Fuzzy Private Matching (Extended Abstract)

TL;DR

This paper addresses the fuzzy private matching problem, proposing two new protocols that enable private matching with similarity tolerance, correcting previous solutions, and analyzing their efficiency and security in semi-honest settings.

Contribution

The paper introduces two novel fuzzy private matching protocols with improved efficiency and correctness, and explores alternative methods based on Hamming distance and oblivious transfer.

Findings

First protocol has bit message complexity O(n * C(T, t) * (T log|D| + k))

Second protocol improves to O(n T (log|D| + k)) complexity

Protocols based on Hamming distance and oblivious transfer offer alternative performance trade-offs.

Abstract

In the private matching problem, a client and a server each hold a set of $n$ input elements. The client wants to privately compute the intersection of these two sets: he learns which elements he has in common with the server (and nothing more), while the server gains 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 \emph{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. is incorrect. Subsequently we present two fuzzy private matching protocols. The first, simple, protocol has bit message complexity $O(n \binom{T}{t} (T \log{|D|}+k))$. The second, improved, protocol has a much better bit message complexity of $O(n T (\log{|D|}+k))$, but here the client incurs a O(n) factor time complexity. Additionally, we present protocols based on the computation of the Hamming distance and on oblivious transfer, that have different, sometimes more efficient, performance characteristics.