With the advent of innovative wireless technologies and the rapid growth of diverse connected devices, ensuring communication security has become a critical challenge for the future massively connected beyond 5th generation (B5G) wireless networks. The physical layer security (PLS) approach leverages the inherent physical medium characteristics of communication networks to provide secure communications. In particular, the wireless channel-based secret key generation (SKG) is a PLS approach that creates symmetric keys for message encryption/decryption by exploiting the randomness inherent in wireless channels while relying on the channel to be reciprocal between the nodes. This work proposes a novel SKG algorithm that emphasizes the pre-processing and quantization stages with the aim to increase the key generation rate (KGR) and the key agreement rate (KAR) between the legitimate nodes. The algorithm employs biasing of selective samples and sliding-window weighted averaging of the Generalized Gamma fading channel samples based on the channel’s average contiguous duration (ACD) metric, a second-order fading statistic, to enhance the channel reciprocity. The proposed scheme may also be used to improve the key randomness rate (KRR) by using a non-contiguous multi-level quantization strategy that evenly sets the quantization intervals to accommodate a similar number of channel samples across these intervals. Thus, a desired trade-off between the KGR, KAR, and KRR to meet operational requirements can be achieved with the proposed scheme. Finally, a comprehensive analysis of the performance gains of the proposed scheme in relation to other notable works is conducted by investigating the impact of several channel and algorithmic parameters on the KGR, KAR, and KRR of these schemes.
Ensuring reliable and secure communications in the increasingly pervasive beyond
5thgeneration (B5G) wireless networks is one of the key research challenges. Within the physical layer security (PLS) paradigm, the secret key generation (SKG) technique exploits the wireless channel’s randomness to generate symmetric secret keys for message encryption/decryption by legitimate communication nodes. The SKG procedure involves various steps such as wireless channel probing, quantization, information reconciliation, and privacy amplification to render effective symmetric secret key bits. This work proposes a novel multi-level channel quantization scheme, which for the given distribution of the channel envelopes’ gain, ensures an identical likelihood of the envelope samples falling into each quantization interval. Inspired by the classical companding transform (CT), the proposed probability integral transform (PIT)–based quantization scheme works in three sequential steps. First, average contiguous duration (ACD), a second-order fading statistics metric, is considered to select and bias the channel samples that are more likely to fall in the same quantization interval. Subsequently, by using an invertible transform the envelope values are transformed into samples drawn from a uniform distribution, which are then processed through a uniform quantizer. The proposed PIT-based transformation and quantization scheme aims to enhance the trade-offs between the SKG performance metrics namely the key generation rate (KGR), key disagreement rate (KDR), and the key randomness properties. A comprehensive performance analysis of the proposed PIT-based quantization scheme for generalized gamma (GG) fading channels is conducted and its performance is evaluated in relation to several channel and system parameters. Moreover, a comparative analysis of the proposed scheme with its counterparts in the literature is also provided to demonstrate its relative performance gains, where our proposed scheme is observed to outperform the existing schemes. Notably, when the correlation of the reciprocal channel is set to
ρ=0.8, the samples excursion qualification threshold is set to
L=3, and GG fading conditions set as defined by
α=2,
ξ=1, and
υ=1, the proposed algorithm, which employs sample biasing and transformation, offers an average improvement of 0.02% in KGR and 0.15% in KDR performance compared to the conventional UQ scheme. Additionally, the algorithm demonstrates superior performance in all considered eight the National Institute of Standards and Technology (NIST) randomness tests, exemplified by an average P-value of 0.78 in the frequency monobit test. Furthermore, for the considered system and channel parameters the proposed algorithm provides an average improvement of 0.06% in KDR compared to cumulative distribution function (CDF)-based non-uniform quantization (CDF-NUQ).
The wireless channel-based Secret Key Generation (SKG) algorithms aim at securing the wireless link against unauthorized eavesdropping by exploiting the channel’s randomness for generating matching secret keys at the legitimate nodes for message encryption/decryption. To counter differences in hardware and noise conditions at the legitimate nodes, which can lead to key mismatch, the SKG algorithms typically include the intermediate steps of sampling, quantization, information reconciliation, and privacy amplification. These steps collectively aim to improve the performance trade-offs between Key Generation Rate (KGR), Key Agreement Probability (KAP), and Secret Key Randomness (SKR) properties. This paper derives a closed-form expression for the Average Contiguous Duration (ACD) of Generalized Gamma (GG) fading wireless channels. The ACD is a recently introduced novel quantifier for characterizing the second-order statistics of fading channels, which includes Average Fade Duration (AFD) as its special case. The proposed GG fading ACD expression is shown to include, as its special cases, the ACD for commonly observed fading distributions such as Gamma, Nakagami-
m , and Rayleigh. By exploiting the derived GG ACD expression, a multi-level quantization scheme for SKG is proposed that determines suitable quantization intervals for identical likelihood of an equal number of consecutive channel samples falling in each quantization interval. A comprehensive comparative analysis of the proposed ACD-based quantization for SKG is conducted in relation to conventional Uniform Quantization (UQ) and Cumulative Distribution Function (CDF)-based Non-Uniform Quantization (NUQ) schemes. The presented numerical results confirm the superior performance trade-off between KGR and KAP offered by the proposed ACD-based quantization in relation to that offered by UQ and CDF-based NUQ.
