 
Summary: Constructing elliptic curves
with known number of points
over a prime field #
Amod Agashe
Max Planck Institut, Bonn
and University of Texas, Austin
October 2, 2002
# These slides can be obtained from
http://www.ma.utexas.edu/users/amod/mymath.html
Abstract: In applications of elliptic curves to
cryptography, one often needs to construct elliptic
curves with known number of points over a prime
field Fn , where n is a prime. Atkin suggested the use
of complex multiplication to construct such curves.
One of the steps in this method is the calculation of a
certain Hilbert class polynomial HD (X) modulo n for
a certain fundamental discriminant D. The usual way
of doing this is to compute HD (X) over the integers
and then reduce modulo n. We suggest the use of a
modified version of the Chinese remainder theorem to
