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

Chan, Chung and Mukherjee, Manuj and Kashyap, Navin and Zhou, Qiaoqiao (2019) Upper Bounds via Lamination on the Constrained Secrecy Capacity of Hypergraphical Sources. In: IEEE TRANSACTIONS ON INFORMATION THEORY, 65 (8). pp. 5080-5093.

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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 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.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON INFORMATION THEORY
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	Copyright of this article belongs to IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Keywords:	Secret key agreement; multiterminal source model; hypergraphical sources; secrecy capacity
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	13 Nov 2019 05:41
Last Modified:	13 Nov 2019 05:41
URI:	http://eprints.iisc.ac.in/id/eprint/63399

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