A method is proposed that allows each individual party to an elliptic curve cryptosystem to quickly determine its own unique pair of finite field and Weierstrass equation, in such a way that the resulting pair provides adequate security. Although the choice of Weierstrass equations allowed by this proposal is limited, the number of possible finite fields is unlimited. The proposed method allows each participant to select its elliptic curve cryptosystem parameters in such a way that the security is not affected by attacks on any other participant unless unanticipated progress is made affecting the security for a particular Weierstrass equation irrespective of the underlying finite field. Thus the proposal provides more security than elliptic curve cryptosystems where all participants share the same Weierstrass equation and finite field. It also offers much faster and less complicated parameter initialization than elliptic curve cryptosystems where each participant randomly selects its own unique Weierstrass equation and thus has to solve the cumbersome point counting problem