Pierrick Gaudry
École polytechnique, Paris
Counting points on elliptic curves in characteristic 2
with the Arithmetic-Geometric Mean (AGM) method.
Thursday 6 December 2001, 3:05-4pm
Carslaw Lecture Theatre 273
Computing the number of points of an elliptic curve defined over a
large finite field of characteristic 2 is one of the most tricky part
of the development of an elliptic curve cryptosystem. A few years
ago, Satoh proposed a new algorithm based on the computation of the
canonical p-adic lifting of the curve. We will first recall some
basics and the general lines of Satoh's algorithm. Based on an idea
of Mestre, we will then explain how the Arithmetic-Geometric Mean can
be used to speed-up the computations and provides an easy extension to
the case of genus 2 curves.
|