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arXiv:2003.03592

Strong Secrecy for General Multiple-Access Wiretap Channels

Manos Athanasakos, N. Kalouptsidis

Published Mar 7, 2020• 1 citation
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Abstract

This paper is concerned with the general multiple access wiretap channel and the existence of codes that accomplish reliability and strong secrecy. Information leakage to the eavesdropper is assessed by the variational distance metric, whereas the average error probability is bounded by modifying Feinsteins Lemma. We derive an achievable strong secrecy rate region by utilizing the resolvability theory for the multiple-access channel in terms of information-spectrum methods.

DOI
10.48550/arxiv.2003.03592

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This paper is concerned with the general multiple access wiretap channel and the existence of codes that accomplish reliability and strong secrecy. Information leakage to the eavesdropper is assessed by the variational distance metric, whereas the average error probability is bounded by modifying Feinsteins Lemma. We derive an achievable strong secrecy rate region by utilizing the resolvability theory for the multiple-access channel in terms of information-spectrum methods.
We derive a rate region which is achievable by the Wiretap MAC with Common Message under the strong secrecy criterion. We follow Devetak's approach to establishing strong secrecy. Using the concentration of the normed sum of bounded i.i.d. random variables around its mean, it is possible to show the existence of a code where the channel outputs at the eavesdropper are almost independent of the messages. The encoders may use a certain amount of common randomness. We give the example of a channel where the availability of common randomness is necessary for secret transmission.
We derive lower bounds to the second-order coding rates for the wiretap channel. The decoding error probability and the information leakage measured in terms of the variational distance secrecy metric are fixed at some constants εrand εsrespectively. We leverage on the connection between wiretap channel coding and channel resolvability to derive tighter secrecy bounds than those available in the literature. We then use central limit theorem-style analysis to evaluate these bounds for the discrete memoryless wiretap channel with cost constraints and the Gaussian wiretap channel.
This paper investigates the information-theoretic secrecy problem for a K-user discrete memoryless (DM) multiple-access wiretap (MAC-WT) channel. Instead of using the weak secrecy criterion characterized by information leakage rate, we adopt the strong secrecy metric defined by information leakage to better protect the confidential information. We provide an achievable rate region and prove its achievability by providing a coding scheme and analyzing the output statistics in terms of (average) variational distance. We show that the rate region obtained in previous works on the subject is a special case of ours. We also show that the achievability proof in such works is incomplete, because it is assumed that certain inequalities hold while they may not in some cases. We solve this problem by constructing an inequality structure for the rates of all users’ secret and redundant messages, and analyzing the conditions required to maintain this structure.
We investigate an approach to physical-layer security based on the premise that the coding mechanism for secrecy over noisy channels is fundamentally tied to the notion of resolvability. Instead of considering capacity-based constructions, which associate to each message a sub-code whose rate approaches the capacity of the eavesdropper’s channel, we consider resolvability-based constructions, which associate to each message a sub-code whose rate is beyond the resolvability of the eavesdropper’s channel. We provide evidence that resolvability is a more powerful and perhaps more fundamental coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels. Specifically, we show that, at least for binary symmetric wiretap channels, random capacity-based constructions fail to approach the strong secrecy capacity while resolvability-based constructions achieve it. We then obtain the secrecy-capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics, which generalizes existing results. Finally, we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information, compound and mixed channels, as well as the secret-key capacity of source models for secret-key agreement. By tying secrecy to resolvability, we obtain achievable rates for stronger secrecy metrics and with simpler proofs than previously derived. Index Terms information-theoretic security, wiretap channel, secret-key agreement, information-spectrum, resolv-ability, wireless channels.
This paper strengthens the known secrecy results for a k-transmitter multiple access channel (MAC) with an external eavesdropper from weak to strong without any rate loss on the achievable region. More specifically, the results are derived under a strong secrecy metric defined by the information leakage to the eavesdropper, instead of the weaker secrecy criteria defined by the information leakage rate or the (average) variation distance. To this end, different approaches are taken to analyze the information leakage and the decoding error probability. Interestingly, both the secrecy and error exponents could be characterized by the (conditional) Rényi mutual information in a concise form. Thus, the region is guaranteed with both information leakage and decoding error probability decreasing exponentially in the code length. Our technique for strong secrecy analysis reflects the resolvability for the k-transmitter MAC; while our error exponent could be regarded as a generalization of Gallager's error exponent.
This paper investigates the capacity region of a discrete memoryless (DM) multiple access wiretap (MAC-WT) channel where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver but only the confidential messages need to be protected from the eavesdropper. By using random coding, we find an achievable secrecy rate region, within which perfect secrecy can be realized, i.e., all users can communicate with the legitimate receiver with arbitrarily small probability of error, while the confidential information leaked to the eavesdropper tends to zero.