Secret Sharing over Fast-Fading MIMO Wiretap Channels

Abstract

Secret sharing over the fast-fading MIMO wiretap channel is considered. A source and a destination try to share secret information over a fast-fading MIMO channel in the presence of an eavesdropper who also makes channel observations that are different from but correlated to those made by the destination. An interactive, authenticated public channel with unlimited capacity is available to the source and destination for the secret sharing process. This situation is a special case of the "channel model with wiretapper" considered by Ahlswede and Csiszár. An extension of their result to continuous channel alphabets is employed to evaluate the key capacity of the fast-fading MIMO wiretap channel. The effects of spatial dimensionality provided by the use of multiple antennas at the source, destination, and eavesdropper are then investigated.

A remark on secret-key generation over correlated fading channels

“…Proposition 1: An achievable rate using the jointbinning scheme in [10] for the Gaussian fading channel with receiver-only CSI and a Gaussian input distribution x ∼ CN (0, P ) is:…”

“…The result can be extended to continuous valued channel gains using quantization arguments. We omit the details in this paper, but refer the reader to [10], [15] for a similar analysis.…”

“…When the output symbols at the receiver (y r ) and eavesdroppers (y e ) are conditionally independent given the input symbol x, i.e., y r ↔ x ↔ y e holds then C = max p(x) I(x; y r |y e ). Building upon these results, reference [10] establishes the secret-key capacity for a class of fading channels. The fading coefficients are sampled i.i.d.…”

“…The secret-key generation codebook is then used conditioned on this knowledge at all the terminals. We observe that the capacity achieving technique in [10], [12] that involves joint binning of the receiver output and channel gains is sub-optimal. We then extend these results to the case when the transmitter also has access to a noisy CSI of the legitimate receiver.…”

“…While the capacity results in [10], [12] provide useful fundamental limits, they crucially depend on the fading channel gains of the receiver and the eavesdropper being independent. When this condition does not hold, the proposed coding schemes may not be optimal.…”