{"id":182090,"date":"2009-03-10T00:00:00","date_gmt":"2009-10-31T09:21:11","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/msr-research-item\/abelian-surfaces-with-a-given-number-of-points\/"},"modified":"2018-07-19T08:26:09","modified_gmt":"2018-07-19T15:26:09","slug":"abelian-surfaces-with-a-given-number-of-points","status":"publish","type":"msr-video","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/video\/abelian-surfaces-with-a-given-number-of-points\/","title":{"rendered":"Abelian surfaces with a given number of points"},"content":{"rendered":"<div class=\"asset-content\">\n<p>This is a report on joint work with Everett Howe and Kristin Lauter.<\/p>\n<p>I will discuss the genus 2 analogue of the problem of efficiently constructing an elliptic curve over a finite field with a prescribed number N of points. If N is provided with its prime factorization, the elliptic construction I gave with Broker is heuristically polynomial time outside a zero density subset of input values N. I will explain why the analogous construction to obtain abelian surfaces of given order N is intrinsically exponential.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a report on joint work with Everett Howe and Kristin Lauter. I will discuss the genus 2 analogue of the problem of efficiently constructing an elliptic curve over a finite field with a prescribed number N of points. If N is provided with its prime factorization, the elliptic construction I gave with Broker [&hellip;]<\/p>\n","protected":false},"featured_media":194449,"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-182090","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\/Pg8lz-W7aC8","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182090","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\/182090\/revisions"}],"predecessor-version":[{"id":496121,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182090\/revisions\/496121"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/media\/194449"}],"wp:attachment":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/media?parent=182090"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=182090"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=182090"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=182090"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=182090"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=182090"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=182090"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=182090"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=182090"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=182090"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}