{"id":185468,"date":"2010-10-20T00:00:00","date_gmt":"2010-10-27T07:38:47","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/f4-traces-and-index-calculus-on-elliptic-curves-over-extension-fields\/"},"modified":"2016-08-22T11:28:40","modified_gmt":"2016-08-22T18:28:40","slug":"f4-traces-and-index-calculus-on-elliptic-curves-over-extension-fields","status":"publish","type":"msr-video","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/video\/f4-traces-and-index-calculus-on-elliptic-curves-over-extension-fields\/","title":{"rendered":"F4 Traces and Index Calculus on Elliptic Curves Over Extension Fields"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Recently, Gaudry and Diem have proposed an index calculus method for the resolution of the DLP on elliptic curves defined over extension fields. In this talk, I will first present a variant of this method that enables to decrease the asymptotic complexity of the DLP on E(Fqn) for a large range of q and n, then introduce a second improvement provided by the use of F4 traces for polynomial system solving. Finally, I will give a practical example of our index calculus variant to the oracle-assisted Static Diffie-Hellman Problem.<\/p>\n<p>This is a joint work with Antoine Joux.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Recently, Gaudry and Diem have proposed an index calculus method for the resolution of the DLP on elliptic curves defined over extension fields. In this talk, I will first present a variant of this method that enables to decrease the asymptotic complexity of the DLP on E(Fqn) for a large range of q and n, [&hellip;]<\/p>\n","protected":false},"featured_media":195810,"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":[],"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-185468","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/w0q4rG49lfk","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185468","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185468\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media\/195810"}],"wp:attachment":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media?parent=185468"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=185468"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=185468"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=185468"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=185468"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=185468"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=185468"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=185468"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=185468"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=185468"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}