Background talks:
Eisenträger: (10--11) Isogeny graphs in cryptography
Poonen: (11:30--12:30) TBA
Research talks:
Eisenträger (2:30--3:30) Computing supersingular endomorphism rings
Poonen: (4--5) TBA
Abstracts:
Isogeny graphs in cryptography (Eisenträger I)
How can maps between elliptic curves be used to build cryptographic systems? This talk presents supersingular isogenies as one approach to post-quantum cryptography. We introduce supersingular isogeny graphs and discuss a cryptographic construction based on the hardness of pathfinding in these graphs. No background in cryptography will be assumed.
Computing supersingular endomorphism rings (Eisenträger II)
The hardness of computing endomorphism rings of supersingular elliptic curves is central to the security of isogeny-based cryptography. This talk introduces the endomorphism ring problem and presents a new algorithm for recovering the full endomorphism ring from partial information. We explain the mathematical ideas behind the algorithm, including higher-dimensional isogenies, quaternion algebras, and Bruhat–Tits trees. This is joint work with Gabrielle Scullard.