On Channel Transforms to Enhance Reciprocity and Quantization in Physical-Layer Secret Key Generation
Ensuring reliable and secure communications in the increasingly pervasive beyond <inline-formula> <tex-math notation="LaTeX">$5{^{\text {th}}}$ </tex-math></inline-formula> generation (B5G) wireless networks is one of the key research challenges. Within the physical...
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2025-01-01
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| author | Ghalib Hussain Syed Junaid Nawaz Shurjeel Wyne Mohammad N. Patwary |
| author_facet | Ghalib Hussain Syed Junaid Nawaz Shurjeel Wyne Mohammad N. Patwary |
| author_sort | Ghalib Hussain |
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| description | Ensuring reliable and secure communications in the increasingly pervasive beyond <inline-formula> <tex-math notation="LaTeX">$5{^{\text {th}}}$ </tex-math></inline-formula> generation (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 to <inline-formula> <tex-math notation="LaTeX">$\rho =0.8$ </tex-math></inline-formula>, the samples excursion qualification threshold is set to <inline-formula> <tex-math notation="LaTeX">$L=3$ </tex-math></inline-formula>, and GG fading conditions set as defined by <inline-formula> <tex-math notation="LaTeX">$\alpha =2$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\xi =1$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$\upsilon =1$ </tex-math></inline-formula>, 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). |
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| publishDate | 2025-01-01 |
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| spelling | doaj-art-1f9dd42c943d4d8dba27d8bd1fd9dbc42025-01-03T00:01:58ZengIEEEIEEE Access2169-35362025-01-011325627210.1109/ACCESS.2024.352310510816322On Channel Transforms to Enhance Reciprocity and Quantization in Physical-Layer Secret Key GenerationGhalib Hussain0https://orcid.org/0000-0002-1425-316XSyed Junaid Nawaz1https://orcid.org/0000-0001-5448-2170Shurjeel Wyne2https://orcid.org/0000-0001-9532-2288Mohammad N. Patwary3https://orcid.org/0000-0003-2878-5295Department of Electrical and Computer Engineering, COMSATS University Islamabad (CUI), Islamabad, PakistanDepartment of Electrical and Computer Engineering, COMSATS University Islamabad (CUI), Islamabad, PakistanDepartment of Electrical and Computer Engineering, COMSATS University Islamabad (CUI), Islamabad, PakistanFaculty of Science and Engineering, University of Wolverhampton, Wolverhampton, U.K.Ensuring reliable and secure communications in the increasingly pervasive beyond <inline-formula> <tex-math notation="LaTeX">$5{^{\text {th}}}$ </tex-math></inline-formula> generation (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 to <inline-formula> <tex-math notation="LaTeX">$\rho =0.8$ </tex-math></inline-formula>, the samples excursion qualification threshold is set to <inline-formula> <tex-math notation="LaTeX">$L=3$ </tex-math></inline-formula>, and GG fading conditions set as defined by <inline-formula> <tex-math notation="LaTeX">$\alpha =2$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\xi =1$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$\upsilon =1$ </tex-math></inline-formula>, 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).https://ieeexplore.ieee.org/document/10816322/6Gbeyond 5Gkey bitsphysical layer securityquantizationsecret key generation |
| spellingShingle | Ghalib Hussain Syed Junaid Nawaz Shurjeel Wyne Mohammad N. Patwary On Channel Transforms to Enhance Reciprocity and Quantization in Physical-Layer Secret Key Generation IEEE Access 6G beyond 5G key bits physical layer security quantization secret key generation |
| title | On Channel Transforms to Enhance Reciprocity and Quantization in Physical-Layer Secret Key Generation |
| title_full | On Channel Transforms to Enhance Reciprocity and Quantization in Physical-Layer Secret Key Generation |
| title_fullStr | On Channel Transforms to Enhance Reciprocity and Quantization in Physical-Layer Secret Key Generation |
| title_full_unstemmed | On Channel Transforms to Enhance Reciprocity and Quantization in Physical-Layer Secret Key Generation |
| title_short | On Channel Transforms to Enhance Reciprocity and Quantization in Physical-Layer Secret Key Generation |
| title_sort | on channel transforms to enhance reciprocity and quantization in physical layer secret key generation |
| topic | 6G beyond 5G key bits physical layer security quantization secret key generation |
| url | https://ieeexplore.ieee.org/document/10816322/ |
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