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IEEE International Symposium on Information Theory (ISIT)

Secret-key sharing based on layered broadcast coding over fading channels

Xiaojun Tang, Ruoheng Liu, Predrag Spasojević, H. Vincent Poor

Published Jun 1, 2009• 9 citations
Publisher

Abstract

A secret-key sharing strategy based on layered broadcast coding is introduced for slow fading channels. In the model considered, Alice wants to share a key with Bob while keeping the key secret from a passive eavesdropper, Eve. Both Alice-Bob and Alice-Eve channels are assumed to undergo slow fading, and perfect channel state information (CSI) is assumed to be known only at the receivers during the transmission. Layered coding facilitates adapting the reliably decoded rate at Bob to the actual channel state without CSI available at Alice. The index of a reliably decoded layer is sent back to Alice via a public and error-free channel, which is exploited by Alice and Bob to generate the secret key. In this paper, the secrecy key rate is derived. In addition, the optimal power distribution over coded layers is characterized. It is shown that layered coding can increase the secrecy key rate significantly compared with single-level coding.

DOI
10.1109/isit.2009.5205823

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A secret-key sharing strategy based on layered broadcast coding is introduced for slow fading channels. In the model considered, Alice wants to share a key with Bob while keeping the key secret from a passive eavesdropper, Eve. Both Alice-Bob and Alice-Eve channels are assumed to undergo slow fading, and perfect channel state information (CSI) is assumed to be known only at the receivers during the transmission. Layered coding facilitates adapting the reliably decoded rate at Bob to the actual channel state without CSI available at Alice. The index of a reliably decoded layer is sent back to Alice via a public and error-free channel, which is exploited by Alice and Bob to generate the secret key. In this paper, the secrecy key rate is derived. In addition, the optimal power distribution over coded layers is characterized. It is shown that layered coding can increase the secrecy key rate significantly compared with single-level coding.
A secret-key generation scheme based on a layered broadcasting strategy is introduced for slow-fading channels. In the model considered, Alice wants to share a key with Bob while keeping the key secret from Eve, who is a passive eavesdropper. Both Alice-Bob and Alice-Eve channels are assumed to undergo slow fading, and perfect channel state information (CSI) is assumed to be known only at the receivers during the transmission. In each fading slot, Alice broadcasts a continuum of coded layers and, hence, allows Bob to decode at the rate corresponding to the fading state (unknown to Alice). The index of a reliably decoded layer is sent back from Bob to Alice via a public and error-free channel and used to generate a common secret key. In this paper, the achievable secrecy key rate is first derived for a given power distribution over coded layers. The optimal power distribution is then characterized. It is shown that layered broadcast coding can increase the secrecy key rate significantly compared to single-level coding.
A (layered) broadcast approach is studied for the fading wiretap channel without the channel state information (CSI) at the transmitter. Two broadcast schemes, based on superposition coding and embedded coding, respectively, are developed to encode information into a number of layers and use stochastic encoding to keep the corresponding information secret from an eavesdropper. The layers that can be successfully and securely transmitted are determined by the channel states to the legitimate receiver and the eavesdropper. The advantage of these broadcast approaches is that the transmitter does not need to know the CSI to the legitimate receiver and the eavesdropper, but the scheme still adapts to the channel states of the legitimate receiver and the eavesdropper. Three scenarios of block fading wiretap channels with stringent delay constraints are studied, in which either the legitimate receiver's channel, the eavesdropper's channel, or both channels are fading. For each scenario, the secrecy rate that can be achieved via the broadcast approach developed in this paper is derived, and the optimal power allocation over the layers (or the conditions on the optimal power allocation) is also characterized. A notion of probabilistic secrecy, which characterizes the probability that a certain secrecy rate of decoded messages is achieved during one block, is also introduced and studied for scenarios when the eavesdropper's channel is fading. Numerical examples are provided to demonstrate the impact of the CSI at the transmitter and the channel fluctuations of the eavesdropper on the average secrecy rate. These examples also demonstrate the advantage of the proposed broadcast approach over the compound channel approach.
Consider a wireless transmission from Alice to Bob in the presence of an eavesdropper, Eve. We propose a technique to allow Alice to send a message such that Bob can decode it but Eve can get little information about the message. This scenario is a classic example of the wiretap channel, for which several researchers have begun to develop practical schemes. However, we consider a challenging version in which the channel from Alice to Eve may be as good or better than the channel from Alice to Bob. There have been no practical secrecy coding techniques that have been developed for this scenario. The key to allow secret communication in such a scenario is feedback from Bob to Alice (which Eve can also observe). The scheme we develop uses reliability-based hybrid automatic-repeat-request (RB-HARQ) over a fast fading channel to provide a decoding advantage at Bob. Bob requests information about received symbols that suffer from deep fades. The retransmitted symbols improve Bobpsilas ability to decode the message faster than at Eve, who sees retransmission of bits with random reliabilities. We evaluate the proposed scheme by performance measures such as the probability of successful decoding and the equivocation rate at Eve.
We consider a secret communication scenario where Alice wants to transmit secretly to Bob in presence of a passive eavesdropper Eve. The Alice-Bob channel is a fixed-SNR AWGN channel, while the Alice-Eve channel is a fast Rayleigh fading channel, with the channel states only known to Eve. Alice knows the statistics of Alice-Eve channel, but not the exact realizations. We investigate the achievable secrecy rates for this channel model with Gaussian signaling and discrete signaling. For Gaussian signaling, several transmission strategies according to the main channel's relative channel gain are proposed and evaluated. For discrete signaling, achievable secrecy rates with Quadrature Amplitude Modulation (QAM) are evaluated. When Bob's channel is much better than Eve's channel, simple Gaussian signaling can perform close to the upper bound, and is better than the rate achieved with M-QAM. When Bob's channel gain is on average worse than the eavesdropper's average channel gain, positive secrecy rate can still be achieved for Gaussian signaling with artificial noise injection and a burst signaling strategy. Moreover, M-QAM can outperform Gaussian signaling. The key factor that enables secret communication in this case is that both M-QAM and artificial noise limit the leakage of information when Eve's channel is unusually good.
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.
The use of secret keys in broadcast channels with receiver side information is studied. The particular scenario is analyzed where a transmitter wants to send two confidential messages to two receivers, while keeping an external eavesdropper ignorant. Each receiver has one of the confidential messages as side information available for decoding. In addition to that, the transmitter shares independent secret keys of arbitrary rates with both receivers. The secret keys can be used in different ways: They can act as one-time pads to encrypt the confidential messages or they can be used as randomization resources for wiretap coding. Both approaches are discussed and an achievable rate region based on superposition coding is established for the one-time pad approach. For the wiretap coding approach, the secrecy capacity for degraded channels is derived. In the optimal coding scheme, the available secret keys are used as the randomization part of the wiretap code to keep the eavesdropper ignorant. In establishing the capacity region, a new upper bound on the sum-rate is derived. This bound shows that in an optimal coding scheme, in the degraded case, the total equivocation-rate of the (opposite) secret-keys at the legitimate receivers must equal the equivocation-rate of the secret-keys at the eavesdropper, when informed about the messages.