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IEEE International Symposium on Information Theory (ISIT)

On an upper bound of the secrecy capacity for a general wiretap channel

H. Koga, N. Sato

Published Jan 1, 2005• 13 citations
Publisher

Abstract

This paper is concerned with coding theorems for a generalized wiretap channel. In the problem of the wiretap channel it is important to characterize the secrecy capacity, i.e., the maximum achievable rate of information securely transmitted from a sender to a legitimate receiver in the presence of a wiretapper. In our model, channels are not restricted to memoryless channels. We first define the secrecy capacity Csand evaluate Csfrom information-spectrum approach. We give a new upper bound of Csnot including auxiliary random variables and explore conditions under which the obtained upper bound becomes tight for the cascaded wiretap channel

DOI
10.1109/isit.2005.1523623

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This paper is concerned with coding theorems for a generalized wiretap channel. In the problem of the wiretap channel it is important to characterize the secrecy capacity, i.e., the maximum achievable rate of information securely transmitted from a sender to a legitimate receiver in the presence of a wiretapper. In our model, channels are not restricted to memoryless channels. We first define the secrecy capacity Csand evaluate Csfrom information-spectrum approach. We give a new upper bound of Csnot including auxiliary random variables and explore conditions under which the obtained upper bound becomes tight for the cascaded wiretap channel
In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted code word symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases, and is termed as the generalized wiretap channel for that reason. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at the wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the generalized wiretap channel by the secrecy capacity when the tapped subset is randomly chosen by nature.
In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted codeword symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the new wiretap channel model by the secrecy capacity when the tapped subset is randomly chosen by nature.
In this paper, a new wiretap channel (WTC) model with a discrete memoryless (DM) main channel and a wiretapper who noiselessly observes a fixed portion, of her choice, of the transmitted symbols, while observing the remaining transmitted symbols through another DM channel (DMC), is considered. The strong secrecy capacity of the model is identified. The achievability is established using the output statistics of random binning framework which exploits the duality between source and channel coding problems. The converse is derived by upper bounding the secrecy capacity of an equivalent model with the secrecy capacity of a DM-WTC. This result generalizes both the classical DM-WTC and the WTC-II with a DM main channel.
The wiretap channel with secret keys models the problem of secure communication in the presence of a non-legitimate eavesdropper, where the transmitter and legitimate receiver share a secret key of finite rate. This communication scenario is studied for compound channels. An achievable strong secrecy rate is presented and a multi-letter upper bound is derived. For degraded compound wiretap channels with secret keys the strong secrecy capacity is established. Finally, the case of channel state information at the transmitter is discussed and the secrecy capacity is established for this case as well.
We derive a lower bound on the secrecy capacity of a compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. [1], thus establishing a full coding theorem in this case. We achieve this with a stronger secrecy criterion and the maximum error probability criterion, and with a decoder that is robust against the effect of randomization in the encoding. This relieves us from the need of decoding the randomization parameter, which is in general impossible within this model. Moreover, we prove a lower bound on the secrecy capacity of a compound wiretap channel without channel state information and derive a multiletter expression for the capacity in this communication scenario.
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.