This study introduces a decentralized approach to secure wireless communication using a cryptographic secret key generation algorithm among distributed nodes. The system model employs Gaussian prime numbers, ensuring the collaborative generation of a secret key. Pre-processing and post-processing functions enable to generate a secret key across the network. An error model evaluates aspects like thermal noise power and channel estimation errors, while simulations assess the success rate to factorize the norm of the secret key. It is observed that path loss-induced large scale fading emerges as a critical component impacting information and power loss. The robustness of the proposed model under fading channel conditions is evaluated with a success rate. Additionally, it is also observed that the tolerance value set in the factorization algorithms has a significant impact on the success rate. Furthermore, the success rate is compared in two scenarios, one with 2 users and another with 3 users, to provide a comprehensive evaluation of the system performance.

翻译：本研究提出一种去中心化的安全无线通信方法，采用分布式节点间的密码学密钥生成算法。系统模型采用高斯素数，确保密钥的协同生成。预处理与后处理函数支持全网范围的密钥生成。通过误差模型评估热噪声功率与信道估计误差等因素，并借助仿真分析密钥范数分解的成功率。研究发现，由路径损耗引发的大尺度衰落是影响信息与功率损耗的关键因素。所提模型在衰落信道条件下的鲁棒性通过成功率进行评估。此外，研究还发现分解算法中设置的容差值对成功率具有显著影响。最后，通过对比2用户与3用户两种场景下的成功率，对系统性能进行了综合评估。