Secure physical-layer key generation protocol and key encoding in wireless communications

Wireless communication between two nodes in a multi-path, multi-hop network does not require that the forward transmission path and the reverse one are the same. However, if a physical-layer security scheme based on mutual channel-state-information (CSI) is used, they at least have to make sure that they use the same channels for secret-key generation. A protocol is proposed in this paper to achieve that purpose in a secure manner. An information-theoretic analysis of physical-layer key generation given in states that there are vulnerable key symbols that might be estimated by eavesdroppers. In this paper, we show how to protect those key symbols by means of physical-layer key encoding. We provide necessary and sufficient conditions on the code in order to achieve perfect secrecy, even when the eavesdropper knows the code, and derive the asymptotic code rate accordingly. We also discuss how to design the code when the number of vulnerable key symbols are not known.