The problem of secure two-party vector dominance requires the comparison of two vectors in an "all-or-nothing" way. In this paper we provide a solution to this problem based on the semi-honest model. It is reduced to the problem of privacy preserving prefix test, and an additive threshold homomorphic encryption is used to protect those privacies while computing the results of all of the prefix tests. Our solution has advantages of efficiency and security in comparison with other solutions.
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