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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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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
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.
Secure Degrees of Freedom of the Gaussian Multiple Access Wiretap Channel
"... Abstract—We show that the sum secure degrees of freedom (d.o.f.) of the Kuser Gaussian multiple access (MAC) wiretap channel is K(K−1). Our achievability is based on real interferK(K−1)+1 ence alignment and structured cooperative jamming. Each user divides its message into K − 1 submessages, and ..."
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Cited by 10 (6 self)
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Abstract—We show that the sum secure degrees of freedom (d.o.f.) of the Kuser Gaussian multiple access (MAC) wiretap channel is K(K−1). Our achievability is based on real interferK(K−1)+1 ence alignment and structured cooperative jamming. Each user divides its message into K − 1 submessages, and sends a linear combination of signals carrying these submessages together with a structured cooperative jamming signal. All cooperative jamming signals are aligned in a single dimension at the legitimate receiver allowing for reliable decoding of the message carrying signals by the legitimate receiver. Each cooperative jamming signal is aligned with K − 1 message signals at the eavesdropper limiting the information leakage rate to the eavesdropper. We provide a matching converse establishing the exact sum secure d.o.f. of the Gaussian MAC wiretap channel as
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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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
Secure Degrees of Freedom of KUser Gaussian Interference Channels: A Unified View
, 2013
"... 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) ..."
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Cited by 5 (4 self)
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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) 2K−1. We show converses for ICEE and ICCM, which imply a converse for ICCMEE. We show achievability for ICCMEE, which implies achievability for ICEE and ICCM. We develop the converses by relating the channel inputs of interfering users to the reliable rates of the interfered users, and by quantifying the secrecy penalty in terms of the eavesdroppers’ observations. Our achievability uses structured signaling, structured cooperative jamming, channel prefixing, and asymptotic real interference alignment. While the traditional interference alignment provides some amount of secrecy by mixing unintended signals in a smaller subspace at every receiver, in order to attain the optimum sum secure d.o.f., we incorporate structured cooperative jamming into the achievable scheme, and intricately design the structure of all of the transmitted signals jointly.
MISO Broadcast Channels with Confidential Messages and Alternating CSIT
"... Abstract—We study the twouser multipleinput singleoutput (MISO) broadcast channel with confidential messages under the assumption of alternating channel state information at the transmitter (CSIT). We consider two alternating states: PD and DP which occur for an equal fraction of time. In state P ..."
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Cited by 3 (3 self)
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Abstract—We study the twouser multipleinput singleoutput (MISO) broadcast channel with confidential messages under the assumption of alternating channel state information at the transmitter (CSIT). We consider two alternating states: PD and DP which occur for an equal fraction of time. In state PD, the CSIT of the channel to the first receiver is available perfectly without delay (P) while that of the second receiver is available with a delay of one channel use (D); in state DP, the roles of the receivers are reversed. We characterize the exact secure degrees of freedom (s.d.o.f.) region of this system, and show as a corollary that the sum s.d.o.f. is 3 2. We observe that this sum s.d.o.f. is the same as what can be achieved by the states PP and DD occurring for equal fraction of time. Though the s.d.o.f. of the system in the states PD and DP is not known individually, we are able to establish the s.d.o.f. region when the two states alternate and occur for an equal fraction of the time. I.
Secure degrees of freedom region of the Gaussian multiple access wiretap channel
 In Asilomar Conference
, 2013
"... Abstract — [1] showed that the sum secure degrees of freedom (s.d.o.f.) of the Kuser Gaussian multiple access (MAC) wiretap channel is K(K−1) K(K−1)+1. In this paper, we determine the entire s.d.o.f. region of the Kuser Gaussian MAC wiretap channel. The converse follows from a middle step in the c ..."
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Cited by 3 (2 self)
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Abstract — [1] showed that the sum secure degrees of freedom (s.d.o.f.) of the Kuser Gaussian multiple access (MAC) wiretap channel is K(K−1) K(K−1)+1. In this paper, we determine the entire s.d.o.f. region of the Kuser Gaussian MAC wiretap channel. The converse follows from a middle step in the converse of [1]. The achievability follows from exploring the polytope structure of the converse region, determining its extreme points, and then showing that each extreme point can be achieved by an muser MAC wiretap channel with K−m helpers, i.e., by setting K−m users ’ secure rates to zero and utilizing them as pure (structured) cooperative jammers. A byproduct of our result is that the sum s.d.o.f. is achieved only at one corner point of the s.d.o.f. region. I.
MIMO Broadcast Channel with an Unknown Eavesdropper: Secrecy Degrees of Freedom
"... Abstract—We study a multiantenna broadcast channel with two legitimate receivers and an external eavesdropper. We assume that the channel matrix of the eavesdropper is unknown to the legitimate terminals but satisfies a maximum rank constraint. As our main result we characterize the associated secr ..."
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Abstract—We study a multiantenna broadcast channel with two legitimate receivers and an external eavesdropper. We assume that the channel matrix of the eavesdropper is unknown to the legitimate terminals but satisfies a maximum rank constraint. As our main result we characterize the associated secrecy degrees of freedom for the broadcast channel with common and private messages. We show that a direct extension of the singleuser wiretap codebook does not achieve the secrecy degrees of freedom. Our proposed optimal scheme involves decomposing the signal space into a common subspace, which can be observed by both receivers, and private subspaces which can be observed by only one of the receivers, and carefully transmitting a subset of messages in each subspace. We also consider the case when each user’s private message must additionally remain confidential from the other legitimate receiver and characterize the s.d.o.f. region in this case. Index Terms—Information theoretic security, broadcast channels, wiretap channels, generalized singular value decomposition, MIMOME channel. I.
Secure Degrees of Freedom Region of the TwoUser MISO Broadcast Channel with Alternating CSIT∗
, 2015
"... The two user multipleinput singleoutput (MISO) broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1, I2 ∈ {P,D,N}, and the forms P, D and N correspond to p ..."
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Cited by 2 (2 self)
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The two user multipleinput singleoutput (MISO) broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1, I2 ∈ {P,D,N}, and the forms P, D and N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between 9 possible states corresponding to all possible values of I1I2, with each state occurring for λI1I2 fraction of the total duration. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where λI1I2 = λI2I1. The main technical contributions include developing a) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints which also highlight the synergistic benefits of interstate coding for secrecy, b) new converse proofs via local statistical equivalence and channel enhancement; and c) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f. 1