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arXiv:0807.0942 · IEEE Transactions on Information Theory

Secrecy via Sources and Channels

Vinod M. Prabhakaran, Krishnan Eswaran, Kannan Ramchandran

Published Jul 13, 2012• 31 citations
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Abstract

Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. This problem of secret communication and secret-key generation when two resources are available-correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve which is independent of the sources is studied. The goal is to characterize the fundamental tradeoff between the rates of the secret message and secret key. An achievable solution and proof of its optimality for the parallel channels and sources case when each subchannel and source component satisfies a degradation order (either in favor of the legitimate receiver or the eavesdropper) is presented. This includes the case of jointly Gaussian sources and an additive Gaussian channel, for which the secrecy region is evaluated.

DOI
10.1109/tit.2012.2208579

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Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. This problem of secret communication and secret-key generation when two resources are available-correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve which is independent of the sources is studied. The goal is to characterize the fundamental tradeoff between the rates of the secret message and secret key. An achievable solution and proof of its optimality for the parallel channels and sources case when each subchannel and source component satisfies a degradation order (either in favor of the legitimate receiver or the eavesdropper) is presented. This includes the case of jointly Gaussian sources and an additive Gaussian channel, for which the secrecy region is evaluated.
Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. We study this problem of secret communication and secret key generation when two resources are available – correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve which is independent of the sources. We are interested in characterizing the fundamental trade-off between the rates of the secret message and secret key. We present an achievable solution and prove its optimality for the parallel channels and sources case when each sub-channel and source component satisfies a degradation order (either in favor of the legitimate receiver or the eavesdropper). This includes the case of jointly Gaussian sources and an additive Gaussian channel, for which the secrecy region is evaluated. I.
Alice and Bob want to share a secret key and to communicate an independent message, both of which they desire to be kept secret from an eavesdropper Eve. We study this problem of secret communication and secret key generation when two resources are available — correlated sources at Alice, Bob, and Eve, and a noisy broadcast channel from Alice to Bob and Eve. No other resource, in particular, no other channel is available. We are interested in characterizing the fundamental trade-off between the rates of the secret message and secret key. We present an achievable solution based on a separation architecture and prove its optimality under three settings: when Eve’s source and channel are degraded versions of Bob’s, and either Bob’s source or channel is by itself useless in generating a secret key.
Alice wants to send Bob a secret message in the presence of an eavesdropper Eve. Alice has two resources available: a noisy broadcast channel and source observations correlated with observations at Bob and Eve. We consider two cases, the first in which the source observations and channel are independent and the second in which they can depend on each other. For the independent case, we consider a strategy that exploits the sources and channels separately and show this separation strategy is optimal for a class of sources and channels that includes a Gaussian example. For the case in which the sources and channels depend on each other, this separation strategy does not work, and an optimal strategy has yet to be established. For this setting, we improve on the best known upper bound to the secret message capacity.
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.
In this paper, we consider the problem of secret key generation with one-way communication through both a rate-limited public channel and a rate-limited secure channels where the public channel is from Alice to Bob and Eve and the secure channel is from Alice to Bob. In this model, we do not pose any constraints on the sources, i.e. Bob is not degraded to or less noisy than Eve. We obtain the optimal secret key rate in this problem, for the vector Gaussian sources setting. The characterization is derived by suitably applying the enhancement argument, and Proving a new extremal inequality. The extremal inequality can be seen as coupling of two extremal inequalities, which are related to the degraded compound MIMO Gaussian broadcast channel, and the vector generalization of Costa's entropy power inequality, accordingly.