{"id":182084,"date":"2009-03-10T00:00:00","date_gmt":"2009-10-31T09:20:54","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/msr-research-item\/genus-2-curves-with-a-given-number-of-points\/"},"modified":"2018-07-19T08:25:39","modified_gmt":"2018-07-19T15:25:39","slug":"genus-2-curves-with-a-given-number-of-points","status":"publish","type":"msr-video","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/video\/genus-2-curves-with-a-given-number-of-points\/","title":{"rendered":"Genus-2 curves with a given number of points"},"content":{"rendered":"<div class=\"asset-content\">\n<p>This is a report on joint work with Kristin Lauter and Peter Stevenhagen.<\/p>\n<p>Broker and Stevenhagen have shown that in practice it is not hard to produce an elliptic curve (over some finite field) with a given number N of points, provided that the factorization of N is known. In his talk this week, Stevenhagen will show that the natural generalization of this method to produce genus-2 curves with a given number of points on their Jacobian is an exponential algorithm.<\/p>\n<p>I will consider the related problem of constructing a genus-2 curve over some finite field such that the curve itself has a given number N of points. The idea of &#8220;explicit gluings&#8221; of pairs of elliptic curves leads to a solution for most values of N; I will discuss this, and other, applications of explicit gluings.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a report on joint work with Kristin Lauter and Peter Stevenhagen. Broker and Stevenhagen have shown that in practice it is not hard to produce an elliptic curve (over some finite field) with a given number N of points, provided that the factorization of N is known. In his talk this week, Stevenhagen [&hellip;]<\/p>\n","protected":false},"featured_media":194446,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[13558],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-182084","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/bI8z1p1ASJ4","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":1,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182084\/revisions"}],"predecessor-version":[{"id":496118,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182084\/revisions\/496118"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/media\/194446"}],"wp:attachment":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/media?parent=182084"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=182084"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=182084"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=182084"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=182084"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=182084"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=182084"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=182084"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=182084"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=182084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}