Computing endomorphism rings of supersingular elliptic curves

Abstract: Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of the recently proposed isogeny-based cryptosystems. In this talk we give a new algorithm for computing the endomorphism ring of a supersingular elliptic curve. The algorithm works by first computing two cycles in the l-isogeny graph that create an order in the endomorphism ring of the curve E. Then we determine which maximal order containing this order is the endomorphism ring of E. This is joint work with Hallgren, Leonardi, Morrison and Park.

number theory

Audience: researchers in the topic

Front Range Number Theory Day

Series comments: Description: Short research conference on number theory

The FRNTD is a twice-yearly conference that brings together number theorists working on the Front Range. We are excited to be able to open our virtual doors to number theorists around the world this semester. Please see the website for the schedule, further details, and registration.