  We propose a scheme by which two parties can secretely and simultaneously
exchange messages. The scheme requires the two parties to share entanglement
and both to perform Bell-state measurements. Only two out of the four Bell
states are required to be distinguished in the Bell-state measurements, and
thus the scheme is experimentally feasible using only linear optical means.
Generalizations of the scheme to high-dimensional systems and to multipartite
entanglement are considered. We show also that the proposed scheme works even
if the two parties do not possess shared reference frames.
