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arXiv:1407.5572 · IEEE Transactions on Information Theory

Secrecy Capacity Region of Some Classes of Wiretap Broadcast Channels

Meryem Benammar, Pablo Piantanida

Published Jul 31, 2015• 24 citations
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Abstract

This paper investigates the secrecy capacity of the wiretap broadcast channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a broadcast channel (BC) while keeping them secret from the eavesdropper. We derive a nontrivial outer bound on the secrecy capacity region of this channel which, in absence of security constraints, reduces to the best known outer bound to the capacity of the standard BC. An inner bound is also derived, which follows the behavior of both the best known inner bound for the BC and the wiretap channel. These bounds are shown to be tight for the deterministic BC with a general eavesdropper, the semideterministic BC with a more noisy eavesdropper, and the wiretap BC where users exhibit a less noisiness order between them. Finally, by rewriting our outer bound to encompass the characteristics of parallel channels, we also derive the secrecy capacity region of the product of two inversely less noisy BCs with a more noisy eavesdropper. We illustrate our results by studying the impact of security constraints on the capacity of the WBC with binary erasure and binary symmetric components.

DOI
10.1109/tit.2015.2463279

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This paper investigates the secrecy capacity of the wiretap broadcast channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a broadcast channel (BC) while keeping them secret from the eavesdropper. We derive a nontrivial outer bound on the secrecy capacity region of this channel which, in absence of security constraints, reduces to the best known outer bound to the capacity of the standard BC. An inner bound is also derived, which follows the behavior of both the best known inner bound for the BC and the wiretap channel. These bounds are shown to be tight for the deterministic BC with a general eavesdropper, the semideterministic BC with a more noisy eavesdropper, and the wiretap BC where users exhibit a less noisiness order between them. Finally, by rewriting our outer bound to encompass the characteristics of parallel channels, we also derive the secrecy capacity region of the product of two inversely less noisy BCs with a more noisy eavesdropper. We illustrate our results by studying the impact of security constraints on the capacity of the WBC with binary erasure and binary symmetric components.
This work investigates the secrecy capacity region of the Wiretap Broadcast Channel (WBC) where an encoder communicates two private messages over a Broadcast Channel (BC) while keeping both messages secret from the eavesdropper. Our main result is the derivation of a novel outer bound and an inner bound on the secrecy capacity region of this setting. These results allow us to characterize the capacity region for three non-degraded classes of WBCs: the deterministic and the semi-deterministic WBC with a more noisy eavesdropper, and the WBC when users exhibit less noisiness order between them.
This work investigates the secrecy capacity region of a class of Wiretap Broadcast Channel (WBC) where a source wishes to send two independent messages to two receivers in the presence of an external eavesdropper. We focus on the class of parallel WBC and more precisely on the product of two reversely less-noisy BC with a more noisy eavesdropper. We fully characterize the capacity region of such a setting through a novel powerful outer bound that relies on a careful single letter expression, followed by a non-trivial equivalent formulation of the resulting rate region. This outer bound turns out to be tight with the inner bound we derive for the setting under study.
In this paper, the individual secrecy of two-way wiretap channel is investigated, where two legitimate users' messages are separately guaranteed secure against an external eavesdropper. For one thing, in some communication scenarios, the joint secrecy is impossible to achieve both positive secrecy rates of two users. For another, the individual secrecy satisfies the secrecy demand of many practical communication systems. Thus, firstly, an achievable secrecy rate region is derived for the general two-way wiretap channel with individual secrecy. In a deterministic channel, the region with individual secrecy is shown to be larger than that with joint secrecy.Secondly, outer bounds on the secrecy capacity region are obtained for the general two-way wiretap channel and for two classes of special two-way wiretap channels.The gap between inner and outer bounds on the secrecy capacity region is explored via the binary input two-way wiretap channels and the degraded Gaussian two-way wiretap. Most notably, the secrecy capacity regions are established for the XOR channel and the degraded Gaussian two-way wiretap channel.Furthermore, the secure sum-rate of the degraded Gaussian two-way wiretap channel under the individual secrecy constraint is demonstrated to be strictly larger than that under the joint secrecy constraint.
We study the two-transmitter two-receiver channel with confidential messages channel under a secrecy constraint, exploring the effect of a single eavesdropper on the secure communication rate. A general achievable secrecy rate region and an outer bound are derived for the degraded version of this channel. An example is provided in which the inner and outer bound meet. For the general non-degraded channel, another outer bound is derived and a special case is highlighted in which the inner and outer bound meet. Our inner bound recovers the known inner bounds for the multiple-access wiretap channel, broadcast channel with confidential messages, and the compound MAC channel.
In this paper, secure communication over a broadcast channel with multiple legitimate receivers and an external eavesdropper is investigated. Two different secrecy measures are considered. The first criterion is a conservative one known as joint secrecy, where the mutual leakage of all confidential messages must be small. The second criterion is a less conservative constraint known as individual secrecy, where the individual leakage of each confidential message must be small. At first, we consider the degraded multi-receiver wiretap broadcast channel and manage to establish the individual secrecy capacity region. Our encoding scheme applies a careful combination of the standard techniques of wiretap random coding and Shannon's one time pad encoding, where the confidential messages of the weak receivers are used as secret keys for the stronger ones. The validity of this technique is due to the properties of the degraded broadcast channel and the secrecy requirements of the individual secrecy criterion. Our result indicates that the individual secrecy capacity region is in fact larger than the joint one established in earlier literature. The established capacity region is then used to derive the individual secrecy capacity regions of the Gaussian single-input single-output and degraded Gaussian multiple-input multiple-output multi-receiver wiretap broadcast channels. Furthermore, we present an achievable rate region for the general two-receiver wiretap broadcast channel under both the joint and the individual secrecy criterion. Comparing these two rate regions suggests that even for the general case, the individual secrecy criterion might be able to provide a larger rate region compared with the joint one.
We study secure communication in which two confidential messages are transmitted over a broadcast channel to two legitimate receivers, while keeping an eavesdropper ignorant. Each legitimate receiver is interested in decoding one confidential message, while having the other one as side information. In order to measure the secrecy of the communication, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide an achievable rate region and a matching multi-letter outer bound presenting a multi-letter description for the capacity region. We further investigate the class of more capable channels and provide a single-letter converse establishing the secrecy capacity region, not only for more capable channels but less noisy and degraded channels as well. Our results indicate that the secrecy capacity for individual secrecy is higher than the one for joint secrecy, as one message can be used as a secret key for the other one.