20 years ago, Diffie and Hellman conceived the idea of exponential key exchange, now commonly known as Diffie-Hellman key agreement. Today, the long-predicted wide-scale commercial deployment of cryptographic technology is finally occurring. As designers seek to provide implementations of public-key cryptography which offer adequate security while minimizing the computational requirements thereof, various options are available regarding parameter selection and other design choices. We examine a subset of options intended to reduce the computational costs of Diffie-Hellman key agreement protocols, and their related security implications.