This paper proposes a vector-quantization-based secret key generation (SKG) procedure to efficiently extract shared secret keys from correlated channel observations at two communicating terminals, Alice and Bob. Most existing SKG schemes utilize scalar quantization to extract secret key bits separately from each individual channel observation. This approach is simple to implement but yields higher key disagreement probability (or lower key entropy) compared with vector-quantization-based approaches. However, regardless of the quantizer design, quantization for SKG often suffers from the so-called cell-boundary problem, which occurs when the channel observations at Alice and Bob lie close to the quantization cell boundaries, resulting in high probability of key disagreement. In this paper, a general SKG procedure that utilizes sample and quantizer selection techniques to avoid this problem is first proposed. The vector quantizer adopted in the above procedure is designed by minimizing the quadratic distortion between the true channel vector and the noisy observation at Alice (or Bob). Then, by considering the case where the eavesdropper (Eve) may observe a channel vector that is correlated with that observed by Alice and Bob, a clustered key mapping scheme that assigns each secret key to multiple quantization cells in different clusters is also proposed to induce additional randomness at Eve and, thus, maintain high conditional key entropy. The effectiveness of the proposed schemes is demonstrated through computer simulations.
This paper proposes a vector-quantization-based secret key generation (SKG) procedure to efficiently extract shared secret keys from correlated channel observations at two communicating terminals, Alice and Bob. Most existing SKG schemes utilize scalar quantization to extract secret key bits separately from each individual channel observation. This approach is simple to implement but yields higher key disagreement probability (or lower key entropy) compared with vector-quantization-based approaches. However, regardless of the quantizer design, quantization for SKG often suffers from the so-called cell-boundary problem, which occurs when the channel observations at Alice and Bob lie close to the quantization cell boundaries, resulting in high probability of key disagreement. In this paper, a general SKG procedure that utilizes sample and quantizer selection techniques to avoid this problem is first proposed. The vector quantizer adopted in the above procedure is designed by minimizing the quadratic distortion between the true channel vector and the noisy observation at Alice (or Bob). Then, by considering the case where the eavesdropper (Eve) may observe a channel vector that is correlated with that observed by Alice and Bob, a clustered key mapping scheme that assigns each secret key to multiple quantization cells in different clusters is also proposed to induce additional randomness at Eve and, thus, maintain high conditional key entropy. The effectiveness of the proposed schemes is demonstrated through computer simulations.
Vector quantization schemes are proposed to extract secret keys from correlated wireless fading channels. By assuming that the channel between two terminals are reciprocal, its estimates can be used as the common randomness for generating secret keys at the two terminals. Most schemes in the literature assume that channels are independent over time and utilize scalar quantization on each element of the estimated channel vector to generate secret key bits. These schemes are simple to implement but yield high key disagreement probability (KDP) at low SNR and low key entropy when channels are highly correlated. In this work, two vector quantization schemes, namely, the minimum key disagreement probability (MKDP) and the minimum quadratic distortion (MQD) secret key generation schemes, are proposed to effectively extract secret keys from correlated channel estimates. The vector quantizers are derived using KDP and QD as the respective distortion measures. To further reduce KDP, each channel vector is first pre-multiplied by an appropriately chosen unitary matrix to rotate the vector away from quantization cell boundaries. The MKDP scheme achieves the lowest KDP but requires high complexity whereas the MQD scheme yields lower complexity but at the cost of slightly increased KDP. Computer simulations are provided to demonstrate the effectiveness of the proposed vector quantization schemes.
The growth of IoT in 6G networks necessitates efficient, lightweight security solutions for generating secure symmetric keys in low-power devices, as traditional public-key cryptography is inadequate due to complexity and overhead. In this paper, we propose a novel approach for physical layer key generation using channel reciprocity-based methods. Our contribution lies in the development of a unique feature-extraction method that reduces signal dimensions, enhances computational efficiency, and improves shared key accuracy. Additionally, we introduce an innovative Equalized Fuzzy C-Means (EFCM) vector quantization scheme that ensures clusters of equal size and maximizes entropy and randomness. Existing vector quantization schemes have communication overhead to address high Bit Error Rate (BER) through the exchanging of information over the channel. This can cause information leakage to a potential eavesdropper, which is addressed in our scheme by eliminating this communication overhead. Simulation results demonstrate the superiority of our approach, achieving higher key entropy, lower BER, and improved security compared to traditional scalar quantization and Principal Component Analysis-KMeans (PCA-KM) methods. The proposed scheme offers a promising solution for secure key generation in 6G networks and addresses the challenges posed by IoT devices' limited capabilities.
