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Entropy

An Efficient Advantage Distillation Scheme for Bidirectional Secret-Key Agreement

Yan Feng, Xueqin Jiang, Jia Hou, Hui‐Ming Wang, Yi Xian Yang

Published Sep 18, 2017• 5 citations
Publisher

Abstract

The classical secret-key agreement (SKA) scheme includes three phases: (a) advantage distillation (AD), (b) reconciliation, and (c) privacy amplification. Define the transmission rate as the ratio between the number of raw key bits obtained by the AD phase and the number of transmitted bits in the AD. The unidirectional SKA, whose transmission rate is 0 . 5, can be realized by using the original two-way wiretap channel as the AD phase. In this paper, we establish an efficient bidirectional SKA whose transmission rate is nearly 1 by modifying the two-way wiretap channel and using the modified two-way wiretap channel as the AD phase. The bidirectional SKA can be extended to multiple rounds of SKA with the same performance and transmission rate. For multiple rounds of bidirectional SKA, we have provided the bit error rate performance of the main channel and eavesdropper’s channel and the secret-key capacity. It is shown that the bit error rate (BER) of the main channel was lower than the eavesdropper’s channel and we prove that the transmission rate was nearly 1 when the number of rounds was large. Moreover, the secret-key capacity C s was from 0 . 04 to 0 . 1 as the error probability of channel was from 0 . 01 to 0 . 15 in binary symmetric channel (BSC). The secret-key capacity was close to 0 . 3 as the signal-to-noise ratio increased in the additive white Gaussian noise (AWGN) channel.

DOI
10.3390/e19090505

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The classical secret-key agreement (SKA) scheme includes three phases: (a) advantage distillation (AD), (b) reconciliation, and (c) privacy amplification. Define the transmission rate as the ratio between the number of raw key bits obtained by the AD phase and the number of transmitted bits in the AD. The unidirectional SKA, whose transmission rate is 0 . 5, can be realized by using the original two-way wiretap channel as the AD phase. In this paper, we establish an efficient bidirectional SKA whose transmission rate is nearly 1 by modifying the two-way wiretap channel and using the modified two-way wiretap channel as the AD phase. The bidirectional SKA can be extended to multiple rounds of SKA with the same performance and transmission rate. For multiple rounds of bidirectional SKA, we have provided the bit error rate performance of the main channel and eavesdropper’s channel and the secret-key capacity. It is shown that the bit error rate (BER) of the main channel was lower than the eavesdropper’s channel and we prove that the transmission rate was nearly 1 when the number of rounds was large. Moreover, the secret-key capacity C s was from 0 . 04 to 0 . 1 as the error probability of channel was from 0 . 01 to 0 . 15 in binary symmetric channel (BSC). The secret-key capacity was close to 0 . 3 as the signal-to-noise ratio increased in the additive white Gaussian noise (AWGN) channel.
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.
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.
The three-phase process of achieving secret sharing over a wiretap channel are, respectively, advantage distillation, information reconciliation, and privacy amplification. In this paper, we first generalize the extended orthogonal space time block codes (EO-STBCs). Then, based on the generalized EO-STBCs (GEO-STBCs) and the feedback bits from the legitimate receiver, we propose a new advantage distillation scheme for multiple-input multiple-output (MIMO) wiretap channels. Simulation results show that the bit error rate (BER) performance gain up to 4.2 dB is obtained by the legitimate receiver over the eavesdropper at the BER of 10−5. Moreover, it is shown that the feedback performance gain of the proposed advantage distillation scheme grows exponentially with signal-to-noise ratio (SNR).
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.
Underwater acoustic communications (UWACs) are being adopted in several applications, and their security mechanisms require periodically renewed symmetric keys among legitimate devices. To this end, a secret key agreement (SKA) exploiting the UWAC context can be implemented. In this paper, we focus on one step of the source-based SKA protocol, i.e., the advantage distillation, when the legitimate users pre-process the channel measurement to increase the agreement while decreasing the attacker's knowledge about the key. We propose to learn the advantage distillation process by using a dataset of observed channels from the legitimate parties and the attacker, respectively. In turn, also the attacker uses such data to extract the key from its own underwater channel observations. The key extraction functions are derived through a computationally efficient data-driven adversarial strategy based on a metric related to the secret key rate that can be computed with a lower computational cost. The proposed strategy is tested considering experimental UWAC data, derived from a sea experiment. Results prove the quick convergence of the algorithm and the advantage of using the proposed techniques.
We consider a physical layer-based secret-key-agreement (SKA) scenario where Alice and Bob aim at extracting a common bit sequence, which should remain secret to Eve, by quantizing a random number obtained from measurements of their communication channel. We propose an asymmetric advantage distillation protocol where i) Alice quantizes her measurement and sends partial information on it over an authenticated public side channel, and ii) Bob (and Eve) quantizes his measurement by exploiting the partial information. The partial information on the position of the measurement in the quantization interval allows Bob to obtain a quantized value closer to that of Alice. Such strategies are shown to increase the lower bound of the secret key rate.