The rapid technological advancements in wireless networks have resulted in tremendous increase in the number of connected user and machine-type wireless devices. Physical Layer Security (PLS) has a strong potential for providing security to wireless links in massively connected future wireless networks. The key-based PLS methods aim at generating secret key bits for data encryption/decryption at the legitimate communication nodes by exploiting the randomness inherent in wireless channels. This work proposes a novel secret key-bits extraction algorithm named Moving-Window Wrapped-Envelope Secret Key Generation (MWWE-SKG). The proposed algorithm uses first-order statistics from a sliding temporal window of channel samples to select the channel quantization interval for each window from circularly wrapped channel envelope samples. The differences in hardware noise conditions at the legitimate nodes lead to differences in the measurement of ideally reciprocal channels, which further leads to a mismatch in the generated secret key bits, whereas the channel statistics of the same links are more likely to remain unchanged for a reasonably large length of time window over the channel samples. An extensive analysis on the performance of the proposed algorithm is conducted, where the proposed algorithm is observed to provide a promising trade-off between the critical SKG performance metrics namely the Key Generation Rate (KGR), Bit Mismatch Probability (BMP), and the Key Randomness Property (KRP). Furthermore, a comparative performance analysis of the proposed algorithm with other notable techniques is also conducted to demonstrate the superior performance of the proposed algorithm.
Physical layer security (PLS) techniques hold promise for augmenting secure communications in the 5thgeneration of mobile wireless networks. Secret key generation (SKG) is a PLS technique which exploits the wireless propagation channel's randomness to generate symmetric key bits for information encryption and decryption. This work proposes symmetric key generation based on non-uniform quantization of the received signal strength (RSS) samples of a Nakagami-
m fading channel. The proposed strategy for non-uniform quantization for SKG aims to set quantization thresholds for maximal key randomness and high values of key generation rate (KGR) and key agreement probability (KAP). Finally, a framework is proposed to use single node RSS measurements, readily available in the literature, to generate RSS samples at the other link end. This framework facilitates the testing of new SKG algorithms that require simultaneous RSS measurements by the legitimate nodes, which are not readily available in the open literature. The effectiveness of the proposed SKG scheme is validated through Monte Carlo methods and the National Institute of Standards and Technology (NIST) test suite for assessing the randomness of the generated key sequence.
Physical Layer-based Secret Key Generation (PLSKG) between the legitimate nodes from the reciprocal wireless channel is a vastly studied area of Physical Layer Security (PLS). PLSKG aims to secure the wireless link between the legitimate nodes by symmetrically encrypting the wirelessly transmitted information via a secret key that is extracted from the common randomness of the stochastic wireless channel. PLSKG encompasses the intermediate steps of channel sampling, quantization, information reconciliation, and privacy amplification. The PLSKG algorithms are evaluated in terms of quantifiers such as Key Generation Rate (KGR), Key Agreement Probability (KAP), and randomness. The practical PLSKG algorithms (level-crossing algorithms) extract a secret key by analyzing the channel samples and assigning bit sequences to the channel samples lying in different quantization regions. Level-crossing algorithms are lossy and extract a secret key from the central samples of matched excursions between the legitimate nodes. This results in a reduced KGR as there is a scarcity of such matched excursions considering the fast variations of the wireless link between the legitimate nodes. This paper proposes a Two-Round Channel Parsing (TRCP) algorithm that exploits the correlation between the excursion lengths of the channel samples in addition to the sample correlation. TRCP effectively utilize the channel samples by reducing the sample losses incurred by lossy quantizers exploring a new dimension of correlated excursions of the channel samples between legitimate nodes. Simulation results demonstrate that the proposed TRCP scheme enhances the KGR and KAP performance of the secret key and also passes the National Institute of Standards and Technology (NIST) test suite of randomness.
As Beyond 5thGeneration (B5G) networks expand, securing communication links remains a challenge. Physical Layer Security (PLS) is a promising paradigm, and this work explores wireless channel-based Secret Key Generation (SKG) by proposing an Extended Huffman Coding (EHC) framework to enhance quantization stage. While non-uniform coding is common in Analog-to-Digital (A2D) conversion, it remains largely unexplored in SKG due to key mismatch risks. To address this, we propose a Huffman Coding (HC)-inspired framework that generates binary codes using reversed HC principles and extends them by sequentially altering the Least Significant Bit (LSB), ensuring equal-length unique codes for quantization levels while enhancing generation rate, agreement, and randomness. Additionally, histogram/ Probability Density Function (PDF) matching aligns quantization level probabilities at legitimate nodes to minimize mismatches while exchanging minimal statistical information without compromising secrecy. Unlike conventional quantization, which relies on predetermined codes vulnerable to eavesdropping, our scheme dynamically computes quantization codes at runtime, adding an extra layer of security. Moreover, while conventional HC avoids codes of a level to be a subcode of another level, SKG benefits when one code is a subcode of another, making detection harder. Instead of compression, as desired in conventional A2D conversion, SKG requires longer and random keys that reliably match at legitimate nodes, which our scheme ensures. Simulations are conducted under Rice-fading conditions that evaluate the impact of variations in the Rician K-factor on SKG performance. The proposed method is assessed using key SKG metrics named: Key Agreement Rate (KAR), Key Generation Rate (KGR), and Key Randomness Rate (KRR) (employing the NIST test suite). The obtained results demonstrate the potential of our proposed scheme for secure and scalable SKG solutions in future networks.