## 7 Performance Evaluation
### Computation Cost  
The computation cost is calculated by the execution time of all cryptographic operations in each protocol. I consider the time of computing an XOR negligible, as the operation is extremely fast. In addition, the difference between the execution times of a biohash function and a one-way hash function is too small [29]. For simplicity, they are assumed to \begin{table}
\begin{tabular}{c c c} \hline \hline
**Protocols** & **Total Communication Rounds** & **Total Cost of \(P_{i}\) and \(S_{m}\)\((\)bits\()\)** \\ \hline [PERSON] et al. [22] & 2 & 512 \\ [PERSON] et al. [24] & 3 & 1344 \\ [PERSON] et al. [25] & 3 & 5736 \\ [PERSON] et al. [26] & 2 & 3072 \\ [PERSON] and [PERSON] [27] & 3 & 1376 \\ [PERSON] & 2 & 1088 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of communication cost. Figure 5: Total length of transcripts of different protocols [22; 24; 25; 26; 27]. be similar. I denote the following cryptographic functions and operations for the evaluation in this subsection. * \(T_{FE}\): Time of running fuzzy extraction function. * \(T_{CM}\): Time of running a Chebyshev chaotic polynomial mapping. * \(T_{PM}\): Time of operating an EC point multiplication. * \(T_{PA}\): Time of operating an EC point addition. * \(T_{SED}\): Time of running a symmetric encryption or symmetric decryption. * \(T_{M}\): Time of calculating a modular squaring. * \(T_{QR}\): Time of calculating a square root module \(N\). * \(T_{H}\): Time of running a hash function. The result of the comparison of computational cost of multiple protocols is presented in Table 5 and Figure 6. Based on the result, for each communication session, the proposed protocol is more efficient than [PERSON] and [PERSON]'s [27] protocol. The incurred costs in the works of [PERSON] et al. [22], [PERSON] et al. [25] and [PERSON] et al. [26] are less than the ones in my protocol, [PERSON] et al. 's [24] protocol and [PERSON] and [PERSON]'s [27] protocol. Nevertheless, my protocol provides support for more functional properties and is better than the ones of [PERSON] et al. [22], [PERSON] et al. [25] and [PERSON] et al. [26] in terms of communicational efficiency. Furthermore, I consider a scenario where a single patient is using multiple U-healthcare services. Since the cost-saving SC-SSO solution is employed in my work, some operations before smart card verification, such as \(\sigma_{i}=\epsilon_{i}\oplus h\left(ID_{i}^{*}\left|PW_{i}^{*}\right|\left| \left|h_{bio}\left(B_{i}^{*}\right)\right.\right)\right.\) and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Protocols**} & **Time Complexities** & **Time Estimation** & **Time Complexities** & **Time Estimation** & **Total Time** \\  & **of \(P_{i}\) Side** & **of \(P_{i}\) Side \((\mathbf{ms})\)** & **of \(S_{m}\) Side** & **of \(S_{m}\) Side** \((\mathbf{ms})\) & **Estimation \((\mathbf{ms})\)** \\ \hline [PERSON] et al. [22] & \(T_{M}+T_{SED}+9T_{H}\) & \(\approx\)0.00744 & \(T_{QR}+2T_{SED}+8T_{H}\) & \(\approx\)1.17560 & \(\approx\)1.18304 \\ [PERSON] et al. [24] & \(T_{FE}+4T_{PM}+9T_{H}\) & \(\approx\)2.54621 & \(3T_{PM}+5T_{H}\) & \(\approx\)1.52745 & \(\approx\)4.07366 \\ [PERSON] et al. [25] & \(2T_{CM}+2T_{SED}+7T_{H}\) & \(\approx\)0.06353 & \(2T_{CM}+2T_{SED}+5T_{H}\) & \(\approx\)0.06215 & \(\approx\)0.12568 \\ [PERSON] et al. [26] & \(2T_{CM}+11T_{H}\) & \(\approx\)0.06521 & \(2T_{CM}+9T_{H}\) & \(\approx\)0.06383 & \(\approx\)0.12904 \\ [PERSON] and [PERSON] [27] & \(4T_{PM}+2T_{PA}+7T_{H}\) & \(\approx\)2.05063 & \(4T_{PM}+T_{PA}+5T_{H}\) & \(\approx\)2.04235 & \(\approx\)4.09298 \\ [PERSON] & \(4T_{PM}+T_{SED}+4T_{H}\) & \(\approx\)2.03530 & \(3T_{PM}+T_{SED}+2T_{H}\) & \(\approx\)1.52592 & \(\approx\)3.56122 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of computation cost. Figure 6: Computational cost of a single communication session in different protocols [22; 24; 25; 26; 27]. \(V_{i}\overset{?