Two methods are developed that can be applied to generate secret keys automatically from fading propagation channels that are reciprocal but have arbitrary (i.e. non Gaussian) statistics. Such methods may be necessary for physical-layer key generation in cases where the line-of-sight (LOS) component produces Rician channel statistics, not only because channel quantization based on Gaussian statistics will not provide equally probable symbols, but also because the symbol error rate (SER) and efficiency analysis based on Gaussian channels does not reflect true performance. An improved channel quantization method compared to [1], [2] is developed, where the empirical cumulative distribution function (cdf) of the channel is used directly to ensure equal probability of the key symbols. The results show that LOS channels can have slightly better SER performance than strictly Gaussian channels, especially at low SNR. Second, the idea of positional coding is developed, where a secret key can be transmitted by dividing empirical channel observations into multiple codewords and conveying a secret message from Alice to Bob in the sequence of channels fed forward from Alice to Bob. Analysis of the method illustrates that key mismatch rate can be made arbitrarily low by properly selecting the codeword length.
Two methods are developed that can be applied to generate secret keys automatically from fading propagation channels that are reciprocal but have arbitrary (i.e. non Gaussian) statistics. Such methods may be necessary for physical-layer key generation in cases where the line-of-sight (LOS) component produces Rician channel statistics, not only because channel quantization based on Gaussian statistics will not provide equally probable symbols, but also because the symbol error rate (SER) and efficiency analysis based on Gaussian channels does not reflect true performance. An improved channel quantization method compared to [1], [2] is developed, where the empirical cumulative distribution function (cdf) of the channel is used directly to ensure equal probability of the key symbols. The results show that LOS channels can have slightly better SER performance than strictly Gaussian channels, especially at low SNR. Second, the idea of positional coding is developed, where a secret key can be transmitted by dividing empirical channel observations into multiple codewords and conveying a secret message from Alice to Bob in the sequence of channels fed forward from Alice to Bob. Analysis of the method illustrates that key mismatch rate can be made arbitrarily low by properly selecting the codeword length.
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.
The reciprocity of the wireless channel is the basis of the secret key generation on the physical layer as an emerging method for information security enhancement. Due to the duplex mode of communication systems, the channel responses detected by two connected legitimate nodes are not completely reciprocal. In this paper, an efficient physical layer secret key generation scheme is proposed based on an autoencoder to extract reciprocal features from weakly correlated channel estimates. The encoder part after training is equipped at both nodes to generate features for quantization in various channel environments. Simulation results show lower mean squared error (MSE) and better mutual information of the extracted features comparing to the most efficient linear generation method, the principal component analysis (PCA) based one. It reveals the great potential to generate symmetric secret keys with better performance, particularly in low SNR scenarios.
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).
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 secret key generation exploits the reciprocal channel randomness for key generation and has proven to be an effective addition security layer in wireless communications. However, static or scarcely random channels require artificially induced dynamics to improve the secrecy performance, e.g., using intelligent reflecting surface (IRS). One key challenge is that the induced random phase from IRS is also reflected in the direction to eavesdroppers (Eve). This leakage enables Eve nodes to estimate the legitimate channels and secret key via a globally known pilot sequence. To mitigate the secret key leakage issue, we propose to exploit random matrix theory to inform the design of a new physical layer secret key generation (PL-SKG) algorithm. We prove that, when sending appropriate random Gaussian matrices, the singular values of Alice's and Bob's received signals follow a similar probability distribution. Leveraging these common singular values, we propose a random Gaussian matrix based PL-SKG (RGM PL-SKG), which avoids the usages of the globally known pilot and thereby prevents the aforementioned leakage issue. Our results show the following: (i) high noise resistance which leads to superior secret key rate (SKR) improvement (up to 300%) in low SNR regime, and (ii) general improved SKR performance against multiple colluded Eves. We believe our combination of random matrix theory and PL-SKG shows a new paradigm to secure the wireless communication channels.
The generation of secret keys from reciprocal wireless channel by exploiting their randomness nature, is an emerging area of interest to provide secure communication. One of the main challenges in this domain is to increase the secret key length, extracted from the shared channel coefficients between two legitimate communication parties, while maintaining its randomness and uniformity. In this work, we develop a practical key generation method, based on channel quantization with singular value decomposition (CQSVD), which is capable of significantly increasing the generated secret key in MIMO systems. This is achieved through quantizing the phases and amplitudes of the estimated MIMO channel coefficient's matrix by using an alternative form of SVD, where the key sequence is extracted from the orthogonal basis functions of the decomposed channel. In this method, it is shown that for an M ×M antenna system, with M2independent channel fading coefficients, a secret key sequence of length 2M3can be generated. The extracted key sequence is transformed to a random phase sequence, which is then used to manipulate the transmitted data on a symbol level basis rather than bit level-basis, to provide more secure communication. The comparative simulation results show that the proposed CQSVD method outperforms the state of the art secret key generation methods.