https://manbolq.xyz/posts/trxctf-2026/ Recent content in TRX CTF-2026 writeups on manbolq's Blog Hugo -- gohugo.io en Wed, 29 Apr 2026 00:00:00 +0000 https://manbolq.xyz/posts/trxctf-2026/whatthehecc2/ Wed, 29 Apr 2026 00:00:00 +0000 https://manbolq.xyz/posts/trxctf-2026/whatthehecc2/ <p>This challenge involves hyperelliptic curves and understanding the Cantor&rsquo;s algorithm to be able to construct a relationship that can be used to extract some small roots using the Coppermisth algorithm.</p> <p>We are given a <code>chall.sage</code> file that, first of all, sets up some parameters:</p> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-python" data-lang="python"><span style="display:flex;"><span>p <span style="color:#f92672">=</span> <span style="color:#ae81ff">94235683804629271565982999971710609375595046800623466974818400769289845080223265348096429515360903332205728922039831445325696288131469248632324474133225349921788521516761748848030075106682083159721250623229343087538822420218805346047462578541418450143242476874246298541119785973740522737514515994196626057947</span> </span></span><span style="display:flex;"><span>Zp <span style="color:#f92672">=</span> Zmod(p) </span></span><span style="display:flex;"><span>R<span style="color:#f92672">.&lt;</span>x<span style="color:#f92672">&gt;</span> <span style="color:#f92672">=</span> PolynomialRing(Zp) </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span>a <span style="color:#f92672">=</span> <span style="color:#ae81ff">50388745719041913460291516577153707251851589986907343887836950814620908576049743625336406788413868434770966202375151155498184781903665587711680037916397047153196612649839072989391148224527332860455558388897073964777769901562543742670098611486382534056016050623712004728700806297510524525947953184925678738191</span> </span></span><span style="display:flex;"><span>b <span style="color:#f92672">=</span> <span style="color:#ae81ff">77079665980869941586534539811707525781544605363177140690146778399875761035230354698555185675543136711786384579448967682817286610411073515757944721339483414323574243444638341503092366359064263273232684465918634617514909696812221857920483650952488398729514231494850081371324567953025480739514958298506881528450</span> </span></span><span style="display:flex;"><span>F <span style="color:#f92672">=</span> x<span style="color:#f92672">**</span><span style="color:#ae81ff">5</span> <span style="color:#f92672">+</span> a<span style="color:#f92672">*</span>x<span style="color:#f92672">**</span><span style="color:#ae81ff">3</span> <span style="color:#f92672">+</span> b<span style="color:#f92672">*</span>x </span></span><span style="display:flex;"><span>H <span style="color:#f92672">=</span> <span style="color:#ae81ff">0</span> </span></span><span style="display:flex;"><span> </span></span><span style="display:flex;"><span>C <span style="color:#f92672">=</span> HyperellipticCurve(F, H) </span></span><span style="display:flex;"><span>J <span style="color:#f92672">=</span> C<span style="color:#f92672">.</span>jacobian()(Zp) </span></span></code></pre></div><p>In the general case, a hyperelliptic curve is defined as:</p>