Achieving perfect secrecy capacity of an asymmetric bidirectional relay channel

In this paper, we propose a perfectly secure transmission scheme for an asymmetric bidirectional relay channel. The scheme is based on nested lattice coding with keys generated at both legitimate nodes, consisting of unshared random dithers. These keys are indexed by the past secret mutual transmissions and kept secret from other nodes. This model allows legitimate users to transmit safely their secret messages jointly with the artificial noise (dither) without the help of any dedicated internal or external jamming source. Besides, this scheme achieves perfect secrecy at the best known rate for the relay channel in presence of not only an untrusted relay, but also one passive eavesdropper at uplink and one at downlink, even if both eavesdropper channels are noiseless.