## 6 Comparisons and Performance Evaluation
### Performance Evaluation  
In Table 2, we summarize the computation cost of the proposed protocols where E denotes the cost of a modulo exponentiation computation.  
Besides, we show the benchmark of Crypto++, which is a C++ class library of cryptographic computations, in Table 3[29]. The benchmark is measured by running Crypto++ on a machine with Intel Celleron 450 MHz CPU under Windows 2000. Furthermore, we also list the hardware specifications of some recently popular mobile devices in Table 4[30]. In Table 4, we also implemented RSA Cryptography system to check if our proposed system is practically efficient. According to Tables 3 and 4, we can objectively say that our protocols can be implemented and efficiently executed in the present mobile devices. Consequently, our anonymous authentication protocols can be performed in a reasonable time when a mobile user takes her/his mobile device to roa  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multicolumn{5}{c}{**Privacy**} & \multicolumn{5}{c}{**Property**} \\ \cline{2-9}  & \multicolumn{3}{c}{**Hiding ID from:**} & \multicolumn{5}{c}{**Credit-Based**} \\ \cline{2-9}  & **H** & **V** & **E** & **NoR** & **S** & **T** & **R** & **Chargeability** \\ \hline Ours & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\
[6] & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\bigcirc\) & \(\bigtriangleup\) & \(\bigtriangleup\) & \(\bigtriangleup\) & \(\times\) \\
[7] & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) \\
[8] & \(\times\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\times\) & \(\times\) \\
[9] & \(\times\) & \(\times\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\times\) & \(\bigcirc\) \\
[10] & \(\times\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\bigcirc\) & \(\times\) & \(\times\) & \(\bigcirc\) \\
[11] & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) \\
[12] & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) \\
[26] & \(\times\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\times\) \\
[27] & \(\times\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\bigcirc\) & \(\times\) & \(\times\) & \(\times\) \\
[28] & \(\times\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\bigcirc\) & \(\bigcirc\) & \(\times\) & \(\times\) \\ \hline \hline \end{tabular} H: Home domain; V: Visiting domain; E: Eavesdroppers; NoR: Hard to derive relation between any two rounds; S: Secure channel; T: Traceability (Tracing a criminal user); R: Revokeability (Revoking the privacy of a user when necessary); \(\bigcirc\): Achieving the feature; \(\times\): Not achieving the feature; \(\bigtriangleup\): Not realizing the feature.  
\end{table}
Table 1: Comparisons.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Operation** & **Mobile User (\(MS\))** & **The System (\(V\)+\(H\))** \\ \hline Requesting a ticket & 4E & 6E \\ Using a ticket & 3E & 2E \\ Termination & 3E & 8E \\ \hline \hline \end{tabular}
\end{table}
Table 2: Computation evaluation.