On the diversity-multiplexing tradeoff of secret-key agreement over multiple-antenna channels

We consider secret-key agreement with public discussion over Rayleigh fading quasi-static channels. First, the secret-key diversity gain and the secret-key multiplexing gain are defined. Then, the secret-key diversity multiplexing tradeoff (DMT) is established. The eavesdropper is shown to “steal” only transmit antennas. We show that likewise the DMT without secrecy constraint, the secret-key DMT is the same either with or without full channel state information (CSI) at the transmitter (CSI-T). This insensitivity of secret-key DMT toward CSI-T highlights a fundamental difference between secret-key agreement and the wiretap channel whose secret DMT depends crucially on CSI-T. Several secret-key DMT-achieving schemes are presented in case of full CSI-T.