  In this paper, we study an information-theoretic secret sharing problem,
where a dealer distributes shares of a secret among a set of participants under
the following constraints: (i) authorized sets of users can recover the secret
by pooling their shares, and (ii) non-authorized sets of colluding users cannot
learn any information about the secret. We assume that the dealer and
participants observe the realizations of correlated Gaussian random variables
and that the dealer can communicate with participants through a one-way,
authenticated, rate-limited, and public channel. Unlike traditional secret
sharing protocols, in our setting, no perfectly secure channel is needed
between the dealer and the participants. Our main result is a closed-form
characterization of the fundamental trade-off between secret rate and public
communication rate.
