break a fourth-round candidate highlights the risks involved in standardizing the next generation of encryption algorithms.<\/p>\n<p>Last month, the US Department of Commerce&#8217;s National Institute of Standards and Technology, or NIST, selected <a href=\"https:\/\/arstechnica.com\/information-technology\/2022\/07\/nist-selects-quantum-proof-algorithms-to-head-off-the-coming-cryptopocalypse\/\">four post-quantum computing encryption algorithms<\/a> to replace algorithms like RSA, Diffie-Hellman, and elliptic curve Diffie-Hellman, which are unable to withstand attacks from a quantum computer.<\/p>\n<p>In the same move, NIST advanced four additional algorithms as potential replacements pending further testing in hopes one or more of them may also be suitable encryption alternatives in a post-quantum world. The new attack breaks SIKE, which is one of the latter four additional algorithms. The attack has no impact on the four PQC algorithms selected by NIST as approved standards, all of which rely on completely different mathematical techniques than SIKE.<\/p>\n<h2>Getting totally SIKEd<\/h2>\n<p>SIKE\u2014short for <a href=\"https:\/\/sike.org\/\">Supersingular Isogeny Key Encapsulation<\/a>\u2014is now likely out of the running thanks to research that was published over the weekend by researchers from the <a href=\"https:\/\/www.esat.kuleuven.be\/cosic\/\">Computer Security and Industrial Cryptography<\/a> group at KU Leuven. The paper, titled <a href=\"https:\/\/eprint.iacr.org\/2022\/975.pdf\">An Efficient Key Recovery Attack on SIDH (Preliminary Version)<\/a>, described a technique that uses complex mathematics and a single traditional PC to recover the encryption keys protecting the SIKE-protected transactions. The entire process requires only about an hour\u2019s time. The feat makes the researchers, Wouter Castryck and Thomas Decru eligible for a $50,000 reward from NIST.<\/p>\n<p>\u201cThe newly uncovered weakness is clearly a major blow to SIKE,\u201d David Jao, a professor at the University of Waterloo and co-inventor of SIKE, wrote in an email. \u201cThe attack is really unexpected.\u201d<\/p>\n<p>The advent of public key encryption in the 1970s was a major breakthrough because it allowed parties who had never met to securely trade encrypted material that couldn\u2019t be broken by an adversary. Public key encryption relies on asymmetric keys, with one private key used to decrypt messages and a separate public key for encrypting. Users make their public key widely available. As long as their private key remains secret, the scheme remains secure.<\/p>\n<aside class=\"ad_wrapper\" aria-label=\"In Content advertisement\"> <span class=\"ad_notice\">Advertisement <\/span> <\/aside>\n<p>In practice, public key cryptography can often be unwieldy, so many systems rely on key encapsulation mechanisms, which allow parties who have never met before to jointly agree on a symmetric key over a public medium such as the Internet. In contrast to symmetric-key algorithms, key encapsulation mechanisms in use today are easily broken by quantum computers. SIKE, before the new attack, was thought to avoid such vulnerabilities by using a complex mathematical construction known as a supersingular isogeny graph.<\/p>\n<p>The cornerstone of SIKE is a protocol called SIDH, short for Supersingular Isogeny Diffie-Hellman. The research paper published over the weekend shows how SIDH is vulnerable to a theorem known as \u201cglue-and-split\u201d developed by mathematician Ernst Kani in 1997, as well as tools devised by fellow mathematicians Everett W. Howe, Franck Lepr\u00e9vost, and Bjorn Poonen in 2000. The new technique builds on what\u2019s known as the \u201cGPST adaptive attack,\u201d described in a <a href=\"https:\/\/eprint.iacr.org\/2016\/859.pdf\">2016 paper<\/a>. The math behind the latest attack is guaranteed to be impenetrable to most non-mathematicians. Here\u2019s about as close as you\u2019re going to get:<\/p>\n<p>\u201cThe attack exploits the fact that SIDH has auxiliary points and that the degree of the secret isogeny is known,\u201d <a href=\"https:\/\/www.math.auckland.ac.nz\/~sgal018\/\">Steven Galbraith<\/a>, a University of Auckland mathematics professor and the \u201cG\u201d in the GPST adaptive attack, explained in a <a href=\"https:\/\/ellipticnews.wordpress.com\/2022\/07\/31\/breaking-supersingular-isogeny-diffie-hellman-sidh\/\">short writeup<\/a> on the new attack. \u201cThe auxiliary points in SIDH have always been an annoyance and a potential weakness, and they have been exploited for fault attacks, the GPST adaptive attack, torsion point attacks, etc.