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Asilomar Conference on Signals, Systems and Computers (ACSSC)

On Secure Signaling for the Gaussian Multiple Access Wire-tap Channel

Ender Tekin, Semih Serbetli, Aylin Yener

Published Mar 22, 2006• 51 citations
Publisher

Abstract

Abstract — We consider the Gaussian Multiple Access Wire-Tap Channel (GMAC-WT) where multiple users communicate with the intended receiver in the presence of an intelligent and informed wire-tapper (eavesdropper). The wire-tapper receives a degraded version of the signal at the receiver. We assume that the wire-tapper is as capable as the intended receiver, and there is no other shared secret key. We consider two different secure communication scenarios: (i) keeping the wire-tapper totally ignorant of the message of any group of users even if the remaining users are compromised, (ii) using the secrecy of the other users to ensure secrecy for a group of users. We first derive the outer bounds for the secure rate region. Next, using Gaussian codebooks, we show the achievability of a secure rate region for each measure in which the wire-tapper is kept perfectly ignorant of the messages. We also find the power allocations that yield the maximum sum rate, and show that upper bound on the secure sum rate can be achieved by a TDMA scheme. We present numerical results showing the new rate region and compare it with that of the Gaussian Multiple-Access Channel (GMAC) with no secrecy constraints. I.

DOI
10.1109/acssc.2005.1600069

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arXiv:0704.3035•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2007•24 citations
Abstract — We consider the Gaussian Multiple Access Wire-Tap Channel (GMAC-WT) where multiple users communicate with the intended receiver in the presence of an intelligent and informed wire-tapper (eavesdropper). The wire-tapper receives a degraded version of the signal at the receiver. We assume that the wire-tapper is as capable as the intended receiver, and there is no other shared secret key. We consider two different secure communication scenarios: (i) keeping the wire-tapper totally ignorant of the message of any group of users even if the remaining users are compromised, (ii) using the secrecy of the other users to ensure secrecy for a group of users. We first derive the outer bounds for the secure rate region. Next, using Gaussian codebooks, we show the achievability of a secure rate region for each measure in which the wire-tapper is kept perfectly ignorant of the messages. We also find the power allocations that yield the maximum sum rate, and show that upper bound on the secure sum rate can be achieved by a TDMA scheme. We present numerical results showing the new rate region and compare it with that of the Gaussian Multiple-Access Channel (GMAC) with no secrecy constraints. I.
We consider the Gaussian multiple access wire-tap channel (GMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed wire-tapper who receives a degraded version of the signal at the receiver. We define a suitable security measure for this multi-access environment. We derive an outer bound for the rate region such that secrecy to some pre-determined degree can be maintained. We also find, using Gaussian codebooks, an achievable such secrecy region. Gaussian codewords are shown to achieve the sum capacity outer bound, and the achievable region coincides with the outer bound for Gaussian codewords, giving the capacity region when inputs are constrained to be Gaussian. We present numerical results showing the new rate region and compare it with that of the Gaussian multiple-access channel (GMAC) with no secrecy constraints
We consider the Gaussian multiple access wire-tap channel (GMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed wire-tapper who receives a degraded version of the signal at the receiver. We define suitable security measures for this multiaccess environment. Using codebooks generated randomly according to a Gaussian distribution, achievable secrecy rate regions are identified using superposition coding and time-division multiple access (TDMA) coding schemes. An upper bound for the secrecy sum-rate is derived, and our coding schemes are shown to achieve the sum capacity. Numerical results are presented showing the new rate region and comparing it with the capacity region of the Gaussian multiple-access channel (GMAC) with no secrecy constraints, which quantifies the price paid for secrecy.
We consider the General Gaussian Multiple Access Wire-Tap Channel (GGMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed eavesdropper. We define two suitable secrecy measures, termed individual and collective, to reflect the confidence in the system for this multi-access environment. We determine achievable rates such that secrecy to some pre-determined degree can be maintained, using Gaussian codebooks. We also find outer bounds for the case when the eavesdropper receives a degraded version of the intended receiver's signal. In the degraded case, Gaussian codewords are shown to achieve the sum capacity for collective constraints. In addition, a TDMA scheme is shown to also achieve sum capacity for both sets of constraints. Numerical results showing the new rate region are presented and compared with the capacity region of the Gaussian Multiple-Access Channel (GMAC) with no secrecy constraints. We then find the secrecy sum-rate maximizing power allocations for the transmitters, and show that a cooperative jamming scheme can be used to increase achievable rates in this scenario.
We consider the General Gaussian Multiple Access Wire-Tap Channel (GGMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed eavesdropper who is as capable as the intended receiver, but has different channel parameters. We aim to provide perfect secrecy for the transmitters in this multi-access environment. Using Gaussian codebooks, an achievable secrecy region is determined and the power allocation that maximizes the achievable sum-rate is found. Numerical results showing the new rate region are presented. It is shown that the multiple-access nature of the channel may be utilized to allow users with zero single-user secrecy capacity to be able to transmit in perfect secrecy. In addition, a new collaborative scheme is shown that may increase the achievable sum-rate. In this scheme, a user who would not transmit to maximize the sum rate can help another user who (i) has positive secrecy capacity to increase its rate, or (ii) has zero secrecy capacity to achieve a positive secrecy capacity.
The general Gaussian multiple-access wiretap channel (GGMAC-WT) and the Gaussian two-way wiretap channel (GTW-WT) are considered. In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other over a common Gaussian channel, with an eavesdropper listening through a GMAC. A secrecy measure that is suitable for this multiterminal environment is defined, and achievable secrecy rate regions are found for both channels. For both cases, the power allocations maximizing the achievable secrecy sum rate are determined. It is seen that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, a new scheme cooperative jamming is proposed, where users who are prevented from transmitting according to the secrecy sum rate maximizing power allocation policy ldquojamrdquo the eavesdropper, thereby helping the remaining users. This scheme is shown to increase the achievable secrecy sum rate. Overall, our results show that in multiple-access scenarios, users can help each other to collectively achieve positive secrecy rates. In other words, cooperation among users can be invaluable for achieving secrecy for the system.
We consider two-way wire-tap channels, where two users are communicating with each other in the presence of an eavesdropper, who has access to the communications through a multiple-access channel. We find achievable rates for two different scenarios, the Gaussian two-way wire-tap channel, (GTW-WT), and the binary additive two-way wire-tap channel, (BATW- WT). It is shown that the two-way channels inherently provide a unique advantage for wire-tapped scenarios, as the users know their own transmitted signals and in effect help encrypt the other user's messages, similar to a one-time pad. We compare the achievable rates to that of the Gaussian multiple-access wiretap channel (GMAC-WT) to illustrate this advantage.