One significant challenge in building grids between organizations with heterogeneous security systems is the need to express and enforce security policies that specify the users in one organization (the source domain) who are allowed to access the resources in another organization (the target domain). This requires linking the syntax and semantics of security assertions referring to users and their attributes in the source domain to those referring to resources in the target domain. This paper suggests some basic requirements for solving this problem, in particular, an abstract form of interdomain security assertion (IDSA) relying, for instance, on globally meaningful URIs (Uniform Resource Identifiers) to refer to users, resources, and their attributes. This canonical abstract form IDSA is, however, used strictly for assertion mapping purposes. It may - but need not - be visible in any concrete security assertion syntax in any domain. The paper further suggests different scenarios in which URIs for users, resources, and attributes defined in one domain can be mapped to semantically meaningful references - with varying degrees of granularity and accountability - in another domain where they would otherwise be meaningless. © 2004 IBM.