Leírás
Abstract:
Elliptic curves are certain algebraic curves that arise naturally when
studying many classical problems and they provide a link between number
theory, geometry and algebra.
Their surprising abelian group structure makes them prolific in number
theory, with applications to famous conjectures such as Fermat's Last
Theorem, and in cryptography, with encryption standards employed by the
biggest computer companies such as Google and Facebook.
Also, although the study of elliptic curves dates back to the ancient
greeks, there are still many open problems such as the famous
Birch-Swinnerton-Dyer conjecture, one of the seven millenium problems.
This mini course will focus on studying elliptic curves over finite fields
and their applications to cryptography.