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European Wireless Conference

Secret key agreement on wiretap channel with transmitter side information

Ashish J. Khisti

Published Jan 1, 2010• 11 citations
Publisher

Abstract

The secret-key agreement problem over wiretap channels controlled by a state parameter is studied. The entire state sequence is known (non-causally) to the sender but not to the receiver and the eavesdropper. Upper and lower bounds on the secret-key capacity are established both with and without public discussion. In absence of public-discussion, our lower bound is strictly better than the best known lower bound for transmitting an independent secret message. This illustrates that the coding schemes for secret-key agreement are substantially different than secret-message transmission. For the special case of Gaussian channels, we establish the secret-key capacity when the legitimate receiver's signal-to-noise-ratio is greater than 0 dB. When a public discussion channel is available between the sender and the receiver, upper and lower bounds on the secret-key capacity are again established. These bounds coincide, yielding the capacity, when then the channels of the receiver and the eavesdropper satisfy an independent noise condition.

DOI
10.1109/ew.2010.5483458

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Secret key agreement on wiretap channels with transmitter side information

Ashish J. Khisti

Secret-key agreement protocols over wiretap channels controlled by a state parameter are studied. The entire state sequence is known (non-causally) to the sender but not to the receiver and the eavesdropper. Upper and lower bounds on the secret-key capacity are established both with and without public discussion. The proposed coding scheme involves constructing a codebook to create common reconstruction of the state sequence at the sender and the receiver and another secret-key codebook constructed by random binning. For the special case of Gaussian channels, with no public discussion, - the secret-key generation with dirty paper problem, the gap between our bounds is at-most 1/2 bit and the bounds coincide in the high signal-to-noise ratio and high interference-to-noise ratio regimes. In the presence of public discussion our bounds coincide, yielding the capacity, when then the channels of the receiver and the eavesdropper satisfy an in- dependent noise condition.

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We study secret-key agreement protocols over a wiretap channel controlled by a state parameter. The secret-key capacity is established when the wiretap channel is discrete and memoryless, the sender and receiver are both revealed the underlying state parameter, and no public discussion is allowed. An optimal coding scheme involves a two step approach — (i) design a wiretap codebook assuming that the state parameter is also known to the eavesdropper (ii) generate an additional secret key by exploiting the uncertainty of the state parameter at the eavesdropper. When unlimited public discussion is allowed between the legitimate terminals, we provide an upper bound on the secret-key capacity and establish its tightness when the channel outputs of the legitimate receiver and eavesdropper satisfy a conditional independence property. Numerical results for an on-off fading model suggest that the proposed coding schemes significantly outperform naive schemes that either disregard the contribution of the common state sequence or the contribution of the underlying channel.

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We study secret-key agreement with public discussion over a flat-fading wiretap channel model. The fading gains are correlated across the receivers and sampled independently at each time. Perfect receiver channel state information (CSI) is assumed, whereas a noisy CSI of the main channel is also available to the transmitter. We propose lower and upper bounds on the capacity. Our lower bound is achieved by a coding scheme that involves a separate binning of the receiver CSI sequence and its channel output sequence. In general it improves upon the joint-binning schemes considered in earlier works. Our upper and lower bounds coincide, establishing the capacity, when either the transmitter has no CSI or when the channel gains of the legitimate receiver and the eavesdropper are statistically independent.

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In this paper, the problem of secret key agreement in state-dependent multiple access channels with an eavesdropper is studied. For this model, the channel state information is non-causally available at the transmitters; furthermore, a legitimate receiver observes a degraded version of the channel state information. The transmitters can partially cooperate with each other using a conferencing link with a limited rate. In addition, a backward public channel is assumed between the terminals. The problem of secret key sharing consists of two rounds. In the first round, the transmitters wish to share a common key with the legitimate receiver. Lower and upper bounds on the common key capacity are established. In a special case, the capacity of the common key is obtained. In the second round, the legitimate receiver agrees on two independent private keys with the corresponding transmitters using the public channel. Inner and outer bounds on the private key capacity region are characterized. In a special case, the inner bound coincides with the outer bound. We provide some examples to illustrate our results.

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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.

