Nearly optimal private convolution

Nadia Fawaz, Shanmugavelayutham Muthukrishnan, Aleksandar Nikolov

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    We study algorithms for computing the convolution of a private input x with a public input h, while satisfying the guarantees of (ε, δ)-differential privacy. Convolution is a fundamental operation, intimately related to Fourier Transforms. In our setting, the private input may represent a time series of sensitive events or a histogram of a database of confidential personal information. Convolution then captures important primitives including linear filtering, which is an essential tool in time series analysis, and aggregation queries on projections of the data. We give an algorithm for computing convolutions which satisfies (ε, δ)-differentially privacy and is nearly optimal for every public h, i.e. is instance optimal with respect to the public input. We prove optimality via spectral lower bounds on the hereditary discrepancy of convolution matrices. Our algorithm is very efficient - it is essentially no more computationally expensive than a Fast Fourier Transform.

    Original languageEnglish (US)
    Title of host publicationAlgorithms, ESA 2013 - 21st Annual European Symposium, Proceedings
    Pages445-456
    Number of pages12
    DOIs
    StatePublished - Sep 24 2013
    Event21st Annual European Symposium on Algorithms, ESA 2013 - Sophia Antipolis, France
    Duration: Sep 2 2013Sep 4 2013

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume8125 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other21st Annual European Symposium on Algorithms, ESA 2013
    CountryFrance
    CitySophia Antipolis
    Period9/2/139/4/13

    Fingerprint

    Convolution
    Privacy
    Linear Filtering
    Time series analysis
    Computing
    Time Series Analysis
    Fast Fourier transform
    Fast Fourier transforms
    Histogram
    Discrepancy
    Time series
    Fourier transform
    Aggregation
    Optimality
    Fourier transforms
    Agglomeration
    Projection
    Query
    Lower bound

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Fawaz, N., Muthukrishnan, S., & Nikolov, A. (2013). Nearly optimal private convolution. In Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings (pp. 445-456). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8125 LNCS). https://doi.org/10.1007/978-3-642-40450-4_38

    Nearly optimal private convolution. / Fawaz, Nadia; Muthukrishnan, Shanmugavelayutham; Nikolov, Aleksandar.

    Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings. 2013. p. 445-456 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8125 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Fawaz, N, Muthukrishnan, S & Nikolov, A 2013, Nearly optimal private convolution. in Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8125 LNCS, pp. 445-456, 21st Annual European Symposium on Algorithms, ESA 2013, Sophia Antipolis, France, 9/2/13. https://doi.org/10.1007/978-3-642-40450-4_38
    Fawaz N, Muthukrishnan S, Nikolov A. Nearly optimal private convolution. In Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings. 2013. p. 445-456. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-40450-4_38
    Fawaz, Nadia ; Muthukrishnan, Shanmugavelayutham ; Nikolov, Aleksandar. / Nearly optimal private convolution. Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings. 2013. pp. 445-456 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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