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Entropy 2017, 19(10), 545; https://doi.org/10.3390/e19100545

Compressed Secret Key Agreement:Maximizing Multivariate Mutual Information per Bit

Institute of Network Coding, The Chinese University of Hong Kong, Hong Kong, China
Received: 5 July 2017 / Revised: 2 October 2017 / Accepted: 3 October 2017 / Published: 14 October 2017
(This article belongs to the Special Issue Information-Theoretic Security)
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Abstract

The multiterminal secret key agreement problem by public discussion is formulated with an additional source compression step where, prior to the public discussion phase, users independently compress their private sources to filter out strongly correlated components in order to generate a common secret key. The objective is to maximize the achievable key rate as a function of the joint entropy of the compressed sources. Since the maximum achievable key rate captures the total amount of information mutual to the compressed sources, an optimal compression scheme essentially maximizes the multivariate mutual information per bit of randomness of the private sources, and can therefore be viewed more generally as a dimension reduction technique. Single-letter lower and upper bounds on the maximum achievable key rate are derived for the general source model, and an explicit polynomial-time computable formula is obtained for the pairwise independent network model. In particular, the converse results and the upper bounds are obtained from those of the related secret key agreement problem with rate-limited discussion. A precise duality is shown for the two-user case with one-way discussion, and such duality is extended to obtain the desired converse results in the multi-user case. In addition to posing new challenges in information processing and dimension reduction, the compressed secret key agreement problem helps shed new light on resolving the difficult problem of secret key agreement with rate-limited discussion by offering a more structured achieving scheme and some simpler conjectures to prove. View Full-Text
Keywords: secret key agreement; source compression; rate-limited discussion; communication complexity; dimension reduction; multivariate mutual information secret key agreement; source compression; rate-limited discussion; communication complexity; dimension reduction; multivariate mutual information
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Chan, C. Compressed Secret Key Agreement:Maximizing Multivariate Mutual Information per Bit. Entropy 2017, 19, 545.

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