  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.
