Key Generation Over Wiretap Models With Non-Causal Side Information

Abstract

The key agreement problem over a state-dependent wiretap channel with a parallel one-way public channel in the forward direction is studied. It is assumed that the channel state information (CSI) is non-causally known at the transmitter. In this paper, the effect of the public channel and the CSI on the key generation is investigated, and the key capacity as a function of public channel capacity $C_{\!_{P}}$ , $C_{\!_{K}}(C_{\!_{P}}\!)$ , is sought for a discrete memoryless (DM) model and a Gaussian model, in which the CSI is an additive white Gaussian interference. For each model, a lower bound and an upper bound on the key capacity are derived, and $C_{\!_{K}}(\infty )$ is achieved as the bounds are asymptotically tight. For any DM wiretap channel, it is shown that there exists a finite capacity $C^{*}_{\!_{P}}$ beyond which $C_{\!_{K}}(C_{\!_{P}}\!)=C_{\!_{K}}(C^{*}_{\!_{P}}\!)$ . If the CSI is also fully known at the legitimate receiver, it is proved that the public channel has no effect on the key capacity. For the Gaussian model, the achievable key rate is a strictly increasing function of $C_{\!_{P}}$ in general. In addition, $C_{\!_{K}}(C_{\!_{P}}\!)$ is attained in both the low signal-to-interference ratio (SIR) regime and the high SIR regime. In the low SIR regime, the public channel cooperates with the transmitter for the key generation from the known interference. In the high SIR regime, however, the public channel makes negligible contribution to the key generation.