## 5 Performance Evaluation of BSNCare+
\begin{table}
\begin{tabular}{c c} \hline \hline
**Environment** & **Description** \\ \hline \multirow{3}{*}{Raspberry PI 2} & Broadcom BCM2836 @ 1 GHz Quad-Core ARM Cortex-A7 Architecture. \\  & 1 GB DDR2 RAM \\  & SanDisk 16 GB Class 10 SD Card \\ \hline Operating System & Raspbian2016/03 \\ \hline Programming Language & Oracle Java 8 ARM \\ \hline Programming IDE & Eclipse 3.8 \\ \hline Crypto API & The Bouncy Castle Crypto APIs [13] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Implementation Environment. of the total computation cost. Based on these two observations, we find that although the SHA-3 hash function dominates the efficiency of the BSNCare+, it has space for efficiency improvement if the protocol message during the authentication phase can be more-carefully designed to fit the characteristics of the SHA-3 hash function. For example, we find that the efficiency of the SHA-3 hash function will be downgraded to a lower level once the input sequence exceeds the multiple of 576 bits, which is one of the defaulted block sizes of the SHA-3 hash function. In that case, an interesting result, i.e., the SHA-3 hash function may be more suitable for communication protocols with short messages, is observed. Finally, the computation cost for implementing the authentication phase without \(T_{seq}\) is investigated in which, in total, an execution time of 7.540 ms is needed for performing 4 times the random number generations, 8 times the bitwise exclusive-or operations and 16 times teh SHA-3 hash function. Similarly, Table 6 presents the detailed implementation of the authentication phase without \(T_{seq}\). The same trend is obtained as that observed in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Operations in the System Implementation**} & \multicolumn{1}{c}{**Execution Time (ms)**} \\ \hline
4 times of 96-bit random number generations, i.e., \(N_{i}\), \(N_{j}\), \(N_{s1}\) and \(N_{s2}\) & 0.2783 \\
8 times of bitwise exclusive-or operations & 0.2078 \\
4 times of SHA-3 function with 512-bit input sequence, i.e., \(M_{1}\) and \(M_{2}\) & 0.02 \\
2 times of SHA-3 function with 608-bit input sequence, i.e., \(T\tau\) & 0.802 \\
2 times of SHA-3 function with 704-bit input sequence, i.e., \(V_{2}\) & 1.04 \\
2 times of SHA-3 function with 800-bit input sequence, i.e., \(SK_{js}\) & 1.006 \\
2 times of SHA-3 function with 896-bit input sequence, i.e., \(AID_{i}\) & 1.038 \\
2 times of SHA-3 function with 1024-bit input sequence, i.e., \(V_{3}\) & 0.866 \\
2 times of SHA-3 function with 1120-bit input sequence, i.e., \(SK_{is}\) & 0.928 \\
2 times of SHA-3 function with 2208-bit input sequence, i.e., \(V_{1}\) & 3.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The details of the implementation of the authentication phase without \(T_{seq}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Phase** & **Computation Cost** & **Execution Time (ms)** \\ \hline Registration Phase & (2+\(k\)) RN + (2+\(k\)) H 1 & 47.34 ms (with \(k=100\)) \\ \hline \multirow{4}{*}{Authentication Phase with \(T_{seq}\)} & \(BS_{i}\): 1 RN + 3 XOR + 5H & 1.969 ms (20.44\%) \\  & \(MG_{j}\): 1 RN + 1 XOR + 4H & 2.848 ms (29.56\%) \\  & _Server_: 2 RN + 4 XOR + 9H & 4.817 ms (50.00\%) \\  & Total: 4 RN + 8 XOR + 18H & 9.634 ms \\ \hline \multirow{4}{*}{Authentication Phase without \(T_{seq}\)} & \(BS_{i}\): 1 RN + 3 XOR + 4H & 1.451 ms (19.24\%) \\  & \(MG_{j}\): 1 RN + 1 XOR + 4H & 2.319 ms (30.76\%) \\ \cline{1-1}  & _Server_: 2 RN + 4 XOR + 8H & 3.770 ms (50.00\%) \\ \cline{1-1}  & Total: 4 RN + 8 XOR + 16H & 7.540 ms \\ \hline \hline \end{tabular}  
* \(k\) is the size of _SID_, which contains \(ksid_{h}\) values, in the implementation, \(k=100\). RN means a random number. XOR means a bitwise exclusive-or operation. H means the one-way hash function, i.e., SHA-3 (512 bits).  
\end{table} 
Table 4: Execution Time of the BSNCare+.