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24
Providing Secrecy With Structured Codes: Tools and Applications to TwoUser Gaussian Channels
, 2009
"... Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured c ..."
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Cited by 45 (17 self)
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Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured codes are useful for providing secrecy, and show how to compute the secrecy rate when structured codes are used. In particular, we solve the problem of bounding equivocation rates with one important class of structured codes, i.e., nested lattice codes. Having established this result, we next demonstrate the use of structured codes for secrecy in twouser Gaussian channels. In particular, with structured codes, we prove that a positive secure degree of freedom is achievable for a large class of fully connected Gaussian channels as long as the channel is not degraded. By way of this, for these channels, we establish that structured codes outperform Gaussian random codes at high SNR. This class of channels include the twouser multiple access wiretap channel, the twouser interference channel with confidential messages and the twouser interference wiretap channel. A notable consequence of this result is that, unlike the case with Gaussian random codes, using structured codes for both transmission and cooperative jamming, it is possible to achieve an arbitrary large secrecy rate given enough power.
Secure Degrees of Freedom of the Gaussian Wiretap Channel with Helpers
"... Abstract — The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the secure d.o.f. of the Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap cha ..."
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Cited by 22 (16 self)
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Abstract — The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the secure d.o.f. of the Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap channel with a helper is 1. Our achievable scheme is based on 2 real interference alignment 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 secure d.o.f. in this case is M
Ergodic Secret Alignment
, 2012
"... In this paper, we introduce two new achievable schemes for the fading multiple access wiretap channel (MACWT). In the model that we consider, we assume that perfect knowledge of the state of all channels is available at all the nodes in a causal fashion. Our schemes use this knowledge together wit ..."
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Cited by 21 (17 self)
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In this paper, we introduce two new achievable schemes for the fading multiple access wiretap channel (MACWT). In the model that we consider, we assume that perfect knowledge of the state of all channels is available at all the nodes in a causal fashion. Our schemes use this knowledge together with the timevarying nature of the channel model to align the interference from different users at the eavesdropper perfectly in a onedimensional space while creating a higher dimensionality space for the interfering signals at the legitimate receiver, hence allowing for better chance of recovery. While we achieve this alignment through signal scaling at the transmitters in our first scheme (scalingbased alignment), we let nature provide this alignment through the ergodicity of the channel coefficients in the second scheme [ergodic secret alignment (ESA)] [1], [2]. For each scheme, we obtain the resulting achievable secrecy rate region. We show that the secrecy rates achieved by both schemes in the twouser fading MACWT scale with signaltonoise ratio (SNR) as 1 2 log(SNR). Hence, we show the suboptimality of the independent identically distributed (i.i.d.) Gaussian signalingbased schemes with and without cooperative jamming by showing that the secrecy rates achieved using i.i.d. Gaussian signaling with cooperative jamming do not scale with SNR. In addition, we introduce an improved version of our ESA scheme where we incorporate cooperative jamming to achieve higher secrecy rates. Moreover, we derive the necessary optimality conditions for the power control policy that maximizes the secrecy sum rate achievable by our ESA scheme when used solely and with cooperative jamming. Finally, we discuss the extension of the proposed schemes to the case where there are more than two users and show that, for theuser fading MACWT, each of the two schemes achieves secrecy sum rate that scales with SNR as 1 log(SNR).
Secure Degrees of Freedom of Onehop Wireless Networks
, 2012
"... We study the secure degrees of freedom (d.o.f.) of onehop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel, Gaussian broadcast channel with confidential messages, Gaussian interference channel with confidential messages, and Gaussian multiple a ..."
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Cited by 19 (12 self)
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We study the secure degrees of freedom (d.o.f.) of onehop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel, Gaussian broadcast channel with confidential messages, Gaussian interference channel with confidential messages, and Gaussian multiple access wiretap channel. The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the secure d.o.f. of the Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap channel with a helper is 1 2. Our achievable scheme is based on real interference alignment 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 secure d.o.f. in this case is M M+1. We then generalize this approach to more general network structures with multiple messages. We show that the sum secure d.o.f. of the Gaussian broadcast channel with confidential messages and M helpers is 1, the sum secure d.o.f. of the twouser interference channel with confidential messages is 2 3, the sum secure d.o.f. of the twouser interference channel with confidential messages and M helpers is 1, and the sum secure d.o.f. of the Kuser multiple access wiretap channel is
Secure Degrees of Freedom for Gaussian Channels with Interference: Structured Codes Outperform Gaussian Signaling
"... Abstract—In this work, we prove that a positive secure degree of freedom is achievable for a large class of real Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wiretap channel, the 2user interference channel with confidential ..."
