Amid the escalating concerns over internet security, quantum cryptography stands out as a highly promising solution for significantly enhancing the security of networking systems, emerging among them is the quantum key distribution (QKD) with the function of creating secret session keys a breeze when leveraging the intriguing properties of quantum mechanics. This study is rooted in the BB84 QKD method, where in the distribution process in the quantum realm is simulated to derive a shared key via a public channel connecting two clients with the assistance of a server, utilizing the quantum inspire (QI) platform to generate qubits within the BB84 protocol. The results, the findings regarding the performance of BB84 reveal that when the server is set up, and the key size increases to 4000 bits, the process of sending module takes 16.215 sec, the transfer module takes approximately 5.2 hours, the receive module takes 1.257 sec to finish the process for the final session key share. This indicates a noteworthy enhancement in the execution speed of QKD employing the BB84 protocol, which now holds the potential for reinforcing network security using quantum computing systems.