In this talk, we discuss the general supersingular isogeny problem, the foundational hardness assumption underpinning isogeny-based cryptography. We implement and optimize the best attack against this problem \u2013 the Delfs-Galbraith algorithm \u2013 to explicitly determine its concrete complexity. We then develop an improved algorithm that employs a novel method of rapidly determining whether a polynomial has any roots in a subfield. Our improved attack decreases the concrete complexity by a factor of at least 4, an advantage that increases as the parameters (i.e., the underlying prime p) grow.<\/p>\n
As a result, we shed new light on the concrete hardness of the general supersingular isogeny problem, which has immediate implications on the bit-security of schemes like B-SIDH and SQISign for which Delfs\u2013Galbraith is the best-known classical attack.<\/p>\n
This is based on joint work with Craig Costello and Jia Shi.<\/p>\n","protected":false},"excerpt":{"rendered":"
In this talk, we discuss the general supersingular isogeny problem, the foundational hardness assumption underpinning isogeny-based cryptography. We implement and optimize the best attack against this problem \u2013 the Delfs-Galbraith algorithm \u2013 to explicitly determine its concrete complexity. We then develop an improved algorithm that employs a novel method of rapidly determining whether a polynomial […]<\/p>\n","protected":false},"featured_media":864951,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"research-area":[13546,13558],"msr-video-type":[],"msr-locale":[268875],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-864948","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-computational-sciences-mathematics","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/XzdcRcb65UM","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/864948"}],"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":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/864948\/revisions"}],"predecessor-version":[{"id":864984,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/864948\/revisions\/864984"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/864951"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=864948"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=864948"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=864948"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=864948"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=864948"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=864948"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}