In today’s world security of information is of utmost importance. Traditionally symmetric and asymmetric cryptographic methods are used to keep information secure. But they face problems of high computational complexity and key management infrastructure. These issues can be resolved by Physical layer key generation (PLKG) schemes which use channel properties to generate a symmetric key. A basic PLKG system consists of probing the wireless channel, quantizing the probed samples and converting them into bits, error detection and correction between the quantized output bits and privacy amplification using secure hash functions. Quantization plays a critical role in PLKG in order to obtain the symmetric secret keys. This paper proposes Vector Quantization with Affinity Propagation Clustering (VQAPC). When the two legitimate users (Alice and Bob) assign a set of samples to different quantization regions, there will be difference in the quantization results which is called as Assignment Disagreement Rate(ADR). Simulation is done using MATLAB software. The proposed quantization method-VQAPC gives very low ADR as compared to the existing methods.
Secret key generation at physical layer has attracted more and more attentions as an emerging cryptography method. Compared to traditional security approaches, secret key generation at physical layer not only avoids the problem of key distribution, but also holds high efficiency and low complexity in application. Based on the principle of channel reciprocity, Alice and Bob both estimate the channel conditions and extract shared keys from this source of common randomness. In this paper, we first analyze the basic steps (channel estimation, sample quantization and key reconciliation) of secret key generation, key match rate with different quantization levels and key reconciliation times are also simulated. While in practical situations, different non-reciprocity factors affect the channel estimation step, key match rate can be greatly decreased and hardly meet real time cryptography requirements. In order to increase the key match rate, the unified framework of physical layer key generation has been extended to utilizing multiple observations of wireless channels to generate secret keys. An improved key generation approach with multiple observations can well deal with discrepancies between transceivers and keep increasing the key match rate. Theoretical analysis and simulation results both validate the significant improvement due to multiple observations. With an increased number of observations on both sides, the desired key match rate can be achieved much greater than with a single observation, and also the probability of key recovery by Eve can be decreased.
Ensuring reliable and secure communications in the increasingly pervasive beyond5thgeneration (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 toρ=0.8, the samples excursion qualification threshold is set toL=3, and GG fading conditions set as defined byα=2,ξ=1, andυ=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).
Two legitimate parties, referred to as Alice and Bob, wish to generate secret keys from the wireless channel in the presence of an eavesdropper, referred to as Eve, in order to use such keys for encryption and decryption. In general, the secret key rate highly depends on the coherence time of the channel. In particular, a straightforward method of generating secret keys in static environments results in ultra-low rates. In order to resolve this problem, we introduce a low-complexity method called induced randomness. In this method, Alice and Bob independently generate local randomness to be used together with the uniqueness of the wireless channel coefficients in order to enable high-rate secret key generation. In this work, two scenarios are considered: first, when Alice and Bob share a direct communication channel, and second, when Alice and Bob do not have a direct link and communicate through an untrusted relay. After exchanging the induced randomness, post-processing is done by Alice and Bob to generate highly-correlated samples that are used for the key generation. Such samples are then converted into bits, disparities between the sequences generated by Alice and Bob are mitigated, and the resulting sequences are then hashed to compensate for the information leakage to the eavesdropper and to allow consistency checking of the generated key bit sequences. We utilize semantic security measures and information-theoretic inequalities to upper bound the probability of successful eavesdropping attack in terms of the mutual information measures that can be numerically computed. Given certain reasonable system parameters this bound is numerically evaluated to be 2-31and 2-10.57in the first and the second scenario, respectively.