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Endomorphism Rings in Cryptography.

open access: yes, 2011
La cryptographie est devenue indispensable afin de garantir la sécurité et l'intégrité des données transitant dans les réseaux de communication modernes. Ces deux dernières décennies, des cryptosystèmes très efficaces, sûr et riches en fonctionnalités ont été construits à partir de variétés abéliennes définies sur des corps finis. Cette thèse contribue
openaire   +3 more sources

Lattices in Tate modules. [PDF]

open access: yesProc Natl Acad Sci U S A, 2021
Poonen B, Rybakov S.
europepmc   +1 more source

Splittings and Endomorphism Rings

open access: yes
Finding a nontrivial endomorphism of a given supersingular elliptic curve is a hardness assumption of isogeny-based cryptography. We prove the reduction from it to the problem of finding a splitting of a given principally polarized abelian surface.
Min-Yi Shen, Péter Kutas
core  

Endomorphism Algebras of Equivariant Exceptional Collections [PDF]

open access: yes
Given an action of a finite group on a triangulated category with a suitable strong exceptional collection, a construction of Elagin produces an associated strong exceptional collection on the equivariant category.
Krug, Andreas, Nikolov, Erik
core   +1 more source

Another look at rational torsion of modular Jacobians. [PDF]

open access: yesProc Natl Acad Sci U S A, 2022
Ribet KA, Wake P.
europepmc   +1 more source

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