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The authors consider the problem of computing the intersection of private datasets of two parties, where the datasets contain lists of elements taken from a large domain. This problem has many applications for online collaboration. They present protocols, based on the use of homomorphism encryption and balanced hashing, for both semi-honest and malicious environments. For lists of length k, they obtain O(k) communication overhead and O(k ln ln k) computation. The protocol for the sem honest environment is secure in the standard model, while the protocol for the malicious environment is secure in the random oracle model.
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