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Secure communication in stochastic wireless networks – Part II: Maximum rate and collusion
 IEEE Trans. Inf. Forens.Security
, 2012
"... Abstract—In Part I of this paper, we introduced the intrinsically secure communications graph (graph)—a random graph which describes the connections that can be established with strong secrecy over a largescale network, in the presence of eavesdroppers. We focused on the local connectivity of the ..."
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Cited by 26 (4 self)
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Abstract—In Part I of this paper, we introduced the intrinsically secure communications graph (graph)—a random graph which describes the connections that can be established with strong secrecy over a largescale network, in the presence of eavesdroppers. We focused on the local connectivity of thegraph, and proposed techniques to improve it. In this second part, we characterize the maximum secrecy rate (MSR) that can be achieved between a node and its neighbors. We then consider the scenario where the eavesdroppers are allowed to collude, i.e., exchange and combine information. We quantify exactly how eavesdropper collusion degrades the secrecy properties of the network, in comparison to a noncolluding scenario. Our analysis helps clarify how the presence of eavesdroppers can jeopardize the success of wireless physicallayer security. Index Terms—Colluding eavesdroppers, physicallayer security, secrecy capacity, stochastic geometry, wireless networks. I.
Percolation and connectivity in the intrinsically secure communications graph
 IEEE Trans. Inf. Theory
, 2012
"... Abstract—The ability to exchange secret information is critical to many commercial, governmental, and military networks. The intrinsically secure communications graph (graph) is a random graph which describes the connections that can be securely established over a largescale network, by exploitin ..."
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Cited by 9 (3 self)
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Abstract—The ability to exchange secret information is critical to many commercial, governmental, and military networks. The intrinsically secure communications graph (graph) is a random graph which describes the connections that can be securely established over a largescale network, by exploiting the physical properties of the wireless medium. This paper aims to characterize the global properties of the graph in terms of 1) percolation on the infinite plane, and 2) full connectivity on a finite region. First, for the Poisson graph defined on the infinite plane, the existence of a phase transition is proven, whereby an unbounded component of connected nodes suddenly arises as the density of legitimate nodes is increased. This shows that longrange secure communication is still possible in the presence of eavesdroppers. Second, full connectivity on a finite region of the Poisson graph is considered. The exact asymptotic behavior of full connectivity in the limit of a large density of legitimate nodes is characterized. Then, simple, explicit expressions are derived in order to closely approximate the probability of full connectivity for a finite density of legitimate nodes. These results help clarify how the presence of eavesdroppers can compromise longrange secure communication. Index Terms—Connectivity, percolation, physicallayer security, stochastic geometry, wireless networks.
The Secrecy Capacity Region of the Gaussian MIMO Broadcast Channel
, 2009
"... In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wiretapper also receives the transmitted signal via another MIMO channel. First we assumed that the channels are degraded and ..."
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In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wiretapper also receives the transmitted signal via another MIMO channel. First we assumed that the channels are degraded and the wiretapper has the worst channel. We establish the capacity region of this scenario. Our achievability scheme is a combination of the superposition of Gaussian codes and randomization within the layers which we will refer to as Secret Superposition Coding. For the outerbound, we use the notion of enhanced channel to show that the secret superposition of Gaussian codes is optimal. We show that we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged. Then we extend the result of the degraded case to nondegraded case. We show that the secret superposition of Gaussian codes along with successive decoding cannot work when the channel is not degraded. we develop an Secret Dirty Paper Coding (SDPC) scheme and show that SDPC is optimal for this channel. Finally, We investigate practical characterizations for the specific scenario in which the transmitter and the eavesdropper have multiple antennas, while both intended receivers have a single antenna. We characterize the secrecy capacity region in terms of generalized eigenvalues of the receivers channel and the eavesdropper channel. We refer to this configuration as the MISOME case. In high SNR we show that the capacity region is a convex closure of two rectangular regions.
Gaussian MIMO multireceiver wiretap channel
, 2009
"... Abstract — We consider the Gaussian multipleinput multipleoutput (MIMO) multireceiver wiretap channel, and derive the secrecy capacity region of this channel for the most general case. We first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same num ..."
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Abstract — We consider the Gaussian multipleinput multipleoutput (MIMO) multireceiver wiretap channel, and derive the secrecy capacity region of this channel for the most general case. We first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices exhibit a positive semidefinite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas, however there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that a variant of dirtypaper coding with Gaussian signals is optimal. I.
Intrinsically Secure Communication in LargeScale Wireless Networks
"... The ability to exchange secret information is critical to many commercial, governmental, and military networks. Informationtheoretic security widely accepted as the strictest notion of security relies on channel coding techniques that exploit the inherent randomness of the propagation channels ..."
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Cited by 1 (1 self)
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The ability to exchange secret information is critical to many commercial, governmental, and military networks. Informationtheoretic security widely accepted as the strictest notion of security relies on channel coding techniques that exploit the inherent randomness of the propagation channels to significantly strengthen the security of digital communications systems. Motivated by recent developments in the field, this thesis aims at a characterization of the fundamental secrecy limits of largescale wireless networks. We start by introducing an informationtheoretic definition of the intrinsically secure communications graph (iSgraph), based on the notion of strong secrecy. The iSgraph is a random geometric graph which captures the connections that can be securely established over a largescale network, in the presence of spatially scattered eavesdroppers. Using fundamental tools from stochastic geometry, we analyze how the spatial densities of legitimate and eavesdropper nodes influence various properties of the Poisson iSgraph, such as the distribution of node degrees, the node isolation probabil
On MMSE Properties and IMMSE Implications in Parallel MIMO Gaussian Channels
"... Abstract—This paper extends the “single crossing point ” property of the scalar MMSE function, derived by Guo, Shamai and Verdú (first presented in ISIT 2008), to the parallel degraded MIMO scenario. It is shown that the matrix Q(t), which is the difference between the MMSE assuming a Gaussian input ..."
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Abstract—This paper extends the “single crossing point ” property of the scalar MMSE function, derived by Guo, Shamai and Verdú (first presented in ISIT 2008), to the parallel degraded MIMO scenario. It is shown that the matrix Q(t), which is the difference between the MMSE assuming a Gaussian input and the MMSE assuming an arbitrary input, has, at most, a single crossing point for each of its eigenvalues. Together with the IMMSE relationship, a fundamental connection between Information Theory and Estimation Theory, this new property is employed to derive results in Information Theory. As a simple application of this property we provide an alternative converse proof for the broadcast channel (BC) capacity region under covariance constraint in this specific setting. I.
Research Article An MMSE Approach to the Secrecy Capacity of the MIMO Gaussian Wiretap Channel
"... This paper provides a closedform expression for the secrecy capacity of the multipleinput multiple output (MIMO) Gaussian wiretap channel, under a powercovariance constraint. Furthermore, the paper specifies the input covariance matrix required in order to attain the capacity. The proof uses the ..."
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This paper provides a closedform expression for the secrecy capacity of the multipleinput multiple output (MIMO) Gaussian wiretap channel, under a powercovariance constraint. Furthermore, the paper specifies the input covariance matrix required in order to attain the capacity. The proof uses the fundamental relationship between information theory and estimation theory in the Gaussian channel, relating the derivative of the mutual information to the minimum meansquare error (MMSE). The proof provides the missing intuition regarding the existence and construction of an enhanced degraded channel that does not increase the secrecy capacity. The concept of enhancement has been used in a previous proof of the problem. Furthermore, the proof presents methods that can be used in proving other MIMO problems, using this fundamental relationship. Copyright © 2009 Ronit Bustin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.