Construction of Elliptic Curves with Complex Multiplication

By Canbay Ozkan

An abstract model of an elliptic curve is designed as a Java-based application. In this abstract model we implement two distinct elliptic curve types: the Weierstrass curve and the twisted Edwards curve. This model will be used in the algorithm for elliptic curve construction with complex multiplication, in short the CM-method. We implement the elliptic curve primality proving algorithm (ECPP) developed by Atkin/Morain as an application of the CM-method. Instead of using pseudocode, the algorithms are represented explicitly as source code simultaneously with the underlying theory. Finally, we analyze a probable acceleration of the Atkin-Morain's ECPP algorithm by replacing the Weierstrass curve by the twisted Edwards curve."

• Format: Paperback
• Language: English
• ISBN: 3639449754
• ISBN13: 9783639449754
• Release Date: September 2012
• Publisher: AV Akademikerverlag
• Length: 124 Pages
• Weight: 0.42 lbs.
• Dimensions: 0.3" x 6.0" x 9.0"