The focus of this paper is on the public communication required for
generating a maximal-rate secret key (SK) within the multiterminal source model
of Csisz{\'a}r and Narayan. Building on the prior work of Tyagi for the
two-terminal scenario, we derive a lower bound on the communication complexity,
RSKβ, defined to be the minimum rate of public communication needed
to generate a maximal-rate SK. It is well known that the minimum rate of
communication for omniscience, denoted by RCOβ, is an upper bound on
RSKβ. For the class of pairwise independent network (PIN) models
defined on uniform hypergraphs, we show that a certain "Type S"
condition, which is verifiable in polynomial time, guarantees that our lower
bound on RSKβ meets the RCOβ upper bound. Thus, PIN
models satisfying our condition are RSKβ-maximal, meaning that the
upper bound RSKββ€RCOβ holds with equality. This allows
us to explicitly evaluate RSKβ for such PIN models. We also give
several examples of PIN models that satisfy our Type S condition.
Finally, we prove that for an arbitrary multiterminal source model, a stricter
version of our Type S condition implies that communication from
\emph{all} terminals ("omnivocality") is needed for establishing a SK of
maximum rate. For three-terminal source models, the converse is also true:
omnivocality is needed for generating a maximal-rate SK only if the strict Type
S condition is satisfied. Counterexamples exist that show that the
converse is not true in general for source models with four or more terminals.Comment: Submitted to the IEEE Transactions on Information Theory. arXiv admin
note: text overlap with arXiv:1504.0062