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International Conference on Modern Problems of Radio Engineering, Telecommunications and Computer Science

Gaussian wiretap channel with collaborative wiretappers

Slava Voloshynovskiy, Taras Holotyak, Ivan Prudyus

Published May 7, 2012• 0 citations
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Abstract

Abstract—In this paper, we consider the compound wiretap channel with collaborative wiretappers. Contrarily to [1], where the wiretappers act independently, we analyze the setup when the wiretappers form a coalition, which shares the observed data within the coalition. The goal of coalition consists in learning the secret message communicated to the legitimate user by sharing their observations to produce the best possible estimate thus benefiting from available redundancy. We analyze the secrecy capacity for the Gaussian data and correlated observations. As the result, we provide the estimate of the impact of coalition of wiretappers on reduction of secrecy capacity. Index Terms—Wiretap channel, secrecy capacity, collaborative wiretappers. I.

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Abstract—In this paper, we consider the compound wiretap channel with collaborative wiretappers. Contrarily to [1], where the wiretappers act independently, we analyze the setup when the wiretappers form a coalition, which shares the observed data within the coalition. The goal of coalition consists in learning the secret message communicated to the legitimate user by sharing their observations to produce the best possible estimate thus benefiting from available redundancy. We analyze the secrecy capacity for the Gaussian data and correlated observations. As the result, we provide the estimate of the impact of coalition of wiretappers on reduction of secrecy capacity. Index Terms—Wiretap channel, secrecy capacity, collaborative wiretappers. I.
The wiretap channel models the communication scenario where two legitimate users want to communicate in such a way that an external wiretapper is kept ignorant. In this paper the wiretap channel with side information is studied, where the wiretapper has additional side information about the transmitted message available for decoding. The corresponding secrecy capacity is derived and shown to be equal to the one of the classical wiretap channel without side information available at the wiretapper. Further, the capacity-achieving code structure is analyzed and properties are identified. Finally, channel uncertainty is taken into account and the results are extended to the compound wiretap channel with side information.
The wiretap channel models the communication scenario where two legitimate users want to communicate in such a way that a wiretapper is kept ignorant. In this paper, the wiretap channel with side information is studied, where the wiretapper has additional side information available. This side information allows the wiretapper to restrict the transmitted message to a certain subset of messages before further postprocessing. Two different criteria are employed to model the secrecy of the confidential message: the information theoretic criterion of strong secrecy and a signal-processing-inspired criterion based on the decoding performance of the wiretapper. For the latter, the wiretapper is required to have the worst decoding performance regardless of the specific decoding strategy that is used. It is shown that both criteria are equivalent in terms of secrecy capacity. Furthermore, the secrecy capacity equals the one of the classical wiretap channel without side information available at the wiretapper. In addition, the corresponding capacity-achieving code structure and optimal transceiver design are characterized and properties are identified. Finally, extensions to channel uncertainty and multiple wiretappers are discussed.
The compound wiretap channel provides a general framework for studying secrecy communication under channel uncertainty. Characterizing the secrecy capacity of nondegraded compound wiretap channels is a challenging problem in information theory. This paper considers the class of parallel Gaussian compound wiretap channels with only one possible channel realization for the legitimate receiver and characterizes the secrecy capacity. (Such parallel Gaussian compound wiretap channels are generally nondegraded.) Moreover, it is shown that the proposed coding scheme strictly outperforms the best known single-letter scheme with Gaussian codebooks.
We study the two-user one-eavesdropper discrete memoryless compound wiretap channel, where the transmitter sends a common confidential message to both users, which needs to be kept perfectly secret from the eavesdropper. We provide a new achievable secrecy rate which is shown to be potentially better than the best known lower bound for the secrecy capacity of this compound wiretap channel. We next consider the two-user one-eavesdropper Gaussian multiple-input multiple-output (MIMO) compound wiretap channel. We obtain an achievable secrecy rate for the Gaussian MIMO compound wiretap channel by using dirty-paper coding (DPC) in the achievable scheme we provided for the discrete memoryless case. We show that the corresponding achievable secrecy rate achieves at least half of the secrecy capacity of the two-user one-eavesdropper Gaussian MIMO wiretap channel. We also obtain the secrecy capacity of the two-user one-eavesdropper Gaussian MIMO compound wiretap channel when the eavesdropper is degraded with respect to one of the two users.
The concept of the wiretap channel was first proposed by Wyner. He considered the case in which data is to be transmitted reliably over a discrete memoryless main channel to a legitimate receiver. The wiretapper views the output of the main channel through another discrete memoryless channel. It is assumed that the wiretapper knows the code being used and his only handicap is the additional noise in his signal. The problem is to maximize the transmission rate R to the legitimate receiver and the equivocation d of the wiretapper. In this dissertation, the additive white Gaussian noise wiretap channel is introduced and the set of all achievable (R,d) pairs is determined explicitly through the use of certain special properties of the Gaussian channel. Some useful characterizations of a special class of wiretap channels are also explored. A model of the wiretap channel with feedback is proposed. It turns out that with the introduction of feedback, even when the main channel is inferior to the wiretapper's channel, it is still possible to reliably communicate with the legitimate receiver in complete secrecy. The binary erasure wiretap channel with feedback is examined and inner and outer bounds on the achievable (R,d) region are given. Finally, a scheme for enlarging the capacity region of multiple-access channels using feedback is analyzed. It is shown that conditions under which an enlargement is possible are fairly weak, indicating that feedback can almost increase the capacity region. (Author)
The wiretap channel models the communication scenario where two legitimate users want to communicate in such a way that an external wiretapper is kept ignorant. In this paper, the wiretap channel with side information is studied, where the wiretapper has additional side information about the transmitted message available for post-processing. The secrecy of the message is modeled by the decoding performance of the wiretapper. It is required for the wiretapper to have worst behavior of decoding performance regardless of the decoding strategy that is used. The secrecy capacity is derived and shown to be equal to the one of the classical wiretap channel without side information available at the wiretapper. Further, the corresponding optimal transceiver design is characterized.