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.
Highlights
In information-theoretic security, the problem of secret key agreement by public discussion concerns a group of users discussing in public to generate a common secret key that is independent of their discussion
Inspired by the idea of decremental secret key agreement and its application to the constrained secret key agreement problem, we have formulated a multiterminal secret key agreement problem with a more general source compression step that applies beyond the hypergraphical source model
While a single-letter characterization of the compressed secrecy capacity and admissible entropy limit remains unknown, single-letter bounds have been derived and they are likely to be tight for the hypergraphical model, and possibly more general source models such as the finite linear source model [47]
Summary
In information-theoretic security, the problem of secret key agreement by public discussion concerns a group of users discussing in public to generate a common secret key that is independent of their discussion. The problem was first formulated by Maurer [1] and Ahlswede and Csiszár [2] under a private source model involving two users who observe some correlated private sources. Public discussion was shown to be useful in generating the secret key; i.e., it strictly increases the maximum achievable secret key rate, called the secrecy capacity. This phenomenon was discovered in [3] in a different formulation. It was shown that the capacity can be achieved by one-way public discussion (i.e., with only one of the users discussing in public)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
