Functionally Private Approximations of Negligibly-Biased Estimators

Authors André Madeira, S. Muthukrishnan

Thumbnail PDF


  • Filesize: 251 kB
  • 12 pages

Document Identifiers

Author Details

André Madeira
S. Muthukrishnan

Cite AsGet BibTex

André Madeira and S. Muthukrishnan. Functionally Private Approximations of Negligibly-Biased Estimators. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 323-334, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


We study functionally private approximations. An approximation function $g$ is {\em 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 $L_p$-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-random {\em functions} (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 {\em any} problem. Our second application result states that every problem in some subclasses of \SP of hard counting problems admit efficient and functionally private approximation protocols. This result is based on a functionally private approximation for the \SDNF 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.
  • Functional privacy
  • privacy
  • data streams
  • #P-complete


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail