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IEEE Signal Processing Letters

On Secrecy Capacity of Helper-Assisted Wiretap Channel with an Out-of-Band Link

Lingxiang Li, Zhi Chen, Jun Fang

Published Jan 30, 2015• 2 citations
Publisher

Abstract

We consider a physical layer security problem where there is a source, an external helper, a legitimate receiver, and an eavesdropper, each equipped with one antenna. We assume that an additional out-of-band link from the source to the helper is available to improve the transmission security rate. A two-stage cooperative scheme is proposed. The proposed scheme consists of an information sharing stage and a cooperative transmission stage. Specifically, in the information sharing stage the source informs the helper of the signal to be transmitted, while in the cooperative transmission stage the source and the helper cooperate to transmit the signal to the legitimate receiver. Under this framework, we determine the optimal weights associated with this scheme and examine the secrecy capacity of the helper-assisted wiretap channel. The optimal weight design problem is generally nonconvex. To deal with this issue, an algorithm involving a one-dimensional search is developed. On the other hand, an analytical lower bound on the secrecy capacity is derived. Based on this lower bound, we further analyze the sufficient and necessary condition to ensure a positive secrecy capacity and derive the maximal achievable secure degrees of freedom, which are shown to be exactly the same as those of the multi-input single-output (MISO) wiretap channel.

DOI
10.1109/lsp.2015.2398674

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We consider a physical layer security problem where there is a source, an external helper, a legitimate receiver, and an eavesdropper, each equipped with one antenna. We assume that an additional out-of-band link from the source to the helper is available to improve the transmission security rate. A two-stage cooperative scheme is proposed. The proposed scheme consists of an information sharing stage and a cooperative transmission stage. Specifically, in the information sharing stage the source informs the helper of the signal to be transmitted, while in the cooperative transmission stage the source and the helper cooperate to transmit the signal to the legitimate receiver. Under this framework, we determine the optimal weights associated with this scheme and examine the secrecy capacity of the helper-assisted wiretap channel. The optimal weight design problem is generally nonconvex. To deal with this issue, an algorithm involving a one-dimensional search is developed. On the other hand, an analytical lower bound on the secrecy capacity is derived. Based on this lower bound, we further analyze the sufficient and necessary condition to ensure a positive secrecy capacity and derive the maximal achievable secure degrees of freedom, which are shown to be exactly the same as those of the multi-input single-output (MISO) wiretap channel.
We study the secrecy capacity of a helper-assisted Gaussian wiretap channel with a source, a legitimate receiver, an eavesdropper and an external helper, where each terminal is equipped with multiple antennas. Determining the secrecy capacity in this scenario generally requires solving a nonconvex secrecy rate maximization (SRM) problem. To deal with this issue, we first reformulate the original SRM problem into a sequence of convex subproblems. For the special case of single-antenna legitimate receiver, we obtain the secrecy capacity via a combination of convex optimization and one-dimensional search, while for the general case of multi-antenna legitimate receiver, we propose an iterative solution. To gain more insight into how the secrecy capacity of a helper-assisted Gaussian wiretap channel behaves, we examine the achievable secure degrees of freedom (s.d.o.f.) and obtain the maximal achievable s.d.o.f. in closed-form. We also derive a closed-form solution to the original SRM problem which achieves the maximal s.d.o.f.. Numerical results are presented to illustrate the efficacy of the proposed schemes.
We investigate the secrecy capacity of Gaussian wiretap channel with a source, an external helper, an eavesdropper and a single-antenna legitimate receiver where the former three terminals are equipped with NaN_aNa​, NjN_jNj​ and NeN_eNe​ antennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we recast the original nonconvex secrecy rate maximization (SRM) problem into a sequence of convex optimization problems. In doing so, the secrecy capacity can be obtained using a combination of convex optimization and a one-dimensional search. On the other hand, to gain more insight into how the secrecy capacity behaves, we study the secure degrees of freedom (s.d.o.f.) and quantify its connection with system parameters, where our result proves that the s.d.o.f. equal to 1 can be achieved if and only if N_e<N_a+N_j-1. As a by-product, we give a suboptimal but closed-form solution to the original SRM problem for the scenario where N_e<N_a+N_j-1.Numerical results are presented to validate the theoretical findings and illustrate the efficacy of the proposed schemes.
This paper considers secrecy communication from a signal processing point of view, and studies the maximal achievable secrecy degrees of freedoms (S.D.o.F.) of a helper-assisted Gaussian wiretap channel, consisting of a source, a legitimate receiver, an eavesdropper and an external helper. Each terminal is equipped with multiple antennas. We first propose a cooperative secrecy transmission scheme, and show that it achieves the maximal secrecy degrees of freedom. We then propose a heuristic method, through which, we solve analytically the optimization problem associated with the proposed cooperative secrecy transmission scheme. By this way, we obtain the maximal achievable S.D.o.F. and also the precoding matrices which achieve the maximal S.D.o.F. in closed-form.
We investigate the secrecy capacity of Gaussian wiretap channel with a source, an external helper, an eavesdropper and a single-antenna legitimate receiver where the former three terminals are equipped with Na, Njand Neantennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we recast the original nonconvex secrecy rate maximization (SRM) problem into a sequence of convex optimization problems. In doing so, the secrecy capacity can be obtained using a combination of convex optimization and a one-dimensional search. On the other hand, to gain more insight into how the secrecy capacity behaves, we study the secure degrees of freedom (s.d.o.f.) and quantify its connection with system parameters, where our result proves that the s.d.o.f. equal to 1 can be achieved if and only if Nea+Nj-1. As a by-product, we give a suboptimal but closed-form solution to the original SRM problem for the scenario where Nea+Nj-1.Numerical results are presented to validate the theoretical findings and illustrate the efficacy of the proposed schemes.
We study the Gaussian MISO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, where the transmitter and the helper have an arbitrary number of antennas but the intended receiver and the eavesdropper have only one antenna. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. Assuming Gaussian signaling at the helper, we obtain the optimal beamformers at the transmitter and the helper that achieve the secrecy capacity.
We study the secrecy capacity of Gaussian wiretap channel aided by an external jammer/helper. Both the transmitter and the intended receiver are equipped with a single antenna, while the eavesdropper and the jammer are equipped withMMMandNNNantennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we consider a null-space jamming scheme which totally nulls out the jamming signal at the legitimate receiver, and derive lower and upper bounds on its maximal achievable secrecy rateRN{R_N}RN​. The relationship between the average secrecy capacityCˉN{\bar C_N}CˉN​of Gaussian wiretap channel and the average secrecy rateRˉN{\bar R_N}RˉN​achieved by the null-space jamming scheme is investigated, and we prove thatRˉN≤CˉN≤RˉN+1{\bar R_N} \leq {\bar C_N} \leq {\bar R_{N + 1}}RˉN​≤CˉN​≤RˉN+1​. Based on this inequality and the derived lower and upper bounds onRN{R_N}RN​, the upper and lower bounds on the average secrecy capacity of Gaussian wiretap channel aided by an external jammer can be obtained, where our result shows that whenN>MN > MN>M, the average secrecy capacity increases linearly with the total transmit power; while whenN≤M−1N \leq M - 1N≤M−1, there exists a performance ceiling on it.