Abstract
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- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> , 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.
Highlights
The rollout of 5th Generation (5G) communication networks commenced in 2019 with Release-15 of 3rd Generation Partnership Project (3GPP) [1]
The Secret Key Generation (SKG) algorithms typically consist of channel sampling, channel quantization (Alice and Bob decide on channelrange thresholding scheme for channel observations so that measured channel samples can be transformed to secret key bits), information reconciliation (Alice and Bob minimize mismatch between their extracted key sequences by exchanging samples indices or using parity check codes etc.), and privacy amplification (Alice and Bob use a family of universal hash functions to transform their matched sequences into a final key not known to Eve) [13]
In order to optimize the performance trade-off between Key Generation Rate (KGR) and Secret Key Randomness (SKR), we propose that the minimum excursion length threshold L may be suitably set with reference to the Average Contiguous Duration (ACD) floor value, i.e., L ∝ floor(Ψ)
Summary
The rollout of 5th Generation (5G) communication networks commenced in 2019 with Release-15 of 3rd Generation Partnership Project (3GPP) [1]. Secret key distribution and management infrastructure could become challenging in some modern modes of communications like Device-to-Device (D2D) communications due to limited device resources [8] This motivates the use of symmetric secret key extraction from the common wireless channel, which requires no assistance from the server. The SKG algorithms typically consist of channel sampling (legitimate nodes sample the reciprocal channel by alternately exchanging probing signals), channel quantization (Alice and Bob decide on channelrange thresholding scheme for channel observations so that measured channel samples can be transformed to secret key bits), information reconciliation (Alice and Bob minimize mismatch between their extracted key sequences by exchanging samples indices or using parity check codes etc.), and privacy amplification (Alice and Bob use a family of universal hash functions to transform their matched sequences into a final key not known to Eve) [13]. The performance of SKG algorithms is generally evaluated in terms of Key Generation Rate (KGR), Key Agreement Probability (KAP), and Secret Key Randomness (SKR) properties [10], and the quantizer design significantly affects these characteristics
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