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<ul>
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<li class="toctree-l1"><a class="reference internal" href="/example-rsa-keys/">Generating RSA Keys</a>
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</li>
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<li class="toctree-l1"><a class="" href="/example-curves.md">Generating Curves</a>
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<li class="toctree-l1"><a class="reference internal" href="/example-curves/">Generating Curves</a>
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</ul>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../example-rsa-keys/">Generating RSA Keys</a>
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</li>
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<li class="toctree-l1"><a class="" href="../example-curves.md">Generating Curves</a>
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<li class="toctree-l1"><a class="reference internal" href="../example-curves/">Generating Curves</a>
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</ul>
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<title>Generating Curves - CryptoTools documentation</title>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../introduction/">Introduction</a>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../installation/">Installation</a>
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</ul>
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<p class="caption"><span class="caption-text">Low-level cryptographic</span></p>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../number-theory/">Number theory</a>
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<li class="toctree-l1"><a class="reference internal" href="../group-theory/">Group theory</a>
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</li>
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<li class="toctree-l1"><a class="reference internal" href="../curves/">Curves</a>
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</li>
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</ul>
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<p class="caption"><span class="caption-text">Public Keys</span></p>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../rsa/">RSA</a>
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</li>
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</ul>
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<p class="caption"><span class="caption-text">Utils</span></p>
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<li class="toctree-l1"><a class="reference internal" href="../utils/">Utils</a>
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</li>
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</ul>
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<p class="caption"><span class="caption-text">Examples</span></p>
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<ul class="current">
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<li class="toctree-l1"><a class="reference internal" href="../example-rsa-keys/">Generating RSA Keys</a>
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</li>
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<li class="toctree-l1 current"><a class="reference internal current" href="#">Generating Curves</a>
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<ul class="current">
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<li class="toctree-l2"><a class="reference internal" href="#a-weierstrass-curve">A Weierstrass Curve</a>
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</li>
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<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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<div class="section" itemprop="articleBody">
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<h1 id="generating-elliptic-curves">Generating Elliptic Curves</h1>
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<p>In the following section, we are going to see how to generate Elliptic Curves and draw the curve with Python.</p>
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<h2 id="a-weierstrass-curve">A Weierstrass Curve</h2>
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<p>The python code below draw a Weierstrass Curve:</p>
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<pre><code>#!/usr/bin/env python3
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import matplotlib.pyplot as plt
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from Cryptotools.Groups.curve import Curve
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a = 3
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b = 8
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curve = Curve(a, b, Curve.WEIERSTRASS)
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x = curve.x
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curve.generatePoints()
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y = curve.y
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yn = curve.yn
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points = curve.getPoints()
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plt.figure(figsize=(10, 6))
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plt.plot(x, y, color='b', label=f'$y^2 = x^3 + {a}x + {b}$')
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plt.plot(x, yn, color='b', )
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plt.legend()
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plt.show()
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</code></pre>
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</div>
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</div><footer>
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<div class="rst-footer-buttons" role="navigation" aria-label="Footer Navigation">
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<a href="../example-rsa-keys/" class="btn btn-neutral float-left" title="Generating RSA Keys"><span class="icon icon-circle-arrow-left"></span> Previous</a>
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<ul class="current">
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</ul>
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</li>
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<li class="toctree-l1"><a class="" href="../example-curves.md">Generating Curves</a>
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<li class="toctree-l1"><a class="reference internal" href="../example-curves/">Generating Curves</a>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../example-rsa-keys/">Generating RSA Keys</a>
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</li>
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<li class="toctree-l1"><a class="" href="../example-curves.md">Generating Curves</a>
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<li class="toctree-l1"><a class="reference internal" href="../example-curves/">Generating Curves</a>
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</li>
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</ul>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="example-rsa-keys/">Generating RSA Keys</a>
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</li>
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<li class="toctree-l1"><a class="" href="example-curves.md">Generating Curves</a>
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<li class="toctree-l1"><a class="reference internal" href="example-curves/">Generating Curves</a>
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</li>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../example-rsa-keys/">Generating RSA Keys</a>
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</li>
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<li class="toctree-l1"><a class="" href="../example-curves.md">Generating Curves</a>
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<li class="toctree-l1"><a class="reference internal" href="../example-curves/">Generating Curves</a>
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</ul>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../example-rsa-keys/">Generating RSA Keys</a>
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</li>
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<li class="toctree-l1"><a class="" href="../example-curves.md">Generating Curves</a>
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<li class="toctree-l1"><a class="reference internal" href="../example-curves/">Generating Curves</a>
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</li>
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</ul>
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</div>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../example-rsa-keys/">Generating RSA Keys</a>
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</li>
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<li class="toctree-l1"><a class="" href="../example-curves.md">Generating Curves</a>
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<li class="toctree-l1"><a class="reference internal" href="../example-curves/">Generating Curves</a>
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</li>
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</ul>
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</div>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../example-rsa-keys/">Generating RSA Keys</a>
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</li>
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<li class="toctree-l1"><a class="" href="../example-curves.md">Generating Curves</a>
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<li class="toctree-l1"><a class="reference internal" href="../example-curves/">Generating Curves</a>
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</li>
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</ul>
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</div>
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<ul>
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<li class="toctree-l1"><a class="reference internal" href="../example-rsa-keys/">Generating RSA Keys</a>
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</li>
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<li class="toctree-l1"><a class="" href="../example-curves.md">Generating Curves</a>
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<li class="toctree-l1"><a class="reference internal" href="../example-curves/">Generating Curves</a>
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</li>
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</ul>
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</div>
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