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1 files changed, 8 insertions, 7 deletions
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@@ -1,7 +1,7 @@
1<!doctype html> 1<!doctype html>
2<html lang="en"> 2<html lang="en">
3<head> 3<head>
4 <title>Elliptic Curves and the ECM algorithm</title> 4 <title>Elliptic Curves and the ECM Algorithm</title>
5 <meta name="viewport" content="width=device-width" /> 5 <meta name="viewport" content="width=device-width" />
6 6
7 <!-- Import MathJax script --> 7 <!-- Import MathJax script -->
@@ -36,6 +36,7 @@
36 .slide ul { margin-left: 1.5vw; } 36 .slide ul { margin-left: 1.5vw; }
37 .slide ol { margin-left: 1.5vw; } 37 .slide ol { margin-left: 1.5vw; }
38 .slide p { margin-left: 1.5vw; } 38 .slide p { margin-left: 1.5vw; }
39 .slide li { margin: 3.0vh 0; }
39 40
40 .slide.titlepage p, a { text-align: center; } 41 .slide.titlepage p, a { text-align: center; }
41 .slide.titlepage span.title { font-size: 3.6vw; font-weight: bold; } 42 .slide.titlepage span.title { font-size: 3.6vw; font-weight: bold; }
@@ -93,7 +94,7 @@ background-blend-mode: overlay;">
93<div class="slide" tabindex="-1"> 94<div class="slide" tabindex="-1">
94<h1>The integers</h1> 95<h1>The integers</h1>
95 96
96<img alt="The number line" src="images/number-line.svg" 97<img alt="The number line" src="images/number-line.png"
97 style="width: 70%; margin-left: 15%; margin-right: 15%;"/> 98 style="width: 70%; margin-left: 15%; margin-right: 15%;"/>
98 99
99<ul> 100<ul>
@@ -410,7 +411,7 @@ def factorize(n: int) -> list:
410 411
411 f = find_factor(n) 412 f = find_factor(n)
412 413
413 return factorize(n) + factorize(n//f) 414 return factorize(f) + factorize(n//f)
414</code></pre> 415</code></pre>
415 416
416<ul> 417<ul>
@@ -438,7 +439,7 @@ def find_factor(n: int) -> int:
438<div> 439<div>
439<p><strong>To find a factor of \(n\):</strong><p> 440<p><strong>To find a factor of \(n\):</strong><p>
440<ol> 441<ol>
441<li>Take a random Elliptic Curve \(E\) 442<li>Take a random elliptic curve \(E\)
442and a random point \(P\) of \(E\)</li> 443and a random point \(P\) of \(E\)</li>
443<li>Take a <em>suitable number \(m\)</em></li> 444<li>Take a <em>suitable number \(m\)</em></li>
444<li>Try to compute \(m\cdot P = P+P+\cdots+P\quad\) (\(m\) times) 445<li>Try to compute \(m\cdot P = P+P+\cdots+P\quad\) (\(m\) times)
@@ -484,7 +485,7 @@ background-blend-mode: overlay;">
484Q: Aren't we just computing the \(\operatorname{GCD}\) with random numbers? 485Q: Aren't we just computing the \(\operatorname{GCD}\) with random numbers?
485</strong></p> 486</strong></p>
486<p> 487<p>
487A: Yes, but Elliptic Curve operations produce "good candidates" 488A: Yes, but elliptic curve operations produce "good candidates"
488for these random numbers. 489for these random numbers.
489</p> 490</p>
490</div> 491</div>
@@ -504,7 +505,7 @@ Pollard's \(p-1\) Algorithm</a>, but ECM is faster.</p>
504<h1>Elliptic Curve Method - Questions</h1> 505<h1>Elliptic Curve Method - Questions</h1>
505<div class="centertext"> 506<div class="centertext">
506<p><strong> 507<p><strong>
507Q: Are there objects that are more complicated than Elliptic Curves 508Q: Are there objects that are more complicated than elliptic curves
508and can make the method even faster? 509and can make the method even faster?
509</strong></p> 510</strong></p>
510<p>A: Yes, there are higher-dimensional 511<p>A: Yes, there are higher-dimensional
@@ -594,7 +595,7 @@ background-blend-mode: overlay;">
594 // Function to add a footer to every slide. 595 // Function to add a footer to every slide.
595 function slideFooter() { 596 function slideFooter() {
596 const start = "<div class=\"footer\"><table class=\"footer-table\"><tr>"; 597 const start = "<div class=\"footer\"><table class=\"footer-table\"><tr>";
597 const title = "Elliptic Curves and the ECM algorithm" 598 const title = "Elliptic Curves and the ECM Algorithm"
598 const link = "<a href=https://tronto.net/talks/ecm>tronto.net/talks/ecm</a>"; 599 const link = "<a href=https://tronto.net/talks/ecm>tronto.net/talks/ecm</a>";
599 const end = "</tr></table></div>"; 600 const end = "</tr></table></div>";
600 const content = 601 const content =

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