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arXiv:1509.04075 · IEEE Transactions on Information Theory

Secure Transmission on the Two-Hop Relay Channel With Scaled Compute-and-Forward

Zhijie Ren, Jasper Goseling, Jos H. Weber, Michael Gastpar

Published Sep 28, 2017• 11 citations
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Abstract

In this paper, we consider communication on a two-hop channel in which a source wants to send information reliably and securely to the destination via a relay. We consider both the untrusted relay case and the external eavesdropper case. In the untrusted relay case, the relay behaves as an eavesdropper, and there is a cooperative node, which sends a jamming signal to confuse the relay when it is receiving from the source. In the external eavesdropper case, the relay is trusted, and there is an external node eavesdropping the communication. We propose two secure transmission schemes using the scaled compute-and-forward technique. One of the schemes is based on a random binning code, and the other one is based on a lattice chain code. It is proved that in the high signal-to-noise-ratio (SNR) scenario and/or the limited relay power scenario, if the destination is used as the jammer, both schemes outperform all existing schemes and achieve the upper bound. In particular, if the SNR is large and the source, the relay, and the cooperative jammer have identical power and channels, both schemes achieve the upper bound for secrecy rate, which is merely 1/2 bit per channel use lower than the channel capacity without secrecy constraints. We also prove that one of our schemes achieves a positive secrecy rate in the external eavesdropper case in which the relay is trusted and there exists an external eavesdropper.

DOI
10.1109/tit.2017.2757503

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In this paper, we consider communication on a two-hop channel in which a source wants to send information reliably and securely to the destination via a relay. We consider both the untrusted relay case and the external eavesdropper case. In the untrusted relay case, the relay behaves as an eavesdropper, and there is a cooperative node, which sends a jamming signal to confuse the relay when it is receiving from the source. In the external eavesdropper case, the relay is trusted, and there is an external node eavesdropping the communication. We propose two secure transmission schemes using the scaled compute-and-forward technique. One of the schemes is based on a random binning code, and the other one is based on a lattice chain code. It is proved that in the high signal-to-noise-ratio (SNR) scenario and/or the limited relay power scenario, if the destination is used as the jammer, both schemes outperform all existing schemes and achieve the upper bound. In particular, if the SNR is large and the source, the relay, and the cooperative jammer have identical power and channels, both schemes achieve the upper bound for secrecy rate, which is merely 1/2 bit per channel use lower than the channel capacity without secrecy constraints. We also prove that one of our schemes achieves a positive secrecy rate in the external eavesdropper case in which the relay is trusted and there exists an external eavesdropper.
We consider a source-destination pair that can communicate only through an unauthenticated intermediate relay node. In this two-hop communication scenario, where the cooperation from the relay node is essential, we investigate whether achieving non-zero secrecy rate is possible. Specifically, we treat the relay node as an eavesdropper from whom the source information needs to be kept secret, despite the fact that its cooperation in relaying this information is needed. We find that a positive secrecy rate is indeed achievable, with the aid of the destination node or an external node that jams the relay, i.e., by cooperative jamming. We derive an upper bound on the secrecy rate by means of an eavesdropper-relay separation argument. We remark that this upper bound is the first of its kind in Gaussian channels with cooperative jamming. The upper bound is strictly smaller than the channel capacity without secrecy constraints. The achievable secrecy rates are found using stochastic encoding and compress-and-forward at the relay. Numerical results show that the gap between the bound and the achievable rate is small when the relay's power is larger than the power of the jammer and the source. In essence, this paper shows that a cooperative jammer enables secure communication to take place using an untrusted relay which would be otherwise impossible.
A two-hop channel is considered, in which the source wants to send information to the destination while keeping the information confidential from the relay. A novel lattice chain and compute-and-forward based scheme is proposed in which the destination provides cooperative jamming. Channel state information is used at the source and the destination to scale the encoding lattices for the message and the jamming signal according to the channel gains. We compare the achievable secrecy rate of our scheme with an upper bound and with the achievable secrecy rate of other schemes. It follows that our scheme outperforms all existing schemes except in the low power region.
We consider a source-destination pair that can only communicate through an untrusted intermediate relay node. The intermediate node is willing to employ a designated relaying scheme to facilitate reliable communication between the source and the destination. Yet, the information it relays needs to be kept secret from it. In this two-hop communication scenario, where the use of the untrusted relay node is essential, we find that a positive secrecy rate is achievable. The center piece of the achievability scheme is the help provided by either the destination node with transmission capability, or an external "good samaritan" node. In either case, the helper performs cooperative jamming that confuses the eavesdropping relay and disables it from being able to decipher what it is relaying. We next derive an upper bound on the secrecy rate for this system. We observe that the gap between the upper bound and the achievable rate vanishes as the power of the relay node goes to infinity. Overall, the paper presents a case for intentional interference, i.e., cooperative jamming, as an enabler for secure communication.
We consider a Gaussian network consisting of a source that aims to communicate to its legitimate destination via an untrusted relay node in the presence of an external eavesdropper. The source wishes to send two independent messages to the destination: one message must be kept secret from the external eavesdropper only, while the other message must be kept secret from the external eavesdropper and the untrusted relay both. We identify achievable secure rates under these layered secrecy constraints. Considering a two-hop half-duplex setup, we employ the destination as a cooperative jammer in the first phase in order to help provide secrecy from the relay and the external eavesdropper, and the source as a cooperative jammer in the second phase in order to detriment the external eavesdropper. The source encodes its messages using stochastic encoding and security embedding coding. We provide the secrecy analysis and present numerical results to demonstrate the performance of the proposed achievability technique. Our study points to the value of the source serving as a cooperative jammer as well as the need for power control policies at the legitimate nodes in order to ensure secrecy in this system.
We consider a source-destination pair that can only communicate through an untrusted intermediate relay node. The intermediate node is willing to employ a designated relaying scheme to facilitate reliable communication between the source and the destination. Yet, the information it relays needs to be kept secret from it. In this two-hop communication scenario, where the use of the untrusted relay node is essential, we find that a positive secrecy rate is achievable. The center piece of the achievability scheme is the help provided by either the destination node with transmission capability, or an external "good samaritan" node. In either case, the helper performs cooperative jamming that confuses the eavesdropping relay and disables it from being able to decipher what it is relaying. We next derive an upper bound on the secrecy rate for this system. We observe that the gap between the upper bound and the achievable rate vanishes as the power of the relay node goes to infinity. Overall, the paper presents a case for intentional interference, that is, cooperative jamming, as an enabler for secure communication.
We study, using information-theoretic security methods, the so-called symmetric two-hop channel with an untrusted relay. In this model, a source wants to send its message reliably and securely to the destination through an honest but curious relay. The relay acts as a passive eavesdropper. Our investigation, in line with the relevant literature, seeks to determine what rate, termed secrecy rate, is achievable. To do that, we consider a typical setting, with the destination cooperating with the source, sending a 'scrambling' signal to conceal the message from the relay. To derive the achievable secrecy rate, we propose a novel scheme based on nested lattice codes. We show that our scheme outperforms all existing schemes and it achieves the outer bound for this channel model within 0.33 bits.