Fuzzy Private Matching

In the private matching problem, a client and a server each hold a set of n elements as their input. The client wants to privately compute the intersection of these two sets: the client learns the elements it has in common with server (and nothing more), while the server obtains no information at all. In certain applications it would be useful to have a private matching protocol that reports a match even if two elements are only similar instead of equal. Such a private matching protocol is called fuzzy, and is useful, for instance, when elements may be inaccurate or corrupted by errors. We consider the fuzzy private matching problem, in a semi-honest environment. Elements are similar if they match on t out of T attributes. First we show that the original solution proposed by Freedman et al. [FNP04] is not private: the client can “steal” elements even if the sets have no similar elements in common. Following that we present 2 fuzzy private matching protocols. The first, simple, protocol has message complexity O(n ` T t ́ ). The second, improved, protocol has message complexity O(nT ), but here the client incurs a O(n ` T t ́ ) time complexity penalty.