Upper Bounds via Lamination on the Constrained Secrecy Capacity of Hypergraphical Sources

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • Chung Chan
  • Manuj Mukherjee
  • Navin Kashyap
  • Qiaoqiao Zhou

Related Research Unit(s)

Detail(s)

Original languageEnglish
Article number8633870
Pages (from-to)5080-5093
Journal / PublicationIEEE Transactions on Information Theory
Volume65
Issue number8
Online published4 Feb 2019
Publication statusPublished - Aug 2019

Abstract

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 work, 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.

Research Area(s)

  • hypergraphical sources, multiterminal source model, secrecy capacity, Secret key agreement

Citation Format(s)

Upper Bounds via Lamination on the Constrained Secrecy Capacity of Hypergraphical Sources. / Chan, Chung; Mukherjee, Manuj; Kashyap, Navin; Zhou, Qiaoqiao.

In: IEEE Transactions on Information Theory, Vol. 65, No. 8, 8633870, 08.2019, p. 5080-5093.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review