Multi-Key Generation Over a Cellular Model With a Helper

Abstract

The problem of simultaneously generating multiple keys for a cellular source model with a helper is investigated. In the model considered, there are four terminals, $\mathcal {X}_{0}$ , $\mathcal {X}_{1}$ , $\mathcal {X}_{2}$ , and $\mathcal {X}_{3}$ , each of which observes one component of a vector source. Terminal $\mathcal {X}_{0}$ wishes to generate two secret keys $K_{1}$ and $K_{2}$ , respectively, with terminals $\mathcal {X}_{1}$ and $\mathcal {X}_{2}$ under the help of terminal $\mathcal {X}_{3}$ . All terminals are allowed to communicate over a public channel. An eavesdropper is assumed to have access to the public discussion. Both symmetric and asymmetric key generations are considered. In symmetric key generation models, model 1a (with a trusted helper) requires that the two keys are concealed from the eavesdropper, and model 1b (with an untrusted helper) further requires that the two keys are concealed from the helper in addition to the eavesdropper. The asymmetric key generation models 2a and 2b are the same as symmetric key generation models 1a and 1b, respectively, except that the key $K_{2}$ is further required to be concealed from terminal $\mathcal {X}_{1}$ . For all models studied, the key capacity region is established by designing a unified achievable strategy to achieve the cut-set outer bounds. We also study the problem of generating more than two keys and characterize its key capacity region when all the cellular terminals are required to generate independent keys with the base station.