On the Public Communication Needed to Achieve SK Capacity in the Multiterminal Source Model

Mukherjee, Manuj and Kashyap, Navin and Sankarasubramaniam, Yogesh (2016) On the Public Communication Needed to Achieve SK Capacity in the Multiterminal Source Model. In: IEEE TRANSACTIONS ON INFORMATION THEORY, 62 (7). pp. 3811-3830.

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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.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON INFORMATION THEORY
Additional Information:	Copy right for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	22 Oct 2016 10:19
Last Modified:	22 Oct 2016 10:19
URI:	http://eprints.iisc.ac.in/id/eprint/55103

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