Scaling Private Record Linkage using Output Constrained Differential Privacy.

Private record linkage is the problem of identifying pairs of records that are similar as per an input matching rule from databases that are held by two parties that do not trust one another. We identify three key desiderata that a PRL solution must ensure: a proof of end-to-end privacy, communication and computational costs that scale sub-quadratically in the number of input records, perfect precision and high recall of matching pairs. We show that all of the existing solutions for PRL -- including secure 2-party computation (S2PC), and their variants that use non-private or differentially private (DP) blocking -- violate at least one of the three desiderata. particular, S2PC techniques guarantee end-to-end privacy but have either low recall or high cost. We show that DP blocking based techniques do not provide an end-to-end privacy guarantee as DP does not permit the release of any exact answers (including matching records in PRL). In light of this deficiency, we propose a novel privacy model, called output constrained differential privacy, that shares the strong privacy protection of DP, but allows for the truthful release of the output of a certain function applied to the data. We apply this to PRL, and show that protocols satisfying this privacy model permit the disclosure of the true matching records, but their execution is insensitive to the presence or absence of a single non-matching record. We develop novel protocols that satisfy this end-to-end privacy guarantee and permit a tradeoff between recall, privacy and efficiency. Our empirical evaluations on real and synthetic datasets show that our protocols have high recall, scale near linearly in the size of the input databases (and the output set of matching pairs), and have communication and computational costs that are at least 2 orders of magnitude smaller than S2PC baselines.