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Cited by 17 (2 self)
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Abstract—In this work, we prove that a positive secure degree of freedom is achievable for a large class of real Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wiretap channel, the 2user interference channel with confidential messages, the 2user interference channel with an external eavesdropper. Best known achievable schemes to date for these channels use Gaussian signaling. In this work, we show that structured codes outperform Gaussian random codes at high SNR when channel gains are real numbers. I.
Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey
"... This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers, without rely ..."
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Cited by 16 (1 self)
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This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers, without relying on higherlayer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on informationtheoretic security. We then describe the evolution of secure transmission strategies from pointtopoint channels to multipleantenna systems, followed by generalizations to multiuser broadcast, multipleaccess, interference, and relay networks. Secretkey generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of interdisciplinary approaches based on game theory and stochastic geometry. The associated problem of physical layer message authentication is also briefly introduced. The survey concludes with observations on potential research directions in this area.
The Gaussian ManytoOne Interference Channel with Confidential Messages
"... Abstract—We investigate the Kuser manytoone interference channel with confidential messages in which the Kth user experiences interference from all other K − 1 users, and is at the same time treated as an eavesdropper to all the messages of these users. We derive achievable rates and an upper bou ..."
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Cited by 11 (5 self)
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Abstract—We investigate the Kuser manytoone interference channel with confidential messages in which the Kth user experiences interference from all other K − 1 users, and is at the same time treated as an eavesdropper to all the messages of these users. We derive achievable rates and an upper bound on the sum rate for this channel and show that the gap between the achievable sum rate and its upper bound is log 2 (K − 1) bits per channel use under very strong interference, when the interfering users have equal power constraints and interfering link channel gains. The main contributions of this work are: (i) nested lattice codes are shown to provide secrecy when interference is present, (ii) a secrecy sum rate upper bound is found for strong interference regime and (iii) it is proved that under very strong interference and a symmetric setting, the gap between the achievable sum rate and the upper bound is constant with respect to transmission powers. I.
Unified Secure DoF Analysis of KUser Gaussian Interference Channels
"... Abstract—We determine the exact sum secure degrees of freedom (d.o.f.) of the Kuser Gaussian interference channel. We consider three different secrecy constraints: 1) Kuser interference channel with one external eavesdropper (ICEE), 2) Kuser interference channel with confidential messages (ICCM ..."
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Cited by 10 (5 self)
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Abstract—We determine the exact sum secure degrees of freedom (d.o.f.) of the Kuser Gaussian interference channel. We consider three different secrecy constraints: 1) Kuser interference channel with one external eavesdropper (ICEE), 2) Kuser interference channel with confidential messages (ICCM), and 3) Kuser interference channel with confidential messages and one external eavesdropper (ICCMEE). We show that for all of these three cases, the exact sum secure d.o.f. is K(K−1)
On the Sum Secure Degrees of Freedom of TwoUnicast Layered Wireless Networks
"... Abstract—In this paper, we study the sum secure degrees of freedom (d.o.f.) of twounicast layered wireless networks. Without a secrecy constraint, the sum d.o.f. of this class of networks was studied by [1] and shown to take only one of three possible values: 1, 3/2 and 2, for all network configura ..."
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Cited by 7 (4 self)
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Abstract—In this paper, we study the sum secure degrees of freedom (d.o.f.) of twounicast layered wireless networks. Without a secrecy constraint, the sum d.o.f. of this class of networks was studied by [1] and shown to take only one of three possible values: 1, 3/2 and 2, for all network configurations. We consider the setting where the message of each sourcedestination pair must be kept informationtheoretically secure from the unintended receiver. We show that the sum secure d.o.f. can take 0, 1, 3/2, 2 and at most countably many other positive values, which we enumerate. s1 u1 u2 u3 t1 t2 s2 w1 w2 w3