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Identity Management plays a crucial role in many application contexts, including e-Governments, e-Commerce, business intelligence, investigation, and homeland security. The variety of approaches to and techniques for identity management, while addressing some of the challenges, have introduced new problems, especially concerning interoperability and privacy. We focus here on two fundamental issues within this context: (1) a firm unifying semantic foundation for the systematic study of identity management and improved accuracy in reasoning about key properties in identity management system design, and (2) the practical relevance of developing a distributed approach to identity management (as opposed to a centralized one). The proposed mathematical framework is built upon essential requirements of an identity management system (such as privacy, user-control, and minimality), and serves as a starting point for bringing together different approaches in a systematic fashion in order to develop a distributed architecture for identity management.