Helper-assisted asymmetric two key generation

The problem of simultaneously generating an asymmetric key pair with assistance of a helper is studied. In this setting, each of four terminals, i.e., a base station X₀, two cellular nodes X₁ and X₂, and a helper X₃, observes a component of correlated sources. The cellular nodes X₁ and X₂ wish to generate secret keys K₁ and K₂ with the base station X₀, respectively, under the help of terminal X₃. Both keys should be concealed from an eavesdropper that has access to the public discussion, while K₂ is also required to be concealed from terminal X₁. An outer bound on the key capacity region is derived. It is shown to be achievable under certain condition, and hence the key capacity region is characterized under such condition.