Constructing elliptic curves for cryptography
by
Reinier Broker
Microsoft Research

Over the last 20 years, efficient algorithms have been developed to count the number of points of a given elliptic curve over a finite field. We discuss the inverse problem of constructing elliptic curves with a given number of points over a finite field. The difficulty of this problem depends on its exact wording. We present a solution to the problem that easily handles curves of the size occuring in cryptographic practice, and explain why it should be expected to do so.

Date received: January 21, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavi-40.