  In the Open Data approach, governments and other public organisations want to
share their datasets with the public, for accountability and to support
participation. Data must be opened in such a way that individual privacy is
safeguarded. The Privacy Funnel is a mathematical approach that produces a
sanitised database that does not leak private data beyond a chosen threshold.
The downsides to this approach are that it does not give worst-case privacy
guarantees, and that finding optimal sanitisation protocols can be
computationally prohibitive. We tackle these problems by using differential
privacy metrics, and by considering local protocols which operate on one entry
at a time. We show that under both the Local Differential Privacy and Local
Information Privacy leakage metrics, one can efficiently obtain optimal
protocols. Furthermore, Local Information Privacy is both more closely aligned
to the privacy requirements of the Privacy Funnel scenario, and more
efficiently computable. We also consider the scenario where each user has
multiple attributes, for which we define Side-channel Resistant Local
Information Privacy, and we give efficient methods to find protocols satisfying
this criterion while still offering good utility. Finally, we introduce
Conditional Reporting, an explicit LIP protocol that can be used when the
optimal protocol is infeasible to compute, and we test this protocol on
real-world and synthetic data. Experiments on real-world and synthetic data
confirm the validity of these methods.
