The establishment of convenient and reliable cryptographic keys is not always feasible, especially in low-powered wireless devices where a complex key management infrastructure is unaffordable. Physical layer-based key generation approaches, on the other hand, allow two legitimate users to establish a common secret key by exploiting the parameters of the wireless channel, such as the underlying impulse response. In this paper, a fundamental bound on the maximum achievable key generation rate (KGR) over wireless fading channels with asymmetric additive white Gaussian noise (AWGN) is derived. A Nakagami-mfading channel is considered, and the effect of non-reciprocity on the forward and reverse channels correlation is demonstrated. We validate the theoretical platform through simulations using a key generation protocol based on the level crossing rate (LCR) of the fading process. The proposed LCR protocol models the Nakagami channel by utilizing the sum-of-sinusoids approach, where Doppler shift, fading severity, and number-of-paths are taken into account. The proposed protocol also incorporates a two-level quantizer to extract keys, where the channel estimates between a wireless transmitter and receiver can be used as the basis. Besides providing an upper bound on the KGR, the analytical and simulation results intertwine the effect of channel reciprocity with the key generation process.
This paper is concerned with the transmission of confidential message through Nakagami-m fading wireless channel in the presence of multiple eavesdroppers. The eavesdroppers are mutually independent and the information is secure if it cannot be eavesdropped by any eavesdropper. Considering the problem of secret communications between two nodes over Nakagami-m fading channel where a number of eavesdroppers observes their transmissions through other Nakagami-m fading channels, we characterize the probability of non-zero secrecy capacity and secure outage probability to investigate the secrecy capacity in terms of secure outage probability. We also present a formulation of the ergodic secrecy capacity in the presence of multiple eavesdroppers.
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.