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This paper presents Sharp, a framework for secure distributed resource management in an Internet-scale computing infrastructure. The cornerstone of Sharp is a construct to represent cryptographically protected resource claims---promises or rights to control resources for designated time intervals---together with secure mechanisms to subdivide and delegate claims across a network of resource managers. These mechanisms enable flexible resource peering: sites may trade their resources with peering partners or contribute them to a federation according to local policies. A separation of claims into tickets and leases allows coordinated resource management across the system while preserving site autonomy and local control over resources. Sharp also introduces mechanisms for controlled, accountable oversubscription of resource claims as a fundamental tool for dependable, efficient resource management. We present experimental results from a Sharp prototype for PlanetLab, and illustrate its use with a decentralized barter economy for global PlanetLab resources. The results demonstrate the power and practicality of the architecture, and the effectiveness of oversubscription for protecting resource availability in the presence of failures.