The communication complexity of achieving SK capacity in a class of PIN models

The communication complexity of achieving secret key (SK) capacity in the multiterminal source model of Csiszár and Narayan is the minimum rate of public communication required to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by R_CO, is an upper bound on the communication complexity, denoted by R_SK. A source model for which this upper bound is tight is called R_SK-maximal. In this paper, we establish a sufficient condition for R_SK-maximality within the class of pairwise independent network (PIN) models defined on hypergraphs. This allows us to compute R_SK exactly within the class of PIN models satisfying this condition. On the other hand, we also provide a counterexample that shows that our condition does not in general guarantee R_SK-maximality for sources beyond PIN models.