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We consider the problem of efficiently reconciling two similar sets held by different hosts while minimizing the communication complexity, which we call the set reconciliation problem. We describe an approach to set reconciliation based on a polynomial encoding of sets. The resulting protocols exhibit tractable computational complexity and nearly optimal communication complexity when the sets being reconciled are sparse. Also, these protocols can be adapted to work over a broadcast channel, allowing many clients to reconcile with one host based on a single broadcast, even if each client is missing a different subset.