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International Symposium on Wireless Communication Systems

Resource allocation for secret key agreement by LLR thresholding over parallel channels

Alberto Dall’Arche, Stefano Tomasin

Published Aug 1, 2014• 2 citations
Publisher

Abstract

We consider a channel-model based secret key agreement (SKA) over parallel channels, where Alice transmits a random sequence of bits, and Bob selects those having an absolute value of log-likelihood ratio (LLR) larger than a given threshold. Distillation and reconciliation processes follow, independently on each channel. Assuming a total transmit power constraint, we aim at choosing both the LLR threshold and the transmit power on each channel, in order to maximize the secret key throughput (SKT), under a full channel state information of both legitimate and eavesdropper channels. A two-step solution is considered. First the LLR threshold is determined on a per-channel basis for a given power allocation by numerical methods. Then we fit the SKT as a function of the transmit power by an exponential function and the power allocation problem is solved in closed form. Extensive simulation results show accuracy of the fitting function and the importance of the optimization, also for practical reconciliation processes.

DOI
10.1109/iswcs.2014.6933491

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We consider a channel-model based secret key agreement (SKA) over parallel channels, where Alice transmits a random sequence of bits, and Bob selects those having an absolute value of log-likelihood ratio (LLR) larger than a given threshold. Distillation and reconciliation processes follow, independently on each channel. Assuming a total transmit power constraint, we aim at choosing both the LLR threshold and the transmit power on each channel, in order to maximize the secret key throughput (SKT), under a full channel state information of both legitimate and eavesdropper channels. A two-step solution is considered. First the LLR threshold is determined on a per-channel basis for a given power allocation by numerical methods. Then we fit the SKT as a function of the transmit power by an exponential function and the power allocation problem is solved in closed form. Extensive simulation results show accuracy of the fitting function and the importance of the optimization, also for practical reconciliation processes.
We consider the distillation phase of the secret key agreement (SKA) channel model for users connected through parallel additive white Gaussian noise fading channels. Alice sends binary phase shift keying modulated random bits to Bob who selects the subset of bits that have a log-likelihood ratio higher than a given threshold, i.e., they are sufficiently reliable. Alice has either full or partial channel state information (CSI) on her channel to the eavesdropper Eve. The main contributions of this paper are: 1) the derivation of the expression of outage probability when partial CSI is available; 2) the introduction of (outage) secret key throughput (SKT) as a metric in the full (partial) CSI scenario; 3) the derivation of SKT bounds; 4) the proposal of a new power allocation and threshold choice algorithm that maximizes the SKT under an outage probability constraint; and 5) the derivation of a suboptimal version of the allocation algorithm amenable for practical implementation obtained by approximating the objective functions with a closed-form expression. Moreover, we show that when power allocation and thresholds are optimized, per-channel and joint SKA are equivalent.
In this paper we propose novel advantage distillation and reconciliation approaches for secret key agreement (SKA) over additive white Gaussian noise (AWGN) (possibly fading) channels, using binary phase shift keying (BPSK) constellations. For advantage distillation Bob selects bits having an absolute log-likelihood ratio (LLR) larger than some threshold. For reconciliation, Alice transmits the syndrome of the selected bits with respect to a globally pre-shared forward error correcting (FEC) code. We show that the syndrome transmission does not diminish the advantage of Bob over Eve on the key knowledge, thus being an efficient solution. For the proposed scheme we derive both a lower bound on the achievable secret key rate with ideal wiretap coding, and the effective throughput achieved by using practical codes.
A transmission between two agents, Alice and Bob, over a set of parallel sub-channels is overheard by a third agent Eve, through a second set of parallel sub-channels. All subchannels are flat with random and independent gains and additive white Gaussian noise (AWGN). Alice splits the total amount of available power among the sub-channels, with the purpose of maximizing the communication rate to Bob, under reliability and secrecy constraints. To this end, two schemes are considered. In one case the secret message is encoded with a single wiretap code and then split among the sub-channels. In the latter case the secret message is first split into a number of sub-messages, each separately encoded and transmitted on a different sub-channel. The achievable secrecy rates under a constraint on the secrecy outage probability (SOP) are derived and closed form expressions for Rayleigh fading sub-channels are obtained. In order to limit the complexity of resources optimization (power and rates) we also consider suboptimal solutions based on the selection of active sub-channels over which power is split either equally or according to a waterfilling algorithm with respect to the Alice-Bob channel.
Physical layer approaches for generating secret encryption keys for wireless systems using channel information have attracted increased interest from researchers in recent years. This paper presents a new approach for calculating log-likelihood ratios (LLRs) for secret key generation that is based on one-bit quantization of channel measurements and the difference between channel estimates at legitimate reciprocal nodes. The studied secret key agreement approach, which implements advantage distillation along with information reconciliation using Slepian-Wolf low-density parity-check (LDPC) codes, is discussed and illustrated with numerical results obtained from simulations. These results show the probability of bit disagreement for keys generated using the proposed LLR calculations compared with alternative LLR calculation methods for key generation based on channel state information. The proposed LLR calculations are shown to be an improvement to the studied approach of physical layer secret key agreement.
Abstract The novel advantage distillation (AD) scheme for secret key agreement (SKA) scheme over relay communication system for the wiretap channel model is proposed. For the case where there are noiseless both the main channel and the eavesdropper’s channel, the SKA scheme for the noiseless relay communication (SKA-NRC) system is proposed. In this scheme, random sequences qA and qB are used as artificial interference to prevent eavesdropping. Simulation results show that with the proposed SKA schemes, the bit error ratio (BER) of eavesdropper Eve maintains stably at 0.5, while legitimate users Alice and Bob are able to get much lower BERs.
Physical layer approaches for generating secret encryption keys for wireless systems using channel information has attracted increased interest from researchers in recent years. This paper presents a new approach for secret key generation that is based on one-bit quantization of channel measurements along with log-likelihood ratios (LLRs) that are calculated based on the difference between channel estimates at legitimate reciprocal nodes. The proposed approach, which implements advantage distillation along with information reconciliation using Slepian-Wolf low-density parity check (LDPC) codes, is discussed and illustrated with numerical results obtained from simulations. These show the probability of bit disagreement for keys generated through the proposed approach and compare it with that of alternative methods for key generation based on channel state information.