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<title>Elliptic Curve point addition (𝔽ₚ)</title>
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<h1>Elliptic Curve point addition (𝔽<sub>p</sub>)</h1>
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<li class="field">ℝ</li>
<li><a href="reals-add.html">Addition</a></li>
<li><a href="reals-mul.html">Multiplication</a></li>
<li class="field">𝔽<sub>p</sub></li>
<li><a href="modk-add.html" class="active">Addition</a></li>
<li><a href="modk-mul.html">Multiplication</a></li>
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<div id="plot" class="box"></div>
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<div id="curve-coefficients" class="parameters">
<p>Curve:</p>
<div class="parameter curve-coefficient"><label for="coefficient-a">a</label><input id="coefficient-a" name="a" value="2" type="number" step="1"></div>
<div class="parameter curve-coefficient"><label for="coefficient-b">b</label><input id="coefficient-b" name="b" value="3" type="number" step="1"></div>
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<div id="field-coefficients" class="parameters">
<p>Field:</p>
<div class="parameter curve-coefficient"><label for="coefficient-p">p</label><input id="coefficient-p" name="p" value="97" type="number" step="1"></div>
<div class="placeholder"></div>
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<div id="point-p-coordinates" class="parameters">
<p><em>P</em>:</p>
<div class="parameter point-coordinate"><label for="point-p-x">x</label><input id="point-p-x" name="px" value="17" type="number" step="1"></div>
<div class="parameter point-coordinate"><label for="point-p-y">y</label><input id="point-p-y" name="py" value="10" type="number" step="1"></div>
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<div id="point-q-coordinates" class="parameters">
<p><em>Q</em>:</p>
<div class="parameter point-coordinate"><label for="point-q-x">x</label><input id="point-q-x" name="qx" value="95" type="number" step="1"></div>
<div class="parameter point-coordinate"><label for="point-q-y">y</label><input id="point-q-y" name="qy" value="31" type="number" step="1"></div>
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<div id="point-r-coordinates" class="parameters">
<p><em>R</em> = <em>P</em> + <em>Q</em></span>:</p>
<div class="parameter point-coordinate result"><label for="point-r-x">x</label><input id="point-r-x" name="rx" step="any" readonly></div>
<div class="parameter point-coordinate result"><label for="point-r-y">y</label><input id="point-r-y" name="ry" step="any" readonly></div>
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<div id="summary">
<p>Point addition over the elliptic curve <span class="curve-equation"></span> in 𝔽<sub class="field-order"></sub>.</p>
<p>The curve has <span class="curve-order"></span> points (including the point at infinity).</p>
<p class="curve-singular-warning"><strong>Warning:</strong> this curve is singular.</p>
<p class="composite-warning"><strong>Warning:</strong> <em>p</em> is not a prime.</p>
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<p>This tool was created for <a href="http://andrea.corbellini.name/2015/05/17/elliptic-curve-cryptography-a-gentle-introduction/">Elliptic Curve Cryptography: a gentle introduction</a>.</p>
<p>It's free software, released under the <a href="http://opensource.org/licenses/MIT">MIT license</a>, hosted on <a href="https://github.com/andreacorbellini/ecc">GitHub</a> and served by <a href="http://rawgit.com/">RawGit</a>.</p>
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