Large-scale science and engineering is frequently done through the interaction of collaborating groups, heterogeneous computing resources, information systems, and instruments, all of which are geographically and organizationally dispersed. The overall motivation for "Grids" is to enable the routine interactions of these resources to enhance this type of large-scale science and engineering, and thus substantially increase the computing and data handling capabilities available to science and engineering projects. However, even if this environment works in every other way, it will not be viable if it is constantly disrupted by hackers and their kin. Distributed applications are potentially more vulnerable than conventional scientific problem solving environments because there are substantially more targets to attack in order to impact a single application. Much of the overall security of Grids is inherited from the security of the underlying systems. There are, however, some security considerations at the Grid level that are independent of the underlying systems, and we focus on this latter aspect.