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#factorization

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🧿🪬🍄🌈🎮💻🚲🥓🎃💀🏴🛻🇺🇸<p>&gt; Researchers claim to have used a <a href="https://mastodon.social/tags/quantumComputer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>quantumComputer</span></a> to factor a 2,048-bit <a href="https://mastodon.social/tags/RSA" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>RSA</span></a> integer.</p><p>&gt; But the RSA number evaluated was the product of two prime factors that were too close together.</p><p>&gt; As with a parlor magician's card deck that's been stacked for a card trick</p><p>&gt; <a href="https://mastodon.social/tags/Quantum" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Quantum</span></a> <a href="https://mastodon.social/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>factorization</span></a> is performed using sleight-of-hand numbers that have been selected to make them very easy to factorize using a <a href="https://mastodon.social/tags/physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>physics</span></a> experiment</p><p><a href="https://www.theregister.com/2025/07/17/quantum_cryptanalysis_criticism/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">theregister.com/2025/07/17/qua</span><span class="invisible">ntum_cryptanalysis_criticism/</span></a></p><p><a href="https://mastodon.social/tags/quantumComputing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>quantumComputing</span></a> <a href="https://mastodon.social/tags/computerScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>computerScience</span></a> <a href="https://mastodon.social/tags/cryptography" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>cryptography</span></a></p>
Jon Awbrey<p>Riffs and Rotes • Happy New Year 2025<br>• <a href="https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/01</span><span class="invisible">/01/riffs-and-rotes-happy-new-year-2025/</span></a></p><p>\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)</p><p>\( \text{Then} ~ 2025<br>= 81 \cdot 25<br>= 3^4 5^2 \)</p><p>\( = {p_2}^4 {p_3}^2<br>= {p_2}^{{p_1}^{p_1}} {p_3}^{p_1}<br>= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_2}}^{p_1}<br>= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_{p_1}}}^{p_1} \)</p><p>No information is lost by dropping the terminal 1s. Thus we may write the following form.</p><p>\[ 2025 = {p_p}^{p^p} {p_{p_p}}^p \]</p><p>The article linked below tells how forms of that sort correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”. The riff and rote for 2025 are shown in the next two Figures.</p><p>Riff 2025<br>• <a href="https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.png" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.files.wordp</span><span class="invisible">ress.com/2025/01/riff-2025.png</span></a></p><p>Rote 2025<br>• <a href="https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.png" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.files.wordp</span><span class="invisible">ress.com/2025/01/rote-2025.png</span></a></p><p>Reference —</p><p>Riffs and Rotes<br>• <a href="https://oeis.org/wiki/Riffs_and_Rotes" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">oeis.org/wiki/Riffs_and_Rotes</span><span class="invisible"></span></a></p><p><a href="https://mathstodon.xyz/tags/Arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Arithmetic</span></a> <a href="https://mathstodon.xyz/tags/Combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Combinatorics</span></a> <a href="https://mathstodon.xyz/tags/Computation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Computation</span></a> <a href="https://mathstodon.xyz/tags/Factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Factorization</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GraphTheory</span></a> <a href="https://mathstodon.xyz/tags/GroupTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GroupTheory</span></a> <br><a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/Primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Primes</span></a> <a href="https://mathstodon.xyz/tags/Recursion" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Recursion</span></a> <a href="https://mathstodon.xyz/tags/Representation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Representation</span></a> <a href="https://mathstodon.xyz/tags/RiffsAndRotes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>RiffsAndRotes</span></a></p>
badkeys<p>I previously helped discover that RSA keys in certificates generated by printers from Canon and Fuji could be factorized with the centuries-old Fermat factorization algorithm <a href="https://fermatattack.secvuln.info/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">fermatattack.secvuln.info/</span><span class="invisible"></span></a> <a href="https://infosec.exchange/tags/rsa" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>rsa</span></a> <a href="https://infosec.exchange/tags/factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>factorization</span></a> <a href="https://infosec.exchange/tags/fermat" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fermat</span></a></p>
Erwin Schrödinger Institute<p>We are happy to announce that a new thematic programme with 5 focus weeks just got started at <br><span class="h-card"><a href="https://mathstodon.xyz/@ESIVienna" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>ESIVienna</span></a></span><br>! 🥳 Check out the details below ⏬</p><p>📅 31st July - 1st September 2023 📅<br>📌 Schrödinger Lecture Hall 📌</p><p>▫️ Programme description ▫️<br><a href="https://esi.ac.at/events/e476/" rel="nofollow noopener" target="_blank"><span class="invisible">https://</span><span class="">esi.ac.at/events/e476/</span><span class="invisible"></span></a></p><p>📚 Subject: <a href="https://mathstodon.xyz/tags/QuantumFieldTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>QuantumFieldTheory</span></a> at the Frontiers of the <a href="https://mathstodon.xyz/tags/StrongInteraction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>StrongInteraction</span></a><br>📓Week 1: Finite-Mass and <a href="https://mathstodon.xyz/tags/Electroweak" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Electroweak</span></a> Effects in <a href="https://mathstodon.xyz/tags/gaugetheories" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>gaugetheories</span></a><br>📕 Week 2: <a href="https://mathstodon.xyz/tags/Singularity" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Singularity</span></a> Structure of Quantum Field Theory Beyond the Leading Power<br>📗 Week 3: <a href="https://mathstodon.xyz/tags/Factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Factorization</span></a> Violation and the <a href="https://mathstodon.xyz/tags/Space" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Space</span></a> of Universal Functions<br>📘 Week 4: Simulation of the All Order Structure of Scattering Amplitudes<br>📙 Week 5: Multi-Variable Techniques for All Order Resummations in QFT</p><p>(see the motion picture at <a href="https://twitter.com/ESIVienna/status/1686002264878530561" rel="nofollow noopener" target="_blank"><span class="invisible">https://</span><span class="ellipsis">twitter.com/ESIVienna/status/1</span><span class="invisible">686002264878530561</span></a>)</p><p><span class="h-card"><a href="https://fediscience.org/@univienna" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>univienna</span></a></span></p>