BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Renate Scheidler (University of Calgary) DTSTART:20230313T180000Z DTEND:20230313T190000Z DTSTAMP:20260423T052447Z UID:NTC/13 DESCRIPTION:Title: Ori enteering on Supersingular Isogeny Volcanoes Using One Endomorphism\nb y Renate Scheidler (University of Calgary) as part of Lethbridge number th eory and combinatorics seminar\n\nLecture held in University of Lethbridge : M1040 (Markin Hall).\n\nAbstract\nElliptic curve isogeny path finding ha s many applications in number theory and cryptography. For supersingular c urves\, this problem is known to be easy when one small endomorphism or th e entire endomorphism ring are known. Unfortunately\, computing the endomo rphism ring\, or even just finding one small endomorphism\, is hard. How difficult is path finding in the presence of one (not necessarily small) e ndomorphism? We use the volcano structure of the oriented supersingular is ogeny graph to answer this question. We give a classical algorithm for pat h finding that is subexponential in the degree of the endomorphism and lin ear in a certain class number\, and a quantum algorithm for finding a smoo th isogeny (and hence also a path) that is subexponential in the discrimin ant of the endomorphism. A crucial tool for navigating supersingular orien ted isogeny volcanoes is a certain class group action on oriented elliptic curves which generalizes the well-known class group action in the setting of ordinary elliptic curves.\n LOCATION:https://researchseminars.org/talk/NTC/13/ END:VEVENT END:VCALENDAR