Differentially private approximate pattern matching

Teresa Anna Steiner*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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Abstract

Differential privacy is the de facto privacy standard in data analysis and widely researched in various application areas. On the other hand, analyzing sequences, or strings, is essential to many modern data analysis tasks, and those data often include highly sensitive personal data. While the problem of sanitizing sequential data to protect privacy has received growing attention, there is a surprising lack of theoretical studies of algorithms analyzing sequential data that preserve differential privacy while giving provable guarantees on the accuracy of such an algorithm. The goal of this paper is to initiate such a study.
Specifically, in this paper, we consider the k-approximate pattern matching problem under differential privacy, where the goal is to report or count all substrings of a given string S which have a Hamming distance at most k to a pattern P , or decide whether such a substring exists. In our definition of privacy, individual positions of the string S are protected. To be able to answer queries under differential privacy, we allow some slack on k, i.e. we allow reporting or counting substrings of S with a distance at most (1 + γ)k + α to P, for a multiplicative error γ and an additive error α. We analyze which values of α and γ are necessary or sufficient to solve the k-approximate pattern matching problem while satisfying ϵ-differential privacy. Let n denote the length of S. We give
-an ϵ-differentially private algorithm with an additive error of O−1 log n) and no multiplicative error for the existence variant;
-an ϵ-differentially private algorithm with an additive error O−1 max (k, log n) · log n) for the counting variant;
-an ϵ-differentially private algorithm with an additive error of O−1 log n) and multiplicative error O(1) for the reporting variant for a special class of patterns.
The error bounds hold with high probability. All of these algorithms return a witness, that is, if there exists a substring of S with distance at most k to P, then the algorithm returns a substring of S with distance at most (1 + γ)k + α to P. Further, we complement these results by a lower bound, showing that any algorithm for the existence variant which also returns a witness must have an additive error of Ω(ϵ−1 log n) with constant probability.
Original languageEnglish
Title of host publicationProceedings of the 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)
Volume287
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publication date2024
Pages18
Article number94
DOIs
Publication statusPublished - 2024
Event15th Innovations in Theoretical Computer Science Conference - Berkeley, United States
Duration: 30 Jan 20242 Feb 2024

Conference

Conference15th Innovations in Theoretical Computer Science Conference
Country/TerritoryUnited States
CityBerkeley
Period30/01/202402/02/2024
SeriesLeibniz International Proceedings in Informatics, LIPIcs
ISSN1868-8969

Keywords

  • Differential privacy
  • Pattern matching

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