# A Secure Blockchain-Based Authentication and Key Agreement Scheme for 3 GPP 5G Networks
## 6 Performance Evaluation
### Energy Consumption for UE  
Since mobile devices have limited battery life, a security protocol with the strongest security and the least energy consumption is always preferable. To evaluate the energy consumption for UE two factors should be considered: data transmission energy and the energy for the execution of the cryptographic functions. For the data transmission energy, the data transfer power model in [37] is adopted to estimate the energy consumption. Thus, the energy cost for uplink transmission of the UE is in Equation (39) and the energy cost for the downlink is in Equation (40), where \(\alpha_{u}\)= 438.39 mW/Mbps, \(\alpha_{d}\) = 51.97 mW/Mbps, \(\beta\) = 1288.04 mW, \(t_{udr}\) is the uplink throughput, \(t_{ddr}\) is the downlink throughput, \(t_{ul}\) is the transmission time spent on the uplink, and \(t_{dl}\) is the transmission time spent on the downlink. We further assume that the uplink and downlink throughput follow the dense urban 5G service requirement in TS 22.261 [36], so that \(t_{udr}\) = 50 Mbps and \(t_{ddr}\) = 300 Mbps.  
\[E_{ul}=(\alpha_{u}t_{udr}+\beta)\cdot t_{ul} \tag{39}\]  
Figure 8: Total communication delays.  
\[E_{dl}=(\alpha_{d}t_{ddr}+\beta)\cdot t_{dl} \tag{40}\]  
On the other hand, for the energy consumption for the execution of cryptographic functions, the measure of energy cost approximation in [38] is taken. In [38], all experiments were conducted using a battery-powered Compaq iPAQ H3670 PDA. It was equipped with an Intel SA-1110 StrongARM processor clocked at 206 MHz, 64 MB of RAM, and 16 MB of FlashROM. Moreover, the energy cost of ECDH public key generation \(E_{ECDH,gen}\) was 276.7 mJ, the ECDH common key derivation \(E_{ECDH,ck}\) was 163.5 mJ, the ECDSA signature generation \(E_{ECDSA,sign}\) was 134.2 mJ, and the ECDSA signature validation \(E_{ECDSA,new}\) was 196.23 mJ. For the energy cost of symmetric key-based operations, the symmetric key-based encryption \(E_{sym.}\) was \(9.92+2.29l\) uJ, where \(l\) was the number of bytes of the cleartext. The HMAC operation \(E_{HMAC}\) was 1.16 mJ, and hash operation \(E_{hash}\) was 0.76 mJ. For the ECIES operations, since it was a hybrid encryption combining both CDH problems and a key encapsulation mechanism (KEM), the cost of the ECIES encryption was estimated as \(E_{ECDH,gen}+E_{ECDH,ck}+E_{sym}=440.20992+0.00229l\) mJ.  
Finally, by combining all parameters above with the unknown attack model stated in Section 6.1.2, the average UE energy consumption for different protocols is simulated in Figure 9. It shows that all the schemes providing perfect forward and backward secrecy, including the 5 GSBA [4], SE-AKA [20], and BB-AKA 5G [10], consume a similar amount of energy in a situation without any unknown attacks. When the unknown attack probability increases, the 5 GSBA unavoidably uses more energy because of the increased SUCI generation. However, the 5 GSBA still consumes less energy than the BB-AKA 5G. On the other hand, although the 5G-AKA uses the least energy, its power-saving symmetric key-based cryptosystem makes it vulnerable to many other known attacks.