On Differentially Private String Distances

Jerry Yao-Chieh Hu, Erzhi Liu, Han Liu, Zhao Song, Lichen Zhang

Keywords: edit distance, data structure, differential privacy

TL;DR: We design the first differentially private data structures for estimating Hamming and edit distances that are both time and space efficient.

Abstract:

Given a database of bit strings $A_1,\ldots,A_m\in \\{0,1\\}^n$, a fundamental data structure task is to estimate the distances between a given query $B\in \\{0,1\\}^n$ with all the strings in the database. In addition, one might further want to ensure the integrity of the database by releasing these distance statistics in a secure manner. In this work, we propose differentially private (DP) data structures for this type of tasks, with a focus on Hamming and edit distance. On top of the strong privacy guarantees, our data structures are also time- and space-efficient. In particular, our data structure is $\epsilon$-DP against any sequence of queries of arbitrary length, and for any query $B$ such that the maximum distance to any string in the database is at most $k$, we output $m$ distance estimates. Moreover,

* For Hamming distance, our data structure answers any query in $\widetilde O(mk+n)$ time and each estimate deviates from the true distance by at most $\widetilde O(k/e^{\epsilon/\log k})$;

* For edit distance, our data structure answers any query in $\widetilde O(mk^2+n)$ time and each estimate deviates from the true distance by at most $\widetilde O(k/e^{\epsilon/(\log k \log n)})$.

For moderate $k$, both data structures support sublinear query operations. We obtain these results via a novel adaptation of the randomized response technique as a bit flipping procedure, applied to the sketched strings.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

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Submission Number: 7798