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IEEE Communications Letters

Secret Key Agreement by LLR Thresholding and Syndrome Feedback over AWGN Channel

Stefano Tomasin, Francesco Trentini, Nicola Laurenti

Published Jan 1, 2014• 11 citations
Publisher

Abstract

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.

DOI
10.1109/lcomm.2013.112513.131744

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arXiv:2403.16180•IEEE Open Journal of the Communications Society•Jan 1, 2024•7 citations
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.
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.
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.
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.
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.
New near-capacity continuous-variable quantum key distribution (CV-QKD) reconciliation schemes are proposed, where both the authenticated classical channel (ClC) and the quantum channel (QuC) for QKD are protected by separate forward error correction (FEC) coding schemes. More explicitly, all of the syndrome-based QKD reconciliation schemes found in literature rely on syndrome-based codes, such as low-density parity-check (LDPC) codes. Hence at the current state-of-the-art the channel codes that cannot use syndrome decoding such as the family of convolutional codes (CCs) and polar codes cannot be directly applied. Moreover, the ClC used for syndrome transmission in these schemes is generally assumed to be idealistically error-free, where the realistic additive white Gaussian noise (AWGN) and Rayleigh fading of the ClC have not been taken into account. To circumvent this limitation, a new codeword-based -rather than syndrome-based -QKD reconciliation scheme is proposed, where Alice sends an FEC-protected codeword to Bob through a ClC, while Bob sends a separate FEC protected codeword to Alice through a QuC. Upon decoding the codeword received from the other side, the final key is obtained by applying a simple modulo-2 operation to the local codeword and the decoded remote codeword. As a result, first of all, the proposed codeword-based QKD reconciliation system ensures protection of both the QuC and of the ClC. Secondly, the proposed system has a similar complexity at both sides, where both Alice and Bob have an FEC encoder and an FEC decoder. Thirdly, the proposed system makes QKD reconciliation compatible with a wide range of FEC schemes, including polar codes, CCs and irregular convolutional codes (IRCCs), where a near-capacity performance can be achieved for both the QuC and for the ClC. Our simulation results demonstrate that thanks to the proposed regime, the performance improvements of the QuC and of the ClC benefit each other, hence leading to an improved secret key rate (SKR) that inches closer to both the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound and to the maximum achieveable rate bound.