We study a discrete memoryless two-way wiretap channel under strong one-sided secrecy, where User 1's message is confidential and User 2's message is not required to be secret. We develop non-adaptive and key-assisted adaptive inner bounds from a common resolvability estimate for selected index components. For the adaptive construction, we prove a multiround leakage theorem that accounts both for information revealed about a key before its later use and for the possibility that an encoder uses an incorrectly decoded key. The proof includes an ideal-to-implemented coupling, deterministic codebook selection, and a growing-round argument that removes the initialization-rate loss. We eliminate the internal component rates exactly and characterize the adaptive gain at each fixed auxiliary distribution. For an open two-parameter family of binary channels, we also prove a converse for arbitrary non-adaptive stochastic codes and obtain an operational adaptive-versus-non-adaptive separation. For one representative channel, the complete non-adaptive strong one-sided secrecy capacity region is identified exactly.
We study a discrete memoryless two-way wiretap channel under strong one-sided secrecy, where User 1's message is confidential and User 2's message is not required to be secret. We develop non-adaptive and key-assisted adaptive inner bounds from a common resolvability estimate for selected index components. For the adaptive construction, we prove a multiround leakage theorem that accounts both for information revealed about a key before its later use and for the possibility that an encoder uses an incorrectly decoded key. The proof includes an ideal-to-implemented coupling, deterministic codebook selection, and a growing-round argument that removes the initialization-rate loss. We eliminate the internal component rates exactly and characterize the adaptive gain at each fixed auxiliary distribution. For an open two-parameter family of binary channels, we also prove a converse for arbitrary non-adaptive stochastic codes and obtain an operational adaptive-versus-non-adaptive separation. For one representative channel, the complete non-adaptive strong one-sided secrecy capacity region is identified exactly.
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.
This paper studies the secrecy results for the two-way wiretap channel (TW-WC) with an external eavesdropper under a strong secrecy metric. Employing non-adaptive coding, we analyze theinformation leakageand the decoding error probability, and derive inner bounds on the secrecy capacity regions for the TW-WC under strong joint and individual secrecy constraints. For the TW-WC without cost constraint, both the secrecy and error exponents could be characterized by theconditional Rényi mutual informationin a concise and compact form. And, some special cases secrecy capacity region and sum-rate capacity results are established, demonstrating that adaption is useless in some cases or the maximum sum-rate that could be achieved by non-adaptive coding. For the TW-WC with cost constraint, we consider the peak cost constraint and extend our secrecy results by using the constant composition codes. Accordingly, we characterize both the secrecy and error exponents bya modification of Rényi mutual information, which yields inner bounds on the secrecy capacity regions for the general discrete memoryless TW-WC with cost constraint. Our method works even when a pre-noisy processing is employed based on a conditional distribution in the encoder and can be easily extended to other multi-user communication scenarios.
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.
This paper investigates the achievable region of a K-user discrete memoryless (DM) multiple access wiretap (MAC-WT) channel, where each user transmits both secret and open (i.e., non-confidential) messages. All these messages are intended for the legitimate receiver (Bob), while the eavesdropper (Eve) is only interested in the secret messages. In the achievable coding strategy, the confidential information is protected by open messages and also by the introduction of auxiliary messages. When introducing an auxiliary message, one has to ensure that, on one hand, its rate is large enough for protecting the secret message from Eve and, on the other hand, the resulting sum rate (together with the secret and open message rate) does not exceed Bob’s decoding capability. This yields an inequality structure involving the rates of all users’ secret, open, and auxiliary messages. To obtain the rate region, the auxiliary message rates must be eliminated from the system of inequalities. A direct application of the Fourier-Motzkin elimination procedure is elusive since a) it requires that the number of users K is explicitly given, and b) even for small$K = 3, 4, \ldots $, the number of inequalities becomes extremely large. We prove the result for general K through the combined use of Fourier-Motzkin elimination procedure and mathematical induction. This paper adopts the strong secrecy metric, characterized by information leakage. To prove the achievability under this criterion, we analyze the resolvability region of a K-user DM-MAC channel (not necessarily a wiretap channel). In addition, we show that users with zero secrecy rate can play different roles and use different strategies in encoding their messages. These strategies yield non-redundant (i.e., not mutually dominating) rate inequalities. By considering all possible coding strategies, we provide a new achievable region for the considered channel, and show that it strictly improves those already known in the existing literature by considering a specific example.
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.
Recently, a secrecy measure based on list-reconstruction has been proposed, in which a wiretapper is allowed to produce a list of 2mRLreconstruction sequences and the secrecy is measured by the minimum distortion over the entire list. In this paper, we show that this list secrecy problem is equivalent to the one with secrecy measured by a new quantity lossy equivocation, which is proved to be the minimum optimistic one-achievable source coding rate (the minimum coding rate needed to reconstruct the source within target distortion with positive probability for infinitely many blocklengths) of the source with the wiretapped signal as two-sided information, and also can be seen as a lossy extension of conventional equivocation. Upon this (or list) secrecy measure, we study source-channel secrecy problem in the discrete memoryless Shannon cipher system with noisy wiretap channel. Two inner bounds and an outer bound on the achievable region of secret key rate, list rate, wiretapper distortion, and distortion of legitimate user are given. The inner bounds are derived by using uncoded scheme and (operationally) separate scheme, respectively. Thanks to the equivalence between lossy-equivocation secrecy and list secrecy, information spectrum method is leveraged to prove the outer bound. As special cases, the admissible region for the case of degraded wiretap channel or lossless communication for legitimate user has been characterized completely. For both these two cases, separate scheme is proved to be optimal. Interestingly, however, separation indeed suffers performance loss for other certain cases. Besides, we also extend our results to characterize the achievable region for Gaussian communication case. As a side product, optimistic lossy source coding has also been addressed.