## 6 Performance Evaluation
### Computational Cost Analysis  
The computational cost is primarily determined by the number and type of cryptographic operations performed by each entity during the online authentication phase. Registration phase costs are amortized as they are one-time operations. We use the following estimated execution times for common cryptographic operations, which are representative values found in the recent IoD security literature (e.g., [PERSON] et al. [5], [PERSON] et al. [1], and values from [PERSON] [8] where applicable):  
* \(T_{H}\) (SHA-256 hash): \(\approx\) 0.0025 ms [5];
* \(T_{FE}\) (Fuzzy Extractor-Rec): \(\approx\) 0.0098 ms [5];
* \(T_{S}\) (AES-128 Enc/Dec): \(\approx\) 0.0046 ms [5];
* \(T_{KDF}\) (PBKDF2-SHA256, simplified for derivation): \(\approx\)2 \(\times\)\(T_{H}\) = 0.0050 ms (estimation, actual PBKDF2 can be higher due to iterations but here it is used for key derivation not password stretching from low-entropy input).  
**Bio-2 FA-IoD computational cost (authentication phase):**
* **Operator's** device (OD): 1. \(\times\)\(T_{FE}\) = 0.0098 ms; 2. Local key \(K_{O}\) regeneration (\(KDF(P_{ID_{O}},Salt_{2})\)): 1. \(\times\)\(T_{KDF}\) = 0.0050 ms; 3. \(RP_{ID_{O}}\) decryption (\(D_{K_{O}}(C_{RP})\)): 1. \(\times\)\(T_{S}\) = 0.0046 ms; 4. Session key KS generation (\(KDF(P_{ID_{O}},T_{ID})\)): 1. \(\times\)\(T_{KDF}\) = 0.0050 ms; 5. OTAC encryption (\(E_{KS}(PINI)\|T_{ID}\|RP_{ID_{O}}\)): 1. \(\times\)\(T_{S}\) = 0.0046 ms. _Total OD cost_: 0.0098 + 0.0050 + 0.0046 + 0.0050 + 0.0046 + 0.029 **ms**.
* **Ground** control station (GCS): 1. Session key \(KS_{GCS}\) generation (\(KDF(P_{ID_{O}},T_{ID})\)): 1. \(\times\)\(T_{KDF}\) = 0.0050 ms; 2. OTAC decryption (\(D_{KS_{GCS}}(OTAC)\)): 1. \(\times\)\(T_{S}\) = 0.0046 ms; 3. \(RPMD^{\prime}_{ID_{O}}\) calculation (\(H(RP^{\prime}_{ID_{O}}\|Salt_{1})\)): 1. \(\times\)\(T_{H}\) = 0.0025 ms. _Total GCS cost_: 0.0050 + 0.0046 + 0.0025 + **0.0121 ms**.  
**Total** protocol computational cost (online phase): 0.029 ms (OD) + 0.0121 ms (GCS) = 0.0411 ms. **Comparison with other schemes:** Table 3 presents a comparative overview of computational costs. The proposed Bio-2 FA-IoD, with a total estimated cost of **0.0411 ms**, demonstrates significantly lower computational overhead compared to schemes that rely heavily on asymmetric cryptography, such as ECC (e.g., [PERSON] et al. [13], with costs around 0.448 ms) or HECC (e.g., HCALA by [PERSON] et al. [2], at 3.3873 ms). Its cost is comparable to, and slightly higher than, the PUF and biometric-based scheme by [PERSON] et al. [5] (**0.0388** ms), which involves PUF operations directly in the authentication flow for multiple entities. In contrast, [PERSON] et al.'s scheme [1], while using symmetric primitives, involves more operations, leading to a higher cost (**17.79** ms). The EPUF-based authentication by [PERSON] et al. [11] also reports very low computational costs for its core logic (excluding PUF read time), comparable to our proposal (\(\approx\)0.016 ms). The efficiency of Bio-2 FA-IoD stems from its reliance on a minimal set of fast symmetric operations (AES) and hashing (SHA-256) for the core online authentication loop, with the biometric processing localized to the OD. This makes it exceptionally well suited for real-time IoD operations on resource-constrained devices, performing significantly faster than many ECC/HECC or HMAC-based protocols.