Optimal Singular Value Decomposition Based Pre-coding for Secret Key Extraction from Correlated Orthogonal Frequency Division Multiplexing Sub-channels
Amir Aliabadian, Mohammad Reza Zahabi, Majid Mobini
Secret key extraction is a crucial issue in physical layer security and a less complex and, at the same time, a more robust scheme for the next generation of 5G and beyond. Unlike previous works on this topic, in which Orthogonal Frequency Division Multiplexing (OFDM) sub-channels were considered to be independent, the effect of correlation between sub-channels on the secret key rate is addressed in this paper. As an assumption, a realistic model for dependency among sub-channels is considered. Benchmarked by simulation, the result shows that the key exchange rate may decline by up to 72% due to the correlation of sub-channels. A new approach for efficient key extraction is used in this study. To do this, a Singular Value Decomposition based (SVD-based) pre-coding is utilized to alleviate the sub-channels correlation and the channel noise. The low computational complexity of our proposed approach makes it a promising candidate for developing secure and high-speed networks. Results obtained through simulation indicate that applying pre-coding on the measured correlated data resulted in a minimum gain of 9 dB. In addition, the result also depicts the advantage of SVD versus other pre-coding techniques, namely PCA, DCT, and WT.
Secret key extraction is a crucial issue in physical layer security and a less complex and, at the same time, a more robust scheme for the next generation of 5G and beyond. Unlike previous works on this topic, in which Orthogonal Frequency Division Multiplexing (OFDM) sub-channels were considered to be independent, the effect of correlation between sub-channels on the secret key rate is addressed in this paper. As an assumption, a realistic model for dependency among sub-channels is considered. Benchmarked by simulation, the result shows that the key exchange rate may decline by up to 72% due to the correlation of sub-channels. A new approach for efficient key extraction is used in this study. To do this, a Singular Value Decomposition based (SVD-based) pre-coding is utilized to alleviate the sub-channels correlation and the channel noise. The low computational complexity of our proposed approach makes it a promising candidate for developing secure and high-speed networks. Results obtained through simulation indicate that applying pre-coding on the measured correlated data resulted in a minimum gain of 9 dB. In addition, the result also depicts the advantage of SVD versus other pre-coding techniques, namely PCA, DCT, and WT.
Key generation from the randomness of wireless channels is a promising technique to establish a secret cryptographic key securely between legitimate users. This paper proposes a new approach to extract keys efficiently from the channel responses of individual orthogonal frequency-division multiplexing (OFDM) subcarriers. The efficiency is achieved by: 1) fully exploiting randomness from time and frequency domains and 2) improving the cross-correlation of the channel measurements. Through the theoretical modeling of the time and frequency autocorrelation relationship of the OFDM subcarrier's channel responses, we can obtain the optimal probing rate and use multiple uncorrelated subcarriers as random sources. We also study the effects of non-simultaneous measurements and noise on the cross-correlation of the channel measurements. We find that the cross-correlation is mainly impacted by noise effects in a slow fading channel and use a low-pass filter to reduce the key disagreement rate and extend the system's working signal-to-noise ratio range. The system is evaluated in terms of randomness, key generation rate, and key disagreement rate, verifying that it is feasible to extract randomness from both time and frequency domains of the OFDM subcarrier's channel responses.
Orthogonal frequency division multiplexing (OFDM) is such a vital waveform scheme that is utilized in fifth-generation (5G) communication systems as well as the previous one. Since the usage scenarios of 5G are quite wide, the security of those systems is currently an open and critical issue. In this paper, a promising paradigm is proposed for enhancing physical layer (PHY) security in OFDM systems. Two independent secret keys are extracted by legitimate users quantizing the channel measurements. Those key sequences are exchanged via a novel artificial noise (AN) injection method which does not result in a key mismatch. Bit error rate (BER) versus signal-to-noise ratio (SNR) performance of the adversary is still low even if the malicious node has better channel than the legitimate user. After agreement upon the same key, both legitimate parties directly employ key sequence and inter-carrier interference matrix caused by the local oscillators to produce a secrecy matrix. This matrix enables secure communication by inserting it into the transmission design.