Iran Workshop on Communication and Information Theory (IWCIT)•May 1, 2013•0 citations
The secret-key agreement problem over wiretap channels controlled by a state parameter is studied. The entire state sequence is known (non-causally) to the sender but not to the receiver and the eavesdropper. Upper and lower bounds on the secret-key capacity are established both with and without public discussion. In absence of public-discussion, our lower bound is strictly better than the best known lower bound for transmitting an independent secret message. This illustrates that the coding schemes for secret-key agreement are substantially different than secret-message transmission. For the special case of Gaussian channels, we establish the secret-key capacity when the legitimate receiver's signal-to-noise-ratio is greater than 0 dB. When a public discussion channel is available between the sender and the receiver, upper and lower bounds on the secret-key capacity are again established. These bounds coincide, yielding the capacity, when then the channels of the receiver and the eavesdropper satisfy an independent noise condition.
Secret-key agreement protocols over wiretap channels controlled by a state parameter are studied. The entire state sequence is known (non-causally) to the sender but not to the receiver and the eavesdropper. Upper and lower bounds on the secret-key capacity are established both with and without public discussion. The proposed coding scheme involves constructing a codebook to create common reconstruction of the state sequence at the sender and the receiver and another secret-key codebook constructed by random binning. For the special case of Gaussian channels, with no public discussion, - the secret-key generation with dirty paper problem, the gap between our bounds is at-most 1/2 bit and the bounds coincide in the high signal-to-noise ratio and high interference-to-noise ratio regimes. In the presence of public discussion our bounds coincide, yielding the capacity, when then the channels of the receiver and the eavesdropper satisfy an in- dependent noise condition.
We study the capacity of secret-key agreement over a wiretap channel with state parameters. The transmitter, the legitimate receiver, and the eavesdropper are connected by a discrete memoryless wiretap channel with a memoryless state sequence. The transmitter and the legitimate receiver generate a secret-key that must be concealed from the eavesdropper. We assume that the state sequence is known noncausally to the transmitter and no public discussion channel is available. We derive lower and upper bounds on the secret-key capacity. The lower bound involves a source-channel codebook for constructing a common reconstruction sequence at the legitimate terminals and then mapping this sequence to a secret-key using a secret-key codebook. For the special case of Gaussian channels with additive interference (secret-keys from dirty paper channel) our bounds differ by 0.5 bit/symbol and coincide in the high signal-to-noise-ratio and high interference-to-noise-ratio regimes. In another special case-symmetric channel state information (CSI)-when the legitimate receiver is also revealed the state sequence, we establish optimality of our lower bound. In addition, only causal side information at the transmitter and the receiver suffices to attain the secret-key capacity in the case of symmetric CSI.
We study secret-key agreement protocols over a wiretap channel controlled by a state parameter. The secret-key capacity is established when the wiretap channel is discrete and memoryless, the sender and receiver are both revealed the underlying state parameter, and no public discussion is allowed. An optimal coding scheme involves a two step approach — (i) design a wiretap codebook assuming that the state parameter is also known to the eavesdropper (ii) generate an additional secret key by exploiting the uncertainty of the state parameter at the eavesdropper. When unlimited public discussion is allowed between the legitimate terminals, we provide an upper bound on the secret-key capacity and establish its tightness when the channel outputs of the legitimate receiver and eavesdropper satisfy a conditional independence property. Numerical results for an on-off fading model suggest that the proposed coding schemes significantly outperform naive schemes that either disregard the contribution of the common state sequence or the contribution of the underlying channel.
We study secret-key agreement with public discussion over a flat-fading wiretap channel model. The fading gains are correlated across the receivers and sampled independently at each time. Perfect receiver channel state information (CSI) is assumed, whereas a noisy CSI of the main channel is also available to the transmitter. We propose lower and upper bounds on the capacity. Our lower bound is achieved by a coding scheme that involves a separate binning of the receiver CSI sequence and its channel output sequence. In general it improves upon the joint-binning schemes considered in earlier works. Our upper and lower bounds coincide, establishing the capacity, when either the transmitter has no CSI or when the channel gains of the legitimate receiver and the eavesdropper are statistically independent.
In this paper, the problem of secret key agreement in state-dependent multiple access channels with an eavesdropper is studied. For this model, the channel state information is non-causally available at the transmitters; furthermore, a legitimate receiver observes a degraded version of the channel state information. The transmitters can partially cooperate with each other using a conferencing link with a limited rate. In addition, a backward public channel is assumed between the terminals. The problem of secret key sharing consists of two rounds. In the first round, the transmitters wish to share a common key with the legitimate receiver. Lower and upper bounds on the common key capacity are established. In a special case, the capacity of the common key is obtained. In the second round, the legitimate receiver agrees on two independent private keys with the corresponding transmitters using the public channel. Inner and outer bounds on the private key capacity region are characterized. In a special case, the inner bound coincides with the outer bound. We provide some examples to illustrate our results.
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.