<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BARRETO, Paulo S. L. M.</style></author><author><style face="normal" font="default" size="100%">Galbraith, Steven D.</style></author><author><style face="normal" font="default" size="100%">hÉigeartaigh, Colm Ó’</style></author><author><style face="normal" font="default" size="100%">Scott, Michael</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Efficient pairing computation on supersingular Abelian varieties</style></title><secondary-title><style face="normal" font="default" size="100%">Designs, Codes and Cryptography</style></secondary-title><short-title><style face="normal" font="default" size="100%">Des Codes Crypt</style></short-title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">3/2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.springerlink.com/content/48403647105q3451/</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">42</style></volume><pages><style face="normal" font="default" size="100%">239 - 271</style></pages><abstract><style face="normal" font="default" size="100%">&lt;div class=&quot;Abstract&quot;&gt;&lt;a name=&quot;Abs1&quot;&gt;&lt;/a&gt;&lt;span class=&quot;AbstractHeading&quot;&gt;Abstract&amp;nbsp;&amp;nbsp;&lt;/span&gt;We present a general technique for the efficient computation of pairings on Jacobians of supersingular curves. This formulation, which we call the eta pairing, generalizes results of Duursma and Lee for computing the Tate pairing on supersingular elliptic curves in characteristic 3. We then show how our general technique leads to a new algorithm which is about twice as fast as the Duursma&amp;ndash;Lee method. These ideas are applied to elliptic and hyperelliptic curves in characteristic 2 with very efficient results. In particular, the hyperelliptic case is faster than all previously known pairing algorithms.&lt;/div&gt;</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue></record></records></xml>