Grid security solutions address critical requirements and are constructed from building blocks comprising cryptographic algorithms and protocols. Choosing the most appropriate algorithms and protocols requires an ongoing evaluation of performance and security properties, given continuing advances in system performance, optimizations, security analyses, and cryptographic techniques. Today, the Globus Toolkit's Grid Security Infrastructure (GSI) is a leading provider of security solutions based on the RSA cryptosystem. Recently, cryptosystems based on bilinear pairings have been proposed as an alternative with the promise of increased efficiency and scalability. In this work we evaluate this alternative compared to Elliptic Curve Cryptography (ECC) and RSA in terms of their computation and communication overheads for today's Grid systems. Our analysis and experiments lead us to conclude that RSA continues to be a good choice for the foreseeable future. Furthermore, our results are intuitively aligned with the high-performance, high-bandwidth, and high-latency nature of Grid systems.