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SUMMARY:Post-quantum key exchange using class group actions on oriented su
persingular elliptic curves
DTSTART:20231123T130000Z
DTEND:20231123T140000Z
DTSTAMP:20240228T220600Z
UID:indico-event-10716@indico.math.cnrs.fr
DESCRIPTION:Speakers: Arthur Herlédan Le Merdy\n\nThe Diffie-Hellman sche
me is the most well-known key exchange protocol. However\, its security re
lies on the Discrete Logarithm problem which is not a difficult problem fo
r quantum computers. In this presentation\, we will first focus on the tas
k of adapting Diffie-Hellman to a post-quantum context by replacing the cy
clic groups in Diffie-Hellman by group actions. We will see how elliptic c
urves and isogenies can be used as a framework for realizing this task. In
particular\, we will introduce the notion of orientations — embeddings
from quadratic number fields into endomorphism rings of supersingular elli
ptic curves — and see how they induce suitable group actions for this ob
jective. Finally\, we will study the computational complexity of computing
the endomorphism ring of supersingular elliptic curves given an orientati
on\, which is an important problem that naturally arises from these constr
uctions.\n\nhttps://indico.math.cnrs.fr/event/10716/
URL:https://indico.math.cnrs.fr/event/10716/
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