Distortion maps for elliptic curves over finite fields

Abstract: If P is a torsion point on an elliptic curve over a finite field, then a distortion map with respect to P is an endomorphism that maps P outside the cyclic group generated by P. While initially motivated by questions related to cryptography, the algebraic properties and existence conditions of such maps present an interesting problem in its own right, related to the arithmetic of endomorphism rings. In this talk, we will discuss the arithmetic of distortion maps and provide a criterion for a map to be a distortion map, as well as a complete classification regarding their existence over finite fields. This is joint work with Nikita Andrusov, Sevag Büyüksimkeşyan, Fabien Pazuki, Mustafa Umut Kazancıoğlu, and Jordi Vilà-Casadevall.

Mathematics

Audience: researchers in the topic

Greek Algebra & Number Theory Seminar