Functionally Private Approximations of Negligibly-Biased Estimators

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-random functions (PRF) (a stronger cryptographic notion than pseudo-random generators) of which can be based on common cryptographic assumptions. The application ...

• Type: Conference
• Year: 2009
• Where: FSTTCS
• Authors: André Madeira, S. Muthukrishnan
• Keywords: Approximation, FSTTCS 2009, Private Approximation, Private Approximation Protocols, Theoretical Computer Science