## 6 Performance Evaluation
### Communication Cost Analysis  
Communication cost is determined by the number of messages exchanged during the authentication phase and their total size in bits.  
* Message \(M_{1}=(ID_{O},OTAC,T_{ID})\);
* Message \(M_{2}=(PIN^{\prime})\). Assuming standard sizes for parameters and AES-128 in CBC mode with a 128-bit IV:
* \(ID_{O}\): e.g., 128 bits (16 bytes).
* \(T_{ID}\) (timestamp): e.g., 32 bits (4 bytes).
* \(PIN\) (nonce): e.g., 128 bits (16 bytes).
* \(RP_{ID_{O}}\) (random password, assumed to be key-like): e.g., 160 bits (20 bytes).
* Plaintext for OTAC: \(PIN(128)+T_{ID}(32)+RP_{ID_{O}}(160)=320\) bits (40 bytes).
* OTAC (ciphertext using AES-128, e.g., CBC mode with IV and padding): Size will be a multiple of 128 bits. For 40-byte plaintext, it will require three blocks plus IV, thus \(3\times 128=384\) bits (48 bytes) including IV or padding.
* Size of \(M_{1}\): \(128(\text{for }ID_{O})+384(\text{for }OTAC)+32(\text{for }T_{ID})=\mathbf{544\ bits}\).
* Size of \(M_{2}\): \(128(\text{for }PIN^{\prime})=\mathbf{128\ bits}\).  
**Total** communication cost: \(544+128=\mathbf{672\ bits}\) (or 84 bytes).  
**Comparison** with other schemes: Table 4 compares the communication overhead. The Bio-2 FA-IoD protocol's total communication cost of \(\mathbf{672\ bits}\) exchanged in two messages is exceptionally low. It is significantly more efficient than many other IoD protocols, such as [PERSON] et al. [5] (**2464** bits, six messages), [PERSON] et al. [1] (**3720** bits, four messages), and HCALA by [PERSON] et al. [2] (**1536** bits, three messages). For example, our protocol reduces bandwidth consumption by approximately 73% compared to [PERSON] et al. [5] and 82% compared to [PERSON] et al. [1]. The EPUF-based protocol by [PERSON] et al. [11] also boasts low communication costs (around 1536 bits, but their message structure is different). This efficiency is critical for IoD networks, where bandwidth may be constrained, communication links may be unreliable, or energy consumed by radio transmission is a significant concern. Reduced communication overhead directly translates to lower energy consumption and improved reliability in potentially lossy wireless channels.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Protocol** & **Messages** & **Total Est. Cost (bits)** & **Source for Comparison** \\ \hline
**Bio-2 FA-IoD (proposed)** & **2** & **672** & Current Estimation \\ [PERSON] et al. [5] & 6 & 2464 & [PERSON] et al. [5] \\ [PERSON] et al. [1] & 4 & 3720 & [PERSON] et al. [1] \\ [PERSON] et al. (HCALA, 2023) [2] & 3 & 1536 & [PERSON] et al. [2] \\ [PERSON] et al. (HOOPOE, 2023) [6] & 2 (D-GSS) & 1280 & [PERSON] et al. [6] \\ [PERSON] et al. (2023) [13] & 2 & 1152 & [PERSON] et al. [13] \\ [PERSON] et al. (EPUF-Auth, 2025) [11] & 2 & 1536 & [PERSON] et al. [11] (192 bytes) \\ \hline \hline \end{tabular} Note: Bold indicates the proposed protocol for emphasis.  
\end{table}
Table 4: Comparative communication costs of authentication phase.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Protocol** & **Total Est. Cost (ms)** & **Primary Cryptographic Primitives** \\ \hline
**Bio-2 FA-IoD (proposed)** & **0.0411** & FE, KDF, AES, SHA-256 \\ [PERSON] et al. [5] & 0.0388 & PUF, FE, Hash \\ [PERSON] et al. [1] & 17.7939 & HMAC-SHA1, Hash, XOR \\ [PERSON] et al. (HCALA, 2023) [2] & 3.3873 & HEC, Hash, AES \\ [PERSON] et al. (HOOPOE, 2023) [6] & 8.343 & AES, RSA, Hash, Signature \\ [PERSON] et al. (2023) [13] & 0.44819 & ECC, Hash, Signature \\ [PERSON] et al. (EPUF-Auth, 2025) [11] & \(\approx\)0.016 & PUF (DRAM), Hash, XOR \\ \hline \hline \end{tabular} Note.: Bold indicates the proposed protocol for emphasis.  
\end{table}
Table 3: Comparative computational costs (ms) of authentication phase.