# Lightweight and Security-Enhanced Key Agreement Protocol Using PUF for IoD Environments
## 8 Performance Analysis
### Computational Cost Analysis  
This work compares and analyzes the computational costs incurred during the key agreement and authentication processes of the proposed protocol and other relevant protocols. The operation time of the ECC point multiplication, HECC multiplication, hash function, fuzzy extractor, symmetric encryption/decryption, and physical unclonable function are denoted by \(T_{ppm},T_{hem},T_{hf},T_{fe},T_{sed}\), and \(T_{puf}\), respectively. To evaluate the computational cost in the IoD environment, we conducted experiments using MIRACL, a cryptography library designed for resource-constrained devices. We simulated two different computational environments: a server (Desktop with an Intel Core i5-11400 @2.60 GHz Hexa-core processor, 24.0 GB of RAM, and a Ubuntu 20.04 LTS 64-bit operating system) and a drone environment (Raspberry Pi with an ARM Cortex-A72 processor and 8.0 GB of RAM operating on the 64-bit version of Ubuntu 20.04 LTS with a GUI). Table 5 lists the execution time for each operation. This work evaluates the computational cost incurred by all operations in the authentication process of these protocols. In [PERSON] et al. 's protocol Nyangaresi et al. (2018), an operator performed 1 fuzzy extractor operation, 11 hash operations, 55 ECC point multiplications, and 2 symmetric encryption/decryption operations. Therefore, we computed the computational cost of the operator as \(1T_{fe}+11T_{hf}+5T_{ppm}+2T_{sed}=13.3905\) ms. The registration authority performed 12 hash operations, 5 ECC point multiplications, and 2 symmetric encryption/decryption operations; thus, the computational cost of the registration authority is \(12T_{hf}+5T_{ppm}+2T_{sed}=11.1668\) ms. The UAV performed four hash operations and one symmetric encryption/decryption operation; hence, we computed the computational \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Notation** & **Description** & **Desktop** & **Raspberry Pi** \\ \hline \(T_{ppm}\) & ECC point multiplication & 0.411 ms & 2.353 ms \\ \(T_{hem}\) & HECC multiplication & 0.2055 ms & 1.1765 ms \\ \(T_{fe}\) & Fuzzy extractor & 0.411 ms & 2.353 ms \\ \(T_{hf}\) & Hash function & 0.001 ms & 0.009 ms \\ \(T_{sed}\) & Symmetric encryption/decryption & 0.001 ms & 0.004 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Execution time for each operation. cost of the UAV as \(4T_{hf}+1T_{sed}=0.0138\ ms\). The total cost for the operator, registration authority, and UAV is \(1T_{fe}+27T_{hf}+10T_{epm}+5T_{sed}=24.5771\) ms. In [PERSON] et al. 's protocol [26], the user performed 11 hash operations and 2 ECC point multiplications; hence, we computed the computational cost of the user as \(11T_{hf}+2T_{epm}=2.2513\) ms. The ground-station server performed six hash operations and one ECC point multiplication; thus, the computational cost of the ground-station server is \(6T_{hf}+1T_{epm}=1.1268\) ms. The drone performed six hash operations; therefore, we computed the computational cost of the drone as \(6T_{hf}=0.0138\) ms. Thus, the total cost for the user, ground-station server, and drone is \(23T_{hf}+3T_{epm}=3.3919\) ms. In [PERSON] et al. 's protocol [27], the user performed 1 fuzzy extractor operation, 13 hash operations, and 2 ECC point multiplications. Therefore, we computed the computational cost of the user as \(1T_{fe}+13T_{hf}+2T_{epm}=6.7079\) ms. The drone gateway performed 26 hash operations, 2 ECC point multiplications, and 1 symmetric encryption/decryption operation; hence, the computational cost of the drone gateway is \(26T_{hf}+2T_{epm}+1T_{sed}=4.5164\) ms. The processor performed 12 hash operations and 2 ECC point multiplications; thus, the computational cost of the processor is \(12T_{hf}+2T_{epm}=4.4796\) ms. The total cost of the user, drone gateway, and processor is \(1T_{fe}+51T_{hf}+6T_{epm}+1T_{sed}=15.7039\) ms. In [PERSON] et al.