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The problem of secure multiparty computation - performing some computation based on distributed, private inputs - has been studied intensively for more than twenty years. This paper includes both "One shot" applications as well as reactive tasks, where the exact computation is not known in advance. The authors extend this line of work by asking whether it is possible to efficiently both update and query secret data. A clearer formulation is, perhaps, to ask whether it is possible to construct efficient datastructures based on secure multiparty computation primitives.
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