  This paper studies the tradeoff in privacy and utility in a single-trial
multi-terminal guessing (estimation) framework using a system model that is
inspired by index coding. There are $n$ independent discrete sources at a data
curator. There are $m$ legitimate users and one adversary, each with some side
information about the sources. The data curator broadcasts a distorted function
of sources to legitimate users, which is also overheard by the adversary. In
terms of utility, each legitimate user wishes to perfectly reconstruct some of
the unknown sources and attain a certain gain in the estimation correctness for
the remaining unknown sources. In terms of privacy, the data curator wishes to
minimize the maximal leakage: the worst-case guessing gain of the adversary in
estimating any target function of its unknown sources after receiving the
broadcast data. Given the system settings, we derive fundamental performance
lower bounds on the maximal leakage to the adversary, which are inspired by the
notion of confusion graph and performance bounds for the index coding problem.
We also detail a greedy privacy enhancing mechanism, which is inspired by the
agglomerative clustering algorithms in the information bottleneck and privacy
funnel problems.
