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</script></nav></div><div class="container mainContainer docsContainer"><div class="wrapper"><div class="post"><header class="postHeader"><h1 id="__docusaurus" class="postHeaderTitle">PAIR</h1></header><article><div><span><p><a name="PAIR"></a></p>
<h2><a class="anchor" aria-hidden="true" id="pair"></a><a href="#pair" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR</h2>
<p><strong>Kind</strong>: global class<br>
<strong>this</strong>: <code>{PAIR}</code></p>
<ul>
<li><a href="#PAIR">PAIR</a>
<ul>
<li><a href="#new_PAIR_new">new PAIR()</a></li>
<li><a href="#PAIR.line">.line()</a></li>
<li><a href="#PAIR.initmp">.initmp()</a></li>
<li><a href="#PAIR.miller">.miller(r, res)</a></li>
<li><a href="#PAIR.another">.another(r, P1, Q1)</a></li>
<li><a href="#PAIR.ate">.ate(P1, Q1)</a></li>
<li><a href="#PAIR.ate2">.ate2(P1, Q1, R1, S1)</a></li>
<li><a href="#PAIR.fexp">.fexp(m)</a></li>
<li><a href="#PAIR.lbits">.lbits()</a></li>
<li><a href="#PAIR.glv">.glv()</a></li>
<li><a href="#PAIR.gs">.gs()</a></li>
<li><a href="#PAIR.G1mul">.G1mul(P, e)</a> ⇒</li>
<li><a href="#PAIR.G2mul">.G2mul(P, e)</a> ⇒</li>
<li><a href="#PAIR.GTpow">.GTpow(d, e)</a> ⇒</li>
</ul></li>
</ul>
<p><a name="new_PAIR_new"></a></p>
<h3><a class="anchor" aria-hidden="true" id="new-pair"></a><a href="#new-pair" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>new PAIR()</h3>
<p>Creates an instance of PAIR</p>
<p><a name="PAIR.line"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairline"></a><a href="#pairline" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.line()</h3>
<p>Line function</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>this</strong>: <code>{PAIR}</code> <br>
<a name="PAIR.initmp"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairinitmp"></a><a href="#pairinitmp" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.initmp()</h3>
<p>prepare for multi-pairing</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>this</strong>: <code>{PAIR}</code> <br>
<a name="PAIR.miller"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairmillerr-res"></a><a href="#pairmillerr-res" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.miller(r, res)</h3>
<p>basic Miller loop</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>this</strong>: <code>{PAIR}</code></p>
<table>
<thead>
<tr><th>Param</th><th>Description</th></tr>
</thead>
<tbody>
<tr><td>r</td><td>FP12 precomputed array of accumulated line functions</td></tr>
<tr><td>res</td><td>FP12 result</td></tr>
</tbody>
</table>
<p><a name="PAIR.another"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairanotherr-p1-q1"></a><a href="#pairanotherr-p1-q1" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.another(r, P1, Q1)</h3>
<p>Precompute line functions for n-pairing</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>this</strong>: <code>{PAIR}</code></p>
<table>
<thead>
<tr><th>Param</th><th>Description</th></tr>
</thead>
<tbody>
<tr><td>r</td><td>array of precomputed FP48 products of line functions</td></tr>
<tr><td>P1</td><td>An element of G2</td></tr>
<tr><td>Q1</td><td>An element of G1</td></tr>
</tbody>
</table>
<p><a name="PAIR.ate"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairatep1-q1"></a><a href="#pairatep1-q1" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.ate(P1, Q1)</h3>
<p>Calculate Miller loop for Optimal ATE pairing e(P,Q)</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>this</strong>: <code>{PAIR}</code> <br>
<strong>Result</strong>: r An element of GT i.e. result of the pairing calculation e(P,Q)</p>
<table>
<thead>
<tr><th>Param</th><th>Description</th></tr>
</thead>
<tbody>
<tr><td>P1</td><td>An element of G2</td></tr>
<tr><td>Q1</td><td>An element of G1</td></tr>
</tbody>
</table>
<p><a name="PAIR.ate2"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairate2p1-q1-r1-s1"></a><a href="#pairate2p1-q1-r1-s1" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.ate2(P1, Q1, R1, S1)</h3>
<p>Calculate Miller loop for Optimal ATE double-pairing e(P,Q).e(R,S)</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>this</strong>: <code>{PAIR}</code> <br>
<strong>Result</strong>: r An element of GT i.e. result of the double pairing calculation e(P,Q).e(R,S)</p>
<table>
<thead>
<tr><th>Param</th><th>Description</th></tr>
</thead>
<tbody>
<tr><td>P1</td><td>An element of G2</td></tr>
<tr><td>Q1</td><td>An element of G1</td></tr>
<tr><td>R1</td><td>An element of G2</td></tr>
<tr><td>S1</td><td>An element of G1</td></tr>
</tbody>
</table>
<p><a name="PAIR.fexp"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairfexpm"></a><a href="#pairfexpm" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.fexp(m)</h3>
<p>Final exponentiation of pairing, converts output of Miller loop to element in GT</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>this</strong>: <code>{PAIR}</code> <br>
<strong>Result</strong>: r m^((p^12-1)/r) where p is modulus and r is the group order</p>
<table>
<thead>
<tr><th>Param</th><th>Description</th></tr>
</thead>
<tbody>
<tr><td>m</td><td>FP12 value</td></tr>
</tbody>
</table>
<p><a name="PAIR.lbits"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairlbits"></a><a href="#pairlbits" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.lbits()</h3>
<p>prepare ate parameter, n=6u+2 (BN) or n=u (BLS), n3=3*n</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>this</strong>: <code>{PAIR}</code> <br>
