{"id":358964,"date":"2017-01-18T00:00:52","date_gmt":"2017-01-18T08:00:52","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=358964"},"modified":"2022-01-04T08:00:43","modified_gmt":"2022-01-04T16:00:43","slug":"quantum-algorithms-number-theory-relevance-cryptography","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/quantum-algorithms-number-theory-relevance-cryptography\/","title":{"rendered":"Quantum Algorithms for Number Theory and their Relevance to Cryptography"},"content":{"rendered":"<p>I will report on recent results about quantum algorithms for solving computational problems in number theory. I will show how they impact the security of certain post-quantum cryptosystems. Shor&#8217;s quantum algorithm for factoring large integers and solving the discrete logarithm problem has been the motivation for an entire new area of research in cryptology: namely &#8220;post-quantum&#8221; cryptography. It consists of designing new cryptographic primitives which will resist attacks from quantum computers. In a recent work in collaboration with Fang Song, I presented a quantum polynomial time algorithm for solving the so-called &#8220;Principal Ideal Problem&#8221; (among other things) in arbitrary fields. We will see how this impacts the security of some ring-based proposals for quantum resistant cryptography. In collaboration with David Jao and Anirudh Sankar, I also described a quantum algorithm which finds an isogeny between two given supersingular curves over a finite field, a hard problem on which some post-quantum cryptosystem rely. Finally, if there is enough time, I&#8217;ll mention some recent work on factorization.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I will report on recent results about quantum algorithms for solving computational problems in number theory. I will show how they impact the security of certain post-quantum cryptosystems. Shor&#8217;s quantum algorithm for factoring large integers and solving the discrete logarithm problem has been the motivation for an entire new area of research in cryptology: namely [&hellip;]<\/p>\n","protected":false},"featured_media":358985,"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":[13552,13558],"msr-video-type":[206954],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-358964","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-hardware-devices","msr-research-area-security-privacy-cryptography","msr-video-type-microsoft-research-talks","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/7YTbf1KkvJs","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/358964","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":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/358964\/revisions"}],"predecessor-version":[{"id":808633,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/358964\/revisions\/808633"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/358985"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=358964"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=358964"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=358964"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=358964"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=358964"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=358964"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=358964"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=358964"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=358964"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=358964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}