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The Interference Wiretap Channel with an Arbitrarily Varying Eavesdropper: Aligning Interference with Artificial Noise
, 2012
"... Abstract—In this work, a Gaussian twouser MIMO interference channel is considered in the presence of an external eavesdropper whose channel is completely unknown to the legitimate communication parties and can be varying in an arbitrary fashion from one channel use to the next. We improve our recen ..."
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Abstract—In this work, a Gaussian twouser MIMO interference channel is considered in the presence of an external eavesdropper whose channel is completely unknown to the legitimate communication parties and can be varying in an arbitrary fashion from one channel use to the next. We improve our recent result by deriving a larger achievable secrecy degrees of freedom region. In the achievable scheme, the transmitter injects artificial noise to confuse the eavesdropper, and at the same time aligns the injected noise with the interference from the other user at the intended receiver. The achieved secure degrees of freedom are shown to be closely connected to the rank of the effective channel matrix through which the eavesdropper observes the artificial noise. The precoding matrix is then designed to ensure that this rank cannot be reduced under any possible Eve’s channel state. I.
GC'11 Workshop on PhysicalLayer Security Gaussian Twoway Wiretap Channel with an Arbitrarily Varying Eavesdropper
"... Abstract—In this work, we derive the secrecy degrees of freedom (s.d.o.f.) region of the Gaussian twoway wiretap channel in which the eavesdropper channel state is arbitrarily varying and is unknown to the legitimate nodes. We prove that the s.d.o.f. region is identical to that when the eavesdroppe ..."
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Abstract—In this work, we derive the secrecy degrees of freedom (s.d.o.f.) region of the Gaussian twoway wiretap channel in which the eavesdropper channel state is arbitrarily varying and is unknown to the legitimate nodes. We prove that the s.d.o.f. region is identical to that when the eavesdropper channel is fixed and globally known. A multistage coding scheme that combines secret key generation and confidential message transmission is developed to prove achievability. The confidentiality guarantee provided in this work is in the sense of strong secrecy.
The Secrecy Capacity of Compound Gaussian MIMO Wiretap Channels
"... Abstract—Strong secrecy capacity of compound wiretap channels is studied. The known lower bounds for the secrecy capacity of compound finitestate memoryless channels under discrete alphabets are extended to arbitrary uncertainty sets and continuous alphabets under the strong secrecy criterion. The ..."
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Abstract—Strong secrecy capacity of compound wiretap channels is studied. The known lower bounds for the secrecy capacity of compound finitestate memoryless channels under discrete alphabets are extended to arbitrary uncertainty sets and continuous alphabets under the strong secrecy criterion. The conditions under which these bounds are tight are given. Under the saddlepoint condition, the compound secrecy capacity is shown to be equal to that of the worstcase channel. Based on this, the compound Gaussian MIMO wiretap channel is studied under the spectral norm constraint and without the degradedness assumption. First, it is assumed that only the eavesdropper channel is unknown, but is known to have a bounded spectral norm (maximum channel gain). The compound secrecy capacity is established in a closed form and the optimal signaling is identified: the compound capacity equals the worstcase channel
Secure DoF of MIMO Rayleigh Block Fading Wiretap Channels with No CSI Anywhere
"... Abstract—We consider the block Rayleigh fading multipleinput multipleoutput (MIMO) wiretap channel with no prior channel state information (CSI) available at any of the terminals. The channel gains remain constant in a coherence time of T symbols, and then change to another independent realization ..."
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Abstract—We consider the block Rayleigh fading multipleinput multipleoutput (MIMO) wiretap channel with no prior channel state information (CSI) available at any of the terminals. The channel gains remain constant in a coherence time of T symbols, and then change to another independent realization. The transmitter, the legitimate receiver and the eavesdropper have nt, nr and ne antennas, respectively. We determine the exact secure degrees of freedom (s.d.o.f.) of this system when T 2min(nt; nr). We show that, in this case, the s.d.o.f. is exactly (min(nt; nr) ne)+(T min(nt; nr))=T. The first term can be interpreted as the eavesdropper with ne antennas taking away ne antennas from both the transmitter and the legitimate receiver. The second term can be interpreted as a fraction of s.d.o.f. being lost due to the lack of CSI at the legitimate receiver. In particular, the fraction loss, min(nt; nr)=T, can be interpreted as the fraction of channel uses dedicated to training the legitimate receiver for it to learn its own CSI. We prove that this s.d.o.f. can be achieved by employing a constant norm channel input, which can be viewed as a generalization of discrete signalling to multiple dimensions. I.
