Two-Party Private Vector Dominance: The All-Or-Nothing Deal

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 Yao's millionaires' problem. In some e-commerce applications, Alice holds an n-dimension secret vector alpha = (a₁, ..., a_n) while Bob holds an n-dimension secret vector beta = (b₁,..., b_n). Alice and Bob want to decide on one of the three possible domination results, alpha beta, beta alpha, 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 a_i > b_i 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