  Consider a source and multiple users who observe the independent and
identically distributed (i.i.d.) copies of correlated Gaussian random
variables. The source wishes to compress its observations and store the result
in a public database such that (i) authorized sets of users are able to
reconstruct the source with a certain distortion level, and (ii) information
leakage to non-authorized sets of colluding users is minimized. In other words,
the recovery of the source is restricted to a predefined access structure. The
main result of this paper is a closed-form characterization of the fundamental
trade-off between the source coding rate and the information leakage rate. As
an example, threshold access structures are studied, i.e., the case where any
set of at least $t$ users is able to reconstruct the source with some
predefined distortion level and the information leakage at any set of users
with a size smaller than $t$ is minimized.
