# A Secure Blockchain-Based Authentication and Key Agreement Scheme for 3 GPP 5G Networks
## 6 Performance Evaluation
### Communication Overhead  
As bandwidth resources in the 5G network are invaluable, smaller communication overhead is always preferred. Thus, we further evaluated the communication overhead in terms of bandwidth consumption and transmission overhead.  
For the bandwidth consumption based on five different security levels suggested by NIST [35], the total message sizes of the related protocols are derived in Figure 7. It shows that our 5 GSBA outperformed all other schemes by achieving the lowest bandwidth consumption. This is because the 5 GSBA authenticates the incoming UE locally using the two-step protocol, which can save redundant forwarding messages.  
For communication delays there are two components: propagation delays and transmission delays. Propagation delay calculations consist of both wired and wireless connections. For the wired connections, we referred to the link between the gNB and the nearest 5 GC functional entities. It is assumed that optical fiber is deployed for all wired connections, and the 5 GC functional entities are geographically distant to the gNB. To simulate a real-life situation, we assumed the distance between the gNB and the nearest 5 GC functional entity to be 1 km, and the distance between two functional entities within the 5 GC to be less than 0.5 km. For the wireless connection, according to the dense urban 5G service requirement in TS 22.261 [36], we assumed that the inter-site distance (ISD) between two  
Figure 6: Average delays under unknown attacks.  
Figure 7: Total bandwidth consumption.  
gNBs was 200 m, and the requesting UE was located to the edge of the coverage of the gNB. Therefore, the distance between the gNB and UE was about 100 m. The transmission delay calculation also consisted of wired and wireless connections. For the wired connections, due to the link of optical fiber, it was assumed that the uplink and downlink speed were both 1 Gbit/s. For the wireless connections, similarly, by following TS 22.261 [36], it was assumed that the uplink speed for UE was 50 Mbit/s and the downlink speed for UE was 300 Mbit/s. For the blockchain-based schemes, it was assumed that blockchain nodes could synchronize new blocks parallelly during the idle time of gNBs. To better reflect the extra communication overhead introduced by blockchains, we included the average delay of downloading one old transaction and uploading one new transaction into the calculation. Finally, by combining all the assumptions above, the sums of propagation and transmission delays are derived in Figure 8.  
Figure 8 shows that the 5 GSBA achieves similar total communication delays from 160-bit to 256-bit key length. Although the total communication delay of the 5 GSBA was marginally higher than that of the 5G-AKA [4] from 384 bit to 512 bit, the 5 GSBA still consumed much less time than that of the BB-AKA 5G [10]. This is because the 5 GSBA saved some propagation delays by consuming the lengthy authentication requests locally in gNBs. Considering that the 256-bit ECC key was accepted in the NIST recommendation [35], the communication delays of the 5 GSBA were very close to that of the 5G-AKA. Overall, the 5 GSBA achieved the right balance between strong security and relatively low communication overhead.