Speaker:
Sabrina Kunzweiler
Affiliation:
INRIA, France
Date:
Wed, 27/03/2024 - 14:30 - 15:30
The classical modular polynomial $\phi_\ell(X,Y) \in \mathbb{Z}[X,Y]$ parametrizes pairs of elliptic curves connected by an isogeny of degree $\ell$.
They play an important role in algorithmic number theory, and are used in many applications, for example in the SEA point counting algorithm.
In this talk, I present a new method for computing modular polynomials. It has the same asymptotic time complexity as the currently best known algorithms, but does not rely on any heuristics.