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IEEE Information Theory Workshop (ITW)

Wiretap channel with shared key

Wei Kang, Nan Liu

Published Aug 1, 2010• 54 citations
Publisher

Abstract

This paper studies the problem of secure communication over a wiretap channel where the transmitter and the legitimate receiver share a secret key, which is concealed from the eavesdropper. We find the secrecy capacity under this scenario. This result generalizes that of Yamamoto, which is applicable only to less noisy wiretap channels, to the general wiretap channel when no distortion is allowed at the legitimate receiver.

DOI
10.1109/cig.2010.5592665

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This paper studies the problem of secure communication over a wiretap channel where the transmitter and the legitimate receiver share a secret key, which is concealed from the eavesdropper. We find the secrecy capacity under this scenario. This result generalizes that of Yamamoto, which is applicable only to less noisy wiretap channels, to the general wiretap channel when no distortion is allowed at the legitimate receiver.
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.
The broadcast channel with independent secret keys models a communication scenario in which a common message has to be securely broadcast to two legitimate receivers keeping an eavesdropper ignorant of it.The transmitter shares an independent secret key of arbitrary rate with each legitimate receiver.Depending on the channel qualities of the legitimate receivers and the eavesdropper, these secret keys must be used as one-time pads to encrypt the message, as fictitious messages for randomization in wiretap coding, or a combination of both to achieve the secrecy capacity.In this paper, communication takes place over independent parallel subchannels and the secrecy capacity is established for these cases, in which all parallel channels follow the same order of degradation.
The problem of secure broadcasting with independent secret keys is studied. The particular scenario is analyzed where a common message has to be broadcasted to two legitimate receivers, while keeping an external eavesdropper ignorant of it. The transmitter shares independent secret keys of arbitrary rates with both legitimate receivers, which can be used in different ways: They can be used as one-time pads to encrypt the common message or they can be used as randomization resources for wiretap coding. Both approaches are studied in this paper. If both legitimate channels are degraded versions of the eavesdropper channel, it is shown that the one-time pad approach is optimal for several cases yielding corresponding capacity expressions. Reversely, the wiretap coding approach is shown to be optimal if the eavesdropper channel is degraded with respect to both legitimate channels establishing capacity in this case as well.
The broadcast channel with independent secret keys is studied. In this scenario, a common message has to be securely broadcast to two legitimate receivers in the presence of an eavesdropper. The transmitter shares with each legitimate receiver an independent secret key of arbitrary rate. These keys can either be used as one-time pads to encrypt the common message or can be interpreted as fictitious messages used as randomization resources for wiretap coding. Both approaches are discussed and the secrecy capacity is derived for various cases. Depending on the qualities of the legitimate and eavesdropper channels, either a one-time pad, wiretap coding, or a combination of both turns out to be capacity-achieving.
The problem of secure broadcasting with independent secret keys is studied. The particular scenario is analyzed in which a common message has to be broadcast to two legitimate receivers, while keeping an external eavesdropper ignorant of it. The transmitter shares independent secret keys of sufficiently high rates with both legitimate receivers, which can be used in different ways: they can be used as one-time pads to encrypt the common message, as fictitious messages for wiretap coding, or as a hybrid of these. In this paper, capacity results are established when the broadcast channels involving the three receivers are degraded. If both legitimate channels are degraded versions of the eavesdropper's channel, it is shown that the one-time pad approach is optimal for several cases, yielding corresponding capacity expressions. Alternatively, the wiretap coding approach is shown to be optimal if the eavesdropper's channel is degraded with respect to both legitimate channels, establishing capacity in this case as well. If the eavesdropper's channel is neither the strongest nor the weakest, an intricate scheme that carefully combines both concepts of one-time pad and wiretap coding with fictitious messages turns out to be capacity-achieving. Finally we also obtain some results for the general non-degraded broadcast channel.
In this paper, we consider the problem of secret key agreement in state-dependent 3-receiver broadcast channels. In the proposed model, there are two legitimate receivers, an eavesdropper and a transmitter where the channel state information is non-causally available at the transmitter. We consider two setups. In the first setup, the transmitter tries to agree on a common key with the legitimate receivers while keeping it concealed from the eavesdropper. Simultaneously, the transmitter agrees on a private key with each of the legitimate receivers that needs to be kept secret from the other legitimate receiver and the eavesdropper. For this setup, we derive inner and outer bounds on the secret key capacity region. In the second setup, we assume that a backward public channel is available among the receivers and the transmitter. Each legitimate receiver wishes to share a private key with the transmitter. For this setup, an inner bound on the private key capacity region is found. Furthermore, the capacity region of the secret key in the state-dependent wiretap channel can be deduced from our inner and outer bounds.