Alice holds a secret integer a while Bob holds a secret integer b, they want to decide on the predicate a > b with no information revealed other than the result. This is the well known Yaos millionaires problem. In some ecommerce applications, Alice holds an n-dimension secret vector a = (a1, ..., an) while Bob holds an n-dimension secret vector ß = (b1, ..., bn). Alice and Bob want to decide on one of the three possible domination results, a succ ß, ß succ a, or no domination exists, with no information revealed other than the result. I.e., in case there is a domination, no information is revealed about any dimension, whereas, in case no domination exists, no information is revealed about the predicate ai > bi for any i = 1, ..., n. In the honest-but-curious scenario and without the help of a third party, in this paper we propose an efficient solution to this problem. We give a complete security proof. Up to our knowledge, no practical solution to this problem — that does not incorporate a third party — has been proposed.
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