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markdown"><header><h1>PAIR</h1></header><a name="PAIR"></a><h2 class="anchor anchorWithStickyNavbar_LWe7" id="pair">PAIR<a class="hash-link" href="#pair" title="Direct link to heading">​</a></h2><p><strong>Kind</strong>: global class<br>
<strong>this</strong>: <code>{&quot;{&quot;}PAIR{&quot;}&quot;}</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><a name="new_PAIR_new"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="new-pair">new PAIR()<a class="hash-link" href="#new-pair" title="Direct link to heading">​</a></h3><p>Creates an instance of PAIR</p><a name="PAIR.line"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairline">PAIR.line()<a class="hash-link" href="#pairline" title="Direct link to heading">​</a></h3><p>Line function</p><p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a><br>
<strong>this</strong>: <code>{&quot;{&quot;}PAIR{&quot;}&quot;}</code> </p><a name="PAIR.initmp"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairinitmp">PAIR.initmp()<a class="hash-link" href="#pairinitmp" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</code> </p><a name="PAIR.miller"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairmillerr-res">PAIR.miller(r, res)<a class="hash-link" href="#pairmillerr-res" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</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><a name="PAIR.another"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairanotherr-p1-q1">PAIR.another(r, P1, Q1)<a class="hash-link" href="#pairanotherr-p1-q1" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</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><a name="PAIR.ate"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairatep1-q1">PAIR.ate(P1, Q1)<a class="hash-link" href="#pairatep1-q1" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</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><a name="PAIR.ate2"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairate2p1-q1-r1-s1">PAIR.ate2(P1, Q1, R1, S1)<a class="hash-link" href="#pairate2p1-q1-r1-s1" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</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><a name="PAIR.fexp"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairfexpm">PAIR.fexp(m)<a class="hash-link" href="#pairfexpm" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</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><a name="PAIR.lbits"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairlbits">PAIR.lbits()<a class="hash-link" href="#pairlbits" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</code> </p><a name="PAIR.glv"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairglv">PAIR.glv()<a class="hash-link" href="#pairglv" title="Direct link to heading">​</a></h3><p>GLV method</p><p><strong>Kind</strong>: static method of <a href="#PAIR"><code>PAIR</code></a><br>
<strong>this</strong>: <code>{&quot;{&quot;}PAIR{&quot;}&quot;}</code> </p><a name="PAIR.gs"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairgs">PAIR.gs()<a class="hash-link" href="#pairgs" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</code> </p><a name="PAIR.G1mul"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairg1mulp-e-">PAIR.G1mul(P, e) ⇒<a class="hash-link" href="#pairg1mulp-e-" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</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><a name="PAIR.G2mul"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairg2mulp-e-">PAIR.G2mul(P, e) ⇒<a class="hash-link" href="#pairg2mulp-e-" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</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><a name="PAIR.GTpow"></a><h3 class="anchor anchorWithStickyNavbar_LWe7" id="pairgtpowd-e-">PAIR.GTpow(d, e) ⇒<a class="hash-link" href="#pairgtpowd-e-" title="Direct link to heading">​</a></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>{&quot;{&quot;}PAIR{&quot;}&quot;}</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></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Docs pages navigation"><a class="pagination-nav__link pagination-nav__link--prev" href="/docs/cryptojs/mpin256"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">MPIN256</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/docs/cryptojs/pair192"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">PAIR192</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#pair" class="table-of-contents__link toc-highlight">PAIR</a><ul><li><a href="#new-pair" class="table-of-contents__link toc-highlight">new PAIR()</a></li><li><a href="#pairline" class="table-of-contents__link toc-highlight">PAIR.line()</a></li><li><a href="#pairinitmp" class="table-of-contents__link toc-highlight">PAIR.initmp()</a></li><li><a href="#pairmillerr-res" class="table-of-contents__link toc-highlight">PAIR.miller(r, res)</a></li><li><a href="#pairanotherr-p1-q1" class="table-of-contents__link toc-highlight">PAIR.another(r, P1, Q1)</a></li><li><a href="#pairatep1-q1" class="table-of-contents__link toc-highlight">PAIR.ate(P1, Q1)</a></li><li><a href="#pairate2p1-q1-r1-s1" class="table-of-contents__link toc-highlight">PAIR.ate2(P1, Q1, R1, S1)</a></li><li><a href="#pairfexpm" class="table-of-contents__link toc-highlight">PAIR.fexp(m)</a></li><li><a href="#pairlbits" class="table-of-contents__link toc-highlight">PAIR.lbits()</a></li><li><a href="#pairglv" class="table-of-contents__link toc-highlight">PAIR.glv()</a></li><li><a href="#pairgs" class="table-of-contents__link toc-highlight">PAIR.gs()</a></li><li><a href="#pairg1mulp-e-" class="table-of-contents__link toc-highlight">PAIR.G1mul(P, e) ⇒</a></li><li><a href="#pairg2mulp-e-" class="table-of-contents__link toc-highlight">PAIR.G2mul(P, e) ⇒</a></li><li><a href="#pairgtpowd-e-" class="table-of-contents__link toc-highlight">PAIR.GTpow(d, e) ⇒</a></li></ul></li></ul></div></div></div></div></main></div></div><footer class="footer"><div class="container container-fluid"><div class="footer__bottom text--center"><div class="margin-bottom--sm"><img src="/img/milagro.svg" class="themedImage_ToTc themedImage--light_HNdA footer__logo"><img src="/img/milagro.svg" class="themedImage_ToTc themedImage--dark_i4oU footer__logo"></div><div class="footer__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.</div></div></div></footer></div>
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