Multiterminal Secret Key Agreement at Asymptotically Zero Discussion Rate

TL;DR

This paper investigates the maximum secret key rate achievable with negligible discussion, providing new characterizations for hypergraphical and linear sources and proposing methods for broader models.

Contribution

It characterizes the secrecy capacity at zero discussion rate for hypergraphical and linear sources, advancing understanding of multiterminal secret key agreement.

Findings

Capacity equals Gács-Körner common information for two users.

Provided efficiently computable capacity characterizations.

Extended techniques to more general source models.

Abstract

In the multiterminal secret key agreement problem, a set of users want to discuss with each other until they share a common secret key independent of their discussion. We want to characterize the maximum secret key rate, called the secrecy capacity, asymptotically when the total discussion rate goes to zero. In the case of only two users, the capacity is equal to the G\'acs-K\"orner common information. However, when there are more than two users, the capacity is unknown. It is plausible that a multivariate extension of the G\'acs-K\"orner common information is the capacity, however, proving the converse is challenging. We resolved this for the hypergraphical sources and finite linear sources, and provide efficiently computable characterizations. We also give some ideas of extending the techniques to more general source models.