  The problem of secure source coding with multiple terminals is extended by
considering a remote source whose noisy measurements are the correlated random
variables used for secure source reconstruction. The main additions to the
problem include 1) all terminals noncausally observe a noisy measurement of the
remote source; 2) a private key is available to all legitimate terminals; 3)
the public communication link between the encoder and decoder is rate-limited;
and 4) the secrecy leakage to the eavesdropper is measured with respect to the
encoder input, whereas the privacy leakage is measured with respect to the
remote source. Exact rate regions are characterized for a lossy source coding
problem with a private key, remote source, and decoder side information under
security, privacy, communication, and distortion constraints. By replacing the
distortion constraint with a reliability constraint, we obtain the exact rate
region also for the lossless case. Furthermore, the lossy rate region for
scalar discrete-time Gaussian sources and measurement channels is established.
