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 and store its observation in a public database such that (i) authorized sets of users can reconstruct the source with some distortion level, and (ii) information leakage to non-authorized sets of colluding users is minimized. In other words, the recovery of the data is restricted to a predefined access structure of the users. One of the main results of this paper is a closed-form characterization of the fundamental trade-off between source coding rate and the information leakage rate when any authorized set of users has "better" side information than any set of unauthorized users.