Results of an Elliptic-Curve-Approach for Use in CryptosystemsReinhard Rauscher, Frank BohnsackThis paper presents new research results concerning cryptosystems based upon elliptic curves. The system developed is similar to that of ElGamal over a finite field F_q. The investigations enfold those elliptic curves with primary characteristics over F_q (q is a prime number). The goal of the study is the determination of dependencies between calculation time required by the cryptosystem and size of the keys and length of messages. Additionally, identifying possible areas vulnerable to attacks are taken into account.