The Computational Wiretap Channel

We present the computational wiretap channel: Alice has some data x and wants to share some computation h(x) with Bob. To do this, she sends f(x), where f is some sufficient statistic for h. An eavesdropper, Eve, is interested in computing another function g(x). We show that, under some conditions on f and g, this channel can be approximated, from Eve's point of view, by the classic Wyner wiretap channel.Comment: Presented at the 56th Annual Allerton Conference on Communication, Control, and Computin

Optimal Binary Differential Privacy via Graphs

We present the notion of \emph{reasonable utility} for binary mechanisms, which applies to all utility functions in the literature. This notion induces a partial ordering on the performance of all binary differentially private (DP) mechanisms. DP mechanisms that are maximal elements of this ordering are optimal DP mechanisms for every reasonable utility. By looking at differential privacy as a randomized graph coloring, we characterize these optimal DP in terms of their behavior on a certain subset of the boundary datasets we call a boundary hitting set. In the process of establishing our results, we also introduce a useful notion that generalizes DP conditions for binary-valued queries, which we coin as suitable pairs. Suitable pairs abstract away the algebraic roles of $\varepsilon,\delta$ in the DP framework, making the derivations and understanding of our proofs simpler. Additionally, the notion of a suitable pair can potentially capture privacy conditions in frameworks other than DP and may be of independent interest