# An Anonymous Offline RFID Grouping-Proof Protocol
## 8 Performance Analysis  
In this section, we analyze the communication overhead of the proposed protocol. The communication overhead denotes the length of the messages transmitted between the reader and tags when they execute the protocol. According to [32], we assume that an elliptic curve with length of 160 bits is used in our schemes. The length of an elliptic curve point is 320 bits. The communicational overhead comparisons about the [PERSON]'s protocol [19], EAGP\({}^{(2)}\) and EAGP are shown in Table 5.  
According to the Table 5, we know that the amount of data transferred in EAGP/EAGP\({}^{(2)}\) and [PERSON]'s protocol is very close. However, our protocols reduce the transmission number to six, this will  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Anonymity**} & \multirow{2}{*}{\begin{tabular}{c} **Location** \\ **Privacy** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **DoP** \\ **Attack** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Tag** \\ **Information** \\ **Protect** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Tag** \\ **Impersonation** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Reader** \\ **Impersonation** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Replay** \\ **Attack** \\ \end{tabular} } \\ \[PERSON] [1] & \(\times\) & \(\times\) & \(\times\) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) \\ [PERSON] [22] & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) \\ [PERSON] [24] & \(\surd\) & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) & \(\surd\) & \(\surd\) \\ [PERSON] [28] & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) \\ [PERSON] [29] & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) \\ [PERSON] [31] & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) & \(\times\) \\ [PERSON] [19] & \(\surd\) & \(\surd\) & \(\times\) & \(\surd\) & \(\times\) & \(\surd\) & \(\surd\) \\ EAGP & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: The comparison of grouping-proof protocols.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Send**} & \multicolumn{3}{c}{**Receive**} & \multirow{2}{*}{**Total Times**} \\ \cline{3-4} \multicolumn{1}{c}{} & \multicolumn{1}{c}{**Total Data (bit)**} & \multicolumn{1}{c}{**Transmission Times**} & \multicolumn{1}{c}{**Total Data (bit)**} & \multicolumn{1}{c}{**Transmission Times**} \\ \hline \multirow{3}{*}{Kang’s} & tag A & 640 & 2 & 1120 & 2 \\  & tag B & 640 & 2 & 1280 & 2 \\  & Reader & 2400 & 4 & 1280 & 4 \\ \hline \multirow{3}{*}{EAGP\({}^{(2)}\)} & tag A & 640 & 2 & 1280 & 2 \\  & tag B & 640 & 1 & 1120 & 1 \\  & Reader & 2240 & 3 & 1280 & 3 \\ \hline \multirow{3}{*}{EAGP} & Tag\({}_{1}\) & 640 & 2 & 1280 & 2 \\  & Tag\({}_{i}\) & 640 & 1 & 1120 & 1 \\  & Tag\({}_{n}\) & 640 & 1 & 1120 & 1 \\  & Reader & \(1120n+160\) & \(n+1\) & 640\(n\) & \(n+1\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: The comparison of communication overhead.  
cut down the communication overhead. When the tag number increases to \(n\) (EAGP), the transmission data amount of each tag is the same as (EAGP\({}^{(2)}\)), EAGP has good scalability in multiple tags condition.