We consider a group of @math trusted and authenticated nodes that aim to create a shared secret key @math over a wireless channel in the presence of an eavesdropper Eve. We assume that there exists a state dependent wireless broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free, noiseless and unlimited rate public channel which is also overheard by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for "linear deterministic" wireless broadcast channels. This model generalizes the packet erasure model studied in literature for wireless broadcast channels. For "state-dependent Gaussian" wireless broadcast channels, we propose an achievability scheme based on a multi-layer wiretap code. Finding the best achievable secret key generation rate leads to solving a non-convex power allocation problem. We show that using a dynamic programming algorithm, one can obtain the best power allocation for this problem. Moreover, we prove the optimality of the proposed achievability scheme for the regime of high-SNR and large-dynamic range over the channel states in the (generalized) degrees of freedom sense.
The main contributions of the paper can be summarized as follows: For the secret key sharing problem among @math trusted nodes that have access to a deterministic broadcast channel and to a public discussion channel, we completely characterize the secret key generation capacity. This result can be considered an extension to the erasure channel case @cite_17 and produces information theoretic secure key regardless of the computational power of the eavesdropper Eve. By using ideas from the code design for deterministic broadcast channels, we devise a coding scheme based on a nested message set, degraded channel wiretap code (also see @cite_10 ). In general, we characterize the achievable secret key generation rate which is given by a non-convex power allocation optimization problem. Moreover, we derive an upper bound on the secrecy rate and show that for the high-SNR, high-dynamic range regime, our proposed scheme is optimal in a degree of freedom sense. Although, in the proposed scheme, the best achievable secrecy rate is described by the solution of a non-convex optimization problem, we the optimization problem by using dynamic programming technique.
@cite_10 @cite_17
2162821768 2546022252
A (layered) broadcast approach is studied for fading wiretap channels. The basic idea is to employ superposition coding to encode information into a number of layers and use stochastic encoding for each layer to keep the corresponding information secret from an eavesdropper. The legitimate receiver successively decodes information one layer after another by canceling the interference caused by the layers that the receiver has already decoded. The advantage of this approach is that the transmitter does not need to know the channel states to the legitimate receiver and the eavesdropper, but can still securely transmit certain layers of information to the legitimate receiver. The layers that can be securely transmitted are determined by the channel states to the legitimate receiver and the eavesdropper. The Gaussian wiretap channel with fixed channel gains is first studied to illustrate the idea of the broadcast approach. Three cases of block fading wiretap channels with a stringent delay constraint are then studied, in which either the legitimate receiver's channel, the eavesdropper's channel, or both channels are fading. For each case, the secrecy rate that can be achieved by using the broadcast approach is obtained, and the optimal power allocation over the layers (or the conditions on the optimal power allocation) is also derived. We consider a group of m trusted nodes that aim to create a shared secret key K over a wireless channel in the presence an eavesdropper Eve. We assume an erasure broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free public channel which is observed by Eve. For this setup we characterize the secret key generation capacity and propose an achievability scheme that is computationally efficient and employs techniques from network coding. Surprisingly, whether we have m = 2 nodes, or an arbitrary number m of nodes, we can establish a shared secret key among them at the same rate, independently of m.1