Results of an elliptic-curve-approach for use in cryptosystems

This paper presents new research results concerning cryptosystems based upon elliptic curves. The system which has been developed is similar to that of T. ElGamal (1985) over a finite field F_q. The investigations cover those elliptic curves with primary characteristics over F_q (2¹⁶⩽q⩽2²⁵⁷ , q is a prime number). The aim 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, possible areas vulnerable to attacks are identified