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Communication complexity refers to the minimum rate of public communicationrequired for generating a maximal-rate secret key (SK) in the multiterminalsource model of Csiszar and Narayan. Tyagi recently characterized thiscommunication complexity for a two-terminal system. We extend the ideas inTyagi's work to derive a lower bound on communication complexity in the generalmultiterminal setting. In the important special case of the complete graphpairwise independent network (PIN) model, our bound allows us to determine theexact linear communication complexity, i.e., the communication complexity whenthe communication and SK are restricted to be linear functions of therandomness available at the terminals.

On the Communication Complexity of Secret Key Generation in the Multiterminal Source Model