Supersingular Elliptic Curves and their Applications to Cryptography

Specialeforsvar ved Astrid Steen Mortensen

Titel: Supersingular Elliptic Curvesand their Applications to Cryptography

 Abstract: This thesis studies the theory of supersingular elliptic curves. First a number of preliminary results about general elliptic curves are presented. This includes a correction of a small error in the article Isogenies entre courbes elliptiques by Velu [24]. The notion of super-singular curves is introduced and the structure of such curves is discussed. After this it is proven that there are infinitely many supersingular primes of any elliptic curve over Q. Finally the cryptographic applications are introduced. One is the so-called MOV-attack and the other is isogeny based cryptography.

Vejleder: Fabien Pazuki
Censor:  Peter Beelen, DTU