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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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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
Strong Secrecy and Reliable Byzantine Detection in the Presence of an Untrusted Relay
 IEEE Transactions on Information Theory
, 2009
"... Abstract—We consider a Gaussian twohop network where the source and the destination can communicate only via a relay node who is both an eavesdropper and a Byzantine adversary. Both the source and the destination nodes are allowed to transmit, and the relay receives a superposition of their transmi ..."
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Cited by 8 (5 self)
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Abstract—We consider a Gaussian twohop network where the source and the destination can communicate only via a relay node who is both an eavesdropper and a Byzantine adversary. Both the source and the destination nodes are allowed to transmit, and the relay receives a superposition of their transmitted signals. We propose a new coding scheme that satisfies two requirements simultaneously: the transmitted message must be kept secret from the relay node, and the destination must be able to detect any Byzantine attack that the relay node might launch reliably and fast. The three main components of the proposed schemearethenestedlattice code, the privacy amplification scheme, and the algebraic manipulation detection (AMD) code. Specifically, for the Gaussian twohop network, we show that lattice coding can successfully pair with AMD codes enabling its first application to a noisy channel model. We prove, using this new coding scheme, that the probability that the Byzantine attack goes undetected decreases exponentially fast with respect to the number of channel uses, while the loss in the secrecy rate, compared to the rate achievable when the relay is honest, can be made arbitrarily small. In addition, in contrast with prior work in Gaussian channels, the notion of secrecy provided here is strong secrecy. Index Terms—Algebraic manipulation detection (AMD) code, Byzantine detection, informationtheoretic secrecy, lattice code, relay channel, strong secrecy. I.
Unimodular Lattices for the Gaussian Wiretap Channel,” available online at http://arxiv.org/abs/1007.0449v1
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Improving Secrecy Rate via Spectrum Leasing for Friendly Jamming
"... Abstract—Cooperative jamming paradigm in secure communications enlists network nodes to transmit noise or structured codewords, in order to impair the eavesdropper’s ability to decode messages to be kept confidential from it. Such an approach can significantly help in facilitating secure communicati ..."
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Cited by 7 (3 self)
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Abstract—Cooperative jamming paradigm in secure communications enlists network nodes to transmit noise or structured codewords, in order to impair the eavesdropper’s ability to decode messages to be kept confidential from it. Such an approach can significantly help in facilitating secure communication between legitimate parties but, by definition, assumes dedicated and/or altruistic nodes willing to act as cooperative jammers. In this paper, it is demonstrated that cooperative jamming leads to meaningful secrecy rate improvements even when this assumption is removed. A distributed mechanism is developed that motivates jamming participation of otherwise noncooperative terminals, by compensating them with an opportunity to use the fraction of legitimate parties ’ spectrum for their own data traffic. With the goal of maximizing their data transmission rate priced by the invested power, cooperative jammers provide the jamming/transmitting power that is generally proportional to the amount of leased bandwidth. The fully decentralized framework is facilitated through a gametheoretic model, with the legitimate parties as the spectrum owners acting as the game leader, and the set of assisting jammers constituting the follower. To facilitate the behavior of noncooperative and competitive multiple jammers, auctioning and power control mechanisms are applied for a follower subgame in a twolayer leaderfollower game framework. Index Terms—Information theoretic security, cooperative jamming, game theory, Stackelberg game, auctions. I.
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
Lattice code design for the rayleigh fading wiretap channel
 in ICC 2011
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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.
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.
Endtoend Secure Multihop Communication with Untrusted Relays is Possible
"... Abstract—We consider a sourcedestination pair that can communicate only through a chain of unauthenticated intermediate relay nodes over AWGN links. In this scenario, it is desirable to use these relays—as otherwise communicating with the destination is impossible—without the relays being able to d ..."
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Abstract—We consider a sourcedestination pair that can communicate only through a chain of unauthenticated intermediate relay nodes over AWGN links. In this scenario, it is desirable to use these relays—as otherwise communicating with the destination is impossible—without the relays being able to decode the information flowing through them. This in turn is tantamount to treating the relays as eavesdroppers from whom the information needs to be kept secret. An important question then becomes that of identifying the limits of reliable and secure communication in this network in the information theoretic sense. In particular, we ask whether it is possible to achieve a nonvanishing perfect secrecy rate regardless of the number of hops. In this work, we find that the answer is yes and show that a constant secrecy rate for an arbitrary number of hops is achievable by employing the combination of a lattice code and a random code. I.
On modulosum computation over an erasure multiple access channel
 in Prodeedings. IEEE International Symposium on Information Theory (ISIT), 2012
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