  Communication complexity refers to the minimum rate of public communication
required for generating a maximal-rate secret key (SK) in the multiterminal
source model of Csiszar and Narayan. Tyagi recently characterized this
communication complexity for a two-terminal system. We extend the ideas in
Tyagi's work to derive a lower bound on communication complexity in the general
multiterminal setting. In the important special case of the complete graph
pairwise independent network (PIN) model, our bound allows us to determine the
exact linear communication complexity, i.e., the communication complexity when
the communication and SK are restricted to be linear functions of the
randomness available at the terminals.