<a name="PAIR.glv"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairglv"></a><a href="#pairglv" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.glv()</h3>
<p>GLV method</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>this</strong>: <code>{PAIR}</code> <br>
<a name="PAIR.gs"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairgs"></a><a href="#pairgs" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.gs()</h3>
<p>Galbraith &amp; Scott Method</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>this</strong>: <code>{PAIR}</code> <br>
<a name="PAIR.G1mul"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairg1mulp-e-"></a><a href="#pairg1mulp-e-" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.G1mul(P, e) ⇒</h3>
<p>Fast point multiplication of a member of the group G1 by a BIG number</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>Returns</strong>: R Member of G1 R=e.P<br>
<strong>this</strong>: <code>{PAIR}</code></p>
<table>
<thead>
<tr><th>Param</th><th>Description</th></tr>
</thead>
<tbody>
<tr><td>P</td><td>Member of G1</td></tr>
<tr><td>e</td><td>BIG multiplier</td></tr>
</tbody>
</table>
<p><a name="PAIR.G2mul"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairg2mulp-e-"></a><a href="#pairg2mulp-e-" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.G2mul(P, e) ⇒</h3>
<p>Multiply P by e in group G2</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>Returns</strong>: R Member of G2 R=e.P<br>
<strong>this</strong>: <code>{PAIR}</code></p>
<table>
<thead>
<tr><th>Param</th><th>Description</th></tr>
</thead>
<tbody>
<tr><td>P</td><td>Member of G2</td></tr>
<tr><td>e</td><td>BIG multiplier</td></tr>
</tbody>
</table>
<p><a name="PAIR.GTpow"></a></p>
<h3><a class="anchor" aria-hidden="true" id="pairgtpowd-e-"></a><a href="#pairgtpowd-e-" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>PAIR.GTpow(d, e) ⇒</h3>
<p>Fast raising of a member of GT to a BIG power</p>
<p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a> <br>
<strong>Returns</strong>: r d^e<br>
<strong>this</strong>: <code>{PAIR}</code></p>
<table>
<thead>
<tr><th>Param</th><th>Description</th></tr>
</thead>
<tbody>
<tr><td>d</td><td>Member of GT</td></tr>
<tr><td>e</td><td>BIG exponent</td></tr>
</tbody>
</table>
</span></div></article></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/cryptojs/mpin256"><span class="arrow-prev">← </span><span>MPIN256</span></a><a class="docs-next button" href="/docs/cryptojs/pair192"><span>PAIR192</span><span class="arrow-next"> →</span></a></div></div></div><nav class="onPageNav"><ul class="toc-headings"><li><a href="#pair">PAIR</a><ul class="toc-headings"><li><a href="#new-pair">new PAIR()</a></li><li><a href="#pairline">PAIR.line()</a></li><li><a href="#pairinitmp">PAIR.initmp()</a></li><li><a href="#pairmillerr-res">PAIR.miller(r, res)</a></li><li><a href="#pairanotherr-p1-q1">PAIR.another(r, P1, Q1)</a></li><li><a href="#pairatep1-q1">PAIR.ate(P1, Q1)</a></li><li><a href="#pairate2p1-q1-r1-s1">PAIR.ate2(P1, Q1, R1, S1)</a></li><li><a href="#pairfexpm">PAIR.fexp(m)</a></li><li><a href="#pairlbits">PAIR.lbits()</a></li><li><a href="#pairglv">PAIR.glv()</a></li><li><a href="#pairgs">PAIR.gs()</a></li><li><a href="#pairg1mulp-e-">PAIR.G1mul(P, e) ⇒</a></li><li><a href="#pairg2mulp-e-">PAIR.G2mul(P, e) ⇒</a></li><li><a href="#pairgtpowd-e-">PAIR.GTpow(d, e) ⇒</a></li></ul></li></ul></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><a href="/" class="nav-home"><img src="/img/milagro.svg" alt="Apache Milagro" width="50" height="100"/></a><div><h5>Docs</h5><a href="/docs/milagro-intro.html">Milagro Intro</a><a href="/docs/amcl-overview.html">Apache Milagro Crypto Library</a><a href="/docs/d-ta-overview.html">Decentralized Trust Authority</a><a href="/docs/zkp-mfa-overview.html">Zero Knowledge Proof MFA</a></div><div><h5>Community</h5><a href="../docs/support">Support</a><a href="../docs/contributor-guide">Contributing</a><a href="https://cwiki.apache.org/confluence/pages/viewpage.action?pageId=115529045" target="_blank" rel="noreferrer noopener">Developer Wiki</a><a href="https://twitter.com/apachemilagro?lang=en" target="_blank" rel="noreferrer noopener">Twitter</a></div><div><h5>More</h5><a href="/blog">Status</a><a href="https://github.com/apache/incubator-milagro-crypto-c">GitHub</a><a class="github-button" href="https://github.com/apache/incubator-milagro" data-icon="octicon-star" data-count-href="/apache/incubator-milagro-crypto/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star this project on GitHub">Star</a></div></section><a href="https://apache.org" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Apache Incubator" width="170" height="45"/></a><section class="copyright"><div>Apache Milagro is an effort undergoing incubation at The Apache Software Foundation (ASF), sponsored by the Apache Incubator. Incubation is required of all newly accepted projects until a further review indicates that the infrastructure, communications, and decision making process have stabilized in a manner consistent with other successful ASF projects. While incubation status is not necessarily a reflection of the completeness or stability of the code, it does indicate that the project has yet to be fully endorsed by the ASF.</div></section><p></p><section class="copyright">Copyright © 2022 The Apache Software Foundation. Apache Milagro, Milagro, Apache, the Apache feather, and the Apache Milagro project logo are either registered trademarks or trademarks of the Apache Software Foundation.</section></footer></div></body></html>