{"version":"1.0","provider_name":"Microsoft Research","provider_url":"https:\/\/www.microsoft.com\/en-us\/research","author_name":"Martin Roetteler","author_url":"https:\/\/www.microsoft.com\/en-us\/research\/people\/martinro\/","title":"A quantum circuit to find discrete logarithms on ordinary binary elliptic curves in depth O(log^2 n) - Microsoft Research","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"42gT7x3ZbP\"><a href=\"https:\/\/www.microsoft.com\/en-us\/research\/publication\/a-quantum-circuit-to-find-discrete-logarithms-on-ordinary-binary-elliptic-curves-in-depth-olog2-n\/\">A quantum circuit to find discrete logarithms on ordinary binary elliptic curves in depth O(log^2 n)<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/publication\/a-quantum-circuit-to-find-discrete-logarithms-on-ordinary-binary-elliptic-curves-in-depth-olog2-n\/embed\/#?secret=42gT7x3ZbP\" width=\"600\" height=\"338\" title=\"&#8220;A quantum circuit to find discrete logarithms on ordinary binary elliptic curves in depth O(log^2 n)&#8221; &#8212; Microsoft Research\" data-secret=\"42gT7x3ZbP\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script type=\"text\/javascript\">\n\/* <![CDATA[ *\/\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/* ]]> *\/\n<\/script>\n","description":"Improving over an earlier construction by Kaye and Zalka, Maslov et al. describe an implementation of Shor&#8217;s algorithm which can solve the discrete logarithm problem on binary elliptic curves in quadratic depth O(n2). In this paper we show that discrete logarithms on such curves can be found with a quantum circuit of depth O(log2 n). [&hellip;]"}