Construction of Elliptic Curves with Complex Multiplication

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 Weierstra 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 Weierstra curve by the twisted Edwards curve.

• | Author: Canbay Özkan
• | Publisher: AV Akademikerverlag
• | Publication Date: Sep 26, 2012
• | Number of Pages: 124 pages
• | Binding: Paperback or Softback
• | ISBN-10: 3639449754
• | ISBN-13: 9783639449754