A secure multidimensional point inclusion protocol
Proceedings of the 9th workshop on Multimedia & security
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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 ecommerce applications, Alice holds an n-dimension secret vector a = (a1, ..., an) while Bob holds an n-dimension secret vector β = (b1, ..., bn). Alice and Bob want to decide on one of the three possible domination results, a\succβ, β\succa, 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.