Slovak University of Technology, Bratislava
Faculty of Informatics and Information Technologies
Degree Course: INFORMATICS
Author: Bc. Pavol Zajac
Diploma thesis: Effective Methods for Generating the Elliptic Curves
Supervisor: doc. RNDr. Ladislav Satko, PhD.
2004, May

In this work we present basic facts about the elliptic curves (EC) and the elliptic curve discrete logarithm problem (ECDLP). Its analytic part contains basic mathematical facts about EC and a brief survey of the elliptic curve cryptography standards. In particular, we focus on the Elliptic Curve Digital Signature Algorithm (ECDSA) and the methods for generating suitable elliptic curves for this algorithm. The main scientific contribution of this project is the statistical analysis of random elliptic curves generation and its impact on the generating of the EC cryptosystem parameters. Results of the research are applied in the software implementation of the electronic signature based on ECDSA. We were able to compare the achieved results with the results of the alternative complex multiplication method.