Physical-Layer Secret and Private Key Generation in Wireless Relay Networks With Correlated Eavesdropping Channels

This paper investigates the performance of key generation between two nodes assisted by a relay in the presence of correlated eavesdropping channels. A cooperative jamming scheme is utilized to impose superimposed channel measurements on the relay and eavesdropper. Both lower and upper bounds on key capacities for both secret key (SK) and private key (PK) generation are evaluated, where the lower bounds are derived by using minimum mean square error and zero forcing methods for channel estimation, and the upper bounds are derived by formulating several enhanced discrete memoryless source (DMS) models. The analytical expressions are further simplified in the high signal-to-noise ratio (SNR) regime. We discover that one of the two legitimate channels should specialize in playing a role of jamming the relay or eavesdropper. We also demonstrate that the derived lower and upper bounds are tight when the eavesdropping channels are lowly or highly correlated. When the eavesdropping channels are uncorrelated, the SK and PK capacities can be determined since the corresponding upper and lower bounds are equal. Moreover, at high SNRs, a constant gap exists between the SK/PK upper and lower bounds as the correlation coefficient becomes one.