1Secure Degrees of Freedom of MIMO Rayleigh Block Fading Wiretap Channels with No CSI Anywhere
"... We consider the block Rayleigh fading multipleinput multipleoutput (MIMO) wiretap channel with no prior channel state information (CSI) available at any of the terminals. The channel gains remain constant within a coherence interval of T symbols, and then change to another independent realization ..."
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We consider the block Rayleigh fading multipleinput multipleoutput (MIMO) wiretap channel with no prior channel state information (CSI) available at any of the terminals. The channel gains remain constant within a coherence interval of T symbols, and then change to another independent realization in the next coherence interval. The transmitter, the legitimate receiver and the eavesdropper have nt, nr and ne antennas, respectively. We determine the exact secure degrees of freedom (s.d.o.f.) of this system when T ≥ 2min(nt, nr). We show that, in this case, the s.d.o.f. is exactly equal to (min(nt, nr) − ne)+(T −min(nt, nr))/T. The first term in this expression can be interpreted as the eavesdropper with ne antennas taking away ne antennas from both the transmitter and the legitimate receiver. The second term can be interpreted as a fraction of the s.d.o.f. being lost due to the lack of CSI at the legitimate receiver. In particular, the fraction loss, min(nt, nr)/T, can be interpreted as the fraction of channel uses dedicated to training the legitimate receiver for it to learn its own CSI. We prove that this s.d.o.f. can be achieved by employing a constant norm channel input, which can be viewed as a generalization of discrete signalling to multiple dimensions. I.
The Effect of Eavesdroppers on Network Connectivity: A Secrecy Graph Approach
"... Abstract—This paper investigates the effect of eavesdroppers on networkconnectivity,usingawiretapmodelandpercolation theory. The wiretap model captures the effect of eavesdroppers on link security. A link exists between two nodes only if the secrecy capacity of that link is positive. Network connec ..."
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Abstract—This paper investigates the effect of eavesdroppers on networkconnectivity,usingawiretapmodelandpercolation theory. The wiretap model captures the effect of eavesdroppers on link security. A link exists between two nodes only if the secrecy capacity of that link is positive. Network connectivity is defined in a percolation sense, i.e., connectivity exists if an infinite connected component exists in the corresponding secrecy graph. We consider uncertainty in location of eavesdroppers, which ismodeled directly at the network level as correlated failures in the secrecy graph. Our approach attempts to bridge the gap between physical layer security under uncertain channel state information and network level connectivity under secrecy constraints. For square and triangular lattice secrecy graphs, we obtain bounds on the percolation threshold, which is the critical value of the probability of occurrence of an eavesdropper, abovewhich network connectivity does not exist. For Poissonsecrecygraphs,degreedistributionandmeanvalueofupper and lower bounds on node degree are obtained. Further, inner and outer bounds on the achievable region for network connectivity are obtained.Bothanalyticandsimulationresultsshowthatuncertainty in location of eavesdroppers has a dramatic effect on network connectivity in a secrecy graph. Index Terms—Connectivity, eavesdropper, lattice, percolation, physical layer security, Poisson, secrecy graph. I.
SECURE DEGREES OF FREEDOM OF WIRELESS NETWORKS
, 2014
"... This dissertation studies the security of wireless interference networks from an informationtheoretic point of view. In this setting, several transmitterreceiver pairs wish to have secure communication against the eavesdropper(s). The central goal of this dissertation is to develop a framework bas ..."
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This dissertation studies the security of wireless interference networks from an informationtheoretic point of view. In this setting, several transmitterreceiver pairs wish to have secure communication against the eavesdropper(s). The central goal of this dissertation is to develop a framework based on informationtheoretic principles to determine the complete solutions for the signaling schemes in different wireless interference networks with large transmit powers, and derive the corresponding fundamental limits in terms of the secure degrees of freedom (s.d.o.f.). First, we study onehop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel with helpers, Gaussian broadcast channel (BC) with confidential messages, Gaussian interference channel (IC) with confidential messages, and Gaussian multiple access (MAC) wiretap channel. The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the s.d.o.f. of the Gaussian wiretap channel with no helpers is zero. We show that the exact s.d.o.f. of the Gaussian wiretap channel with a helper is 1. Our achievable scheme is based on real interference alignment 2 and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact s.d.o.f. in this case is M. We then generalize this approach to more
Wireless Physical Layer Security with Imperfect Channel State Information: A Survey
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SUBMITTED FOR PUBLICATION 1 Secrecy Degrees of Freedom of Wireless X Networks Using Artificial Noise Alignment
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