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arXiv:1301.5136

Secret Key Agreement Using Conferencing in State- Dependent Multiple Access Channels with An Eavesdropper

Bahrami, Mohsen, Ali Bereyhi, Mahtab Mirmohseni, Mohammad Reza Aref

Published Jan 22, 2013• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1301.5136

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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.
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.
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.
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.
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.
In this paper, a generalized multiple access channel (MAC) model for secret key sharing between three terminals is considered. In this model, there are two transmitters and a receiver where all three terminals receive noisy channel outputs. In addition, there is a one-way public channel from the transmitters to the receiver. Each of the transmitters intends to share a secret key with the receiver by using the MAC and the public channel, where the transmitters are eavesdroppers with respect to each other. Two strategies for secret key sharing are considered, namely, the pregenerated key strategy and the two-stage key strategy. For both of them, inner and outer bounds of the secret key capacity region are derived. Furthermore, the effect of the public channel is discussed and the two strategies are compared. In both strategies, it is assumed that the channel outputs at the transmitters are only used for eavesdropping and not as inputs to the encoders. The effect of this assumption in the presence of the public channel is analyzed for some Gaussian MACs.
Strong secrecy communication over a discrete memoryless state-dependent multiple access channel (SD-MAC) with an external eavesdropper is investigated. The channel is governed by discrete memoryless and i.i.d. channel states, and the channel state information (CSI) is revealed to the encoders in a causal manner. The main results of this paper are inner and outer bounds of the capacity region, for which we investigate coding schemes incorporating wiretap coding and secret key agreements between the sender and the legitimate receiver. Two kinds of block Markov coding schemes are proposed. The first is a new coding scheme that uses backward decoding and the Wyner-Ziv coding, and the secret key is constructed from a lossy description of the CSI. The other is an extended version of an existing coding scheme for point-to-point wiretap channels with causal CSI. A numerical example shows that the achievable region given by the first coding scheme can be strictly larger than the second one. However, these two schemes do not outperform each other in general, and there exist some numerical examples in which each coding scheme achieves some rate pairs that cannot be achieved by another scheme. Our established inner bound reduces to some best-known results in the literature as special cases. We further investigate some capacity-achieving cases for state-dependent multiple access wiretap channels (SD-MAWCs) with degraded message sets. It turns out that the two coding schemes are both optimal in these cases.