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Data integrity has to become one of the central concerns of large-scale distributed computing systems such as the grid, whose primary products are the results of computation. In order to maintain the integrity of this data, the system must be resilient to diverse attacks and tampering. The system should also encourage positive influences on its integrity in addition to discouraging or eliminating negative ones. In this paper we develop a model of trust for grid participants based on the use of reputation systems and associated feedback mechanisms.