{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:23:22Z","timestamp":1760145802737,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T00:00:00Z","timestamp":1725408000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Chongqing Electronics Engineering Technology Research Center for Interactive Learning","award":["KJQN202201630","KJZD-K202401604"],"award-info":[{"award-number":["KJQN202201630","KJZD-K202401604"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper explores physical layer group key generation in wireless relay networks with a star topology. In this setup, the relay node plays the role of either a trusted or untrusted central node, while one legitimate node (Alice) acts as the reference node. The channel between the relay and Alice serves as the reference channel. To enhance security during the channel measurement stage, a cooperative jamming-based scheme is proposed in this paper. This scheme allows the relay to obtain superimposed channel observations from both the reference channel and other relay channels. Then, a public discussion is utilized to enable all nodes to obtain estimates of the reference channel. Subsequently, the legitimate nodes can agree on a secret key (SK) that remains secret from the eavesdropper (Eve), or a private key (PK) that needs to be secret from both the relay and Eve. This paper also derives the lower and upper bounds of the SK\/PK capacity. Notably, it demonstrates that there exists only a small constant difference between the SK\/PK upper and lower bounds in the high signal-to-noise ratio (SNR) regime. Simulation results confirm the effectiveness of the proposed scheme for ensuring security and efficiency of group key generation.<\/jats:p>","DOI":"10.3390\/e26090758","type":"journal-article","created":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T08:46:22Z","timestamp":1725439582000},"page":"758","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cooperative Jamming-Based Physical-Layer Group Secret and Private Key Generation"],"prefix":"10.3390","volume":"26","author":[{"given":"Shiming","family":"Fu","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Chongqing University of Education, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tong","family":"Ling","sequence":"additional","affiliation":[{"name":"School of Communications and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Communications and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Li","sequence":"additional","affiliation":[{"name":"College of Computer Science, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3682","DOI":"10.1109\/COMST.2019.2916180","article-title":"Security for 5G and beyond","volume":"21","author":"Ahmad","year":"2019","journal-title":"IEEE Commun. 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