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首页> 外文期刊>IEEE Transactions on Information Theory >Upper Bounds via Lamination on the Constrained Secrecy Capacity of Hypergraphical Sources
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Upper Bounds via Lamination on the Constrained Secrecy Capacity of Hypergraphical Sources

机译：通过分层对超图源的约束保密能力的上限

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摘要

Hypergraphical sources are a natural class of sources for secret key generation, within which different subsets of terminals sharing secrets are allowed to discuss publicly in order to agree upon a global secret key. While their secrecy capacity, i.e., the maximum rate of a secret key that can be agreed upon by the entire set of terminals, is well-understood, what remains open is the maximum rate of a secret key that can be generated when there is a restriction on the overall rate of public discussion allowed. In this paper, we obtain a family of explicitly computable upper bounds on the number of bits of secret key that can be generated per bit of public discussion. These upper bounds are derived using a lamination technique based on the submodularity of the entropy function. In particular, a specific instance of these upper bounds, called the edge-partition bound, is shown to be tight for the pairwise independent network model, a special case of the hypergraphical source when the hypergraph is a graph. The secret key generation scheme achieving this upper bound is the tree-packing protocol of Nitinawarat et al., thereby resolving in the affirmative the discussion rate optimality of the tree-packing protocol.
机译：超图形资源是用于生成密钥的自然类别的资源，在该资源中，共享秘密的终端的不同子集被允许公开讨论，以便就全局密钥达成一致。虽然他们的保密能力（即可以由整个终端集确定的最大密钥秘密率）已得到很好的理解，但开放的仍然是存在密钥时可以生成的最大秘密密钥率。限制公众讨论的整体速度。在本文中，我们获得了每个公开讨论位可以生成的一系列显式可计算的上限。这些上限是使用分层技术根据熵函数的次模量得出的。特别是，这些上限的特定实例（称为边沿分区边界）对于成对独立网络模型来说是紧密的，当超图是图时，这是超图源的一种特殊情况。实现该上限的秘密密钥生成方案是Nitinawarat等人的树包装协议，从而肯定地解决了树包装协议的讨论速率最优性。

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