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IEEE Transactions on Vehicular Technology

Evaluation of Multi-Level Amplitude and Phase Quantization for Coded Secret Key Generation

Meixiang Zhang, Ziyue Zhuang, Sooyoung Kim

Published Apr 18, 2025• 1 citation
Publisher

Abstract

For efficient physical layer secret key generation (SKG), a key challenge is to increase the secret key rate while ensuring low inconsistency, low complexity, and low latency. This paper addresses this issue by proposing efficient amplitude and phase quantization (APQ) methods, integrated with a computationally efficient information reconciliation process. Specifically, systematic polar codes are utilized alongside a compact, universally applicable soft-bit extraction method. Furthermore, performance is optimized through the adaptive selection of quantization and information reconciliation parameters, fully leveraging the universal applicability of the proposed soft-bit estimation technique. Simulation results confirm that the proposed methods significantly reduce the initial key disagreement probability (KDP) while achieving substantial complexity reduction. In addition, the proposed methods achieve higher secret key rate with fewer parity bits.

DOI
10.1109/tvt.2025.3561347

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For efficient physical layer secret key generation (SKG), a key challenge is to increase the secret key rate while ensuring low inconsistency, low complexity, and low latency. This paper addresses this issue by proposing efficient amplitude and phase quantization (APQ) methods, integrated with a computationally efficient information reconciliation process. Specifically, systematic polar codes are utilized alongside a compact, universally applicable soft-bit extraction method. Furthermore, performance is optimized through the adaptive selection of quantization and information reconciliation parameters, fully leveraging the universal applicability of the proposed soft-bit estimation technique. Simulation results confirm that the proposed methods significantly reduce the initial key disagreement probability (KDP) while achieving substantial complexity reduction. In addition, the proposed methods achieve higher secret key rate with fewer parity bits.
Physical layer key generation (PLKG) offers a lightweight and low-complexity key management solution for future emerging wireless communication networks. However, current PLKG schemes face challenges in effective integration with practical communication systems, hindering their practical deployment. To solve this problem, this paper proposes a key generation scheme integrated with the 5 G physical layer protocol, leveraging the Demodulation Reference Signal (DM-RS) to extract channel estimation for PLKG, enabling efficient key generation. Furthermore, a soft-decision quantization method based on Multibit Adaptive Quantization is proposed which makes key reconciliation input compatible with the soft-decision input requirements of the Low-Density Parity-Check (LDPC) decoder in 5G channel coding module. Simulation results demonstrate that the proposed scheme successfully integrates into the 5G standard communication framework while still maintaining favorable key disagreement rate (KDR) performance, the key reconciliation using keys derived by soft-decision quantization method can achieve better key agreement performance than using keys derived by binary quantization.
This letter proposes an efficient information reconciliation coding scheme for physical layer secret key generation. We consider a high-rate key generation system, where multiple key bits are extracted from one Gaussian random variable source, each of which has different reliability depending on its bit level. Although the conventional bit-interleaved coded modulation (BICM)-type reconciliation protects all the key bits by forward error correction (FEC), the computational complexity associated with its encoding and decoding can be a bottleneck in achieving a high secret key rate especially for low-cost devices with limited computational capabilities. To alleviate this complexity issue, we propose a new reconciliation scheme that efficiently reduces the complexity by applying FEC only to the least reliable bits (LRBs). We demonstrate by simulations that the proposed information reconciliation based on partial encoding achieves a lower key bit mismatch rate (BMR) than the conventional BICM-type reconciliation even with lower decoding complexity. Furthermore, we provide a lower bound on the asymptotic BMR of the proposed scheme that is useful for estimating the performance in high signal-to-noise ratio (SNR) regimes.
Physical-layer based secret key generation (SKG) becomes a research focus as it solves key distribution problem which is difficult in traditional cryptographic mechanism. To remove the disagreements caused by imperfect reciprocity of communicating parties, information reconciliation is a critical process in SKG to obtain symmetric keys. Various reconciliation schemes are proposed, e.g. BBBSS, Cascade, BCH code and Turbo code. Reconciliation efficiency is a common evaluation index which takes reconciliation success rate and information leakage rate into account. However, time delay caused by information interaction and computation overhead may affect reconciliation performance under specific scenarios. Therefore, a comprehensive evaluation metric is required to compare existing schemes. Besides, channel condition changes all the time in real mobile communication systems, and most existing reconciliation schemes only work well in certain channel conditions. Hence, a reconciliation scheme which can adapt to time-varying channel condition is required. In this paper, we introduce a novel comprehensive reconciliation efficiency index (CREI) to evaluate existing reconciliation schemes and propose an adaptive information reconciliation scheme selection (AIRSS) protocol to maximize CREI. The simulation results show the superiority of AIRSS and present recommendations of reconciliation scheme selection in different scenarios.
Physical layer key generation is one of the promising candidate technology schemes for communication network encryption as it promises to solve the difficulties in traditional cryptographic mechanisms. However, due to the existence of unequal key bits in the process of key generation, the practical application of physical layer key generation is greatly hindered. In this paper, in order to eliminate the key inconsistency problem, we propose a Polar code-based information reconciliation scheme (PIRS) by combining the design mechanism of the 5th generation (5G) physical control channel processing flow in the 5G physical layer protocol. The Monte Carlo simulation results show that our proposed method can significantly reduce the key disagreement rate (KDR) and increase the key generation rate (KGR) for both parties in communication, even when the signal-to-noise ratio is low.
As an alternative and appealing approach to providing information security in wireless communication systems, secret key generation at physical layer has demonstrated its potential in terms of efficiency and reliability over traditional cryptographic methods. Without the necessity of a management centre for key distribution or reliance on computational complexity, physical layer key generation protocols enable two wireless entities to extract identical and dynamic keys from the randomness of the wireless channels associated with them.\nIn this thesis, the reliability of secret key generation at the physical layer is examined in practical wireless channels with imperfect channel state information (CSI). Theoretical analyses are provided to relate key match rate with channel's signal-to-noise ratio (SNR), degrees of channel reciprocity, and iterations of information reconciliation.\nIn order to increase key match rate of physical layer secret key generation, improved schemes in the steps of channel estimation and sample quantization are proposed respectively. In the channel estimation step, multiple observations of the wireless channels are integrated with a linear processor to provide a synthesized and more accurate estimation of the wireless channel. In the sample quantization step, a magnitude based quantization method with two thresholds is proposed to quantize partial samples, where specific quantization areas are selected to reduce cross-over errors. Significant improvements in key match rate are proven for both schemes in theoretical analysis and numerical simulations. Key match rate can even achieve 100% in both schemes with the assistance of information reconciliation process.\nIn the end, a practical application of physical layer secret key generation is presented, where dynamic keys extracted from the wireless channels are utilized for securing secret data transmission and providing efficient access control.
Physical layer security (PLS) of wireless communications is becoming increasingly significant with the advent of 6G. The reconciliation of channel-based secret key generation (SKG) methods is necessary to avoid inconsistencies after key generation, resulting in increased communication overhead, leakage of key information, and reduced security performance. This paper proposes a fuzzy secret key generation (FSKG) method that does not require the legitimate user to perform a consistency check after fuzzy extraction of the phase, which is used directly to encrypt the constellation rotation of the key. The proposed scheme allows users to code-decode the key bits to reduce the transmission error probability and improve the key consistency, and the simulation results prove that the proposed FSKG scheme outperforms traditional SKG schemes like CQA and CQG. The simulation results also indicate that the best secure key rate can be achieved by applying PSK modulation.