In this paper, we propose a feedback scheme for transmitting secret messages between two legitimate parties, over an eavesdropped communication link. Relative to Wyner's traditional encoding scheme, our feedback-based encoding often yields larger rate-equivocation regions and achievable secrecy rates. More importantly, by exploiting the channel randomness inherent in the feedback channels, our scheme achieves a strictly positive secrecy rate even when the eavesdropper's channel is less noisy than the legitimate receiver's channel. All channels are modeled as binary and symmetric. We demonstrate the versatility of our feedback-based encoding method by using it in three different configurations: the stand-alone configuration, the mixed configuration (when it combines with Wyner's scheme), and the reversed configuration. Depending on the channel conditions, significant improvements over Wyner's secrecy capacity can be observed in all configurations.
In this paper, we propose a feedback scheme for transmitting secret messages between two legitimate parties, over an eavesdropped communication link. Relative to Wyner's traditional encoding scheme, our feedback-based encoding often yields larger rate-equivocation regions and achievable secrecy rates. More importantly, by exploiting the channel randomness inherent in the feedback channels, our scheme achieves a strictly positive secrecy rate even when the eavesdropper's channel is less noisy than the legitimate receiver's channel. All channels are modeled as binary and symmetric. We demonstrate the versatility of our feedback-based encoding method by using it in three different configurations: the stand-alone configuration, the mixed configuration (when it combines with Wyner's scheme), and the reversed configuration. Depending on the channel conditions, significant improvements over Wyner's secrecy capacity can be observed in all configurations.
In this paper, we propose a feedback scheme to achieve a strictly positive secrecy rate over an eavesdropped communication link when the eavesdropper's channel is less noisy than the legitimate receiver's channel. All channels are assumed binary and symmetric (BSC). The proposed scheme exploits the channel randomness inherent in feedback channels. We show that our feedback scheme can further increase the secrecy rate achievable by the Wyner's method when the eaves-dropper's channel is worse. Some pre-/post-processing schemes to intentionally improve and degrade the equivalent wiretapper channels, respectively, are also proposed to further enhance the overall secrecy rate.
This paper studies the problem of secure communication over a wiretap channel p(y,z|x) with a secure feedback link of rate Rf, where X is the channel input, and Y and Z are channel outputs observed by the legitimate receiver and the eavesdropper, respectively. It is shown that the secrecy capacity, the maximum data rate of reliable communication while the intended message is not revealed to the eavesdropper, is upper bounded as Cs(Rf) les maxmin/p(x) {I(X;Y), I(X;Y |Z) + Rf}. The proof of the bound crucially depends on a recursive argument which is used to obtain the single-letter characterization. This upper bound is shown to be tight for the class of physically degraded wiretap channels. A capacity-achieving coding scheme is presented for this case, in which the receiver securely feeds back fresh randomness with rate Rf, generated independent of the received channel output symbols. The transmitter then uses this shared randomness as a secret key on top of Wyner's coding scheme for wiretap channels without feedback. Hence, when a feedback link is available, the receiver should allocate all resources to convey a new key rather than sending back the channel output.
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.
In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf . We shown that the secrecy capacity is bounded. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving scheme is based on both the Wyner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. Finally, we consider several special cases. When state information is available only at the legitimate receiver, the analysis suggests that unlike previous results involving feedback, it is better to use the feedback to send the state information to the transmitter (when possible), rather than send a random key.
In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf. We shown that the secrecy capacity is bounded by Cs ≥ max {p(u|v) p(x|u,v)max min{I(U;Y|v) - I(U;Z|V) + H(V|Z) + Rf, I(U;Y|V)},p(u)p(x|u,v)max min{H(V|Z,U) + Rf, I(U;Y|V)}}. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving scheme is based on both the Wyner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. Finally, we consider several special cases. When state information is available only at the legitimate receiver, the analysis suggests that unlike previous results involving feedback, it is better to use the feedback to send the state information to the transmitter (when possible), rather than send a random key.
We study the interference channel with one-sided generalized feedback and secrecy requirements. In our model Message 1 which is known just to Encoder 1 should be decoded by both receivers. Message 2 - known only to Encoder 2 - should be decoded by Decoder 2 and kept as secret as possible from Decoder 1. The uncertainty of Decoder 1 about Message 2 is measured by means of the equivocation rate. In addition, a noisy feedback is provided to Encoder 2. We derive an achievable rate-equivocation region for this model and an outer bound for the “noisy cribbing” regime that coincides with the inner bound the gap being in the Markov conditions satisfied by one of the auxiliary random variables.