## Abstract

For the multiterminal secret key agreement problem under a private source model, it is known that the communication complexity required to achieve the capacity can be strictly smaller than the minimum rate of communication for omniscience, but a single-letter characterization is not known. We obtain a single-letter lower bound on the communication complexity as well as some conditions for the communication complexity to be maximal (equal to the smallest rate of communication for omniscience). The results are are stated and derived using a meaningful multivariate mutual information measure. They are stronger than existing ones because 1) they apply to a general discrete memoryless multiple source rather than a special source model, 2) the problem formulation allows private randomization by individual users, 3) the bound is single-letter and the condition can be checked easily, and so 4) more scenarios in which the communication complexity is maximal are discovered. We conjecture that the lower bound can be further improved by giving a concrete example.

Original language | English |
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Title of host publication | 2016 IEEE Information Theory Workshop, ITW 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 354-358 |

Number of pages | 5 |

ISBN (Electronic) | 9781509010905 |

DOIs | |

State | Published - 21 Oct 2016 |

Externally published | Yes |

Event | 2016 IEEE Information Theory Workshop, ITW 2016 - Cambridge, United Kingdom Duration: 11 Sep 2016 → 14 Sep 2016 |

### Publication series

Name | 2016 IEEE Information Theory Workshop, ITW 2016 |
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### Conference

Conference | 2016 IEEE Information Theory Workshop, ITW 2016 |
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Country/Territory | United Kingdom |

City | Cambridge |

Period | 11/09/16 → 14/09/16 |

### Bibliographical note

Publisher Copyright:© 2016 IEEE.