ABSTRACT This work proposes a secret key extraction technique from the complex impulse response (CIR) for secure orthogonal frequency division multiplexing (OFDM) wireless communication systems. Using time division duplexing (TDD), the legitimate transceivers exchange pilot tones within the channel coherence time to estimate their CIRs, from which the dominant peaks are selected and quantised into binary sequences using a mean‐referenced Heaviside rule. Simulations are conducted in MATLAB for OFDM systems over Additive White Gaussian Noise (AWGN) and Rayleigh fading channels with Binary Phase Shift Keying (BPSK) and Quadrature Phase Shift Keying (QPSK) modulation schemes. The proposed method is evaluated in terms of randomness, key disagreement rate (KDR), and key generation rate (KGR). For key lengths of 128 bits, 100,000 bits, and 1,000,000 bits, the generated key sequences pass 8, 9 and 15 tests, respectively, in the National Institute of Standards and Technology (NIST) statistical test suite, with all p ‐values greater than 0.01. Since the simulations are performed under ideal reciprocal channel conditions, the keys generated by the two legitimate users are identical, resulting in a KDR of 0 prior to any reconciliation process. In addition, because 16 dominant CIR peaks are extracted from each realisation and each peak contributes one bit, the proposed method achieves a constant KGR of 16 bits per CIR realisation. The results show that the proposed scheme provides a scalable and deterministic key generation mechanism with strong randomness, zero disagreement in simulation, and controllable generation efficiency.
Physical layer secret key generation techniques have spurred much recent research interest. In general, the secret key establishment contains four main procedures: channel sounding, quantization, information reconciliation and privacy amplification. However, to overcome the non- reciprocity and correlation problems in key generation from orthogonal frequency division multiplexing (OFDM) channels, a preprocessing procedure is added to prepare inputs for quantization. This paper demonstrates the optimal preprocessing approach in secret key generation and addresses its practical problems in realization. More specifically, we first build the mathematical model of a preprocessing procedure. Then, we identify that principle component analysis (PCA) can achieve the optimal performance in this model from the perspective of secret key capacity. Next, we discuss the realization steps of PCA algorithm and the corresponding procedures to cooperate with it. The parameter design in matrix partitioning and covariance matrix calculation are also analyzed. Numerical results verify that the proposed PCA preprocessing outperforms other tall unitary transforms and thus, it can be used to generate secret key with high key generation rate (KGR), low key error rate (KER) and good randomness.
As a new way to enhance wireless communication security, secret key generation based on physical layer channel characteristics has emerged. In this paper, we propose a novel secret key generation algorithm based on wireless channel characteristics for orthogonal frequency division multiplexing (OFDM) communication systems. The mean quantization algorithm is applied to quantize the real part and imaginary part of OFDM subcarriers, respectively, which can significantly increase the length of the generated secret key in the OFDM system. To reduce the consistency between the secret keys generated by the eavesdropper and the legitimate communication nodes, a processing method by taking the subcarrier phase as initialization of a scrambling code and scrambling the quantized result is proposed. The simulation and test results show that compared with the existing research, the proposed algorithm can improve the key generation rate (KGR), reduce the key mismatch rate (KMR) and complexity, maintain high randomness, and disturb the eavesdroppers.
Information is regarded as a resource with highest organizational value. Its confidentiality, integrity and authenticity are important for any organization. The broadcast nature of wireless medium makes communication vulnerable to security attacks such as eavesdropping, non-repudiation, denial of service and more. Hence, prior to transmission of information, a secret key is securely exchanged between sender and receiver. Conventional key generation algorithms work at the application layer. However, they suffer from computational overheads and require a reliable third party. Moreover, when system grows complex, these methods start failing considerably. To encounter these issues, a novel key exchange mechanism is proposed which works at the physical layer. The proposed method is based on the concept of self-jamming and exploits the properties of Orthogonal Frequency Division Multiplexing (OFDM). The simulation results show that the proposed scheme has a low Bit Error Rate (BER) for the receiver and high BER for the eavesdropper. It has also been shown that the number of attempts that eavesdropper has to make to guess the correct key are large, thereby decreasing its probability to decode the correct key.