{"id":184957,"date":"2010-06-29T00:00:00","date_gmt":"2010-07-02T20:15:20","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/generalized-algorithm-for-dlp-with-auxiliary-inputs\/"},"modified":"2016-08-22T11:27:36","modified_gmt":"2016-08-22T18:27:36","slug":"generalized-algorithm-for-dlp-with-auxiliary-inputs","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/generalized-algorithm-for-dlp-with-auxiliary-inputs\/","title":{"rendered":"Generalized Algorithm for DLP with Auxiliary Inputs"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The DLP with auxiliary inputs is to find <i>&alpha;<\/i> when <i>g<sup>&alpha;<sup>i<\/sup><\/sup><\/i> (i=0,1,2,&hellip;,d)<i> as well as <\/i>g, g<sup>&alpha;<\/sup><i> are given. Recently, numerous cryptosystems are designed on a weaker variant of this problem. One example is the strong Diffie-Hellman problem. It has been shown that the complexity of this problem is lower than the original DLP by upto <\/i>&radic; d<i> group operations when <\/i>p-1<i> or <\/i>p+1<i> has an appropriate divisor. In this talk, we present a generalization of this algorithm, which can be applied even when <\/i>p-1<i> and <\/i>p+1$ are almost prime. We also discuss how many parameters are susceptible to this attack.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The DLP with auxiliary inputs is to find &alpha; when g&alpha;i (i=0,1,2,&hellip;,d) as well as g, g&alpha; are given. Recently, numerous cryptosystems are designed on a weaker variant of this problem. One example is the strong Diffie-Hellman problem. It has been shown that the complexity of this problem is lower than the original DLP by [&hellip;]<\/p>\n","protected":false},"featured_media":195665,"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-184957","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/8J2hVnsRCuE","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/184957","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/184957\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/195665"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=184957"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=184957"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=184957"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=184957"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=184957"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=184957"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=184957"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=184957"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=184957"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=184957"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}