Functionally private approximations of negligibly-biased estimators

André Madeira, S. Muthukrishnan

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

    Abstract

    We study functionally private approximations. An approximation function g is functionally private with respect to f if, for any input x, g(x) reveals no more information about x than f(x). Our main result states that a function f admits an efficiently-computable functionally private approximation g if there exists an efficiently-computable and negligibly-biased estimator for f. Contrary to previous generic results, our theorem is more general and has a wider application reach. We provide two distinct applications of the above result to demonstrate its flexibility. In the data stream model, we provide a functionally private approximation to the Lp-norm estimation problem, a quintessential application in streaming, using only polylogarithmic space in the input size. The privacy guarantees rely on the use of pseudo-randomfunctions (PRF) (a stronger cryptographic notion than pseudo-random generators) of which can be based on common cryptographic assumptions. The application of PRFs in this context appears to be novel and we expect other results to follow suit. Moreover, this is the first known functionally private streaming result for any problem. Our second application result states that every problem in some subclasses of #P of hard counting problems admit efficient and functionally private approximation protocols. This result is based on a functionally private approximation for the #DNF problem (or estimating the number of satisfiable truth assignments to a Boolean formula in disjunctive normal form), which is an application of our main theorem and previously known results.

    Original languageEnglish (US)
    Title of host publicationFoundations of Software Technology and Theoretical Computer Science, FSTTCS 2009 - 29th Annual Conference, Proceedings
    Pages323-334
    Number of pages12
    DOIs
    StatePublished - Dec 1 2009
    Event29th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2009 - Kanpur, India
    Duration: Dec 15 2009Dec 17 2009

    Publication series

    NameLeibniz International Proceedings in Informatics, LIPIcs
    Volume4
    ISSN (Print)1868-8969

    Conference

    Conference29th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2009
    CountryIndia
    CityKanpur
    Period12/15/0912/17/09

    ASJC Scopus subject areas

    • Software

    Cite this

    Madeira, A., & Muthukrishnan, S. (2009). Functionally private approximations of negligibly-biased estimators. In Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2009 - 29th Annual Conference, Proceedings (pp. 323-334). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 4). https://doi.org/10.4230/LIPIcs.FSTTCS.2009.2329