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SUMMARY:The supersingular Endomorphism Ring and One Endomorphism problems
are equivalent
DTSTART:20231109T130000Z
DTEND:20231109T140000Z
DTSTAMP:20241102T175600Z
UID:indico-event-10715@indico.math.cnrs.fr
DESCRIPTION:Speakers: Benjamin Wesolowski (CNRS\, ENS de Lyon)\n\nThe supe
rsingular Endomorphism Ring problem is the following: given a supersingula
r elliptic curve\, compute all of its endomorphisms. The presumed hardness
of this problem is foundational for isogeny-based cryptography. The One E
ndomorphism problem only asks to find a single non-scalar endomorphism. We
prove that these two problems are equivalent\, under probabilistic polyno
mial time reductions. We prove a number of consequences: on the security o
f cryptosystems\, on the hardness of computing isogenies between supersing
ular elliptic curves\, and on solving the endomorphism ring problem.\n\nht
tps://indico.math.cnrs.fr/event/10715/
URL:https://indico.math.cnrs.fr/event/10715/
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