<\/p>\n<p>He continued:<\/p>\n<blockquote>\n<p>Let <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=E_0&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=E_0&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=E_0&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"E_0\"> be the base curve and let <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=P_0%2C+Q_0+%5Cin+E_0&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=P_0%2C+Q_0+%5Cin+E_0&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=P_0%2C+Q_0+%5Cin+E_0&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"P_0, Q_0 \\in E_0\"> have order <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=2%5Ea&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=2%5Ea&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=2%5Ea&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"2^a\">. Let <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=E%2C+P%2C+Q&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=E%2C+P%2C+Q&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=E%2C+P%2C+Q&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"E, P, Q\"> be given such that there exists an isogeny <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cphi&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cphi&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=%5Cphi&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"\\phi\"> of degree <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=3%5Eb&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=3%5Eb&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=3%5Eb&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"3^b\"> with <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cphi+%3A+E_0+%5Cto+E&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cphi+%3A+E_0+%5Cto+E&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=%5Cphi+%3A+E_0+%5Cto+E&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"\\phi : E_0 \\to E\">, <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cphi%28P_0%29+%3D+P&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cphi%28P_0%29+%3D+P&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=%5Cphi%28P_0%29+%3D+P&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"\\phi(P_0) = P\">, and <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cphi%28Q_0%29+%3D+Q.&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cphi%28Q_0%29+%3D+Q.&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=%5Cphi%28Q_0%29+%3D+Q.&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"\\phi(Q_0) = Q.\"><\/p>\n<p>A key aspect of SIDH is that one does not compute <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cphi&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=%5Cphi&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=%5Cphi&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"\\phi\"> directly, but as a composition of isogenies of degree 3. In other words, there is a sequence of curves <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=E_0+%5Cto+E_1+%5Cto+E_2+%5Cto+%5Ccdots+%5Cto+E&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=E_0+%5Cto+E_1+%5Cto+E_2+%5Cto+%5Ccdots+%5Cto+E&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=E_0+%5Cto+E_1+%5Cto+E_2+%5Cto+%5Ccdots+%5Cto+E&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"E_0 \\to E_1 \\to E_2 \\to \\cdots \\to E\"> connected by 3-isogenies.<\/p>\n<p>Essentially, like in GPST, the attack determines the intermediate curves <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=E_i&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=E_i&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=E_i&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"E_i\"> and hence eventually determines the private key. At step <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=i&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=i&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=i&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"i\"> the attack does a brute-force search of all possible <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=E_i+%5Cto+E_%7Bi%2B1%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=E_i+%5Cto+E_%7Bi%2B1%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=E_i+%5Cto+E_%7Bi%2B1%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"E_i \\to E_{i+1}\">, and the magic ingredient is a gadget that shows which one is correct.<\/p>\n<p>(The above is over-simplified, the isogenies <img decoding=\"async\" class=\"latex\" src=\"https:\/\/s0.wp.com\/latex.php?latex=E_i+%5Cto+E_%7Bi%2B1%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002\" srcset=\"https:\/\/s0.wp.com\/latex.php?latex=E_i+%5Cto+E_%7Bi%2B1%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002 1x, https:\/\/s0.wp.com\/latex.php?latex=E_i+%5Cto+E_%7Bi%2B1%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0&amp;c=20201002&amp;zoom=4.5 4x\" alt=\"E_i \\to E_{i+1}\"> in the attack are not of degree 3 but of degree a small power of 3.)<\/p>\n<\/blockquote>\n<p>More important than understanding the math, Jonathan Katz, an IEEE Member and professor in the department of computer science at the University of Maryland, wrote in an email: \u201cthe attack is entirely classical, and does not require quantum computers at all.\u201d<\/p>\n<p> READ MORE <a href=\"https:\/\/packetstormsecurity.com\/news\/view\/33687\/Post-Quantum-Encryption-Contender-Is-Taken-Out-By-Single-Core-PC-And-1-Hour.html\">HERE<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>READ MORE HERE&#8230;<\/p>\n","protected":false},"author":2,"featured_media":47787,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"colormag_page_layout":"default_layout","footnotes":""},"categories":[60],"tags":[10125],"class_list":["post-47786","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-packet-storm","tag-headlineflawsciencecryptography"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Post-Quantum Encryption Contender Is Taken Out By Single-Core PC And 1 Hour 2026 | ThreatsHub Cybersecurity News<\/title>\n<meta name=\"description\" content=\"ThreatsHub Cybersecurity News | 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