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arXiv:1612.00130 · IEEE Access

Secure Polar Coding for the Two-Way Wiretap Channel

Mengfan Zheng, Meixia Tao, Wen Chen, Cong Ling

Published Jan 1, 2018• 16 citations
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Abstract

In this paper, we consider the problem of polar coding for secure communications over the two-way wiretap channel, where two legitimate users communicate with each other simultaneously, while a passive eavesdropper overhears a combination of their exchanged signals. We design a low complexity polar coded cooperative jamming scheme that achieves the whole secrecy rate region of the general two-way wiretap channel under the strong secrecy criterion. The chaining method is used to make proper alignment of polar indices. The randomness required to be shared between two legitimate users is treated as a limited resource and we show that its rate can be made negligible by increasing the blocklength and the number of chained blocks. For the special case when the eavesdropper channel is degraded with respect to the legitimate ones, a simplified scheme is proposed which can simultaneously ensure reliability and weak secrecy within a single transmission block.

DOI
10.1109/access.2018.2813998

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In this paper, we consider the problem of polar coding for secure communications over the two-way wiretap channel, where two legitimate users communicate with each other simultaneously, while a passive eavesdropper overhears a combination of their exchanged signals. We design a low complexity polar coded cooperative jamming scheme that achieves the whole secrecy rate region of the general two-way wiretap channel under the strong secrecy criterion. The chaining method is used to make proper alignment of polar indices. The randomness required to be shared between two legitimate users is treated as a limited resource and we show that its rate can be made negligible by increasing the blocklength and the number of chained blocks. For the special case when the eavesdropper channel is degraded with respect to the legitimate ones, a simplified scheme is proposed which can simultaneously ensure reliability and weak secrecy within a single transmission block.
We consider strongly secure communication over a discrete memoryless multiple access wiretap channel with two transmitters - no degradation or symmetry assumptions are made on the channel. Our main result is that any rate pair known to be achievable with a random coding like proof, is also achievable with a low-complexity polar coding scheme. Moreover, if the rate pair is known to be achievable without time-sharing, then time-sharing is not needed in our polar coding scheme as well. Our proof technique relies on rate-splitting and different cooperative jamming strategies. Specifically, our coding scheme combines several point-to-point codes that either aim at secretly conveying a message to the legitimate receiver or at performing cooperative jamming. Each point-to-point code relies on a chaining construction to be able to deal with an arbitrary channel and strong secrecy. We assess reliability and strong secrecy through a detailed analysis of the dependencies between the random variables involved in the scheme.
We consider strongly secure communication over a discrete memoryless multiple access wiretap channel with two transmitters. No degradation or symmetry assumptions are made on the channel. Our main result is that any rate pair known to be achievable with a random coding like proof, is also achievable with an explicit and low-complexity polar coding scheme. Moreover, if the rate pair is known to be achievable without time-sharing, then time-sharing is not needed in our polar coding scheme as well. Our proof technique relies on rate-splitting, which introduces two virtual transmitters, and cooperative jamming strategies implemented by these virtual transmitters. Specifically, our coding scheme combines point-to-point codes that either aim at secretly conveying a message to the legitimate receiver or at performing cooperative jamming. Each point-to-point code relies on block Markov encoding to be able to deal with an arbitrary channel and strong secrecy. Consequently, our coding scheme is the combination of inter-dependent block Markov constructions. We assess reliability and strong secrecy through a detailed analysis of the dependencies between the random variables involved in the scheme.
The authors consider the problems of key exchange for one‐time pad along with the problem of rate sacrifice for secure polar coding over the two‐way wiretap channel under the strong security criterion. Based on existing techniques, they present a new hash chaining structure to solve the good bits sacrificing problem for achieving the strong security and constructed encryption embedded secure polar coding scheme for two‐way wiretap channel. To implement a one‐time pad without any key pre‐sharing, they design a secure and reliable transmission for both key and ciphertext coupling with the cooperative jamming strategy, which can also increase the secrecy rate for communication. As proved, extended upper bounds for both achievable secrecy rate pair and effective secrecy rate pair can be achieved under the strong security and reliability criterions.
The authors study cooperative security in the physical layer of wireless systems based on the recently developed polar codes for multiple access channel (MAC). Specifically, the authors first consider the case of a m ‐user MAC with external eavesdropper. Using polar alignment, the authors formulate a discrete optimisation problem where security and reliability criteria can be handled separately over the bases of a set of deterministic binary matrices. A discrete algorithm with incrementally polynomial complexity is used to maximise the uniform sum secrecy rate of users. Moreover, the proposed coding scheme is shown to achieve strong security for any subset of users. The authors next examine the case of minimum number of cooperative helpers to fulfil a feasible secrecy rate requirement at the legitimate user. Here, a low‐complexity suboptimal algorithm is presented with at most one helper more than the optimal solution. Using Tal–Sharov–Vardy implementation of MAC polar codes, secure polar coding is implemented for a 2‐user Gaussian wiretap MAC channel. The upper and lower bound of block error probability are compared, respectively, at the legitimate receiver and the eavesdropper. The results demonstrate clearly that with sufficiently long block length, strong secrecy with respect to the eavesdropper is achieved, while block error probability approaches 0.5.
We consider the problem of secure communications over the two-way wiretap channel under a strong secrecy criterion. We improve existing results by developing an achievable region based on strategies that exploit both the interference at the eavesdropper's terminal and cooperation between legitimate users. We leverage the notion of channel resolvability for the multiple-access channel to analyze cooperative jamming and we show that the artificial noise created by cooperative jamming induces a source of common randomness that can be used for secret-key agreement. We illustrate the gain provided by this coding technique in the case of the Gaussian two-way wiretap channel, and we show significant improvements for some channel configurations.
Achieving information theoretic security with practical coding complexity is of definite interest. This work first focuses on the key agreement problem. For this problem, a new cross-layer secure coding protocol over block fading channels is proposed. The proposed scheme requires only the statistical knowledge about the eavesdropper channel state information (CSI), and, utilizing a privacy amplification technique, reduces the problem of key agreement to a provably secure coding problem per block. Focusing on this secure coding problem, it is shown that polar codes, introduced by Arikan, achieve nonzero perfect secrecy rates for the binary-input degraded wiretap channel while enjoying a remarkably low encoding-decoding complexity. We further show that, in the special case of symmetric main and eavesdropper channels, this coding technique achieves the secrecy capacity. This approach is also extended to the multiple-access channel with a degraded eavesdropper where a nontrivial achievable secrecy region is established. This polar coding method is then utilized in the proposed key agreement protocol, where the secure coding per block is used to create an advantage for the legitimate nodes over the eavesdropper, which is then turned into a private key via the privacy amplification module.