  The problem of reliable function computation is extended by imposing privacy,
secrecy, and storage constraints on a remote source whose noisy measurements
are observed by multiple parties. The main additions to the classic function
computation problem include 1) privacy leakage to an eavesdropper is measured
with respect to the remote source rather than the transmitting terminals'
observed sequences; 2) the information leakage to a fusion center with respect
to the remote source is considered as a new privacy leakage metric; 3) the
function computed is allowed to be a distorted version of the target function,
which allows to reduce the storage rate as compared to a reliable function
computation scenario in addition to reducing secrecy and privacy leakages; 4)
two transmitting node observations are used to compute a function. Inner and
outer bounds on the rate regions are derived for lossless and lossy
single-function computation with two transmitting nodes, which recover previous
results in the literature. For special cases, including invertible and
partially invertible functions, and degraded measurement channels, simplified
lossless and lossy rate region bounds are established, and one region is
evaluated as an example scenario.
