Almost Perfect Privacy for Additive Gaussian Privacy Filters

2016/08/13 by Asoodeh, Shahab, Alajaji, Fady, Linder, Tamas
#Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1608.04001

Abstract

We study the maximal mutual information about a random variable Y (representing non-private information) displayed through an additive Gaussian channel when guaranteeing that only ε bits of information is leaked about a random variable X (representing private information) that is correlated with Y. Denoting this quantity by g_ε(X,Y), we show that for perfect privacy, i.e., ε=0, one has g₀(X,Y)=0 for any pair of absolutely continuous random variables (X,Y) and then derive a second-order approximation for g_ε(X,Y) for small ε. This approximation is shown to be related to the strong data processing inequality for mutual information under suitable conditions on the joint distribution P_XY. Next, motivated by an operational interpretation of data privacy, we formulate the privacy-utility tradeoff in the same setup using estimation-theoretic quantities and obtain explicit bounds for this tradeoff when ε is sufficiently small using the approximation formula derived for g_ε(X,Y).

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