BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Renate Scheidler (University of Calgary) DTSTART:20241024T200000Z DTEND:20241024T210000Z DTSTAMP:20260423T021451Z UID:ANTS/2 DESCRIPTION:Title: Ori enteering with One Endomorphism\nby Renate Scheidler (University of Ca lgary) as part of Calgary Algebra and Number Theory Seminar\n\nLecture hel d in MS 337.\n\nAbstract\nGiven two elliptic curves\, the path finding pro blem asks to find an isogeny (i.e. a group homomorphism) between them\, su bject to certain degree restrictions. Path finding has uses in number theo ry as well as applications to cryptography. For supersingular curves\, thi s problem is known to be easy when one small endomorphism or the entire en domorphism ring are known. Unfortunately\, computing the endomorphism ring \, or even just finding one small endomorphism\, is hard. How difficult i s path finding in the presence of one (not necessarily small) endomorphism ? We use the volcano structure of the oriented supersingular isogeny graph to answer this question. We give a classical algorithm for path finding t hat is subexponential in the degree of the endomorphism and linear in a ce rtain class number\, and a quantum algorithm for finding a smooth isogeny (and hence also a path) that is subexponential in the discriminant of the endomorphism. A crucial tool for navigating supersingular oriented isogeny volcanoes is a certain class group action on oriented elliptic curves whi ch generalizes the well-known class group action in the setting of ordinar y elliptic curves.\n\nThe recorded video Passcode: Z&7TyEGW\n LOCATION:https://researchseminars.org/talk/ANTS/2/ END:VEVENT END:VCALENDAR