Abstract
A user generates <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> independent and identically distributed data rvs with a pmf that must be guarded from a querier. The querier must recover, with a prescribed accuracy, a given function of the data from each of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> independent and identically distributed user-devised query responses. The user chooses the data pmf and the random query responses to maximize distribution privacy as gauged by the divergence between the pmf and the querier's best estimate of it based on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> query responses. Considering an arbitrary function, a basic achievable lower bound, that does not depend on n, is provided for distribution privacy. Next, upper (converse) and lower (achievable) bounds, dependent on n, are developed that converge to said basic bound as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> grows. Explicit strategies for the user and the querier are identified.
Published Version
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