Physical layer key generation (PLKG) methods are widely studied in academia due to their independence from trusted third parties and computational efficiency. However, the security of these methods depends on the statistical testing of the post-processed random sequences, which raises concerns about their reliability. While min-entropy is commonly used to evaluate the quality of random sequences, few studies provide explicit min-entropy estimation results. Additionally, existing methods for min-entropy estimation, such as the NIST SP 800-90B (90B) standard and entropy estimators based on deep neural networks (DNNs), have not been adequately validated in the context of PLKG. In this work, we present the first empirical study of min-entropy estimation tailored for PLKG. We systematically analyze five representative key generation schemes using both public and collected datasets. We first experimentally demonstrate the overestimation and underestimation behaviors of 90B estimators on time-varying data and propose a practical strategy for their use. Then, we formally analyze the limitations of DNN-based estimators and introduce a Bidirectional Temporal Training and Testing strategy to improve estimation accuracy. Furthermore, we provide theoretical and empirical insights into how preprocessing and quantization affect entropy. Our results show that PLKG sequences often exhibit significant local predictability, leading to lower-than-expected entropy values. These findings highlight previously overlooked security risks and provide practical guidance for designing more robust PLKG systems.

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Min-Entropy Estimation for Physical Layer Key Generation: An Empirical Study

  • Dongchi Han,
  • Yuan Ma,
  • Tianyu Chen,
  • Liliang Guan,
  • Xianhui Lu

摘要

Physical layer key generation (PLKG) methods are widely studied in academia due to their independence from trusted third parties and computational efficiency. However, the security of these methods depends on the statistical testing of the post-processed random sequences, which raises concerns about their reliability. While min-entropy is commonly used to evaluate the quality of random sequences, few studies provide explicit min-entropy estimation results. Additionally, existing methods for min-entropy estimation, such as the NIST SP 800-90B (90B) standard and entropy estimators based on deep neural networks (DNNs), have not been adequately validated in the context of PLKG. In this work, we present the first empirical study of min-entropy estimation tailored for PLKG. We systematically analyze five representative key generation schemes using both public and collected datasets. We first experimentally demonstrate the overestimation and underestimation behaviors of 90B estimators on time-varying data and propose a practical strategy for their use. Then, we formally analyze the limitations of DNN-based estimators and introduce a Bidirectional Temporal Training and Testing strategy to improve estimation accuracy. Furthermore, we provide theoretical and empirical insights into how preprocessing and quantization affect entropy. Our results show that PLKG sequences often exhibit significant local predictability, leading to lower-than-expected entropy values. These findings highlight previously overlooked security risks and provide practical guidance for designing more robust PLKG systems.