In this paper, the one-sided secrecy of two-way wiretap channel with feedback is investigated, where the confidential messages of one user through multiple transmissions is guaranteed secure against an external eavesdropper. For one thing, one-sided secrecy satisfies the secure demand of many practical scenarios. For another, the secrecy is measured over many blocks since the correlation between eavesdropper's observation and the confidential messages in successive blocks, instead of secrecy measurement of one block in previous works. Thus, firstly, an achievable secrecy rate region is derived for the general two-way wiretap channel with feedback through multiple transmissions under one-sided secrecy. Secondly, outer bounds on the secrecy capacity region are also obtained. The gap between inner and outer bounds on the secrecy capacity region is explored via the binary input two-way wiretap channels. Most notably, the secrecy capacity regions are established for the XOR channel. Furthermore, the result shows that the achievable rate region with feedback is larger than that without feedback. Therefore, the benefit role of feedback is precisely characterized for two-way wiretap channel with feedback under one-sided secrecy.
In this paper, the one-sided secrecy of two-way wiretap channel with feedback is investigated, where the confidential messages of one user through multiple transmissions is guaranteed secure against an external eavesdropper. For one thing, one-sided secrecy satisfies the secure demand of many practical scenarios. For another, the secrecy is measured over many blocks since the correlation between eavesdropper's observation and the confidential messages in successive blocks, instead of secrecy measurement of one block in previous works. Thus, firstly, an achievable secrecy rate region is derived for the general two-way wiretap channel with feedback through multiple transmissions under one-sided secrecy. Secondly, outer bounds on the secrecy capacity region are also obtained. The gap between inner and outer bounds on the secrecy capacity region is explored via the binary input two-way wiretap channels. Most notably, the secrecy capacity regions are established for the XOR channel. Furthermore, the result shows that the achievable rate region with feedback is larger than that without feedback. Therefore, the benefit role of feedback is precisely characterized for two-way wiretap channel with feedback under one-sided secrecy.
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 investigate the fundamental communication limits when messages are sent via a Gaussian two-way channel, which must at the same time be kept secret from an external eavesdropper. In this two-way wiretap channel that models two legitimate transceivers and an eavesdropping receiver, there are two techniques to provide confidentiality for the messages: one entails the legitimate nodes to jam the eavesdropper, i.e., cooperative jamming, while the other entails generating keys from the feedback signals received by the two legitimate nodes and using them to encrypt the messages. Previous work has shown that both methods can be used concurrently to improve the secrecy rates of a channel with a degradedness condition. In this work, we consider the general case, and derive a new outer bound for the secrecy capacity region of this channel. A case is identified where the loss in secrecy rate, due to ignoring the backward (feedback) link at each legitimate transmitter from the other, is bounded by a constant which only depends on the channel gains. This is the case when the power of the two legitimate nodes increases proportionally. In all other cases, we show that ignoring feedback signals causes unbounded loss in the secrecy rate. The loss is measured as the gap between the achievable rate when the feedback signals are taken into account, and the upper bound when the feedback is not used, and hence is not affected by the choice of the achievable scheme. This result therefore establishes that, for the Gaussian two-way channel with an external eavesdropper, the encoders need to be designed with memory. This is in contrast to the result for this channel in the absence of an eavesdropper.
This paper investigates the problem of secure transmission over a two-user discrete memoryless multiple-access wiretap channel with partial rate-limited feedback (MAC-WT-PLF). The receiver can causally and securely transmit feedback to one of the transmitters at a limited rate. Three achievable rate regions and one outer bound on the secrecy capacity are presented based on three proposed coding schemes and the Sato-type bounding approach. The proposed coding schemes show that the feedback can play multiple roles, i.e., encrypting part of messages, enlarging the size of the dummy message, and increasing the correlation between the channel inputs, to enhance the secrecy performance. Of particular interest is identifying the novel role of enlarging the size of the dummy message at one of the transmitters, which enables both transmitters to benefit from the feedback significantly. In addition, the proposed achievable rate regions and outer bound are computed for the Gaussian MAC-WT-PLF, and comparative numerical results are provided under different eavesdropping cases.
Most practical communication links are bidirectional. In these models, since the source node also receives signals, its encoder has the option of computing its output based on the signals it received in the past. On the other hand, from a practical point of view, it would also be desirable to identify the cases where such an encoder design may not improve communication rates. This question is particularly interesting for the case where the transmitted messages and the feedback signals are subject to eavesdropping. In this paper, we investigate the question of how much impact the feedback has on the secrecy capacity by studying two fundamental models. First, we consider the Gaussian two-way wiretap channel and derive an outer bound for its secrecy capacity region. We show that the secrecy rate loss can be unbounded when feedback signals are not utilized except for a special case we identify, and thus conclude that utilizing feedback can be highly beneficial in general. Second, we consider a half-duplex Gaussian two-way relay channel where the relay node is also an eavesdropper, and find that the impact of feedback is less pronounced compared to the previous scenario. Specifically, the loss in secrecy rate, when ignoring the feedback, is quantified to be less than 0.5 bit per channel use when the relay power goes to infinity. This achievable rate region is obtained with simple time sharing along with cooperative jamming, which, with its simplicity and near optimum performance, is a viable alternative to an encoder that utilizes feedback signals.
This paper studies the two-way wiretap channel (TW-WC) with an external eavesdropper under strong one-sided (mixed) secrecy: only User~1's message is required to be secure from the eavesdropper, while no secrecy constraint is imposed on User~2's message. Secrecy is measured by the information leakage of User~1's message to the eavesdropper. Applying a non-adaptive construction and a one-sided reduction of the key-exchange construction, we obtain exponential error and leakage bounds for every fixed number of adaptive rounds. A quantitative one-time-pad argument propagates the leakage of the key used in the next round, and an explicit padding construction removes the initialization-rate loss for all sufficiently large blocklengths. We derive the corresponding strong mixed-secrecy achievable regions. The non-adaptive construction recovers the previously reported weak one-sided single-letter inner bound under the stronger secrecy criterion. The overall adaptive achievable region includes the non-adaptive construction as a fallback and also contains a key-exchange subregion that can be strictly larger.
In this work, we investigate the problem of secure broadcasting over block-fading wiretap channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having a finite rate feedback on the throughput of multi-user broadcast wiretap channels. We consider that the transmitter is only provided by a b -bits feedback of the main channel state information (CSI) sent by each legitimate receiver, at the beginning of each fading block, over error-free public links with limited capacity. Also, we assume that the transmitter is aware of the statistics of the eavesdropper's CSI but not of its channel's realizations. Under these assumptions of CSI uncertainty, we characterize the ergodic secrecy capacity of the system when a common message is broadcasted to all legitimate receivers, the ergodic secrecy sum-capacity when multiple independent messages are transmitted, and the ergodic secrecy capacity region for the broadcast channel with confidential messages (BCCM). In all three scenarios, we show that as long as the transmitter has some knowledge of the main CSI, obtained even through a 1-bit CSI feedback, a non-zero secrecy rate can still be achieved. The impact of having the feedback sent over a binary erasure channel (BEC) is also investigated for the BCCM case. Here again, and even with the possibility of having the feedback bits erased, a positive secrecy rate can still be achieved as long as the erasure event is not a probability-one event. An asymptotic analysis of the obtained results is provided for the high SNR regime, and the scaling law of the system, when the number of legitimate receivers is large, is also presented.