## Abstract

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 Csiszar and Narayan. Building on the prior work of Tyagi for the two-terminal scenario, we derive a lower bound on the communication complexity, R_{SK}, 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 R_{CO}, is an upper bound on R_{SK}. 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 R_{SK} meets the R_{CO} upper bound. Thus, the PIN models satisfying our condition are R_{SK}-maximal, indicating that the upper bound R_{SK} ≤ R_{CO} holds with equality. This allows us to explicitly evaluate R_{SK} 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 all terminals (omnivocality) is needed for establishing an 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. However, for the source models with four or more terminals, counterexamples exist showing that the converse does not hold in general.

Original language | English |
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Article number | 7416199 |

Pages (from-to) | 3811-3830 |

Number of pages | 20 |

Journal | IEEE Transactions on Information Theory |

Volume | 62 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2016 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2016 IEEE.

## Keywords

- Communication complexity
- PIN model
- Secret key generation
- informationtheoretic security